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Regulation of linear and angular impulse generation: implications for athletic performance

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Regulation of linear and angular impulse generation: implications for athletic performance

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Regulation of Linear and Angular
Impulse Generation: Implications
for Athletic Performance

By
Christopher Daniel Ramos

A Dissertation Presented to the
FACULTY OF THE GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(BIOMEDICAL ENGINEERING)

Dissertation Chair: Jill L. McNitt-Gray
Dissertation Committee Members: David D’Argenio, Philip Requejo, Rand R. Wilcox
Defense Date: August 31, 2017
Degree Conferral Date: December 2017

Copyright 2017 Christopher Ramos
i

Dedication

To my teammates and coaches. Without you I am nothing, and with you I am everything.

ii

Table of Contents
Dedication ........................................................................................................................................ i
Table of Contents ............................................................................................................................ ii
Chapter 1: Introduction ................................................................................................................... 1
Mechanics of Impulse Generation .............................................................................................. 1
References ................................................................................................................................... 6
Chapter 2: Specific Aims and Hypotheses...................................................................................... 7
Specific Aim 1: The Effect of Augmented Feedback on Quick First Step Impulse Generation
and Performance in Volleyball Players....................................................................................... 7
Specific Aim 2: Implications of Multijoint Control Strategies on Linear and Angular Impulse
Generation in Backward Rotating Dives .................................................................................... 8
Specific Aim 3: Differences in Volleyball Block Jumps Initiated With and Without
Momentum .................................................................................................................................. 8
Specific Aim 4: Regulation of Linear Impulse during the Takeoff of the Long Jump ............... 8
Specific Aim 5: Regulation of Linear Impulse and Multijoint Control of the Lower Extremities
during a 180° Change in Horizontal Direction ........................................................................... 9
Chapter 3: Experimental Design ................................................................................................... 10
Experimental Procedures .......................................................................................................... 10
Overview of Participant Tasks .................................................................................................. 10
Calibration Movements ......................................................................................................... 10
Experimental Tasks ............................................................................................................... 10
Data Collection ......................................................................................................................... 10
Kinematics ............................................................................................................................ 10
Kinetics ................................................................................................................................. 12
Lab Setup and Lab Coordinate Systems ............................................................................... 12
Data Processing and Analysis ................................................................................................... 13
Kinematics ............................................................................................................................ 13
Kinetics ................................................................................................................................. 14
Joint Kinetics ........................................................................................................................ 15
Statistics ................................................................................................................................ 16
Chapter 4: The Effect of Augmented Feedback on Quick First Step Impulse Generation and
Performance in Volleyball Players ............................................................................................... 19
Introduction ............................................................................................................................... 19
Methods..................................................................................................................................... 22
Results ....................................................................................................................................... 25
iii

Discussion ................................................................................................................................. 27
References ................................................................................................................................. 30
Chapter 5: Implications of Multijoint Control Strategies on Linear and Angular Impulse
Generation in Backward Rotating Dives ...................................................................................... 33
Introduction ............................................................................................................................... 33
Methods..................................................................................................................................... 35
Results ....................................................................................................................................... 37
Discussion ................................................................................................................................. 42
References ................................................................................................................................. 44
Chapter 6: Differences in Volleyball Block Jumps Initiated With and Without Horizontal
Momentum .................................................................................................................................... 47
Introduction ............................................................................................................................... 47
Methods..................................................................................................................................... 48
Results ....................................................................................................................................... 51
Discussion ................................................................................................................................. 55
References ................................................................................................................................. 58
Chapter 7: Generation of Linear Impulse during the Takeoff of the Long Jump ......................... 62
Introduction ............................................................................................................................... 62
Methods..................................................................................................................................... 64
Results ....................................................................................................................................... 66
Discussion ................................................................................................................................. 72
References ................................................................................................................................. 74
Chapter 8: Regulation of Linear Impulse during the Takeoff of the Long Jump ......................... 76
Introduction ............................................................................................................................... 76
Methods..................................................................................................................................... 78
Results ....................................................................................................................................... 80
Discussion ................................................................................................................................. 86
References ................................................................................................................................. 88
Chapter 9: Generation of Linear Impulse during a 180° Change of Horizontal Momentum ....... 90
Introduction ............................................................................................................................... 90
Methods..................................................................................................................................... 91
Results ....................................................................................................................................... 94
Discussion ................................................................................................................................. 99
References ............................................................................................................................... 101

iv

Chapter 10: Multijoint Control of the Lower Extremities during a 180° Change in Direction .. 106
Introduction ............................................................................................................................. 106
Methods................................................................................................................................... 107
Results ..................................................................................................................................... 110
Discussion ............................................................................................................................... 116
References ............................................................................................................................... 119
Chapter 11: Discussion ............................................................................................................... 122
References ............................................................................................................................... 126
Appendix A: Force Plate Documentation ................................................................................... 127
References ............................................................................................................................... 131

1

Chapter 1: Introduction

Generation of impulse during ground contact is central to success in athletics. Effective impulse
generation often requires that the individual re-configure their body so that they can generate the
linear and angular impulse needed to move in a desired direction. In time dependent activities,
opportunity to generate momentum is limited and requires that the reaction forces be generated
as quickly as possible. Athletes prepare for impulse generation by configuring their bodies so
that they are in a position to generate impulse in the desired direction without delay.
1
For
example, to generate horizontal impulse in the sprint start the athlete positions their total body
center of mass (CM) anterior to their feet so that they can immediately generate the horizontal
reaction forces during foot contact that are needed to move the body down the track.
2–8
To
maximize the horizontal impulse in the shortest amount of time, the athlete must strategically
configure their body segments so that the net joint moments (NJM) generated by muscles
crossing the ankle, knee, and hip can effectively generate required reaction forces in relation to
the CM trajectory. This mechanical demand imposed on the lower extremity during impulse
generation is affected by the magnitude and orientation of the reaction force relative to the lower
extremity segments and moments at the adjacent joint. Studying how individuals accomplish
these mechanical objectives under varying initial momentum and/or configuration conditions
advances our understanding of the control structure and its benefits specific to an individual.
9–12

By determining what problems the athlete needs to solve and designing experiments to
investigate how and why they move, we can determine solutions to help facilitate skill
acquisition and improve athletic performance.

The purpose of the proposed series of studies was to determine how elite-level athletes
effectively regulate impulse generation to satisfy the mechanical objectives of tasks under
contextually relevant training conditions and how this information could be used to improve
performance. These sets of experiments were performed at the Olympic Training Center in Chula
Vista and Indianapolis, in the gymnasium at USC, and a training session conducted by a coach in
the laboratory. High speed video or motion capture techniques were used to determine segment
kinematics during task performance. Reaction forces (RF) generated during foot contact were
simultaneously measured using force plates. In one study, the activation of muscles involved in
generating the RF over time was also monitored using telemetered surface electromyography
(EMG). The realistic circumstances allowed the testing of hypotheses regarding multi-joint
coordination and linear and angular impulse regulation under different initial momentum and
configuration conditions.

Mechanics of Impulse Generation

Tasks involving impulse generation can be broken down into three phases: pre-contact, contact,
and post-contact (Figure 1-1). During the pre-contact phase, the individual prepares for impulse
generation by re-configuring their lower extremity in a position favorable for generating the
required linear and angular impulse needed to perform the task. For example, prior to lead leg
impulse generation in a quick first step, the athlete must reposition their lead foot relative to their
total body CM (Figure 1-2). Foot contact time is typically shorter if the lead foot at contact is
posterior to the CM, while horizontal RF is typically initially negative if the lead foot at contact
is anterior to the CM.
8

2

Figure 1-1: Body configuration, estimated total body center of mass position (•), and reaction forces during the
take-off (i.e. contact) phase of the back somersault. During contact, the athlete generates backward and upward RFs
(white) anterior to the CM, resulting in backwards and upwards translation with backwards rotation (red).

Figure 1-2: Body configuration and estimated total body center of mass position (•) at lead leg initial contact (top),
and associated lead leg horizontal reaction forces (bottom) during contact for a quick first step. Contact time is
typically shorter when lead foot is posterior to CM (blue) and horizontal RF is initially negative when lead foot is
anterior to CM (red) at initial contact.
3

During the contact phase, the individual controls the RF relative to the CM trajectory by
coordinating NJM generation at the ankle, knee, and hip (Figure 1-3). NJM magnitude and
direction during contact can be modified via changes in net joint force (NJF) magnitude, NJF
relative to segment orientation, and / or net joint moment at the distal joint if present (Figure 1-
4).
9
The change in linear and angular momentum achieved during the contact phase becomes the
initial conditions for the post-contact phase of the task. For example, in the take-off phase of a
dive, the diver must generate the vertical, horizontal, and angular momentum needed for the
subsequent flight phase of the dive (Figure 1-3).
10–12

Figure 1-3: Body configuration, estimated total body center of mass position (•), and reaction forces at key events of
the back somersault. During the contact phase, the athlete generates backward and upward RFs (left, yellow)
anterior to the CM, typically resulting in ankle, knee, and hip extensor moments (middle, blue). As these reaction
forces are applied over time to generate linear and angular impulse, they result in backwards and upwards
translation of the total body CM with backwards rotation (right, white).

Figure 1-4: Example free body diagram (without segment weight) for the shank. Knee extensor NJM (top grey
arrow) can be increased by increasing NJF (red arrows) magnitude, increasing relative orientation between the
shank and NJFs, or decreasing ankle extensor NJM (bottom grey arrow).
4

Momentum conditions at contact often vary between tasks and are also expected to affect linear
and angular impulse generation during contact. For example, a dive may be initiated from a
standing position whereas a long jump is initiated with near maximum horizontal momentum
generated during the preceding run-up (Figures 1-1, 1-5). Increasing initial momentum can have
a positive effect on an athlete’s ability to generate impulse by increasing RF magnitude during
contact.
11,13
In these situations, impulse generated can be increased by increasing reaction force
magnitude and / or contact time with the ground. However, for time-dependent tasks such as a
sprint start, it may not be beneficial to increase time and decreasing contact time may be
preferred instead.

Figure 1-5: Kinematic sequence of events for key instances in time (grey lines) and associated horizontal and
vertical reaction forces for the takeoff in a long jump. Resultant RF is depicted in green for each image.

In some cases, the linear and angular momentum at contact is in direct opposition to the
subsequent task direction (such as a 180° change in horizontal direction). Initially the momentum
at contact is reduced to zero and then followed by applying an impulse in the same direction that
acts to propel the individual in the opposite direction (Figure 1-6). During the pre-contact phase,
the athlete can reconfigure their total body CM relative to their feet to favorably affect impulse
generation and / or the upcoming lower extremity mechanical demand during impact and set
themselves up for effect impulse generation in subsequent intervals of contact. During the first
5

part of the contact phase, the athlete can generate impulse in the desired direction resulting in a
reduction of total body CM velocity to zero. During the second part of the contact phase, the
athlete can then generate impulse in the desired direction resulting in movement of the total body
CM in the desired direction.

In tasks initiated without momentum, the generation of linear and angular impulse needed to
achieve the momentum conditions at last contact involves strategic multijoint coordination and
control at the ankle, knee, and hip (tested using joint kinetics in well-practiced goal-directed
tasks such as those performed by elite-level athletes). In tasks initiated with momentum, the
athlete is likely to find ways of effectively utilizing the existing momentum when generating
linear and angular impulse during the contact phase. In these cases, if it is advantageous for
impulse to be generated quickly then an important outcome of the pre-contact phase control is to
initiate foot contact in a body configuration effective for generating the linear and angular
impulse required for successful task performance.

Figure 1-6: Depiction of key events as determined by vertical RF for each leg in a 180° change in horizontal
direction. The Jump In interval is defined from front leg initial contact to zero velocity. The Jump Out interval is
defined from zero velocity to front leg final contact.
6

References
1. Requejo PS, McNitt-Gray JL, Flashner H. An approach for developing an experimentally
based model for simulating flight-phase dynamics. Biol Cybern. 2002;87(4):289-300.
doi:10.1007/s00422-002-0339-9.
2. Raibert MH. Running With Symmetry. Int J Rob Res. 1986;5(4):3-19.
doi:10.1177/027836498600500401.
3. Hodgins JK, Raibert MH. Biped Gymnastics. Int J Rob Res. 1990;9(2):115-128.
4. McMahon T a., Cheng GC. The mechanics of running: How does stiffness couple with
speed? J Biomech. 1990;23(SUPPL. 1):65-78. doi:10.1016/0021-9290(90)90042-2.
5. Seyfarth a., Friedrichs a., Wank V, Blickhan R. Dyanamics of the Long Jump. J Biomech.
1999;32:1259-1267.
6. Ridderikhoff A, Batelaan JH, Bobbert MF. Jumping for distance: control of the external
force in squat jumps. Med Sci Sport Exerc. 1999;31(8):1196-1204.
doi:10.1097/00005768-199908000-00018.
7. Kraan G a., Van Veen J, Snijders CJ, Storm J. Starting from standing; Why step
backwards? J Biomech. 2001;34(2):211-215. doi:10.1016/S0021-9290(00)00178-0.
8. Costa K. Control and Dynamics during Horizontal Impulse Generation. 2004.
9. McNitt-Gray JL, Hester DME, Mathiyakom W, Munkasy B a. Mechanical demand and
multijoint control during landing depend on orientation of the body segments relative to
the reaction force. J Biomech. 2001;34(11):1471-1482. doi:10.1016/S0021-
9290(01)00110-5.
10. Mathiyakom W, McNitt-Gray JL, Wilcox R. Lower extremity control and dynamics
during backward angular impulse generation in backward translating tasks. Exp Brain Res.
2006;169(3):377-388. doi:10.1007/s00221-005-0150-7.
11. Mathiyakom W, McNitt-Gray JL, Wilcox R. Lower extremity control and dynamics
during backward angular impulse generation in forward translating tasks. J Biomech.
2006;39(6):990-1000. doi:10.1016/j.jbiomech.2005.02.022.
12. Mathiyakom W, McNitt-Gray JL, Wilcox RR. Regulation of angular impulse during two
forward translating tasks. J Appl Biomech. 2007;23(2):149-161.
13. Moran K a., Wallace ES. Eccentric loading and range of knee joint motion effects on
performance enhancement in vertical jumping. Hum Mov Sci. 2007;26(6):824-840.
doi:10.1016/j.humov.2007.05.001.
7

Chapter 2: Specific Aims and Hypotheses

The proposed series of studies involve studying multi-joint coordination and control under
different initial momentum and configuration setups. The variations on experimental design were
divided into a series of specific aims (SA) investigating the effects of these differences on
regulation of impulse generation and the implications for performance. SA1 investigates the
effect of using augmented feedback to facilitate improvement. SA2 investigates the relationship
between knee-hip coordination and impulse generation without different initial conditions in
diving. SA3 investigates the effect of having initial momentum in volleyball. SA4 investigates
the relationship between knee-hip coordination and lower extremity demand with different initial
configurations in long jump. Finally, SA5 investigates the relationship between knee-hip
coordination and lower extremity demand with different initial momentum and configuration
differences in basketball.

Specific Aim 1: The Effect of Augmented Feedback on Quick First Step Impulse
Generation and Performance in Volleyball Players

Objective: To determine how augmented feedback on quick first step performance affects
improvement in (a) lead leg linear impulse generation and (b) overall task performance for elite-
level college volleyball players.

The mechanical objective of a quick first step is to maximize horizontal impulse generated as
quickly as possible.

Individuals receiving augmented feedback on knowledge of performance compared to
individuals receiving performance time only will

 Hypothesis 1: improve both lead leg and overall impulse generation more often
8

Specific Aim 2: Implications of Multijoint Control Strategies on Linear and
Angular Impulse Generation in Backward Rotating Dives

Objective: To determine how differences in individual knee-hip extension coordination affects
(a) linear and angular impulse generation and (b) muscle activation during the takeoff phase of
backwards and reverse somersaults performed by national and Olympic level divers.

The mechanical objective of the takeoff phase is to generate sufficient horizontal impulse to clear
the platform and maximize net vertical and angular impulse.

Individuals initiating leg extension with a more fixed knee (KStab) compared to those initiating
knee and hip extension together (KH) will

 Hypothesis 1: have differences in muscle activation patterns of the bi-articular muscles
crossing the knee and hip
 Hypothesis 2: generate greater net angular impulse and less net vertical impulse

because of differences in CM trajectory and segment kinematics relative to the RF.

Specific Aim 3: Differences in Volleyball Block Jumps Initiated With and Without
Momentum

Objective: To determine how the presence of initial momentum affects individual linear impulse
generation during the takeoff phase of a volleyball block jump performed by elite-level college
volleyball players.

The mechanical objective of the takeoff phase is to maximize vertical impulse generated at the
correct time relative to an opponent.

Individuals immediately generating vertical impulse following initial horizontal momentum
compared to after a delay will

 Hypothesis 1: generate more net vertical impulse over a shorter contact time

Specific Aim 4: Regulation of Linear Impulse during the Takeoff of the Long
Jump

Objective: To determine how differences in initial leg angle and leg yield affect linear impulse
generation during the takeoff phase of a long jump performed by national and Olympic level
long jumpers.

The mechanical objective of the takeoff phase of a long jump is to maximize net vertical impulse
generated while minimizing horizontal impulse lost.
9

When individuals initiate contact with a greater leg angle they will

 Hypothesis 1: generate more negative horizontal impulse
 Hypothesis 2: generate more net vertical impulse
 Hypothesis 3: have a longer total contact time
 Hypothesis 4: the increased linear impulses will occur during the impact interval
 Hypothesis 5: the increased linear impulses will result from increased RF magnitude and
contact time

When individuals have less leg yield during contact they will

 Hypothesis 1: generate more negative horizontal impulse
 Hypothesis 2: generate more net vertical impulse
 Hypothesis 3: the increased linear impulses will occur during the impact and / or post-
impact intervals, depending on the individual
 Hypothesis 4: the increased linear impulses will result from increased RF magnitude and
/ or contact time, depending on the individual

Specific Aim 5: Regulation of Linear Impulse and Multijoint Control of the Lower
Extremities during a 180° Change in Horizontal Direction

Objective: To determine how differences in momentum affect (a) linear impulse generation and
(b) the mechanical demand imposed on the front and back legs during the jump in and jump out
intervals of a 180° change in horizontal direction performed by competitive high school
basketball players.

The mechanical objective of the jump in interval is to reduce initial horizontal velocity to zero as
quickly as possible. The mechanical objective of the jump out interval is maximize horizontal
impulse generated as quickly as possible.

When an individual initiates a 180° change in horizontal direction from a further starting distance
compared to a shorter one they will

 Hypothesis 1: generate more horizontal impulse over a longer contact time
 Hypothesis 2: the increased horizontal impulse and contact time will occur only when
reducing initial horizontal velocity to zero
 Hypothesis 3: the increased horizontal impulse will result from increased RFh magnitude
and contact time
 Hypothesis 4: the increase in RF magnitude will result in greater mechanical demand on
the lower extremity
 Hypothesis 5: the distribution of the mechanical demand across the ankle, knee, and hip
will be the same
 Hypothesis 6: have greater leg yield
 Hypothesis 7: the greater mechanical demand and leg yield will result in greater work
done by the lower extremities when reducing initial horizontal velocity to zero
10

Chapter 3: Experimental Design

Experimental Procedures

Male high school level varsity basketball players from the same team (n = 11) were recruited to
participate in this study. Each player was informed and asked consent to serve as a subject in
accordance with the USC Institutional Review Board for Human Subjects. Prior to performance
during data collection, players were able to adjust to the lab space by practicing the 180° change
in horizontal direction on the force plates. All players had time to prepare their bodies to move
(i.e. stretching, performing a self-selected warm-up, etc.).

Overview of Participant Tasks

Calibration Movements
Calibration movements involved a static trial used to measure bodyweight and establish the
mathematical relationship between anatomical and tracking retroreflective markers. Other
calibration movements included functional joint tasks to calculate functional joint axes and
centers of the ankle, knee, and hip.
1,2
Each ankle, knee, and hip joint center calibration
movement used unloaded joint flexion, which is used to calculate function joint axes.

Experimental Tasks
Each player was asked to perform a 180° change in horizontal direction initiated from either 3
meters away from the end of the force plate system (target line) or 7 meters away from the end of
the force plate system, as self-selected by each player prior to collection such that their change in
direction would typically take place with one leg on each plate (Figure 3-3). Players initiated
their movement in reaction to a ball being dropped by their coach through a timing gate. Players
were instructed to jump straight up instead if two balls were dropped in order to prevent players
from leaning and ‘cheating’ in their ready position, and keep comparable trials as consistent as
possible. The players were reminded to perform these movements as they would normally
perform them, and to be as fast as possible from the start of their movement until they passed
through an X marked on the ground in tape 5 meters away from the end of the force plate system
after executing their change in direction.

Data Collection

Kinematics
Recorded Motion
Body segment kinematics were captured simultaneously in the frontal and sagittal planes (30Hz
Panasonic, Newark, NJ, USA & 240Hz Casio, Dover, NJ, USA), and used to verify successful
execution of tasks.

Coordinate Data
Three-dimensional kinematics were recorded using a retro reflective 16-camera motion capture
system (100 Hz, Natural Point, Optitrak, Corvallis, OR, USA) and Acquire3D software (C-
Motion, Germantown, MD, USA). Point residuals were estimated by the Acquire3D software for
11

below 0.60mm during calibration of the lab using the 16 camera setup for each collection.
During recording, cameras sent an external sync pulse to the force data acquisition hardware via
a BNC cable such that the kinematics and kinetics data were synchronized.

Markerset
A custom 32 marker set including anatomic and tracking retroreflective markers (1.2 cm
diameter, B&L Engineering) were applied to the player using an adhesive Velcro-system, skin
adhesive spray, and coban tape (Figure 3-1). The marker set allowed for use of segment
properties presented by DeLeva.
3
Markers were applied and checked by the same experienced
experimenter for all collections to avoid inter-tester differences in landmark locations or
application procedures.

Figure 3-1: Depiction of custom 32 marker set locations. Blue circles denote the 32 markers used during trials,
yellow markers denote the 4 additional markers added during calibration movements.
12

Tracking Markers
Locations of at least three, non-collinear markers affixed to a segment must be known in order to
fully define the orientation of a segment in space over time. These tracking markers were
attached to the shank and thigh segments using methods defined in the literature and previously
tested in our lab by using rigid cuffs. Tracking marker attachment protocol was designed to
minimize error due to movement of the markers relative to the body segment. Sources of error
are marker cuff slippage, marker vibrations on impact, and soft tissue movement.

Prior to collection, four retroreflecitve markers were affixed to each cuff in a configuration
determined by the suggestions presented by Cappozzo et al.: four markers per segment were used
with a mean cluster radius (average of the distance between each marker and the center of
cluster) greater than ten times the standard deviation of expected experimental errors (determined
in pilot studies).
4
The markers were oriented with the longest principal axis along the
longitudinal axis of the segment. The rigid shells were securely fastened to the segment by using
coban tape. Foot tracking markers were applied directly to the shoe. Pelvis tracking markers
were applied to a belt worn by each player. Chest and back tracking markers were applied
directly to the skin. Head tracking markers were applied to a layer of coban worn by each player.
All tracking markers were placed in locations that allowed for natural kinematics used by the
basketball players to execute the change in horizontal direction.

Though there were at least four tracking markers per segment, the three tracking markers used to
define the orientation of a segment were selected based on an automatic detection algorithm that
selected the three markers with the least gaps in raw marker data of the trial and phase of interest
(if gaps were applicable). The reference system was then created such that reference system axes
used the two longest vectors between the three markers, which made the orientation
measurement more robust (smaller vector orientation difference in a longer vector, given the
same displacement of a vector’s endpoint associated with marker residuals/measurement error).

Kinetics
Ground Reaction Forces
Ground reaction forces were measure using two forceplates (0.6 x 0.9 m
2
, 1200 Hz, Kistler,
Amherst, NY, USA), amplified, and digitized (National Instruments A/D board, custom data
collection software). Forceplates were covered with custom flooring (Mondo, Conshohocken,
PA, USA) to preserve the frictional characteristics that the players are accustomed to performing
with (Figure 3-2). These covers were isolated so that they do not transfer force between
forceplates or surrounding flooring. Material properties of the flooring were chosen so that there
was 1:1 correspondence between measured force and force applied to the surface of the flooring
without any elastic deformation of the surface.

Lab Setup and Lab Coordinate Systems
The lab’s reference system is based on the forceplate coordinate system (Figure 3-3). Calibration
markers were screwed into machined holes in the forceplate’s surface during calibration to
ensure alignment between kinetic and kinematic measurements.

13

Figure 3-2: Dual force plates with customized flooring to provide adequate friction characteristics to properly
complete the task while maintaining fidelity of force transmission.

Figure 3-3: Motion capture system relative to the dual force plate system (left) and lab based reference system
relative to the target line (right). 3m and 7m starting positions, and 5m finish line were marked in tape on the
ground.

Data Processing and Analysis

Kinematics
The processing of 3D kinematics was performed using custom Matlab software (The Mathworks,
Natick, MA, USA). After marker data were measured using Acquire3D and identified using
AMASS (C-Motion), C3D files were imported into Visual3D (C-Motion) to export marker data
as a “.txt” file for subsequent processing in Matlab. Upon importing kinematic data, gaps in data
(if applicable) were filled using a cubic spline smoothing Matlab function (“CSAPS”) with a
user-input smoothness factor “p” based on Jackson et al.
5

14

Functional joint centers during calibration movements of the ankle, knee, and hip were
calculated using a custom Visual3D model, and were used to define the endpoints of each
segment. Segment center of masses and total body center of mass (CM) were calculated for
analysis of whole body dynamics using estimates of segment parameters.
3
These measures were
used to provide kinematic context for analysis of kinetics (whole-body and local subsystem).
Segment center of masses enabled comparisons of segment configuration throughout movement.

Kinetics
Reaction forces (RF) in the x, y, and z directions were calculated from voltage to newton
calibration values found in Kistler forceplate documentation (Appendix A). Net linear impulses
during the contact phase (i.e. when players made contact with each force plate) were calculated
for each direction (Eq. 1, 2, and 3). The net linear impulse is the total effect of the force(s) in that
direction over a period of time.

𝑁𝑒𝑡 𝐿 𝑖𝑛𝑒𝑎𝑟 𝐼𝑚𝑝𝑢𝑙𝑠𝑒 𝑥 = ∫ 𝑅𝐹𝑥 𝑑𝑡
𝑡 2
𝑡 1

Eq. 1
𝑁𝑒𝑡 𝐿 𝑖𝑛𝑒𝑎𝑟 𝐼𝑚𝑝𝑢𝑙𝑠𝑒 𝑦 = ∫ 𝑅𝐹𝑦 𝑑𝑡
𝑡 2
𝑡 1

Eq. 2
𝑁𝑒𝑡 𝐿 𝑖𝑛𝑒𝑎𝑟 𝐼𝑚𝑝𝑢𝑙𝑠𝑒 𝑧 = ∫ (𝑅𝐹𝑧 − 𝐵𝑊 ) 𝑑𝑡
𝑡 2
𝑡 1

Eq. 3

Center of pressures were calculated using the method described by the Kistler forceplate
documentation (Appendix A). By using linear impulse in each direction and the CM position
when CM velocity was approximately zero (from kinematics), the CM trajectory was calculated.
This CM trajectory was found to be well-aligned with the CM calculated using markerset data
and estimated body segment parameters in static and motion trials.

Point of wrench application (PWA) was also calculated for each leg (Eq. 4 and 5).
6,7
To account
for the horizontal forces (x and y direction) present in the task, the PWA was used as an
alternative to the center of pressure (CP).
6–8
In the absence of horizontal forces or when vertical
force is much larger than the horizontal forces, the PWA becomes the CP.

𝑋 𝑃𝑊𝐴 =
𝐹 𝑥 𝑀 𝑧 − 𝐹 𝑧 𝑀 𝑦 𝐹 2
−
𝐹 𝑥 2
𝑀 𝑌 − 𝐹 𝑥 𝐹 𝑦 𝑀 𝑥 𝐹 2
𝐹 𝑧
Eq. 1

𝑌 𝑃𝑊𝐴 =
𝐹 𝑧 𝑀 𝑥 − 𝐹 𝑥 𝑀 𝑧 𝐹 2
−
𝐹 𝑥 𝐹 𝑦 𝑀 𝑦 − 𝐹 𝑦 2
𝑀 𝑥 𝐹 2
𝐹 𝑧
Eq. 2

Where Mx, My, and Mz are the moments about each axis of the force plate and F represents the
vector magnitude of the force vector.
15

Joint Kinetics
Joint kinetics during the contact phase of the 180° change in direction were determined for both
the front and back legs using measured ground reaction forces, 3D segment kinematics, and body
segment parameters.
3
The functional joint centers calculated from before were used to define a
leg plane and the axis perpendicular to the leg plane similar to the arm plane defined by Russell
et al.
9
Resultant net joint moments calculated for the ankle, knee, and hip were then represented
perpendicular to leg plane to characterize the mechanical demand imposed on muscles involved
in control of the lower extremities (Figure 3-4). The axis was used to determine how well the net
joint moments aligned with the leg plane.

Figure 3-4: Sagittal (left) and frontal (right) plane views of the leg plane and its perpendicular axis. This axis was
used to determine how well the net joint moments aligned with the leg plane.

Kinematics and kinetics were synchronized by interpolating kinematic data (100 Hz) to match
the kinetic data frequency (1200 Hz) using cubic spline function. The spline function also
automatically differentiated marker and segment center of mass position data to estimate
velocities and accelerations. Net joint forces were calculated using ground reaction forces,
segment masses, segment endpoints, and segment center of mass acceleration.
3

16

Statistics
Robust statistical methods that perform well under non-normality and small sample sizes were
carefully selected for use in this study (personal correspondence with Rand Wilcox). Through
this process a probability-based measurement was identified to determine how likely the value of
interest is to belong in one experimental condition vs. different condition within-subject.
10
This
statistical method is a conservative way to handle statistics in a small sample size without
assuming normality.

Within-player differences were determined using a subset of methods known as a two-state
linear model instead of Student’s T-test due to its limitations when it comes to non-normality,
incorrect assumptions of variance, and unequal sample sizes between conditions.
10
The
probability for each variable of 3m trial being less than any 7m trial was calculated within a
player for each variable, where each player served as their own control (R, open-source).
Assuming local independence (i.e. no order effect for trials within a condition), and that
movement conditions were independent (i.e. not directly tied to each other) for each player, p-
values were calculated for each player using Cliff’s analog of the Wilcoxon-Mann-Whitney
test.
11,12
This method was chosen because it deals well with small numbers of trials per
condition. A modified, step-down Fisher-type method was then applied to control the familywise
error rate (α = 0.05) over multiple comparisons where the level of significance becomes α/k at
each k
th
iteration.
13–15
The current statistics provide more flexibility by allowing
heteroscedasticity across players.
16
As the number of trials increases per condition, Cliff’s
method can achieve lower p-values. The modified, step-down Fisher-type technique is dependent
upon the distribution of p-values for each variable measured because the significance level is
adjusted at each step to compensate for multiple comparisons.
13–15
Therefore, the presentation of
within-player results provides a conservative estimate of significant differences between 180°
change in direction conditions.

17

References
1. Leardini A, Cappozzo A, Catani F, et al. Validation of a functional method for the
estimation of hip joint centre location. J Biomech. 1999;32(1):99-103. doi:10.1016/S0021-
9290(98)00148-1.
2. Piazza SJ, Okita N, Cavanagh PR. Accuracy of the functional method of hip joint center
location: Effects of limited motion and varied implementation. In: Journal of
Biomechanics. Vol 34. ; 2001:967-973. doi:10.1016/S0021-9290(01)00052-5.
3. De Leva P. Adjustments to Zatsiorsky-Seluyanov’s segment inertia parameters. J
Biomech. 1996;29(9):1223-1230. doi:10.1016/0021-9290(95)00178-6.
4. Cappozzo A, Cappello A, Croce UD, Pensalfini F. Surface-marker cluster design criteria
for 3-D bone movement reconstruction. IEEE Trans Biomed Eng. 1997;44(12):1165-1174.
doi:10.1109/10.649988.
5. Jackson KM. Fitting of Mathematical Functions to Biomechanical Data. IEEE Trans
Biomed Eng. 1979;BME-26(2):122-124. doi:10.1109/TBME.1979.326551.
6. Shimba T. Consequences of Force Platform Studies. Natl Rehabiliation Res Bull Japan.
1996;(17):17-23.
7. Zatsiorsky VM. Wrench Representation of the Ground Reaction Force. In: Kinetics of
Human Motion. Vol Champaign, IL: Human Kinetics Publishers; 2002:43-48.
8. Cavanagh PR, Rodgers MM, Iiboshi A. Pressure distribution under symptom-free feet
during barefoot standing. Foot Ankle. 1987;7(5):262-276.
doi:10.1177/107110078700700502.
9. Russell IM, Raina S, Requejo PS, Wilcox RR, Mulroy S, McNitt-Gray JL. Modifications
in Wheelchair Propulsion Technique with Speed. Front Bioeng Biotechnol.
2015;3(October):1-11. doi:10.3389/fbioe.2015.00171.
10. Wilcox RR. Modern Statistics for the Social and Behavioral Sciences: A Practical
Introduction. Boca Raton, FL: CRC Press Taylor & Francis Group; 2012.
11. Cliff N. Ordinal Methods for Behavioral Data Analysis. Mahwah, NJ: Lawrence Erlbaum
Associates, Inc; 1996.
12. Neuhäuser M, Lösch C, Jöckel K-H. The Chen–Luo test in case of heteroscedasticity.
Comput Stat Data Anal. 2007;51(10):5055-5060. doi:10.1016/j.csda.2006.04.025.
13. Hochberg Y. A sharper Bonferroni procedure for multiple tests of significance.
Biometrika. 1988;75(4):800-802. doi:10.1093/biomet/75.4.800.
18

14. Hochberg Y, Tomhane A. Multiple Comparison Procedures. Vol (Hochberg Y, Tamhane
AC, eds.). Hoboken, NJ, USA: John Wiley & Sons, Inc.; 1987.
doi:10.1002/9780470316672.
15. Wilcox RR, Clark F. Robust Multiple Comparisons Based on Combined Probabilities
From Independent Tests. J Data Sci. 2015;13(1):1-11.
16. Crowder M, Hand D. Analysis of Repeated Measures. Vol 1st ed. New York, NY:
Chapman & Hall/CRC; 1990.

19

Chapter 4: The Effect of Augmented Feedback on Quick First Step
Impulse Generation and Performance in Volleyball Players

Introduction

Finding effective methods to facilitate skill-acquisition is central to achieving success in
athletics. Since practice time is typically limited, how practice is organized and feedback to the
athletes delivered can have a significant impact on the effectiveness and progression of athletic
improvement. Considerations for how to facilitate improvement in skill-acquisition include
determining how to use physical practice versus observation of practice, where to direct the
player’s focus of attention / how to deliver feedback, what to deliver as feedback, and when to
deliver feedback.
1
Allowing athletes to observe their own and other teammate’s movements can
give them insight otherwise not obtained by just performing the movement.
2
Directing the
athlete’s focus of attention to the movement effect rather than the movement itself can expedite
the time required to acquire a skill.
3
Delivering augmented feedback that emphasizes successful
performance creates a positive motivational effect that is more effective for learning.
4,5
Finally,
allowing the athlete some control over the progression of practice and when to receive feedback
allows them to learn more effectively.
6–8
When these approaches are used in conjunction, skill-
acquisition can be improved and facilitated more effectively and efficiently.

Allowing the learner to observe movement execution in conjunction with performing the
movement can enhance and expedite learning. While observational practice by itself is not as
effective as physical practice, it is still more effective than no practice at all and has been shown
to make unique learning contributions.
9–11
This is likely due to the similar neural structures
activated and processes used during both observation and physical practice.
12–14
By observing the
movement, the learner may be able to assess strategy effectiveness and extract important
information about coordination patterns that they would otherwise be unable to do while
performing the task.
2
Combining observational and physical practice together has been shown to
be as effective or superior to physical practice alone over the same period of time.
10,11
This
allows the learner to learn via a variety of methods, adding flexibility to practice while at the
same time increasing training efficiency without sacrificing learning effectiveness.
10
In
particular, when learners are partnered together and rotate between observing each other and
performing the movement (dyad practice) their performance is as good or better than learners
performing the movement only, despite only having 50% of the physical practice.
10,11
This
pairing of learners likely results in increased motivation due to competition, a decrease in self-
consciousness as they find themselves in the same learning boat, and anecdotally an increase in
enjoyment.
15
By allowing athletes to partner together and observe practice in addition to physical
preparation, they may be able to improve at a faster rate by increasing training efficiency and
effectiveness.

Providing an external focus of attention during feedback is typically more effective than
providing an internal focus alone. Directing the attention to the effects of the learner’s
movements (external focus) has been shown to be more effective than directing the attention to
the movement itself (such as their leg or foot, which induces an internal focus).
3
This has been
observed across various athletics such as golf (attention was directed to the swing of the club
20

instead of the swing of their arms) and soccer (where attention was directed to the anticipated
trajectory of the ball instead of body parts such as the hand or foot), resulting in greater accuracy
along with other athletics such as basketball, dart throwing, and volleyball.
16–19
An internal focus
may increase the learner’s self-consciousness and self-evaluation, leading them to increase their
attempt to manage their thoughts and responses.
5
In contrast, an external focus of attention may
speed up the learning process by facilitating movement automaticity and allowing the learner to
use automatic processes instead (where as an internal focus may result in a more conscious
control that disrupts the automatic control process and constrains the motor system).
17,20

Evidence for this view has been demonstrated via a reduction in attentional demand and an
increase in more automatic, reflex-type control when performers are given an external focus
compared to an internal one.
20
In addition, this may also lead to an increase in movement
efficiency, as demonstrated by reduced electromyographic (EMG) activity for the same task in
learners adopting an external focus.
4
This method of directing attention has also been shown to
be more effective across different levels of expertise and populations, and even when performing
under pressure.
3,21
Directing athletes to the effect of their movements (external focus) rather than
the movements themselves (internal focus) may facilitate and speed up skill acquisition.

Feedback that emphasizes successful performance rather than that focused on errors provides a
more positive motivational effect on the learner, thereby increasing the effectiveness of learning.
The motivational effects of feedback are also important to consider, since learners with feedback
following ‘good’ trials learn more effectively than learners with feedback following ‘bad’
trials.
22
Providing feedback that emphasizes successful performance likely leads to a positive
motivational effect, whereas feedback centered on errors may induce self-concern that hampers
learning.
4,5
In many cases, bringing attention to these errors may be redundant since learners
typically have a good sense as to how well they perform.
6,23
Successful performance can
subsequently be broken down to either knowledge of results or knowledge of performance.
Knowledge of results refers to overall task performance (such as overall time), while knowledge
of performance refers to how well the movement was executed (looking at how the learner was
able to execute a better overall time) and often requires an outside facilitator / expert to assess.
1

Since both types of augmented feedback adhere to the same learning principles, it is important to
apply them in a manner that increases positive motivational effect even if a ‘bad’ attempt is
being assessed.
1,24
Regardless of which type of feedback is used, creating a positive motivational
effect through feedback delivery is important for increasing learning effectiveness when
coaching athletes.

Allowing the learner to have some control over the direction and execution of practice can
increase the effectiveness of skill acquisition. In both sequential timing tasks and throwing tasks,
having learners decide after which trial to receive feedback has led to more effective learning
than pre-determined feedback timing.
6–8
The frequency of feedback in these studies ranged
greatly from 11% to 97% of trials depending on the learner, suggesting that the ability to
determine when feedback occurs is more important than how often feedback occurs. This effect
may be due to increased motivation and effort as a result of more active involvement and the
ability of the learner to better address their feedback needs when desired (such as after more
successful trials or after a strategy change).
6,25,26
Additionally, when learners had control over
assistive devices such as video analysis, they were able to more successfully learn and adopt
improvements in movement execution.
27
This may have been a result of being able to choose
21

which aspects of the movement to observe, especially in phases when the learner struggled,
thereby affording them the opportunity to identify errors or confirm correct technique in their
own movements. Allowing athletes input as to what to practice, when to receive feedback, and
focus of analysis may expedite and improve skill acquisition of sports-specific movements.

In many sports, effective initiation of a quick first step can be advantageous for task
performance. Individuals often need to read and react to an unexpected event and then quickly
configure their body so that they can quickly redirect the center of mass (CM) trajectory by
generating impulse in a desired direction. Initiating a quick first step from a relatively stationary
position involves adopting postures in which the lead leg center of pressure is behind the CM
prior to initiation of rapid joint extension.
28,29
In this study we investigated the effect of using
augmented feedback to improve quick first step impulse generation prior to performing a
volleyball block jump. Based on previous pilot work, improvements in quick first step horizontal
impulse generation involve faster overall contact time, faster lead leg contact time, greater lead
leg horizontal velocity, greater lead leg average horizontal velocity, quicker time to peak force
associated with rapid joint extension, and shorter times between peak forces generated by the lag
and lead legs (P2P).
30,31

The main purpose of this experiment was to examine the effect of using augmented feedback to
improve quick first step impulse generation in elite-level athletes with athletic context. The
objectives when setting up and delivering augmented feedback was to allow the players to (a) be
able to observe their movements (b) receive augmented feedback regarding their impulse
generation (external focus) from an expert (c) focus on trials that the player ‘liked’ and wanted to
observe and (d) allow the players to determine when they would receive feedback. These players
were also given knowledge of results after each trial in the form of overall performance time in
order to give them different modes of feedback. However, instead of comparing the feedback
group to a control group receiving no feedback at all, they were instead compared to a group
only receiving knowledge of results after each trial to better explore the effect of knowledge of
performance and assess the potential benefit of only using knowledge of results.

Central to the development of a quick first step, we hypothesized that performance could be
enhanced by providing individuals with augmented feedback regarding horizontal-reaction
forces generated during foot contact in conjunction with performance time feedback. To
facilitate skill acquisition and visualize the reaction forces causing the observed movement,
augmented feedback was generated in the form of video replay of the individuals movements
with the lead and lag leg reaction force-time curves overlaid onto the video. To determine the
influence of this augmented feedback on performance, differences in horizontal reaction force-
time characteristics during quick first steps performed following practice with augmented
feedback were compared. Comparisons were made to players who practiced quick first steps
without access to this feedback and were only given their performance time.

22

Methods

Subjects
Thirteen skilled female volleyball players (NCAA Division I top 10 team) between 18 and 22
years of age volunteered to participate in this study. The mean (SD) height was 1.83 m (0.09)
and the mean (SD) mass was 80.13 kg (9.28). All players provided informed consent in
accordance with the Institutional Review Board.

Setup and Task
The experiment took place on a regular indoor-volleyball court with a net. Players faced the net
in their self-selected ‘ready position’ and were instructed to move as quickly as possible into a
volleyball block jump when a tennis ball on the other side of the net was dropped in either the
direction of their more prevalent blocking direction (5 times per round) or less prevalent
blocking direction (2 times per round), depending on their volleyball position. Overall block time
defined as time from first movement to hands over the net was recorded and reported to the
player after each trial using timing gates (Brower, Draper, UT, USA).

Procedure
Each player was instructed to warm up sufficiently prior to the beginning of collection. Baseline
performance was determined by having players complete 2 blocks of 7 performance trials
without any feedback. Seven players (F1 to F7) then practiced 21 trials with timing feedback
after each trial and augmented feedback provided when desired by the player up to 3 times. Six
players (T1 to T6) practiced in a similar manner but were only given timing feedback after each
trial. Ten minutes after practice was completed, all players performed a retention test consisting
of 2 blocks of trials without feedback to determine if any benefit derived from the feedback was
maintained (Figure 4-1).

Data Collected
During each trial, sagittal and coronal kinematics were recorded using high-speed cameras (240
Hz, Casio, Dover, NJ, USA). Vertical and horizontal ground reaction forces (RF) for each leg
were measured for each quick first step at 1,200 Hz using dual force plates (0.6 m x 0.9 m,
Kistler, Amhurst, MA, USA). These sets of data were synchronized at the time of plate
departure.

Augmented Feedback
Reaction force-time curves for both lead and lag legs were overlaid onto frontal plane video (30
Hz, Panasonic, Newark, NJ, USA) and were later used to provide external-focused feedback
between feedback rounds (Figure 4-2). Players were allowed to choose which trial(s) to assess
and when. Feedback was given by a biomechanics expert and was directed primarily toward
quick horizontal impulse generation (area under the RF-time curve) by increasing the force
magnitude (vertical axis) over time (horizontal axis).

23

Figure 4-1: Diagram depicting experimental procedure and timing of feedback. All players first performed 2 rounds
of 7 performance trials without any feedback (Baseline). Augmented feedback and performance time were then
given to 7 of 13 players, while performance time only was given to the remaining 6 players for 3 rounds. After a 10
minute break, all players finished with 2 rounds of 7 performance trials without any feedback (Same Day Retention).

Figure 4-2: Example video frames from the video shown to the players for augmented feedback (RF curves were
overlaid onto 30 Hz video). Attention was directed towards magnitude and rate of horizontal impulse generation.
White boxes and yellow arrows depict key events and label each curve and were not present on the original video,
but were explained to each player beforehand.

Performance Analysis
Overall improvement in players’ horizontal impulse generation was manifested by improvement
in total contact time. Effective improvement in players’ lead leg horizontal impulse generation
was manifested by improvements in multiple parameters associated with quick horizontal
impulse generation in a quick first step (lead leg contact time, lead leg normalized horizontal
impulse, lead leg normalized average horizontal impulse, and lead leg force slope) (Figure 4-3).
Total contact time was determined by finding the difference in time between final contact and
initiation of movement. Lead leg contact time was determined by finding the difference in time
between final contact and start of lead leg RF. Lead leg normalized horizontal impulse ( ∆Vh)
was determined by finding the area under the lead leg horizontal RF-time curve and dividing by
the player’s mass. Normalized average horizontal reaction force was determined by dividing the
lead leg horizontal impulse by the lead leg contact time, and is associated with greater horizontal
RF generation. Lead leg force slope was determined by dividing the lead leg peak horizontal RF
by the difference in time between lead leg peak horizontal RF and start of lead leg horizontal RF,
and is associated with a greater rate of lead leg joint extension.
24

Statistics
Interquartile range (IQR) and 20% trimmed means were calculated to describe the variables
associated with improvement in horizontal impulse generation. Within-player differences were
determined using a subset of methods known as a two-state linear model instead of Student’s T-
test due to its limitations when it comes to non-normality, incorrect assumptions of variance, and
unequal sample sizes between conditions.
32
The probability for each variable of any Baseline
being less than any Same Day Retention trial was calculated within a player for each variable,
where each player served as their own control (R, open-source). Assuming local independence
(i.e. no order effect for trials within a condition), and that conditions were independent (i.e. not
directly tied to each other) for each player, p-values were calculated for each player using Cliff’s
analog of the Wilcoxon-Mann-Whitney test.
33,34
This method was chosen because it deals well
with small numbers of trials per condition. A modified, step-down Fisher-type method was then
applied to control the familywise error rate (α = 0.05) over multiple comparisons where the level
of significance becomes α/k at each kth iteration.
35–37
The current statistics provide more
flexibility by allowing heteroscedasticity across players.
38
As the number of trials increases per
condition, Cliff’s method can achieve lower p-values. The modified, step-down Fisher-type
technique is dependent upon the distribution of p-values for each variable measured because the
significance level is adjusted at each step to compensate for multiple comparisons.
35–37

Therefore, the presentation of within-player results provides a conservative estimate of
significant differences between conditions.

Figure 4-3: Example kinematic sequence of events for key instances in time (start of movement, lag leg peak RF,
start of lead leg force, lead leg peak RF, and end of contact) and associated horizontal reaction forces for each leg.
Resultant RF for each leg is depicted in green for each image. Overall improvement consists of a decrease in total
contact time. Lead leg impulse generation improvement consists of a decrease in peak to peak time, increase in
average lead impulse by decreasing contact time or increasing lead ∆Vh, and / or an increase in lead force slope.
25

Results

Ten minutes following completion of practice, all seven players receiving augmented feedback
showed improvement in total contact time, with six players improving in multiple parameters
associated with effective lead leg impulse generation (Table 4-1, Figures 4-4, 4-5). In contrast,
only three of six players who received time-only feedback improved in total contact time and
multiple parameters associated with effective lead leg impulse generation.

Players receiving augmented feedback in the form of knowledge of performance improved their
overall contact time, suggesting that players were able to get out of their ready position much
faster (Figure 4-4). Total contact time was significantly faster for all seven players receiving
augmented feedback for Same Day Retention compared to Baseline (p < 0.05). In contrast, three
of the six time-only players had a significant decrease in total contact time, with the remaining
players having no significant difference. The mean (range) percent improvement in total contact
time for augmented feedback players compared to time-only players was +7.5% (+11.1%,
+4.0%) and +5.8% (+16.0%, -2.6%), respectively.

Table 4-1: Indication of improvement in performance for each parameter associated with quick first step impulse
generation and overall improvement. F1 to F7 denotes players receiving augmented feedback and performance
time, T1 to T6 denotes players receiving performance time only.  denotes a statistically significant improvement, x
denotes a statistically significant decrease in performance.

26

Figure 4-4: Total contact time for all augmented feedback players (F) and time-only players (T). * denotes
significant improvement (p < 0.05). Players are ordered by decreasing % improvement for each group. Attempts
reflected by circles (black open circles are Baseline trials, blue closed circles are Same Day Retention trials).

Lead leg contact time improved for both augmented feedback and time-only players from
Baseline to Same Day Retention, suggesting that for some players the total contact time
improvement was the result of a faster lead leg (Figure 4-5). Lead leg contact time was
significantly smaller for four of seven players receiving augmented feedback and for two of six
time-only players for Same Day Retention compared to Baseline. The mean (range) percent
improvement in lead leg contact time for augmented feedback players compared to time-only
players was +6.7% (+15.4%, -2.5%) and -5.5% (+31.0%, -8.1%), respectively.

Horizontal velocity generated by the lead leg improved or deteriorated for both groups from
Baseline to Same Day Retention, depending on the individual (Figure 4-5). Lead leg ∆Vh was
significantly larger for two of seven players receiving augmented feedback and significantly
smaller for two players for Same Day Retention compared to Baseline. Lead leg ∆Vh was
significantly larger for one of six time-only players and significantly smaller for two players. The
mean (range) percent improvement in lead leg ∆Vh for augmented feedback players compared to
time-only players was +3.4% (+38.6%, -33.4%) and -5.1% (+47.0%, -19.8%), respectively.

Normalized average horizontal ∆Vh improved for both augmented feedback and time-only
players from Baseline to Same Day Retention, suggesting that they improved their horizontal
force generation during the quick first step (Figure 4-5). Average lead Vh was significantly
larger for four of seven players receiving augmented feedback and significantly smaller for one
player for Same Day Retention compared to Baseline. Two of six time-only players had a
significant increase in average lead Vh, while one player had a significant decrease. The mean
(range) percent improvement in average lead leg horizontal RF for feedback players compared to
time-only players was +10.0% (+40.5%, -31.0%) and -11.4% (+40.3%, -26.3%), respectively.
27

Lead leg force slope improved for both players receiving augmented feedback and time-only
from Baseline to Same Day Retention, suggesting a greater rate of lead leg joint extension
(Figure 4-5). Lead leg force slope was significantly larger for four of seven players receiving
augmented feedback and significantly larger for two of six time-only players for Same Day
Retention compared to Baseline. The mean (range) percent improvement in lead leg force slope
for augmented feedback players compared to time-only players was +15.5% (+34.3%, -4.4%)
and -23.2% (+116.6%, -20.0%), respectively.

Figure 4-5: 20% trimmed mean of select quick first step horizontal impulse variables for all players for Baseline
(black) and Same-Day Retention (blue). Error bars represent interquartile range. All significant differences were
denoted when tested at α = 0.05 level when adjusted for multiple comparison (* denotes significant improvement
between conditions, * denotes significant deterioration between conditions (p < 0.05). Multiple parameters
significantly improved for 6 of 7 feedback players (F) and 3 of 6 time-only players (T).

Discussion

In this study we determined how augmented feedback on quick first step performance affects
improvement in lead leg impulse generation and overall task performance for elite-level college
volleyball players. Within player analysis of participants in this study indicated that players
improved both lead leg and overall impulse generation more often when given augmented
feedback in the form of force-time curves overlaid onto video compared to being given
performance time only. All seven players receiving augmented feedback had a significant
28

reduction in total contact time, with six of the players demonstrating significant improvement in
multiple aspects of lead leg impulse generation. In comparison, only three of six time-only
feedback players had significant improvement in total contact time and lead leg impulse
generation, with the remaining three players showing no improvement in either. In particular,
augmented feedback resulted in more consistent improvement in quick first step performance
with players improving their ability to generate horizontal impulse after only 21 performance
trials. This suggests that allowing elite-level athletes to observe their own movements, focusing
on successful performance of those movements, directing attention towards improvement using
an external focus, and giving them control over the learning process can substantially increase
the chance and degree to which they improve their movement performance. Taking these factors
into consideration when coaching or trying to facilitate improvement is essential for maximizing
athletic performance.

Although in general, the effectiveness of singular aspects of feedback on a learner has been
studied, the combination of these aspects of feedback has not.
1–8
This study examined combining
multiple aspects of feedback, specifically as it pertains to more complex movements such as
those found in athletics instead of those with simplified motor control requirements. Based on
the previous motor control literature, a combination of observation of practice
2
, external focus of
attention
3
, emphasis of successful performance
4,5
, and allowing the player some control over the
feedback process
6–8
was used in an attempt to deliver the ‘best’ possible feedback. This
augmented feedback methodology was assessed using elite volleyball players performing a quick
first step in an athletic context. The experiment demonstrated within its design limitations that
knowledge of performance in the form of augmented feedback results in improvement in quick
first step impulse generation more often than feedback regarding knowledge of results only. All
seven augmented feedback players (knowledge of performance and results) were able to improve
in multiple aspects of impulse generation compared to three of six players receiving only
knowledge of results. This suggests that allowing elite-level athletes to observe their own
movements, focus on successful performance of those movements, be directed towards
improvement using an external focus, and have some control over the learning process can
substantially increase the chance and degree to which they improve their movement
performance.

However, some players still had substantial improvement despite only receiving knowledge of
results. While it may be ideal to use augmented feedback and knowledge of performance to
maximize improvement, at times it may be difficult or unfeasible to use in the context of an
athletic practice. It may be that providing something as simple as concrete knowledge of results
(as opposed to objective terms such as ‘good’ or ‘bad’) in a meaningful context and at the
appropriate time can still enhance the learning process, although how best to approach this
requires further investigation. Ultimately, players were able to improve in a relatively short
period of time using the augmented feedback methodology although the exact effectiveness and
applications to other athletic and non-athletic areas remains to be seen.

The findings from this study are promising given that augmented feedback, in the form of video
replay of the individual’s movements with the lead and lag leg reaction force-time curves
overlaid onto the video, improved a number of movement initiation related parameters and
overall contact time after only 21 performance trials. In particular, this feedback resulted in more
29

consistent improvement in quick first step performance with players improving their ability to
generate horizontal impulse. However, some players were also able to substantially improve their
performance without this augmented feedback when only given their performance time. This
suggests that in some cases, simply making the player aware of their performance result may
lead to an improvement in their quick first step without further feedback. It remains to be seen if
the results of this study are consistent across a larger group and differing athletic populations.

30

References
1. Wulf G, Shea C, Lewthwaite R. Motor skill learning and performance: A review of
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33

Chapter 5: Implications of Multijoint Control Strategies on Linear
and Angular Impulse Generation in Backward Rotating Dives

Introduction

Satisfying mechanical objectives of a task at the total body level involves multijoint control of
the body during interaction with the environment. Observation of complex whole-body
movements such as jumping suggests that the nervous system organizes the human body into a
number of operational subsystems that are coordinated by using some type of hierarchical
control.
1–3
Identification of common multijoint control strategies used by the same individual
under various conditions advances our understanding of the control structure and inherent
priorities specific to an individual.
4
Understanding the implications of different, well-practiced
multijoint control strategies on satisfying the mechanical objectives of the task at the whole body
level is important for skill development that aims to improve task performance.

Linear and angular impulse generation during the take-off phase of well-practiced tasks relies on
the ongoing interaction of the nervous system and the musculoskeletal system during contact
with the ground. The motion of multiple body segments is coordinated so that the position of the
total-body center of mass (CM) relative to the line of action of the reaction force (RF) satisfies
both the linear and angular impulse objectives of the task.
5–9
Regulation of CM position relative
to the RF involves coordination between the trunk and leg subsystems during these weight
bearing tasks. Generation of backward angular impulse during foot contact with the ground is
achieved by orienting the RF anterior to the CM, regardless of translation direction. The
magnitude of the RF is regulated by the rate of lower extremity joint extension,
5,6
whereas the
position of the CM relative to the feet is most sensitive to trunk motion.
10–12
During the take-off
phase of the back somersault (backward translation with backward rotation, BS), backward trunk
and leg rotation increases the perpendicular distance between the CM and RF resulting in
backward angular impulse generation.
13
Although modifications in trunk-leg coordination
provide a mechanism for regulating the position of the CM relative to the RF during impulse
generation, across subject differences in lower extremity segment orientation relative to the RF is
expected to influence how the lower extremities contribute to the linear and angular impulse
required to perform the task.
12
Subsequently, the differences in the control objectives at the total-
body level (i.e. the position of the CM relative to the ground reaction force) is expected to alter
the control and dynamics of the lower extremity subsystem.

The direction and magnitude of the RF relative to the leg and CM is dependent on how joint
motion is controlled via net joint moments (NJM) and activation of specific sets of muscle.
4,12–14

Previous studies have shown that the magnitude of the NJM is sensitive to the orientation of the
RF relative to the lower extremity segments as well as the adjacent joint moment, and that
muscle activation patterns correspond with the NJMs.
4,12,13
When the same individuals
performed back (BS) and reverse (RS) somersaults, the RF-time characteristics and
neuromuscular control strategies used to satisfy the mechanical objectives of the tasks were
34

found to be comparable across tasks (Figure 5-1).
4,13,15
However between subject differences in
joint extension patterns were observed during the push interval of these tasks where individuals
adopted either (a) a more simultaneous knee-hip extension strategy where knee relative to hip
extension angular velocity was similar or (b) a more knee stabilization strategy where knee
relative to hip extension angular velocity was much smaller (Figure 5-3).
1

Figure 5-1: During the BS and RS tasks (left), the diver rotates backwards and translates backwards (BS) or
forwards (RS). Relative magnitudes of net joint moments (NJM) at the knee (k) and hip (h) are noted.
4,13,15
Both
dives are divided into load, tip, and push (right). Force generation is consistent within subject for each dive.

Muscle activation patterns observed during multi-joint goal-directed tasks indicate that uni- and
bi- articular muscles of the lower extremity attached to the pelvis work together synergistically to
regulate trunk motion in relation to the legs.
12
This synergistic activation of the bi-articular
muscles crossing the knee and hip has been observed when investigating how the same
individual generates impulse in two diving tasks performed with (BS) and without backward
rotation (back timer).
4,12,13
In particular, the between task differences in lower extremity joint
kinetics and re-distribution of work done by the ankle, knee, and hip were associated with this
synergistic activation of the bi-articular muscles crossing the knee and hip.
13
However, between
subject differences in muscle activation and advantages in impulse generation have not been
studied, specifically as it relates to between subject differences in joint extension patterns within
and across tasks.

In this study, our focus was to determine if there are mechanical advantages to specific multijoint
control strategies when achieving the same task objectives at the total body level.
4,13
This was
accomplished by investigating differences in two different knee-hip coordination strategies
within task and across subjects for backward angular impulse generating movements. We
35

hypothesized that individuals with slower knee relative to hip extension angular velocity (knee
stabilization strategy) would have delayed activation of the bi-articular muscles crossing the knee
and hip, and increased angular impulse but decreased net vertical impulse generated due to
differences in CM trajectory and RF orientation compared to subjects using a simultaneous knee-
hip extension strategy. We tested this hypothesis by comparing EMG activation of the lower
extremity and impulse generated within individual and across tasks.

Methods

Subjects
Seven (5 male and 2 female) skilled performers (national level divers) between 20 and 26 years
of age participated in this study. The mean (SD) height was 1.82 m (0.17) and the mean (SD)
mass was 65.0 kg (6.9). All subjects provided informed consent in accordance with the
Institutional Review Board.

Tasks
Each subject performed a series of BS and RS take-offs from a force plate onto a landing mat as
part of a dryland training session (Figure 5-1). During the BS take-off, the subject jumped from
the platform (upwards and backwards) and performed one complete backward somersault during
the flight phase and landed feet first on the landing mat. During the RS take-off, the subject
jumped from the platform (upwards and forwards) and performed one complete backward
somersault during the flight phase and landed feet first on the landing mat. The tasks were
blocked and randomized for each subject. Three successful trials of each task were analyzed.

Data Collection
Prior to data collection, subjects warmed up and practiced the experimental tasks until they were
familiar with the experimental set up. Sagittal plane kinematics (200 Hz, C2S NAC Visual
Systems, Burbank, CA USA), reaction forces (0.6x0.9m2, 1200 Hz, Kistler, Amhurst, MA,
USA), and activation patterns of the lower extremity muscles (1x1 cm2, 1200 Hz, Konigsberg,
Pasadena, CA, USA) were simultaneously collected during the performance of each
experimental task. These three sets of data were synchronized at the time of plate departure.

Thirteen body landmarks (vertex, C7, shoulder, elbow, wrist, finger, iliac crest, greater
trochanter, knee, lateral malleolus, heel, 5th metatarsal, and toe) of the side of the body closer to
the camera were manually digitized (Peak Performance, Inc., Englewood, CO, USA). Digitized x
and y coordinates of body landmarks were individually filtered with a fourth order Butterworth
filter (zero phase lag) with cut-off frequencies (5–20 Hz).
16
Body segment parameters of an
athletic population
17
were used to calculate the total body and segment center of mass.

The RF-time characteristics were described using three functional intervals (load, tip, and push)
within the take-off phase of the experimental tasks (Figure 5-2). Positive values of the RF
corresponded to upward vertical and forward horizontal RFs. The orientation of the resultant RF
was defined as an angle of the RF relative to forward horizontal passing through the center of
pressure. Likewise, the angular orientation of each body segment was defined as an angle of the
segment relative to forward horizontal passing through the distal end of the segment.
36

Activation (EMG) of lower extremity muscles (gluteus maximus, semimembranosus, biceps
femoris, rectus femoris, vastus lateralis, tibialis anterior, gastrocnemius, and soleus) acquired
using surface electromyography were filtered using a fourth order recursive Butterworth filter
(zero phase lag, 10–350 Hz bandwidth). The magnitude of muscle activation was quantified
using root-mean-squared (RMS) values (20 ms binned).
18
The RMS values were normalized to
maximum RMS values obtained during isometric manual muscle tests
19
and averaged for each
interval.

Figure 5-2: Multiple events and intervals within the take-off phase of the experimental tasks were defined using
vertical RF. The load interval was defined from initial rise of the vertical RF (initial position (IP)) to the time of first
peak vertical RF (1stPFv). An absence of vertical RF prior to the IP indicated that the performer was not in contact
with the ground. The Tip interval was identified as the time from the peak to the local minimum vertical RF (LMFv).
The Push interval is the time from LMFv to plate departure (PD). The time of 1st BW and 2nd BW corresponded to
the time when the vertical RF equaled to the total BW. These two events occurred prior to the first PFv and PD,
respectively.

Statistical Analysis
Within-subject differences were determined using a subset of methods known as a two-state
linear model instead of Student’s T-test due to its limitations when it comes to non-normality,
incorrect assumptions of variance, and unequal sample sizes between conditions.
20
The
probability for each variable being less between intervals was calculated within a subject for
each variable, where each subject served as their own control (R, open-source). Assuming local
independence (i.e. no order effect for trials within a condition), and that conditions were
independent (i.e. not directly tied to each other) for each subject, p-values were calculated for
each subject using Cliff’s analog of the Wilcoxon-Mann-Whitney test.
21,22
This method was
chosen because it deals well with small numbers of trials per condition. A modified, step-down
Fisher-type method was then applied to control the familywise error rate (α = 0.05) over multiple
comparisons where the level of significance becomes α/k at each kth iteration.
23–25
The current
statistics provide more flexibility by allowing heteroscedasticity across subjects.
26
As the number
37

of trials increases per condition, Cliff’s method can achieve lower p-values. The modified, step-
down Fisher-type technique is dependent upon the distribution of p-values for each variable
measured because the significance level is adjusted at each step to compensate for multiple
comparisons.
23–25
Therefore, the presentation of within-subject results provides a conservative
estimate of significant differences.

Figure 5-3: Example kinematics and reaction force (white arrows) for the take-off phase of the BS performed by two
exemplar subjects. The diver shown in the top panel uses the knee-hip extension strategy whereas the diver shown
on the bottom uses the knee stabilization strategy. Dashed vertical line denotes initiation of hip joint extension.

Results

Lower Extremity Kinematics
Two distinct joint extension strategies were observed during the push interval of the dive (Figure
5-3). Four of seven subjects used a knee-hip extension strategy (KH) by extending the knee and
hip at similar rates immediately following the tip interval. Three of seven subjects used a knee
stabilization strategy (KStab) by keeping the knee initially more fixed while extending the knee
at a slower rate than the hip. Hip rate of joint extension relative to knee joint extension (ωh / ωk)
during the push was larger for KStab compared to KH strategists (Figure 5-4). Lower extremity
segment and joint angles during the push interval of the dive were observed to be subject-
specific and not dependent on extension strategy.

Lower Extremity Muscle Activation
Differences in joint extension strategies were reflected by selective activation of the bi-articular
muscles crossing the knee and hip. KH group demonstrated early onset and prolonged activation
of the bi-articular SM and BF muscles as compared to the KStab group (Figures 5-5, 5-6). KH
38

group had no significant difference in activation of the SM and BF muscles between the first and
second halves of the push interval. KStab group had significantly larger activation of the SM and
BF muscles during the second half of push interval compared to the first half (p < 0.05). While
there were individual differences in muscle activation of the rectus femoris, vastus lateralis,
tibialis anterior, and gastrocnemius muscles as well between the first and second halves of the
push interval, these differences were not reflective of differences in knee-hip coordination
strategy.

Muscle activation strategies were consistent within individual. KH group had no significant
difference in activation of the SM and BF muscles between first and second halves of the push
interval for the RS (Figure 5-5). KStab group had significantly larger activation of the SM and
BF muscles during the second half of push compared to the first half (Figure 5-6).

Impulse Generation
No observed advantage in impulse generation was found based on extension strategy (Figures 5-
7, 5-8). Differences in linear generated were similar when comparing KH versus KStab subjects.
However, three of the seven subjects (KH4, KStab1, and KStab3) generated substantially more
angular impulse compared to the remaining four subjects. This additional angular impulse is
observed to be generated earlier in the dive by redirecting RF anterior to TBCM sooner but did
not appear to be strategy specific (Figure 5-8).

Figure 5-4: Hip versus knee angular velocity during hip extension for the BS for all 7 subjects. KStab subjects have
a larger ratio of hip to knee angular velocity compared to KH subjects at initiation of hip extension.
39

Figure 5-5: Mean (SD) of normalized muscle activation (RMS, 20-ms binned) of the gluteus maximus (GMax),
semimembranosus (SM), biceps femoris (BF), rectus femoris (RFem), vastus lateralis (VL), tibialis anterior (TA),
gastrocnemius (GAS), and soleus (SOL) of an exemplar knee-hip subject. Similar activation patterns were observed
within-group. Knee-hip strategists demonstrated early onset and prolonged activation of the bi-articular SM and BF
muscles compared to their knee stabilization counterparts.
40

Figure 5-6: Mean (SD) of normalized muscle activation (RMS, 20-ms binned) of the gluteus maximus (GMax),
semimembranosus (SM), biceps femoris (BF), rectus femoris (RFem), vastus lateralis (VL), tibialis anterior (TA),
gastrocnemius (GAS), and soleus (SOL) of an exemplar knee stabilization subject. Similar activation patterns were
observed within-group. Within-subject comparison of RMS demonstrates within-task differences in activation of the
semimembranosus and biceps femoris for first half of push versus second half of push for both tasks (*, p < 0.05).
41

Figure 5-7: Mean absolute horizontal (│∆Vh│) and absolute vertical (│∆Vh│) change in velocity for each diver.
Error bars represent standard deviation. No observed advantage in impulse generation was found based on
extension strategy.

Figure 5-8: Moment generated about the total body CM for each instant in time due to RF for all subjects. Three
subjects generated greater angular impulse (KH4, KStab1, and KStab3) by redirecting RF relative to total body CM
earlier compared to the remaining four subjects (KH1, KH2, KH3, and KStab2).

42

Discussion

In this study we determined how differences in individual knee-hip coordination affect impulse
generation and muscle activation during the takeoff phase of backwards and reverse somersaults
performed by national and Olympic level divers. The results of this within subject analysis
indicated that regulation of angular impulse involves coordination between multiple subsystems,
which can be accomplished via at least two different coordination strategies. Either a more hip
dominated or evenly distributed knee-hip extension can be used to satisfy the same linear and
angular impulse requirements of backwards-rotating tasks. Associated differences in lower
extremity extension strategy correspond with selective activation of bi-articular muscles crossing
the knee and hip (semimembranosus and biceps femoris muscles). These differences in selective
activation were consistent within individual even across tasks with similar mechanical objectives
when comparing the backwards to the reverse somersault. However, there was no observed
advantage in impulse generation between coordination strategies. Understanding and studying
the ability of the individual to execute their respective power generation strategy is key to
determining how best to modify technique and facilitate skill improvement.

All trials for a subject were collected on the same day with sufficient rest between trials to
minimize any effect of fatigue or day-to-day variance in performance. The force-time and
magnitude characteristics, kinematics, and muscle activation patterns observed in this study were
consistent with those reported in previous studies.
4,13
The study of elite athlete performance, by
design, limits the sample size and as a result, we chose to use a conservative within-subject
statistical method of comparison where each subject served as their own control. Under
conditions when participation time isn’t as limited, an increase in the number of trials per task
would strengthen the findings.

Different knee-hip coordination patterns can be used to accomplish the same task objectives at
both the local lower extremity and total body level. In this study, individuals used either a more
hip biased (KStab, n = 3) or more balanced (KH, n = 3) rate of joint extension strategy during the
push interval of the takeoff phase to achieve the same mechanical objectives in the BS, as shown
in Figures 5-3 and 5-4. These observed differences in knee-hip extension strategy were
consistent within individual and across tasks, suggesting that individuals may gravitate towards a
preferred coordination strategy when trying to satisfy the mechanical objective of similar tasks.
However, there was no observed advantage for linear or angular impulse generation based on
coordination strategy, as shown in Figures 5-7 and 5-8. This indicates that impulse generation
performance may be specific to the individual and not coordination strategy as it relates to
backwards angular impulse generating tasks such as the BS and RS, although this requires
further investigation using multi-joint modeling to explore ‘what if’ scenarios in coordination
strategy. Specifically, it may be that the ability to redirect the RF relative to the CM independent
of the individual’s knee-hip extension execution is essential to maximizing angular impulse
generation for performance, though how differences in coordination strategy affects this remains
to be seen.

Differences in knee-hip coordination patterns corresponded with differences in selective
activation of the bi-articular knee-flexor hip-extensor muscles. Knee-hip extension individuals
had prolonged activation of the semimembranosus (SM) and biceps femoris (BF) muscles during
43

the tip and push intervals of the BS, as shown in Figure 5-5. In comparison, knee stabilization
individuals had delayed activation of these muscles where selective activation did not occur until
the second half of the push interval, as shown in Figure 5-6. Selective activation of the lower
extremity muscles was used by subjects in this study to satisfy task-specific linear and angular
impulse generation requirements at the whole body level. Activation patterns of both uni- and bi-
articular muscles observed during the take-off phase were similar to those observed during
identical or similar tasks in previous work.
4,13
In particular, activation of the semimembranosus
(SM) and biceps femoris (BF) was used to redirect the reaction force anterior to the center of
mass during backwards-rotating tasks. Activation of the SM and BF muscles during
simultaneous knee and hip joint extension suggests recruitment of these bi-articular muscles may
occur when the muscle-tendon unit is at a preferred, isometric muscle length. When the hip and
knee extend together, the bi-articular muscles shorten at the hip and lengthen at the knee. The
observed differences in bi-articular muscle activation in regulating knee and hip extension
suggests the presence of individual-specific power generation strategies that need to be
considered when modifying technique and individualizing training programs.

Selective activation patterns were consistent within individual across tasks. Knee-hip extension
individuals had prolonged activation of the SM and BF during the tip and push intervals during
the RS as well, while knee stabilization individuals still had delayed activation of these muscles.
The RS has a similar mechanical objective to BS where the subject must generate backwards
angular impulse and upwards net vertical impulse, however, forward translation of the total body
CM is involved instead which requires forwards horizontal impulse. This suggests that
individuals may use a preferred activation and coordination strategy to accomplish tasks with
similar mechanical objectives. During impulse generation in whole body movements, the
nervous system organizes the body into operational subsystems that are coordinated by some
type of hierarchical control.
1–3
Previous study of the control and dynamics of BS and RS tasks at
the total-body level indicates that modification in trunk-leg coordination provides a mechanism
of regulating the position of the CM relative to the RF.
4,13
The results of those studies indicate
that task-specific modification of trunk-leg coordination involves redistribution of the
mechanical work done by the lower extremity NJMs and system scaling the activation of bi-
articular muscles crossing the knee and hip joints. While NJMs were not determined and are
beyond the scope of this study, differences in coordination strategies were reflected by selective
activation of the bi-articular muscles crossing the knee and hip joints, which were consistent
across tasks with similar mechanical objectives.

In summary, the results of this study indicate that regulation of angular impulse involves
coordination between multiple subsystems, which can be accomplished via at least two different
coordination strategies. Either a more hip dominated or evenly distributed knee-hip extension
can be used to satisfy the same linear and angular impulse requirements of backwards-rotating
tasks. Associated differences in lower extremity extension strategy correspond with selective
activation of bi-articular muscles in conjunction with mechanical demand imposed on the knee.
These differences in selective activation were consistent within individual even across tasks with
similar mechanical objectives. However, no advantage in linear or angular impulse generation
was observed. Understanding and studying the ability of the individual to execute their
respective power generation strategy is key to determining how best to modify technique and
facilitate skill improvement.
44

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46

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47

Chapter 6: Differences in Volleyball Block Jumps Initiated With
and Without Horizontal Momentum

Introduction

Performance of a vertical jump in athletic contexts involves effective generation of vertical
impulse while timing the jump relative to an opponent’s movements. Vertical impulse generation
during these well-practiced goal-directed movements involves control of the total body center of
mass (CM) trajectory in relation to the reaction forces (RF) generated during contact with the
environment.
1
Understanding vertical jump performance in realistic contexts assists coaches in
determining how to best prepare their athletes for play during competition.

Initiating a vertical jump with momentum can have a positive effect on an athlete’s ability to
generate vertical force.
1,2
Downward motion of the CM immediately prior to leg extension (e.g.
counter-movement jump) can contribute to greater net vertical impulse generation and
subsequently greater vertical displacement of the CM during the flight phase of the jump.
3–6

Flexion of the lower extremity joints during the countermovement acts to lengthen active
muscle-tendon-units involved in impulse generation.
7–10
Contributing factors thought to increase
muscle force generation include the storage and release of elastic energy generated during the
lengthening phase, tendon elongation, muscle preactivation, and stretch reflex.
4,11–19
While these
mechanisms have been thoroughly explored on their own, their respective contribution to
performance enhancement is still widely debated.
12,20
Furthermore, any potential performance
enhancement associated with lengthening of active muscle-tendon-units prior to force generation
is likely diminished when a delay is introduced prior to shortening.
21–23

In sport-specific contexts, initiating a jump with momentum often leads to greater generation of
net vertical impulse as compared to standing vertical jumps initiated with and without a counter-
movement.
24–26
For example, volleyball players are able to jump higher when hitting a volleyball
when initiating the jump with momentum as compared to stationary counter-movement jumps.
27

If the mechanical demand imposed on the lower extremity exceeds the capacity of the individual
to control the imposed load, then reductions in reaction force generation may occur.
4,22,28
While
adding momentum to the system may assist in increasing jump height, there are also position and
time-dependent aspects of the task performance that must considered when choosing to initiate a
jump with or without momentum. For example, when initiating a volleyball block jump (VBJ)
the horizontal momentum prior to the jump is generated while moving along the net. Adding
momentum to the system through preparatory footwork along the net is expected to increase VBJ
height by augmenting vertical impulse generation.
29,30
A successful VBJ performed during the
course of play, however, requires that the blocker is in an advantageous body position to block
the ball and can time their jump in relation to the set and movements of the opposing hitter.
31–33

Mistiming of the VBJ in relation to the opposing hitter will likely contribute to decrements in
block performance. The need to time the jump with the actions of the opponent may limit the
individual’s ability to use their momentum to assist with vertical impulse generation.

The aim of this study was to use a within-player design to determine if a delay in impulse
generation affects vertical impulse generated during VBJs. We hypothesized that volleyball
48

players would generate more CM vertical velocity during the VBJ when jumping immediately
compared to when pausing before the VBJ. We expected that immediately performing the VBJ
would allow the athlete to take advantage of momentum generated during the lateral movement
along the net, and the greater impulse generated during the take-off phase would contribute to
more time in the air than when pausing before the VBJ. We tested this hypothesis by measuring
the horizontal and vertical reaction forces during the jump phase of the volleyball block and
comparing the net vertical impulse generated as a whole as well as the reaction force-time
characteristics of the lead and lag legs between conditions.

Methods

Subjects
Twelve skilled female volleyball players (NCAA Division I top 5 team) between 18 and 22 years
of age volunteered to participate in this study. The mean (SD) height was 1.83 m (0.09) and the
mean (SD) mass was 80.13 kg (9.28). All players provided informed consent in accordance with
the Institutional Review Board.

Tasks
Each player performed a series of volleyball block jumps (VBJ) by reacting to a stimulus (ball
drop), moving laterally along the net, and then initiating a VBJ immediately after contact versus
with a delay (Figures 6-1, 6-2). Data collection was conducted at the conclusion of a training
session (60 min) that focused on the practice of volleyball specific skills. All players performed 3
rounds of 6 trials (3 trials per round without pause (Immediate) followed by 3 trials with pause
(Delayed)). Rest (20 s) was taken between trials and between rounds (5 min).

Data Collection
During the performance of each VBJ trial, sagittal and coronal plane kinematics were recorded
using high-speed cameras (300 Hz, Casio, Dover, NJ, USA). Vertical and horizontal ground
reaction forces for each leg were measured during each jump at 1200 Hz using dual force plates
(0.6 m x 0.9 m, Kistler, Amherst, NY, USA). These sets of data were synchronized at the time of
departure from the force plates.

Phases
The analysis of the VBJ was divided into three phases. The approach phase was defined as the
beginning of horizontal CM displacement until initial contact with the lead foot on the force
plate (initiation of unilateral foot support). The impulse generation phase of the jump was
defined as the beginning of unilateral foot support to the last instance of toe-off (final contact),
and further divided into an impact (start of impulse generation to local minima between peaks in
lead leg force) and push phase (local minima to end of impulse generation) (Figures 6-1, 6-2).
The flight phase was defined as final contact to the first instance of touchdown on the force
plates.

49

Figure 6-1: Body configuration, lead leg reaction force (solid arrow), and lag leg reaction force (dashed arrow) for
an exemplar player for Delayed VBJ (top). Median (black line) and IQR (grey shading) vertical RF for lead (solid)
and lag (dashed) legs for all trials for an exemplar player for Delayed VBJ (bottom). Player initiated jump used a
CM drop following delay prior to initiating joint extension.

50

Figure 6-2: Body configuration, lead leg reaction force (solid arrow), and lag leg reaction force (dashed arrow) for
an exemplar player for Immediate VBJ (top). Median (black line) and IQR (grey shading) vertical RF for lead
(solid) and lag (dashed) legs for all trials for an exemplar player for Immediate VBJ (bottom).

51

Analysis
Interquartile range (IQR) and 20% trimmed mean were calculated to describe the variables
determined for Delayed and Immediate trials. Net horizontal and vertical impulses were
calculated by integrating lead and lag leg reaction forces during foot contact during the impulse
generation phase. These impulses were normalized by body mass to obtain change in horizontal
velocity of the CM (∆Vh) and change in vertical velocity of the CM (∆Vv) during foot contact.
Lead leg, lag leg, and total contact times were determined from the force-time curves during the
impulse generation phase. Overall flight time was determined from the force-time curves during
the flight phase. Jump height performance was assessed using flight time instead of ∆Vv since
initial vertical velocity prior to impulse generation was variable and unknown. ∆Vv was instead
used to assess performance and execution of conversion of horizontal to vertical momentum as a
direct measure. Peak reaction forces (RF) immediately after contact were normalized by body
weight (BW) and used to reflect mechanical loading during the impact phase. The orientation of
the resultant reaction forces at the time of peak was represented in relation to the frontal and
sagittal plane. Frontal plane angle was defined relative to right horizontal of the player when
facing the net (Figure 6-1). Sagittal plane angle was defined relative to right horizontal away
from the net, with a smaller angle being more posterior to the player.

Statistics
Between condition differences across the group were determined using a standard two-sample
Student’s T-test (α = 0.05). Within-player differences were determined using a subset of methods
known as a two-state linear model instead of Student’s T-test due to its limitations when it comes
to non-normality, incorrect assumptions of variance, and unequal sample sizes between
conditions.
34
The probability for each variable of any Delayed VBJ trial being less than any
Immediate VBJ trial was calculated within a player for each variable, where each player served
as their own control (R, open-source, Table 6-1). Assuming local independence (i.e. no order
effect for trials within a condition), and that jump conditions were independent (i.e. not directly
tied to each other) for each player, p-values were calculated for each player using Cliff’s analog
of the Wilcoxon-Mann-Whitney test (Table 6-1).
35,36
This method was chosen because it deals
well with small numbers of trials per condition. A modified, step-down Fisher-type method was
then applied to control the familywise error rate (α = 0.05) over multiple comparisons where the
level of significance becomes α/k at each k
th
iteration.
37–39
The current statistics provide more
flexibility by allowing heteroscedasticity across players.
40
As the number of trials increases per
condition, Cliff’s method can achieve lower p-values. The modified, step-down Fisher-type
technique is dependent upon the distribution of p-values for each variable measured because the
significance level is adjusted at each step to compensate for multiple comparisons.
37–39

Therefore, the presentation of within-player results provides a conservative estimate of
significant differences between jump conditions.

Results

By design, players took longer to execute their Delayed VBJ compared to their Immediate VBJ.
Across participants, the mean (range) total contact time during Delayed and Immediate was 0.77
(0.55, 1.21) s and 0.47 (0.38, 0.55) s, respectively, with the differences in contact time between
players being much greater for Delayed compared to Immediate. The reduction in CM horizontal
velocity during contact was not significantly different between Delayed and Immediate VBJs
52

(Figure 6-3). The mean (range) ∆Vh during Delayed and Immediate VBJs was 2.14 (1.62, 2.50)
m/s and 2.12 (1.42, 2.49) m/s, respectively.

Players remained in the air longer during Immediate compared to Delayed VBJs, indicating that
they jumped higher. Flight time was significantly longer for Immediate compared to Delayed as
a group, and individually for seven of twelve players (Table 6-1). Of these seven players, only
five players had a higher calculated jump height difference of more than 4 cm with a mean
(range) of 5.29 (4.35, 7.48) cm. The mean (range) flight time for Delayed and Immediate VBJs
was 0.48 (0.44, 0.52) s and 0.51 (0.46, 0.54) s, respectively.

Players generated more net vertical impulse during Immediate compared to Delayed VBJs,
consistent with the observed differences in flight times between conditions (Figure 6-3). ∆Vv
was significantly larger (on average 5%) for Immediate as compared to Delayed VBJs as a
group, and individually for six of twelve players (Table 6-1). The mean (range) ∆Vv during
Delayed and Immediate VBJs were 3.21 (2.74, 3.75) m/s and 3.37 (2.86, 3.87) m/s. These total
changes in vertical velocities for Delayed and Immediate translate into calculated total flight
times of the CM of 0.654 and 0.687 s, respectively.

Figure 6-3: 20% trimmed mean of horizontal velocity lost (∆Vh) and vertical velocity generated (∆Vv) of lead and
lag legs for Delayed (D) and Immediate (I) conditions for all players. Error bars represent interquartile range.
Total ∆Vh and ∆Vv are the summation of lead and lag leg contributions for each condition. All significant
differences were denoted when tested at α = 0.05 level when adjusted for multiple comparison. * total, † lead leg,
and ‡ lag leg ∆Vv significant difference between conditions. Individuals are sorted (1-12) by increasing flight time
during Delayed.

More lead leg net vertical impulse was generated during Immediate compared to Delayed VBJs
(Figure 6-3). Lead leg ∆Vv was significantly larger for Immediate compared to Delayed as a
group, and individually for seven of twelve players (Table 6-1). The mean (range) lead leg ∆Vv
during Delayed and Immediate was 1.66 (1.35, 1.83) m/s and 1.96 (1.58, 2.20) m/s, respectively.

Lag leg net vertical impulse generation during the Immediate VBJ was comparable or less than
that for the Delayed VBJs (Figure 6-3). Lag leg ∆Vv was significantly smaller for Immediate
compared to Delayed as a group, and individually for six of twelve players (Table 6-1). The
mean (range) lag leg ∆Vv during Delayed and Immediate was 1.54 (0.98, 1.94) m/s and 1.40
(0.99, 2.05) m/s, respectively.
53

As a group, lead leg peak RF magnitude was not significantly different for Immediate compared
to Delayed VBJs (Figure 6-4). One of twelve players exhibited significantly larger and one of
twelve exhibited significantly smaller lead leg peak RF for Immediate as compared to Delayed
VBJs (Table 6-1). The mean (range) lead leg peak RF magnitude during impact for Delayed and
Immediate VBJs was 2.25 (1.41, 3.51) BW and 2.16 (1.39, 3.44) BW, respectively. However,
there was no significant difference in reaction force angle in the frontal or sagittal planes
between conditions. The mean (range) lead leg reaction force angle in the frontal plane during
Delayed and Immediate was 70 (66, 77) degrees and 69 (65, 75) degrees, respectively. The mean
(range) lead leg reaction force angle in the sagittal plane during Delayed and Immediate was 96
(80, 102) degrees and 96 (89, 102) degrees, respectively.

As a group, lag leg peak RF magnitude was significantly larger for Immediate compared to
Delayed VBJs (Figure 6-4) and individually for five of twelve players (Table 6-1). The mean
(range) lag leg peak reaction force magnitude during impact for Delayed and Immediate was
1.72 (1.22, 2.49) BW and 2.01 (1.68, 2.59) BW, respectively. However, there was no significant
difference in reaction force orientation in the frontal or sagittal planes between conditions. The
mean (range) lag leg reaction force angle in the frontal plane during Delayed and Immediate was
69 (65, 72) degrees and 69 (65, 72) degrees, respectively. The mean (range) lag leg reaction
force angle in the sagittal plane during Delayed and Immediate VBJs was 91 (87, 96) degrees
and 91 (86, 96) degrees, respectively.

Figure 6-4: 20% trimmed mean of lead and lag leg maximum RF magnitude during impact for Delayed (D) and
Immediate (I) conditions for all players. Error bars represent interquartile range. All significant differences were
denoted when tested at α = 0.05 level when adjusted for multiple comparison. * Lead and lag leg significant
difference between conditions. Individuals are sorted (1-12) by increasing flight time during Delayed.

Two different methods of executing the Delayed VBJ were observed across players. During
high-speed video analysis, five of twelve players had a CM drop prior to initiating joint-
extension (Figure 6-1, Table 6-1), while the remaining seven players initiated joint-extension
without a drop in CM vertical position (Figure 6-5). Peak lead leg force was comparable between
methods and the Delayed VBJ method used was consistent within individual. Neither method of
executing the Delayed VBJ provided a distinct performance advantage over the other.
54

Figure 6-5: Body configuration, lead leg reaction force (solid arrow), and lag leg reaction force (dashed arrow) for
an exemplar player for Delayed VBJ (top). Median (black line) and IQR (grey shading) vertical RF for lead (solid)
and lag (dashed) legs for all trials for an exemplar player for Delayed VBJ (bottom). Player initiated jump and joint
extension immediately following delay without a CM drop.

Overall, several performance and reaction force generation differences were observed between
Delayed and Immediate VBJ. All twelve players took longer to execute their Delayed VBJ and
experienced similar braking horizontal impulse for both conditions. Five of twelve players were
able to increase their calculated jump height by more than 4cm when jumping immediately. Lead
leg net vertical impulse generated was larger for seven of twelve players, while lag leg net
vertical impulse generated was smaller in six of twelve players when jumping immediately,
resulting in a larger total net vertical impulse for six of twelve players. Peak reaction forces for
the lag leg were larger in five of twelve players when jumping immediately, whereas peak
55

reaction forces for the lead leg were either larger, smaller, or the same depending on the
individual. Two different methods of executing the Delayed VBJ were observed, however it did
not have an observable effect on net vertical impulse generated or peak reaction forces
experienced. These findings indicate that jumping immediately with horizontal momentum can
lead to an increased jump height consistent with observed increases in vertical impulse
generation as compared to jumping with a delay. Observed differences in jump height and peak
RFs were found to be player specific (Table 6-1).

Table 6-1: Group and individual total flight times, change in vertical velocities, and lead and lag reaction force
components.
Total Lead Leg Lag Leg
Individual Flight Time (s) ∆Vv (m/s) ∆Vv (m/s) Peak RF (BW) ∆Vv (m/s) Peak RF (BW)
Player VBJ Mean IQR p Mean IQR p Mean IQR p Mean IQR p Mean IQR p Mean IQR p
1
†

D 0.441 0.022
0.016
2.89 0.20
0.016
1.71 0.05
0.016
2.36 0.20
0.880
1.22 0.06
0.016
1.22 0.29
0.016
I 0.491 0.017 3.11 0.14 2.10 0.14 2.30 0.11 0.98 0.12 1.99 0.12
2
D 0.453 0.015
0.045
2.74 0.18
0.005
1.75 0.22
0.140
2.25 0.15
0.330
0.99 0.12
0.670
1.85 0.66
0.690
I 0.461 0.026 2.86 0.12 1.92 0.12 2.18 0.21 0.98 0.06 1.74 0.14
3
†

D 0.461 0.025
0.004
3.05 0.05
0.480
1.70 0.09
0.004
2.04 0.04
0.004
1.36 0.09
0.004
1.58 0.24
< 0.001
I 0.498 0.013 3.13 0.11 2.03 0.17 1.66 0.08 1.08 0.13 2.03 0.34
4
D 0.475 0.004
0.016
3.28 0.05
0.005
1.83 0.11
0.016
3.51 0.46
0.180
1.42 0.04
0.016
1.62 0.30
< 0.001
I 0.491 0.009 3.36 0.03 2.11 0.22 3.44 0.90 1.26 0.27 1.93 0.24
5
†

D 0.478 0.030
0.005
3.32 0.13
0.016
1.54 0.05
0.016
2.16 0.21
0.016
1.78 0.08
0.016
1.62 0.39
0.016
I 0.515 0.021 3.58 0.05 2.20 0.04 2.65 0.09 1.40 0.11 2.22 0.17
6
D 0.479 0.006
0.016
3.39 0.12
0.012
1.73 0.09
0.016
2.46 0.19
0.750
1.69 0.10
0.170
2.24 0.32
0.002
I 0.539 0.023 3.71 0.09 2.11 0.40 2.29 0.19 1.58 0.16 2.59 0.17
7
†

D 0.481 0.006
0.016
3.34 0.15
0.400
1.83 0.19
0.021
2.62 0.53
0.005
1.48 0.18
0.190
1.84 0.39
0.021
I 0.518 0.011 3.51 0.10 2.07 0.18 2.19 0.25 1.47 0.13 2.06 0.27
8
†

D 0.489 0.005
0.016
3.11 0.05
0.005
1.69 0.07
0.016
2.41 0.40
0.800
1.41 0.06
0.097
1.34 0.23
0.005
I 0.505 0.020 3.23 0.18 2.06 0.11 2.47 0.78 1.19 0.23 1.73 0.53
9
D 0.501 0.028
0.045
3.75 0.07
0.330
1.70 0.38
0.016
1.66 0.28
0.016
2.05 0.36
0.007
2.49 0.28
0.710
I 0.508 0.017 3.87 0.23 1.91 0.19 1.58 0.07 1.94 0.19 2.23 0.45
10
D 0.502 0.011
0.140
3.21 0.16
0.110
1.35 0.21
0.190
1.41 0.62
0.890
1.78 0.16
0.770
1.49 0.28
0.190
I 0.518 0.008 3.35 0.14 1.58 0.19 1.39 0.69 1.73 0.18 1.68 0.41
11
D 0.506 0.002
0.210
3.28 0.08
0.380
1.71 0.08
0.079
2.59 0.20
0.400
1.59 0.14
0.016
1.52 0.25
< 0.001
I 0.513 0.018 3.31 0.14 1.85 0.27 2.40 0.23 1.45 0.09 1.97 0.63
12
†

D 0.518 0.005
0.750
3.16 0.13
0.270
1.38 0.16
0.170
1.58 0.64
0.990
1.74 0.11
0.260
1.82 0.24
0.810
I 0.520 0.008 3.35 0.10 1.59 0.27 1.42 0.50 1.70 0.20 1.92 0.10
Increase 7 6 7 1 - 5
Decrease - - - 1 6 -
No Change 5 6 5 10 6 7
Group
VBJ Mean SD p Mean SD p Mean SD p Mean SD p Mean SD p Mean SD p
D 0.482 0.023
0.001*
3.21 0.26
< 0.001*
1.66 0.16
< 0.001*
2.25 0.56
0.205
1.54 0.29
0.001*
1.72 0.36
0.005*
I 0.506 0.019 3.37 0.28 1.96 0.20 2.16 0.59 1.40 0.31 2.01 0.25
p Significant at α = 0.05 level when adjusted for multiple comparisons

p Significant at α = 0.10 level when adjusted for multiple comparisons

p* Group differences based on two-sample Student's T-test at α = 0.05 level

† Player had a CM drop following delay prior to initiating joint-extension in Delayed VBJ

Discussion

In this study, we determined how vertical jump performance in skilled players was affected by
the timing of vertical jump initiation. The results of this within player analysis indicated that
players were able to generate greater change in vertical velocity when initiating a VBJ
immediately as compared to with a delay. However, the resulting jump height increase during the
Immediate VBJ was minimal for most players. The magnitude of these differences between
conditions varied across individuals. Mechanical loading of lead and lag legs during the impact
phase were comparable between VBJ conditions. In these cases, the timing of the VBJ may be
56

more important for some players than the increased jump height when it comes to jumping
performance. The implications for performance in competitive volleyball context are important
to consider when determining whether to use an immediate or delayed VBJ.

All trials for a player were collected on the same day with rest and with adequate rest between
trials so as to minimize any effect of fatigue or day-to-day variance in performance. Players were
allowed to self-select the timing of their block during Immediate and Delayed conditions without
the presence of an opposing hitter in order to reduce variability between trials. Any potential
attenuation by the wood flooring used to cover the force plates is expected to be of similar
magnitude between experimental conditions. The force-time and magnitude characteristics
observed in this study were consistent with those reported in previous studies.
30,41
We also chose
to use a conservative within-player statistical method of comparison where each player served as
their own control. Under conditions when participation time isn’t as limited, an increase in the
number of trials per jump condition would strengthen the findings.

Players in this study modestly increased their net vertical impulse generation when jumping
immediately with initial horizontal momentum as compared to jumping with a delay. Jumping
immediately resulted in a larger lead leg contributions to CM vertical velocity and greater role of
the lead leg in converting horizontal to vertical momentum. Using horizontal momentum to
enhance the player’s ability to generate impulse is consistent with findings that counter-
movements and other momentum inducing techniques prior to leg extension result in increased
force and impulse generation.
3–6
Introducing horizontal momentum prior to the jump induces
conditions that impose active lengthening of muscles involved in impulse generation, resulting in
a stretch-shortening cycle and greater force output whose exact mechanism is widely
debated.
12,20
Although the exact force-enhancing mechanism is uncertain and beyond its scope of
this study, in vivo muscle force following active muscle stretch is observed to be larger than the
force obtained during purely isometric contraction.
11,12,14,15
The residual force generated persists
through concentric shortening following either isometric or eccentric contraction and in theory
allows athletes to generate more net vertical impulse and jump higher due to the larger vertical
force generated over similar time periods. It is likely, however, that the greater impulse
generation observed under the immediate condition involves a combination of factors including
stretch-reflex responses, elastic energy release, muscle preactivation, and tendon elongation
leads specific to greater force output, although it is only recently that these effects have been
studied in conjunction with one another.
4,13,16–20

Successful jumping performance in the context of athletics requires effective height and timing
relative to an opponent. In the case of volleyball blocking, the defensive blocker must time their
jump and arm motion relative to an opponent trying to hit the ball over the net.
31–33
In this study,
the longer flight time in the immediate condition resulted in an increased jump height of more
than 4 cm for only five of the twelve players. These differences were comparable to the
differences found between a squat jump and a counter-movement jump.
3,4
While the modest
increased height difference may give some players an advantage when it comes to blocking,
immediately converting the horizontal momentum to vertical momentum may inhibit their ability
to time the block. Thus, the performance benefit may have been lost in some players when
introducing a delay prior to their jump, suggesting that the positive effect due to active
lengthening was diminished when the players took more time to block.
21–23
Subsequently, for
57

players with a minimal height difference between conditions, having more time to coordinate
their jump relative to an opponent is likely more important than the jump height increase.
Understanding the trade-offs between height and timing for each individual is important when
evaluating vertical jump performance in athletic contexts.

Peak reaction forces during impact were similar within player regardless of jump condition.
Minimal differences were observed in mechanical loading despite being statistically significant.
The peak reaction forces were larger than those reported for squat and countermovement jumps,
yet similar to those generated during the impact phase in landings following a jump or VBJ (~3-
4x BW) across players.
3,42–44
Lead leg mechanical loading was the same as a group when
comparing Delayed to Immediate VBJs, while lag leg mechanical loading was either the same or
minimally larger for Immediate depending on the individual player. In addition, the orientation
of the peak reaction force was consistent across legs and conditions within individual, but did
vary across individuals. While the reaction force results may suggest that for some players using
a delayed movement may reduce lower extremity loading, any differences observed within
individual are minimal. The standard deviation in reaction force magnitude was 0.26 BW and the
standard deviation in reaction force angle was 1.9 degrees within player for all trials within
condition, whereas the standard deviation in reaction force magnitude and angle was larger at
0.66 BW and 4.2 degrees, respectively, across players (Figure 6-4). These results indicate that
the reaction force implications for each condition during the impact phase are more dependent on
the individual player than the addition of horizontal momentum to the VBJ and change in
jumping condition. Subsequently, individual players can be better prepared to handle reaction
force consequences by understanding the individual reaction forces imposed during different
tasks as performed in competition for each individual player.

Understanding the challenges present in a sport and how players navigate them is important
when trying to improve performance. Jumping in athletic contexts such as volleyball blocking
requires planning the jumping movement relative to an opponent so that the player can decide
when to jump such that they will be in the correct location at the right time. Now that we better
understand the importance of evaluating height and timing together when it comes to assessing
jump performance, additional investigation with athletes experimenting in realistic scenarios and
using technology to better assess these tradeoffs may help coaches determine which solutions are
best for each individual athlete.
41,45,46

58

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62

Chapter 7: Generation of Linear Impulse during the Takeoff of the
Long Jump

Introduction

Maximizing horizontal distance traveled during a horizontal jump requires effective regulation of
total body momentum prior to departure from the ground. When initiating a horizontal jump with
initial horizontal velocity, jumpers convert some of their horizontal momentum at contact to
vertical momentum by generating linear and angular impulse during interaction with the ground.
Vertical and horizontal impulse generation during the takeoff phase requires control of the total
body center of mass (CM) trajectory in relation to the reaction forces (RF) generated during
contact with the ground.
1
Understanding how an individual athlete can best generate CM vertical
velocity prior to ground departure is essential to optimizing the horizontal and vertical velocities
of their CM at departure in a way that maximizes their horizontal jump distance.

Initiating a horizontal jump with momentum can have a positive effect on an athlete’s ability to
generate vertical RF.
1,2
Previous research indicates that athletes initiating jumps with momentum
tend generate greater net vertical impulse, resulting in a higher jump
3–6
than when initiating a
jump without momentum. As this initial momentum increases, greater net vertical impulse can
be generated.
7
If however, the mechanical demand imposed on the lower extremity during
contact exceeds the ability of the individual to control said demand, losses in vertical impulse
generation can occur.
4,8,9
During the take-off phases of the long jump or triple jump, it has been
observed that as more horizontal momentum is lost more vertical momentum is gained.
10–12

Thus, in order to maximize vertical jump height and net vertical impulse generated, an athlete
with initial horizontal momentum must increase the negative horizontal impulse generated
during contact while effectively controlling the imposed mechanical demand.

Horizontal momentum regulation during foot contact is largely affected by CM position relative
to the center of pressure. In athletic contexts, adopting an initial posture with contact foot
anterior to the CM typically results in more negative horizontal impulse generated during contact
(commonly known as braking) and a longer contact duration compared to adopting an initial
posture with contact foot directly below or posterior to the CM.
13
The athlete is only able to
initiate lower extremity joint extension when the CM is no longer posterior to the center of
pressure, resulting in initial negative horizontal RF and the inability to immediately generate
positive horizontal impulse.
13
Greater negative horizontal impulse can subsequently be attained
by adopting a posture with the foot further anterior to the CM.

Successful performance of the long jump requires maximizing distance of the body relative to
the take-off board since jump distance is measured from the scratch line to the first mark made
by the body in the sand. In order to maximize the measured distance of the long jump, the jumper
must (a) maximize vertical and horizontal velocity at departure to increase horizontal
displacement, (b) regulate angular velocity in the air via segment configuration to land in the
optimum position, and (c) depart as close to the board as possible.
14–17
The long jump can be
broken down into 4 phases: (1) the approach or run-up (2) the takeoff (3) the flight and (4) the
landing.
14,17
The takeoff phase in the long jump is the last opportunity for a jumper to generate
63

vertical velocity prior to flight.
14
During this phase, horizontal velocity can be maximized by
reducing horizontal impulse lost, while vertical velocity can be maximized by increasing net
vertical impulse generated. As vertical impulse increases during the takeoff, negative horizontal
impulse tends to linearly increase as well.
10–12
An increase in CM vertical velocity achieved at
departure can be shown using projectile equations of motion to be nearly twice as beneficial as a
similar increase in horizontal velocity, suggesting that sacrificing some horizontal momentum for
similar increases in vertical momentum may be beneficial for increasing CM displacement
during the flight phase (Figure 7-1).
10

Figure 7-1: Results from projectile motion calculations for two different example jumps. In Example A, the jumper
has a horizontal takeoff velocity of 9.0 m/s and vertical takeoff velocity of 3.0 m/s, resulting in a horizontal
displacement of 6.73m. In Example B, the jumper has a smaller horizontal takeoff velocity of 8.5 m/s but greater
vertical takeoff velocity of 3.5 m/s instead, resulting in a greater horizontal displacement of 7.10m. A vertical
displacement of 0.5m is assumed for both examples.

While generation of vertical velocity at departure has proven to be advantageous for jump
distance, how an individual can increase CM vertical velocity during the takeoff has not been
thoroughly studied.
14,17,18
Both landing distance for the last stride into the takeoff and the height
of the total body CM at departure are significantly correlated with jump distance.
19
Furthermore,
the same jump distance can be achieved using different takeoff techniques, where increased
losses due to braking impulse do not result in decreased jump distance due to the increased net
vertical impulse generated.
20
Lastly, models such as those developed in Alexander 1990 have
suggested that the key to maximizing jump distance is to maximize horizontal velocity prior to
the takeoff phase while initiating contact at a steeper (i.e. larger) leg angle, indicating that hip
joint center for the contact leg is further behind the ankle joint center (Figure 7-2).
21
Regardless
of takeoff phase strategy or impulse generation, it is key to investigate how each individual
accomplishes their conversion of horizontal to vertical velocity given the multiple solutions
present in horizontal jumping.
11,12

The aim of this study was to investigate the means by which individuals generate vertical
velocity during the takeoff in long jump. We hypothesized that when individuals initiate contact
of the takeoff phase with a greater leg angle, they will generate more negative horizontal and
positive net vertical impulse, have a longer total contact time, and that the increased linear
impulses would occur during the impact interval as a result of increased RF magnitude and
contact time. We tested these hypotheses by measuring the horizontal and vertical RFs during the
takeoff of a long jump and comparing them to leg angle at initial contact.
64

Figure 7-2: Depiction of leg angle (θleg) at initial contact for the takeoff phase of an example jumper for 2 trials.
Leg angle was defined from ankle joint center to hip joint center relative to forward horizontal. Initial leg angle is
smaller for left compared to right trial.

Methods

Subjects
Data from eleven (5 male, 6 female) skilled long jumpers (national and Olympic level) between
23 and 30 years of age were used in this study in accordance with the International Review
Board. The mean (SD) mass was 78.0 kg (7.0) for male and 62.5 kg (4.5) for female jumpers.

Tasks
Collections were performed over the course of 4 years from 2012 to 2016 (some jumpers
participated in multiple collections). Each jumper performed a series of 2-6 long jump takeoffs
as if they were participating in competition or practice. During the long jump takeoff, each
individual attempted to jump as far as possible to achieve the furthest possible jump. Jumpers
were allowed sufficient time prior to data collection to warm-up. Only jumpers with 6 or more
complete jumps were used in this analysis.

Data Collection
Data collection was treated as a component of each jumper’s normal practice or competition.
Sagittal and coronal plane kinematics were recorded using high-speed cameras (240 or 300 Hz,
Casio, Dover, NJ, USA). Vertical and horizontal ground reaction forces (RF) during the takeoff
phase of each jump (last contact) were recorded at 1,200 Hz using a force plate (0.6 m x 0.9 m,
Kistler, Amherst, NY, USA). These sets of data were synchronized at the time of plate departure.
65

Jump Intervals and Events
The RF-time characteristics were described using two functional intervals: impact and post-
impact as described in Ramey 1970 (Figure 7-3).
18
The impact interval was determined to be
from initial contact to the first increase in vertical RF after peak RF. The post-impact interval
was determined from first increase in vertical RF after peak RF to final contact.

Figure 7-3: Kinematic sequence of events for key instances in time (grey lines) and associated horizontal and
vertical reaction forces for the takeoff phase for an example jumper. Resultant RF is depicted in green for each
image. Division of impact and post-impact intervals is labeled.

66

Analysis
Positive values of RF corresponded to vertical and forward horizontal RFs. The orientation of the
resultant RF was defined as an angle of the RF relative to forward horizontal passing through the
center of pressure. Contact time (∆t), average horizontal RF (RFhavg), average vertical RF
(RFvavg), horizontal impulse normalized by body mass (∆Vh), and net vertical impulse
normalized by body mass (∆Vv) were determined for impact interval, post-impact interval, and
in total from the RF-time data for the contact foot during the takeoff phase.

Initial leg angle (θleg) for the contact leg was determined at the initiation of the takeoff phase for
each jumper, and was defined from ankle joint center to hip joint center (lateral malleolus to
greater trochanter) relative to forward horizontal (Figure 7-2).

Statistics
Comparisons between variables on the group level were made using a 1-tailed Pearson
correlation (α = 0.05). Comparison between variables on the individual level were made using
the Winsorized correlation and HC4 method described in Wilcox 2012 (α < 0.05).
22

Results

Changes in CM Horizontal and Vertical Velocity during Take-off
Greater negative horizontal impulse corresponded with greater positive net vertical impulse
generated during the takeoff (Table 7-1). On the group level, decreases in CM horizontal velocity
during take-off were significantly correlated with increases in CM vertical velocity (p < 0.05).

Individually, greater negative horizontal impulse corresponded with greater positive net vertical
impulse generated as well (Table 7-1, Figure 7-4). For 10 of 11 jumpers, decreases in CM
horizontal velocity during take-off were significantly correlated with increases in CM vertical
velocity.

Table 7-1: Individual and group correlations between select variables including initial leg angle (θleg), total
changes in CM velocities (∆Vh, ∆Vv), impact interval changes in CM velocities (∆Vh1, ∆Vv1), post-impact interval
changes in CM velocities (∆Vh2, ∆Vv2), contact time (∆t), and average reaction forces (RFh, RFv).

67

Figure 7-4. Boxplots of horizontal velocity lost (│∆Vh│) (grey) and vertical velocity generated (│∆Vv│) (black) for
each jumper. * denotes significant correlation between ∆Vh and ∆Vv (p < 0.05), † denotes non-significant
correlation (p < 0.10) Jumpers are sorted by increasing median ∆Vv.

Initial Leg Angle and Changes in CM Velocity during Take-off
Greater leg angle at initial contact of the takeoff corresponded with greater impulse generation
(Table 7-1). On the group level, increases in leg angle were significantly correlated with both
decreases in CM horizontal velocity and increases in CM vertical velocity.

Individually, greater leg angle at initial contact of the takeoff resulted in greater impulse
generated as well (Table 7-1, Figure 7-5). For 7 of 11 jumpers, increase in leg angle was
significantly correlated with both decrease in CM horizontal velocity and increase in CM vertical
velocity. Two of the remaining 4 jumpers had a similar correlation, however it was not
significant (p < 0.10). The remaining 2 jumpers had a significant negative correlation between
leg angle and CM horizontal velocity but no correlation between leg angle and CM vertical
velocity.

Sources of Increase in Impulse Generation
Increases in impulse generated during the takeoff corresponded with increases in average RF
magnitude but not contact time (Table 7-1). On the group level, decreases in average horizontal
RF and decreases in horizontal CM velocity were significantly correlated, as were increases in
average vertical RF and increases in vertical CM velocity. Increases in contact time were not
significantly correlated with decreases in horizontal CM velocity or increase in vertical CM
velocity.

68

However individually, increases in impulse generation corresponded with increases in contact
time, average RF, or both depending on the individual (Table 7-1, Figure 7-5). For 3 of 8
jumpers with a significant correlation between increases in leg angle and increases in CM
vertical velocity, increases in CM horizontal and vertical velocity were significantly correlated
with increase in contact time only. For 4 jumpers, increases in CM horizontal and vertical
velocity were significantly correlated with increases in average RF magnitude only. For 1
jumper, increases in CM horizontal and vertical velocity were significantly correlated with both
increases in contact time and average RF.

Figure 7-5: Horizontal velocity lost ( │∆Vh │) (grey) and vertical velocity generated ( │∆Vv │) (black) versus leg
angle (top), contact time (middle), and average RF (bottom) for jumpers with a correlation between leg angle and
change in CM velocity. * denotes significant correlation between variables (p < 0.05), † denotes non-significant
correlation between variables (p < 0.10). Jumpers 1, 6, 8, and 10 increased impulse generation by increasing
contact time only (left). Jumpers 2, 7, and 11 increased impulse generation by increasing average RF only (middle).
Jumpers 3 and 5 increased impulse generation by increasing both contact time and average RF (right). Jumpers 4
and 9 (not shown) had a significant correlation between θleg and ∆Vh but no correlation between θleg and ∆Vv.
Jumpers are sorted by increasing median ∆Vv.
69

Distribution of Impulse during Impact and Post-Impact Intervals
Increases in impulse generated during the takeoff occurred during both the impact and the post-
impact intervals (Table 7-1). On the group level, decreases in the change in CM horizontal
velocity during impact were significantly correlated with decreases in the change in CM
horizontal velocity during the take-off phase. Likewise, increases in CM vertical velocity during
impact were significantly correlated with changes in CM vertical velocity during the take-of
phase. Decreases in CM horizontal velocity during post-impact were significantly correlated with
decreases in CM horizontal velocity during the take-off phase. Likewise, increases in CM
vertical velocity during post-impact was significantly correlated with increases in total CM
vertical velocity the during take-off phase.

However individually, increases in impulse generation during the takeoff occurred during either
the impact, the post-impact, or both depending on the individual (Table 7-1, Figure 7-6). For 2 of
7 jumpers with a significant correlation between increase in leg angle and increase in CM
vertical velocity, significant increases in impulse generation occurred only during the impact
interval. For 2 jumpers, significant increases in impulse generation occurred only during the
post-impact interval. For 2 jumpers, significant increases in impulse generation occurred during
both the impact and post-impact intervals.

Figure 7-6: Median horizontal velocity lost (∆Vh) and vertical velocity generated (∆Vv) of impact (∆Vh 1, ∆Vv 1) and
post-impact (∆Vh 2, ∆Vv 2) intervals for jumpers with a correlation between leg angle and change in CM velocity.
Total ∆Vh and ∆Vv are the summation of impact and post-impact contribution. * denotes correlation for both ∆Vh
vs ∆Vh 1 and ∆Vv vs ∆Vv 1, † for both ∆Vh vs ∆Vh 1 and ∆Vv vs ∆Vv 1 (black for p < 0.05, grey for p < 0.10). Jumpers
4 and 9 (not shown) had a significant correlation between θleg and ∆Vh but no correlation between θleg and ∆Vv.
Jumpers are sorted by increasing median ∆Vv.

Example Comparisons
Example comparison of kinematics and force were made for two exemplar trials for two jumpers
with greater ∆Vv as a result of greater θleg. Jumper 8 had significantly greater ∆Vv as a result of
greater ∆t only during both the impact and post-impact intervals, while Jumper 7 had a
significantly greater ∆Vv as a result of greater RFavg only during the impact interval only
(Figures 7-7, 7-8).
70

Figure 7-7: Example kinematics and RF-time curves for Jumper 8. Jumper had increased ∆Vv generated when
initiating the takeoff with a greater initial leg angle (Trial B) by increasing ∆t during both the impact and post-
impact intervals. Resultant RF is in green.

71

Figure 7-8: Example kinematics and RF-time curves for Jumper 7. Jumper had increased ∆Vv generated when
initiating the takeoff with a greater initial leg angle (Trial B) by increasing RFv avg during the impact interval only.
Resultant RF is in green.
72

Discussion

In this study we determined how horizontal jump performance in skilled jumpers was affected by
initial leg configuration. The results of this within-jumper analysis indicate that when jumpers
initiate the takeoff with larger leg angles, some are able to generate greater increases in CM
vertical velocity. Increases in CM velocity typically occurred at the expense of greater decreases
in CM horizontal velocity at the group level. These greater changes in CM velocity during the
take-off phase corresponded with increases in impulse generation resulting from increased
contact time or average reaction force during either the impact or post-impact interval, depending
on the individual. However, the conclusions at the group level do not necessarily reflect the
findings on the individual level, with eight jumpers having a significant correlation between
larger initial leg angle and increase in CM vertical velocity, for example, while the remaining
three jumpers did not. Initial leg configuration at contact and individual specific impulse
generation strategies are important to consider when determining how an athlete with initial
momentum can increase impulse generation to jump for distance.

The study of elite athlete performance, by design, limits the sample size. In addition, large forces
imposed upon each jumper (often > 15x BW) limited the number of jumps trials per data
collection session. To increase the number of trials per jumper, data was collected over multiple
training sessions to avoid excessive load exposure within a single training session. This approach
provided a means to maximize the number of trials per participant for a within-jumper
correlational analysis. An increase in the number of participants and number of trials per jumper
would strengthen the analysis. The force-time and magnitude characteristics observed in this
study were consistent with those reported in previous studies.
18,23,24
Trials for jumpers were
collected with adequate rest between trials to minimize any fatigue effects. Jumpers were
allowed to self-select their starting distance and initiation away from the long jump board in
order to best mimic practice and competition. Any potential reaction force attenuation by the
track material that was used to cover each force plate or the jumpers’ footwear with spikes was
expected to be minimal and consistent across data collection sessions. The resolution of force
results was particularly valuable in discerning accurate differences in change in CM velocities
between attempts by skilled performers.

Jumpers in this study increased their net vertical impulse generation during take-off when
initiating contact with a larger leg angle. A larger leg angle at contact typically places the foot
further anterior to the total body CM, which contributes to increases in braking horizontal
impulse and RF magnitude during the takeoff phase (Figure 7-5). Placement of the foot further
anterior to the CM at contact has been shown to increase braking horizontal impulse in other
tasks such as sprinting.
13
These findings are also consistent with previous kinematic studies of
the long jump take-off phase.
10–12
The increases in braking horizontal impulse, however, also
result in similar increases in net vertical impulse generated, as shown in Figures 7-4 and 7-5.
Since increases in net vertical impulse generated during take-off contributes to greater CM
vertical velocities at take-off, jumpers will likely have greater time in the air and subsequently
further CM horizontal displacement during the subsequent flight phase as shown in Figure 7-1,
despite decreased takeoff CM horizontal velocity. The increased net vertical impulse generated
should result in further jump distances for each individual for similar initial horizontal velocities
73

given the increased benefit of vertical velocity generation compared to horizontal velocity for the
takeoff phase, although this remains to be seen.
10

Increases in impulse generation were found to correspond with increases in contact time and / or
average vertical reaction force during either the impact or post-impact intervals, depending on
the individual. Any increases in impulse generation were expected to be the result of both
increased contact time and average RF, similar to the increased contact time and RF magnitude
observed in sprint starts.
13
However, only 1 jumper with a significant correlation between
increase in leg angle and increase in CM vertical velocity had increased impulse generation due
to both increased contact time and average RF. The remaining jumpers were instead due to
increased contact time only or increased average RF only, as shown in Figure 7-5. Similarly,
while increased impulse generation was expected to occur during the impact interval and not the
post-impact interval, instead jumpers were able to increase impulse generation during either or
both intervals.
13
Increased impulse generation occurred during both intervals for only 2 jumpers,
while increased impulse generation occurred during the impact only for 2 jumpers and post-
impact only for 2 jumpers, as shown in Figure 7-6.

The conclusions for each individual jumper do not necessarily coincide with the conclusions
determined at the group-level. For example, while there was a significant correlation between
initial leg angle and increase in CM vertical velocity at the group-level (r = 0.49, p < 0.05), this
correlation was not significant for three of the jumpers. This suggests that increasing leg angle at
initial contact of the takeoff phase may not be a mechanism by which to increase vertical
velocity at departure for those individuals. Furthermore, for the eight individuals that did have a
significant correlation, their correlation value was much higher than that determined at the group
level with a median (range) r-value of 0.94 (0.75, 1.00). Even for individuals with a significant
correlation, the means by which net vertical impulse was increased can be different, as shown in
Figures 7-7 and 7-8. It is subsequently important to investigate how each jumper individually can
increase impulse generation to maximize their jump distance and determine what strategy works
best for them, considering that different takeoff solutions can yield the same jump distance
result.
11,12,20
By determining which strategies work best for each jumper rather than which
strategies work in general, coaches can better adapt their workouts and training to the needs of
the individual in order to maximize their jump distance performance.

74

References
1. Mathiyakom W, McNitt-Gray JL, Wilcox R. Lower extremity control and dynamics
during backward angular impulse generation in backward translating tasks. Exp Brain Res.
2006;169(3):377-388. doi:10.1007/s00221-005-0150-7.
2. Mathiyakom W, McNitt-Gray JL, Wilcox R. Lower extremity control and dynamics
during backward angular impulse generation in forward translating tasks. J Biomech.
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3. Bobbert MF, Gerritsen KG, Litjens MC, Van Soest a J. Why is countermovement jump
height greater than squat jump height? Med Sci Sports Exerc. 1996;28(11):1402-1412.
doi:10.1097/00005768-199611000-00009.
4. Moran K a., Wallace ES. Eccentric loading and range of knee joint motion effects on
performance enhancement in vertical jumping. Hum Mov Sci. 2007;26(6):824-840.
doi:10.1016/j.humov.2007.05.001.
5. Hara M, Shibayama A, Takeshita D, Hay DC, Fukashiro S. A comparison of the
mechanical effect of arm swing and countermovement on the lower extremities in vertical
jumping. Hum Mov Sci. 2008;27(4):636-648. doi:10.1016/j.humov.2008.04.001.
6. Lees A, Vanrenterghem J, Clercq DD. Understanding how an arm swing enhances
performance in the vertical jump. J Biomech. 2004;37(12):1929-1940.
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7. Walsh M, Arampatzis A, Schade F, Bruggemann G-P. The Effect of Drop Jump Starting
Height and Contact Time on Power, Work Performed, and Moment of Force. J Strength
Cond Res. 2004;18(3):561-566. doi:10.1519/00124278-200408000-00030.
8. Flitney FW, Hirst DG. Cross-bridge detachment and sarcomere “give” during stretch of
active frog’s muscle. J Physiol. 1978;276:449-465. doi:10.1113/jphysiol.1978.sp012246.
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10. Tiupa V, Aleshinksi S, Primakov I, Pereverzev A. The biomechanics of the movement of
the body’s general center of mass during the long jump (Russian). Teor Prakt Fiz Kul.
1982:11-14.
11. Yu B, Hay JG. Optimum phase ratio in the triple jump. J Biomech. 1996;29(10):1283-
1289. doi:10.1016/0021-9290(96)00048-6.
12. Liu H, Yu B. Effects of phase ratio and velocity conversion coefficient on the
performance of the triple jump. J Sports Sci. 2012;30(14):1529-1536.
doi:10.1080/02640414.2012.713502.
75

13. Costa K. Control and Dynamics during Horizontal Impulse Generation. 2004.
14. Hay JG. The Biomechanics of the Long Jump. Exerc Sport Sci Rev. 1986;14(1):401-446.
15. Bedi JF, Cooper JM. Take off in the long jump-Angular momentum considerations. J
Biomech. 1977;10(9):541-548. doi:10.1016/0021-9290(77)90034-3.
16. Chow JW, Hay JG. Computer simulation of the last support phase of the long jump. Med
Sci Sports Exerc. 2005;37(1):115-123. doi:10.1249/01.MSS.0000150086.13664.32.
17. Hay JG. Citius, altius, longius (faster, higher, longer): The biomechanics of jumping for
distance. J Biomech. 1993;26(SUPPL. 1):7-21. doi:10.1016/0021-9290(93)90076-Q.
18. Ramey M. Force Relationship of the Running Long Jump. Med Sci Sport. 1970;2(3):146-
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19. Hay JG, Nohara H. Techniques used by elite long jumpers in preparation for takeoff. J
Biomech. 1990;23(3):229-239. doi:10.1016/0021-9290(90)90014-T.
20. Seyfarth a., Friedrichs a., Wank V, Blickhan R. Dyanamics of the Long Jump. J Biomech.
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21. Alexander RM. Optimum take-off techniques for high and long jumps. Philos Trans R Soc
Lond B Biol Sci. 1990;329(1252):3-10. doi:10.1098/rstb.1990.0144.
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in long jump take-off. Eur J Appl Physiol Occup Physiol. 1979;41(4):267-274.
doi:10.1007/BF00429743.
24. Muraki Y, Ae M, Koyama H, Yokozawa T. Joint Torque and Power of the Takeoff Leg in
the Long Jump. Int J Sport Heal Sci. 2008;6:21-32. doi:10.5432/ijshs.6.21.

76

Chapter 8: Regulation of Linear Impulse during the Takeoff of the
Long Jump

Introduction

Maximizing horizontal distance traveled during a horizontal jump requires effective regulation of
total body momentum prior to departure from the ground. When initiating a horizontal jump with
initial horizontal velocity, jumpers convert some of their horizontal momentum at contact to
vertical momentum by generating linear and angular impulse during interaction with the ground.
Vertical and horizontal impulse generation during the takeoff phase requires control of the total
body center of mass (CM) trajectory in relation to the reaction forces (RF) generated during
contact with the ground.
1
Understanding how an individual athlete can best generate CM vertical
velocity prior to ground departure is essential to optimizing the horizontal and vertical velocities
of their CM at departure in a way that maximizes their horizontal jump distance.

Initiating a horizontal jump with momentum can have a positive effect on an athlete’s ability to
generate vertical RF.
1,2
Previous research indicates that athletes initiating jumps with momentum
tend generate greater net vertical impulse, resulting in a higher jump
3–6
than when initiating a
jump without momentum. As this initial momentum increases, greater net vertical impulse can
be generated.
7
If however, the mechanical demand imposed on the lower extremity during
contact exceeds the ability of the individual to control said demand, losses in vertical impulse
generation can occur.
4,8,9
During the take-off phases of the long jump or triple jump, it has been
observed that as more horizontal momentum is lost more vertical momentum is gained.
10–12

Thus, in order to optimize the horizontal and vertical velocities of their CM at departure,
horizontal jumpers need to effectively regulate linear and angular impulse generation during last
contact while effectively controlling the mechanical demand imposed on the lower extremity.

Successful performance of the long jump requires maximizing distance of the body relative to
the take-off board since jump distance is measured from the scratch line to the first mark made
by the body in the sand. In order to maximize the measured distance of the long jump, the jumper
must (a) maximize vertical and horizontal velocity at departure to increase horizontal
displacement, (b) regulate angular velocity in the air via segment configuration to land in the
optimum position, and (c) depart as close to the board as possible.
13–16
The long jump can be
broken down into 4 phases: (1) the approach or run-up (2) the takeoff (3) the flight and (4) the
landing.
13,16
The takeoff phase in the long jump is the last opportunity for a jumper to generate
vertical velocity prior to flight.
13
During this phase, horizontal velocity can be maximized by
reducing horizontal impulse lost, while vertical velocity can be maximized by increasing net
vertical impulse generated. As vertical impulse increases during the takeoff, negative horizontal
impulse tends to linearly increase as well.
10–12
An increase in CM vertical velocity achieved at
departure can be shown using projectile equations of motion to be nearly twice as beneficial as a
similar increase in horizontal velocity, suggesting that sacrificing some horizontal momentum for
similar increases in vertical momentum may be beneficial for increasing CM displacement
during the flight phase (Figure 8-1).
10

77

While generation of vertical velocity at departure has proven to be advantageous for jump
distance, how an individual can increase CM vertical velocity during the takeoff has not been
thoroughly studied.
13,16,17
Previous work suggests that when long jumpers initiate the takeoff
phase with a larger leg angle (Figure 8-2), they are able to generate greater negative horizontal
and positive net vertical impulse. The increased impulse generation is a result of increased RF
magnitude and/or duration during either the impact and/or post-impact interval. How the
individual regulates impulse generation while controlling the mechanical demand imposed on the
take-off leg has not been investigated. Research on joint kinetics in the long jump takeoff
18–20
is
largely limited by the inability to measure RFs during take-off under contextually-relevant
conditions. Furthermore, studies that do investigate long jump joint torque and power tend to
report general findings rather than investigating sources of differences in impulse generation, leg
kinematics, and joint kinetics within-jumpers across trials.
20,21
Comparisons of joint torque and
work done reported in the literature tend to focus on the period of leg yielding (when the knee is
flexing) as compared to leg push (when the knee is extending) rather than comparing within
individual across trials when there are differences in impulse generation.
20
By understanding the
differences in impulse generation between trials performed by the same individual, we can find
effective impulse regulation strategies they can use to improve jump performance.
11,12,22

The aim of this study was to determine how individual jumpers generate CM vertical velocity at
departure and maintain horizontal momentum generated during the approach, while controlling
the mechanical demand imposed on the lower extremity. We hypothesized that when individuals
had reduced leg yield, they would generate greater positive net vertical impulse due to increased
contact time and average reaction force during the impact and post-impact intervals. We tested
this hypothesis by measuring the horizontal and vertical RFs during the takeoff of a long jump
and comparing them to digitized kinematics.

Figure 8-1: Results from projectile motion calculations for two different example jumps. In Example A, the jumper
has a horizontal takeoff velocity of 9.0 m/s and vertical takeoff velocity of 3.0 m/s, resulting in a horizontal
displacement of 6.73m. In Example B, the jumper has a smaller horizontal takeoff velocity of 8.5 m/s but greater
vertical takeoff velocity of 3.5 m/s instead, resulting in a greater horizontal displacement of 7.10m. A vertical
displacement of 0.5m is assumed for both examples.

78

Methods

Subjects
Data from seven (5 male, 2 female) skilled long jumpers (national and Olympic level) between
23 and 26 years of age were used in this study in accordance with the International Review
Board. The mean (SD) mass was 72.9 (7.0) kg.

Tasks
Collections were performed over the course of 4 years from 2012 to 2016. Each jumper
performed a series of long jump takeoffs as if they were participating in competition or practice.
During the long jump takeoff, each individual attempted to jump as far as possible to achieve the
longest possible jump. Jumpers were allowed sufficient time prior to data collection to warm-up.

Data Collection
Data collection was treated as a component of each jumper’s normal practice or competition.
Sagittal and coronal plane kinematics were recorded using high-speed cameras (240 or 300 Hz,
Casio, Dover, NJ, USA). Vertical and horizontal ground reaction forces (RF) during the takeoff
phase of each jump (last contact) were recorded at 1,200 Hz using a force plate (0.6 m x 0.9 m,
Kistler, Amherst, NY, USA). These sets of data were synchronized at the time of plate departure.

Twenty-four body landmarks (vertex, C7, right shoulder, elbow, wrist, finger, left shoulder,
elbow, wrist, finger, right iliac crest, greater trochanter, knee, lateral malleolus, heel, 5th
metatarsal, toe, left iliac crest, greater trochanter, knee, lateral malleolus, heel, 5th metatarsal,
and toe) were manually digitized using custom Matlab code for select trials. Digitized x and y
coordinates of body landmarks were individually filtered with a fourth order Butterworth filter
(zero phase lag) with cut-off frequencies (5–20 Hz) based on a method described by Jackson et
al.
23
Body segment parameters of an athletic population
24
were used to calculate the total body
and segment center of mass.

Jump Intervals and Events
The RF-time characteristics were described using two functional intervals: impact and post-
impact as described in Ramey 1970 (Figure 8-3). Impact interval was determined to be from
initial contact to the first increase in vertical RF after peak RF (impact end or transition). Post-
impact interval was determined from first increase in vertical RF after peak RF to final contact.

The kinematic characteristics were described using two functional intervals (leg yield and leg
extension). The leg yield interval was determined to be from initial contact to start of knee
extension as described in Muraki et al 2008. The leg extension interval was determined to be
from start of knee extension to final contact.

Analysis
Positive values of RF corresponded to vertical and forward horizontal RFs. The orientation of the
resultant RF was defined as an angle of the RF relative to forward horizontal passing through the
center of pressure. Contact duration ( ∆t), horizontal impulse normalized by body mass ( ∆Vh),
and net vertical impulse normalized by body mass ( ∆Vv) were determined for impact interval,
post-impact interval, and in total from the RF-time data for the contact foot during final contact.
79

The angular orientation of each body segment was defined as an angle of the segment relative to
forward horizontal passing through the distal end of the segment. Contact leg angle was
determined at the initiation of takeoff for each jumper, and was defined from ankle joint center to
hip joint center (lateral malleolus to greater trochanter). Synchronized RF and kinematic data
were used to calculate net joint force (NJF) and net joint moment (NJM) at the ankle, knee, and
hip using Newtonian equations and inverse dynamics approach.
25
Ankle, knee, and hip extensor
NJMs were presented in positive values. Representative NJMs at the ankle, knee, and hip were
determined at impact peak RF, transition, and post-impact peak RF by taking a 20% trimmed
mean of NJM values at these key events. The ankle, knee, and hip net joint moment powers
(NJMP) were calculated as a product of the NJM and their corresponding joint angular velocity
(JAV).

Initial leg angle (θleg) for the contact leg was determined at the initiation of the takeoff phase for
each jumper, and was defined from ankle joint center to hip joint center (lateral malleolus to
greater trochanter) relative to forward horizontal (Figure 8-2).

Inclusion Criteria
Only jumps performed on the same day for an individual were compared. Two trials were
selected for each individual that (a) had a difference in ∆Vv of greater than 10% or 0.3 m/s and
(b) had sufficient difference in leg yield kinematics. The trial with less ∆Vv generated is denoted
as Trial A, while the trial with more ∆Vv is denoted as Trial B.

Figure 8-2: Depiction of leg angle (θleg) at initial contact for the takeoff phase of an example jumper for 2 trials.
Leg angle was defined from ankle joint center to hip joint center relative to forward horizontal. Initial leg angle is
smaller for left compared to right trial.
80

Figure 8-3: Kinematic sequence of events for key instances in time (grey lines) and associated horizontal and
vertical reaction forces for the takeoff phase for an example jumper. Resultant RF is depicted in green for each
image. Division of impact and post-impact intervals is labeled.

Results

Force and Impulse Generation
All 7 jumpers generated more net vertical impulse for Trial B compared to Trial A (Tables 8-1,
8-2, Figure 8-7). Jumpers 1-4, and 7 had greater ∆Vv generated for Trial B during both the
impact and post-impact intervals. Jumper 5 had greater ∆Vv during the post-impact interval only,
while Jumper 6 had greater ∆Vv during the impact interval only.
81

Jumpers were able to increase their impulse generation using a combination of 4 different
methods (Tables 8-2, 8-3, Figure 8-7). Jumpers 2, 6, and 7 increased their average RF during the
impact interval for Trial B. Jumpers 1, 3, 4 and 6 increased their contact time during the impact
interval. Jumpers 1-3 and 5-7 increased their average RF during the post-impact interval. Jumper
4 was the only jumper that increased their contact time during the post-impact interval.

Leg Kinematics
Jumpers typically had less leg yield when generating more net vertical impulse. Jumpers 1-3 and
5-7 had reduced knee range of motion and knee flexion angular velocity during the yield interval
for Trial B compared to A (Figures 8-4, 8-5). Jumper 4 was the only jumper with greater knee
range of motion and knee flexion angular velocity instead. Jumpers 1-4 and 6 also had reduced
hip range of motion and hip angular velocity during the yield interval (Figures 8-4, 8-5).

Jumpers had slower rotation of the shank over their foot during contact when generating more
net vertical impulse (Figure 8-6). Jumpers 1, 2, and 5-7 had a smaller shank angular velocity
throughout the entire takeoff phase for Trial B. Jumpers 3 and 4 had a smaller shank angular
velocity during the impact interval only.

Initial leg angle was the same or greater when generating more net vertical impulse (Table 8-1,
Figures 8-7). Jumpers 1-4 had a larger leg angle at initial contact, whereas Jumpers 5-7 had a
similar initial leg angle instead.

Table 8-1: Initial leg angle, total contact time, decrease in horizontal velocity, and increase in vertical velocity for
all jumpers. Jumpers are ordered by decreasing % difference in ∆Vv generated.

Jumper % dif mass (kg) Trial θleg ∆t (s) ∆Vh (m/s) ∆Vv (m/s)
1 20% 67.9
A 127° 0.137 -1.22 3.52
B 130° 0.135 -1.83 4.23
2 15% 65.3
A 120° 0.117 -1.29 3.55
B 123° 0.117 -1.75 4.08
3 13% 71.7
A 123° 0.128 -1.33 3.55
B 130° 0.138 -1.72 4.02
4 13% 81.5
A 120° 0.106 -1.18 3.04
B 128° 0.132 -1.55 3.43
5 12% 80.2
A 125° 0.104 -1.58 3.56
B 125° 0.103 -1.51 3.99
6 11% 80.5
A 125° 0.143 -1.33 3.33
B 125° 0.136 -1.74 3.71
7 10% 63.4
A 125° 0.150 -1.42 3.24
B 124° 0.130 -1.46 3.56

82

Table 8-2: Average reaction force, contact time, decrease in horizontal velocity, and increase in vertical velocity for
the impact and post-impact intervals for all jumpers.

Impact Interval Post-Impact Interval
Jumper Trial avg RF ∆t ∆Vh ∆Vv avg RF ∆t ∆Vh ∆Vv
1
A 5.9 0.022 -0.55 1.04 3.4 0.115 -0.66 2.49
B 5.7 0.033 -1.01 1.51 4.0 0.102 -0.83 2.74
2
A 5.8 0.043 -1.07 2.04 3.3 0.074 -0.21 1.52
B 6.9 0.043 -1.35 2.36 3.6 0.073 -0.40 1.73
3
A 6.9 0.026 -0.83 1.50 3.2 0.102 -0.50 2.06
B 6.0 0.033 -1.12 1.65 3.5 0.104 -0.60 2.37
4
A 5.7 0.029 -0.70 1.27 3.6 0.077 -0.48 1.78
B 5.9 0.033 -0.94 1.49 3.1 0.099 -0.61 1.96
5
A 8.1 0.023 -1.06 1.92 2.8 0.082 -0.52 1.66
B 6.4 0.023 -0.76 1.50 3.9 0.079 -0.75 2.50
6
A 5.1 0.033 -0.77 1.29 3.1 0.111 -0.55 2.05
B 5.5 0.040 -1.11 1.74 3.3 0.096 -0.63 1.99
7
A 4.8 0.038 -0.99 1.55 2.7 0.113 -0.43 1.70
B 5.6 0.038 -0.99 1.68 3.3 0.093 -0.47 1.88

Table 8-3: Source of increased vertical impulse generation for all jumpers.  denotes a larger value and x denotes
a smaller value for Trial B compare to A for vertical reaction force magnitude (RFv) and contact time ( ∆t).

Impact Post-Impact
Jumper RFv ∆t RFv ∆t
1

  x
2 



3 x  

4 x  x 
5



6    x
7 

 x

83

Figure 8-4: Kinematics (top), hip-knee angle-angle diagram (bottom left), and joint angular velocities (bottom
right) for Jumper 2. Resultant RF (green vector) and extensor moments (yellow circles) are overlaid at key events.
Red arrows denote initial contact. Jumper has reduced knee and hip range of motion and angular velocity during
impact interval when leg is yielding for Trial B when generating greater ∆Vv.
84

Figure 8-5: Hip versus knee angle (degrees) for all jumpers for Trial A (black) and B (blue). Jumpers are ordered
by decreasing % difference in ∆Vv generated. Jumpers 1-3 and 5-7 have reduced leg yield for Trial B when
generating greater ∆Vv.

Figure 8-6: Leg versus shank angular velocity (deg/s) for all jumpers for Trial A (black) and B (blue). All jumpers
had reduced shank rotation for Trial B when generating greater ∆Vv.

85

Net Joint Moments for Exemplar Jumper
For Trial B, Jumper 2 was able to generate more total ∆Vv (+0.53 m/s) during impact (+0.32
m/s) by increasing reaction force magnitude and during post-impact (+0.21 m/s) by increasing
reaction force magnitude. Initial leg angle was larger, while leg yield and shank angular velocity
were smaller when generating more vertical velocity.

At impact peak RF, demand was hip dominant and more evenly distributed between the knee and
hip when generating more vertical velocity, resulting in increased knee and decreased hip
demand (Figures 8-7, 8-8). Ankle extensor moment was slightly larger (2.3 vs 1.3 Nm/kg), knee
extensor moment was larger (3.4 vs 1.8 Nm/kg), and hip extensor moment was much smaller
(8.8 vs 18.1 Nm/kg) for Trial B compared to A.

At transition from impact to post-impact, demand was knee dominant and similar between trials
(Figure 8-7). Ankle extensor moment was similar (2.9 vs 3.3 Nm/kg), knee extensor moment was
similar (4.9 vs 4.7 Nm/kg), and hip extensor moment was similar (1.6 vs 1.5 Nm/kg) for Trial B.

At post-impact peak RF, demand was also knee dominant and similar between trials (Figure 8-7).
Ankle extensor moment was similar (3.7 vs 3.6 Nm/kg), knee extensor moment was similar (4.2
vs 4.9 Nm/kg), and hip extensor moment was similar (2.2 vs 1.8 Nm/kg) for Trial B.

Figure 8-7: Kinematics, reaction force, net joint moments (NJM), joint angular velocity (JAV), and net joint moment
power (NJMP) versus time for Jumper 2. Resultant RF (green vector), extensor moments (yellow circles), and flexor
moments (cyan circles) are overlaid at key events.
86

Figure 8-8: Configuration and shank and thigh free body diagrams for Jumper 2 at impact interval peak RF.
Resultant RF (green vectors) and extensor moments (yellow circles) are overlaid onto configuration image. Net joint
forces (red vectors) and extensor moments (green circles) are depicted for each free body diagram. RF is more in-
line with the leg for Trial B when generating greater ∆Vv while RF is more anterior to the leg and in-line with the
shank for Trial A when generating less ∆Vv, resulting in larger knee extensor but smaller hip extensor NJM for
Trial B.

Discussion

The aim of this study was to determine how individual jumpers generate CM vertical velocity at
departure while maintaining horizontal momentum generated during the approach. In particular,
we investigated how differences in leg yield affect linear impulse generation during the takeoff
phase of a long jump performed by national and Olympic level long jumpers. We hypothesized
that when individuals had reduced leg yield, they would generate greater positive net vertical
impulse generation due to increased contact time and average reaction force during the impact
and post-impact intervals. Our results indicate that when jumpers had reduced leg yield and
shank rotation, all but one generated more vertical velocity during the takeoff phase. The ability
to both maintain a more rigid knee and reduce shank rotation may improve the chances of being
able to increase impulse generation during the post-impact of the long jump. An exemplar
jumper displayed more evenly distributed demand between the knee and the hip during the
impact interval, which may allow her to sustain and increase her RF through the end of the
impact interval and into the post-impact interval. Net joint moments during transition and the
post-impact intervals were similar between trials for this jumper. Understanding how each
individual jumper is able to regulate and increase impulse generation during the takeoff is
essential for determining how best to improve jump distance performance.

When jumpers had reduced leg yield (both in terms of reduced knee range of motion and knee
flexion angular velocity), they were typically able to generate more vertical velocity during the
takeoff phase. All jumpers except one had reduced leg yield when they were more effective in
generating CM vertical velocity at departure (Figures 8-4 and 8-5). When jumpers had reduced
leg yield, they also had increased RF magnitude during the post-impact. The ability to maintain a
more rigid knee with less ‘give’ during impact may improve the chances of being able to
increase RF magnitude during the post-impact, typically resulting in increased net vertical
87

impulse generation. Furthermore, shank rotation over the foot was much slower for all jumpers
when generating more vertical velocity (Figure 8-6). Regardless of whether post-impact impulse
generation is increased by RF magnitude or contact time, it may be that by reducing rotation of
the shank the jumper is able to increase their opportunity to generate impulse.

Impact net joint moments were more evenly distributed across the leg for Jumper 2 when she had
less leg yield, greater net vertical impulse generated, and larger initial leg angle. Jumper 2 had a
hip to knee ratio closer to 1.0 at impact peak RF when she had reduced leg yield as shown in
Figure 8-8. Distributing the mechanical demand between the knee and the hip together, rather
than the knee or hip by itself, may help this particular jumper to maintain knee rigidity and
reduce ‘give’, thereby allowing them to increase impulse generation later during contact. It may
be that while having a knee and hip moment that is more similar in magnitude results in reduced
leg yield, reducing demand at the hip in favor of increasing demand at the knee is the key to
increasing post-impact impulse generation without the drawbacks of reduced contact time,
although this remains to be seen. The net joint moments observed were typically extensor
moments throughout the takeoff phase across individuals, and were in general similar to values
observed in previous literature across the group, although within individual there were a variety
of moments observed.
20
Whether mechanical demand was knee or hip dominated during impact
or flexor versus extensor did not seem to affect the individual jumper’s ability to generate
impulse during the impact or post-impact intervals. This highlights the need to study and assess
each jumper as an individual to ensure feedback provided by the coach is specific to the
mechanism the individual uses to generate impulse generation during the take-off phase. By
understanding the differences in impulse generation between trials performed by the same
individual, we have been able to identify effective approaches for regulating impulse generation
during take-off. We expect that this level of specificity will prove to be advantageous to coaches
working to improve the performance of individual jumpers.

88

References
1. Mathiyakom W, McNitt-Gray JL, Wilcox R. Lower extremity control and dynamics
during backward angular impulse generation in backward translating tasks. Exp Brain Res.
2006;169(3):377-388. doi:10.1007/s00221-005-0150-7.
2. Mathiyakom W, McNitt-Gray JL, Wilcox R. Lower extremity control and dynamics
during backward angular impulse generation in forward translating tasks. J Biomech.
2006;39(6):990-1000. doi:10.1016/j.jbiomech.2005.02.022.
3. Bobbert MF, Gerritsen KG, Litjens MC, Van Soest a J. Why is countermovement jump
height greater than squat jump height? Med Sci Sports Exerc. 1996;28(11):1402-1412.
doi:10.1097/00005768-199611000-00009.
4. Moran K a., Wallace ES. Eccentric loading and range of knee joint motion effects on
performance enhancement in vertical jumping. Hum Mov Sci. 2007;26(6):824-840.
doi:10.1016/j.humov.2007.05.001.
5. Hara M, Shibayama A, Takeshita D, Hay DC, Fukashiro S. A comparison of the
mechanical effect of arm swing and countermovement on the lower extremities in vertical
jumping. Hum Mov Sci. 2008;27(4):636-648. doi:10.1016/j.humov.2008.04.001.
6. Lees A, Vanrenterghem J, Clercq DD. Understanding how an arm swing enhances
performance in the vertical jump. J Biomech. 2004;37(12):1929-1940.
doi:10.1016/j.jbiomech.2004.02.021.
7. Walsh M, Arampatzis A, Schade F, Bruggemann G-P. The Effect of Drop Jump Starting
Height and Contact Time on Power, Work Performed, and Moment of Force. J Strength
Cond Res. 2004;18(3):561-566. doi:10.1519/00124278-200408000-00030.
8. Flitney FW, Hirst DG. Cross-bridge detachment and sarcomere “give” during stretch of
active frog’s muscle. J Physiol. 1978;276:449-465. doi:10.1113/jphysiol.1978.sp012246.
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13. Hay JG. The Biomechanics of the Long Jump. Exerc Sport Sci Rev. 1986;14(1):401-446.
14. Bedi JF, Cooper JM. Take off in the long jump-Angular momentum considerations. J
Biomech. 1977;10(9):541-548. doi:10.1016/0021-9290(77)90034-3.
15. Chow JW, Hay JG. Computer simulation of the last support phase of the long jump. Med
Sci Sports Exerc. 2005;37(1):115-123. doi:10.1249/01.MSS.0000150086.13664.32.
16. Hay JG. Citius, altius, longius (faster, higher, longer): The biomechanics of jumping for
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Exerc Sport. 1980;51(2):334-348. doi:10.1080/02701367.1980.10605202.
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the Long Jump. Int J Sport Heal Sci. 2008;6:21-32. doi:10.5432/ijshs.6.21.
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1939;10(5):485-491. doi:10.1007/BF02012165.

90

Chapter 9: Generation of Linear Impulse during a 180° Change of
Horizontal Momentum

Introduction

Pushing effectively on the ground is an action central to generation and regulation of linear
momentum in sports. To succeed in athletic environments players must often reconfigure their
bodies to anticipate the need to push in a desired direction, so that the push on the ground is
quick, forceful, and satisfies task performance specifications. Satisfying the mechanical
objectives required by these tasks at the total body level involves multijoint control of the
ongoing interaction between the body and the environment.
1
Studying how individuals
accomplish these mechanical objectives in an attempt to maximize athletic performance under
varying initial momentum and configuration conditions advances our understanding of the
control structure and its benefits specific to an individual.
2–5

Effective horizontal impulse generation requires control of the reaction force (RF) during foot
contact in relation to the CM trajectory. Redirection of initial total body momentum in complex,
multi-joint, goal-directed movements such as running and jumping requires strategic
repositioning of the contact foot relative to the total body CM.
6–9
In contrast, generation of total
body momentum when initial momentum is zero is achieved by re-positioning the total body CM
relative to the contact foot instead.
10,11
In both momentum situations, when the contact foot is
anterior to the total body CM the associated horizontal RF and impulse typically act in
opposition to the CM trajectory.
12
During time-dependent tasks such as a 180° change in
horizontal direction or sprinting, the rate at which impulse is generated must also be considered.
If CM position relative to contact foot inhibits impulse generation for the desired direction then
time to complete the task will increase, whereas if CM position relative to contact foot supports
impulse generation direction then time to complete the task will decrease.
12
In athletics,
regulating total body CM relative to the contact foot can then be used to effectively generate or
redirect horizontal momentum in a desired direction accordingly.

Initiating a movement with momentum can have a positive effect on an athlete’s ability to
generate reaction force.
3,4
In sport-specific contexts, initiating a movement such as a jump with
momentum often leads to greater impulse generation compared to movements without initial
momentum.
13–15
A quick downward motion of the CM immediately prior to leg extension (e.g.
counter-movement jump) has been shown to contribute to greater net vertical impulse generation
and subsequently greater vertical displacement of the CM during the flight phase of the jump.
16–
19
The associated flexion of the lower extremity joints prior to extension results in active
lengthening of muscle-tendon-units involved in impulse generation (often referred to as a stretch-
shorten cycle (SSC)).
20–23
The increased force generated during the shortening phase is thought
to be primarily due to mechanisms such as residual force enhancement, the storage and release of
elastic energy generated during the lengthening phase, tendon elongation, muscle preactivation,
and stretch reflex.
17,24–32
While these mechanisms have been thoroughly explored on their own,
their respective contribution to performance enhancement during the concentric phase of the SSC
is still widely debated.
25,33
Furthermore, this performance enhancement associated with SSC is
observed if shortening immediately follows lengthening of the muscle-tendon-unit, otherwise the
91

stored elastic energy is dissipated and the increased performance benefit is diminished.
34–36

Similarly, initiating a change in horizontal direction with initial momentum may have a similar
beneficial effect on horizontal impulse generation. However, if the mechanical demand imposed
on the lower extremity during the SSC exceeds the capacity of the individual to control the
imposed load, then a sudden reduction in force generation may occur instead.
17,35,37

Being able to change direction quickly and effectively on the court or field is important aspect
for many sports. In sports where teams must score in their opponent’s territory such as football,
basketball, lacrosse, or soccer, players must maintain possession of the ball and evade their
opponents during attack, and reduce space on the court or field to limit attack during defense.
38

Doing both often involves being able to perform a whole-body change in direction or velocity in
response to a stimulus such as the opponent’s movements, typically defined as agility, resulting
in a sudden deceleration of the total body CM.
39–41
In order to succeed at this whole-body
movement, players must develop their perceptual, decision making, and change of direction
speed skills.
42
The change of direction (COD) skill in particular involves varying amounts of
initial horizontal momentum that the player must be able to use effectively by increasing
horizontal impulse generation over a short interval of time. However, while this skill has been
studied in terms of training, technical components, injury analysis, and basic force-time
characteristics, the effect of varying initial horizontal momentum on performance and
mechanical demand has not been thoroughly studied, particularly within individual.
39,43–45

Subsequently, understanding and improving horizontal impulse generation is essential to
succeeding in many of these sports.

In this study, we hypothesized that when individuals initiated a 180° change in horizontal
direction from a further compared to a shorter starting distance, they would generate more
horizontal impulse over a longer contact time, the increased impulse and time would occur only
when reducing initial momentum to zero, and that the increased horizontal impulse would result
from increased horizontal RF magnitude and contact time. We tested these hypotheses by
comparing impulse generation and RF-time characteristics for high school basketball players
performing a series of 180° change in horizontal direction movements initiated from 3m and 7m
away from a target line.

Methods

Subjects
Eleven highly skilled high school male basketball players between 15 and 18 years of age
volunteered to participate in this study. The mean (SD) height was 1.88 m (0.08) and the mean
(SD) mass was 78.4 kg (9.8). All players provided informed consent in accordance with the
Institutional Review Board.

Tasks
Prior to collection, players warmed up and practiced the experimental tasks until they were
familiar with the experimental setup. Each player performed a series of 180° change in
horizontal direction movements initiated from either ~3 meters away (Short) from a target line or
~7 meters away (Long) from a target line in response to a ball being dropped (Figure 9-1).
Players were instructed to move towards the target line and back out through a set of timing
92

gates 5 meters away from the target as quickly as possible. If the ball was dropped to the player’s
left, then they initiated movement to their left and performed the desired movement. If two balls
were dropped, however, then the player jumped straight up. All players performed 4 rounds of up
to 8 trials, alternating rounds between starting at 3m versus starting at 7m.

Data Collection
During the performance of each trial, sagittal and coronal plane kinematics were recorded using
high-speed cameras (240 Hz, Casio, Dover, NJ, USA). Vertical and horizontal ground reaction
forces for each leg were measured during the change in direction movement itself using dual
force plates (1200 Hz, Kistler, Amherst, NY, USA). These sets of data were synchronized at the
time of initial plate contact.

Movement Intervals and Analysis
The RF-time characteristics of the change in direction movement were described using nine key
events and two functional intervals (Jump In and Jump Out) (Figure 9-1). The Jump In was
defined from initial contact with the plates (i.e. front leg initial contact) to time when horizontal
total body CM velocity was approximately zero (A to D). During this interval, the mechanical
objective is to slow the total body CM as quickly as possible and requires that the player reduce
their initial horizontal momentum to zero. Time when horizontal velocity was approximately
zero was determined to coincide with the last local minima in the vertical RF for the back leg,
and was confirmed via video and three-dimensional motion tracking. The Jump Out was defined
from time when horizontal total body CM velocity was approximately zero to final contact (i.e.
front leg final contact) (D to I). During this interval, the mechanical objective is to speed up the
total body CM as quickly as possible in the desired direction of movement and requires that the
player quickly generate horizontal momentum from zero velocity. Normalized horizontal
impulse (∆Vh) and contact times (∆t) were determined for both intervals and in total from the
RF-time data.

Additional intervals were determined from the key events to assess performance (Figure 9-1).
Total Contact Time was defined from initial contact to final contact with the force plates (A to I).
Difference in leg start time (∆start) was defined from front leg initial contact to back leg initial
contact (A to C), and a smaller value for ∆start was associated with the player initiating the
change in direction movement with both feet together compared to rotating their total body CM
over the front leg. Difference in push time (∆push) was defined from front leg initial push to
back leg final contact (E to F), and a larger positive value was associated with the player
generating horizontal impulse sooner. Peak to peak time (P2P) was defined from 1
st
peak vertical
RF to the last peak vertical RF for the front leg (B to H), and a faster time was associated with
having the foot more posterior to the total body CM at the start of the Jump Out. Delay in push
(∆delay) was defined as the local minima (if present) prior to the 2
nd
peak RF for the front leg
(G), and was associated with having the total body CM posterior to the front foot at initiation of
front leg push and/or a drop in the front foot heel during push.
93

Figure 9-1: Example kinematic sequence and associated key events determined from RF-time data for the change in
direction movement for every 0.1 seconds elapsed (top) and associated vertical RFs (bottom). Depiction of key
events as determined by vertical RF for each leg: (A) Front Leg Initial Contact (B) Front Leg 1
st
Peak RF (C) Back
Leg Initial Contact (D) Zero Velocity (E) Front Leg Initial Push (F) Back Leg Final Contact (G) Front Leg Delay
(H) Front Leg 2
nd
Peak RF (I) Front Leg Final Contact. The Jump In interval was defined from front leg initial
contact to zero velocity (A to D). The Jump Out interval was defined from zero velocity to front leg final contact (D
to I).
94

Statistics
Within-player differences were determined using a subset of methods known as a two-state
linear model instead of Student’s T-test due to its limitations when it comes to non-normality,
incorrect assumptions of variance, and unequal sample sizes between conditions.
46
The
probability for each variable of any Short trial being less than any Long trial was calculated
within a player for each variable, where each player served as their own control (R, open-source,
Table 9-1). Assuming local independence (i.e. no order effect for trials within a condition), and
that movement conditions were independent (i.e. not directly tied to each other) for each player,
p-values were calculated for each player using Cliff’s analog of the Wilcoxon-Mann-Whitney
test (Table 9-1).
47,48
This method was chosen because it deals well with small numbers of trials
per condition. A modified, step-down Fisher-type method was then applied to control the
familywise error rate (α = 0.05) over multiple comparisons where the level of significance
becomes α/k at each k
th
iteration.
49–51
The current statistics provide more flexibility by allowing
heteroscedasticity across players.
52
As the number of trials increases per condition, Cliff’s
method can achieve lower p-values. The modified, step-down Fisher-type technique is dependent
upon the distribution of p-values for each variable measured because the significance level is
adjusted at each step to compensate for multiple comparisons.
49–51
Therefore, the presentation of
within-player results provides a conservative estimate of significant differences between
conditions.

Results

Players completed Long compared to Short trials in either (a) a shorter time but the same change
in horizontal momentum or (b) a longer time but with a larger change in horizontal momentum.

Figure 9-2: Total contact time ( ∆t) and change in horizontal velocity ( ∆Vh) for Short (S) and Long (L) trials for all
players. All significant differences were denoted when tested at α = 0.05 level when adjusted for multiple
comparisons. * denotes significant difference in ∆t and ∆Vh. Individuals are sorted (1-11) by increasing %
difference between Long and Short total contact time.

Overall Horizontal Impulse Generation
Total contact time was significantly shorter for Long compared to Short for 4 of 11 players and
significantly longer for 5 of 11 players (p < 0.05) (Table 9-1, Figure 9-2). The remaining 2
players did not have a significant difference in total contact time.
95

Players who had a shorter contact time for Long did not have a difference in horizontal impulse
generated, while players with a longer contact time had increased horizontal impulse generated
(Table 9-1, Figure 9-2). Total ∆Vh was not significantly different for 4 of 4 players with a
shorter total contact time, while total ∆Vh was significantly larger for 5 of 5 players with a
longer total contact time between conditions.

Jump In versus Jump Out
When players had a shorter total contact time for Long compared to Short, it was the result of a
shorter Jump In and not a shorter Jump Out (Table 9-1, Figure 9-3). Jump In ∆t was significantly
smaller for 4 of 4 players, while Jump Out ∆t was not significantly different for 4 of 4 players
between conditions.

When players had a longer contact time for Long, it was the result of both a longer Jump In and
Jump Out (Table 9-1, Figure 9-3). Jump In ∆t was significantly larger for 4 of 5 players, while
Jump Out ∆t was significantly larger for 3 of 5 players between conditions.

There was no difference in impulse generated during the Jump In or the Jump Out for players
with a shorter contact time for Long (Table 9-1, Figure 9-3). Jump In ∆Vh was not significantly
different for 3 of 4 players, and Jump Out ∆Vh was not significantly different for 4 of 4 players
between conditions.

The increased horizontal impulse generated was the result of greater horizontal impulse
generated during the Jump In for players with a longer contact time for Long (Table 9-1, Figure
9-3). Jump In ∆Vh was significantly larger for 4 of 5 players, while Jump Out ∆Vh was not
significantly different for the same 4 players between conditions. The remaining player had a
significantly larger ∆Vh for the Jump Out and not the Jump In.

Figure 9-3: Median contact time ( ∆t) and change in horizontal velocity ( ∆Vh) of Jump In and Jump Out for Short
(S) and Long (L) trials for all players. Error bars represent interquartile range. Total ∆t and ∆Vh are the
summation of Jump In and Jump Out contributions for each condition. All significant differences were denoted when
tested at α = 0.05 level when adjusted for multiple comparison. * total, † Jump In, and ‡ Jump Out significant
difference between conditions. Individuals are sorted (1-11) by increasing % difference between Long and Short
total contact time.

96

Front Leg versus Back Leg
Contribution to horizontal impulse shifted from the front leg to the back leg for players with a
shorter contact time for Long (Table 9-1, Figure 9-4). Front leg % contribution was significantly
smaller for 3 of 4 players between conditions. Additionally, front leg ∆Vh was significantly
smaller for 3 of 4 players, while back leg ∆Vh was significantly larger for 2 of 4 players.

Contribution to horizontal impulse was mostly similar for players with a longer contact time for
Long (Table 9-1, Figure 9-4). Front leg % contribution was significantly smaller for only 2 of 5
players. Additionally, front leg ∆Vh was significantly larger for 3 of 5 players, while back leg
∆Vh was significantly larger for 4 of 5 players.

Figure 9-4: Median change in horizontal velocity ( ∆Vh) of front and back legs for Short (S) and Long (L) trials for
all players. Error bars represent interquartile range. Total ∆Vh is the summation of front and back leg contributions
for each condition. All significant differences were denoted when tested at α = 0.05 level when adjusted for multiple
comparison. * total, † front leg, and ‡ back leg significant difference between conditions. Individuals are sorted (1-
11) by increasing % difference between Long and Short total contact time.

Differences in Foot Contact Initiation
Players with a shorter contact time for Long initiated back leg foot contact sooner between
conditions (Table 9-1, Figure 9-5). ∆start was significantly smaller for 4 of 4 players.
Conversely, players with a longer contact time for Short initiated back leg foot contact at a
similar time between conditions (Table 9-1, Figure 9-6). There was no significant difference in
∆start for 5 of 5 players.

Peak to Peak Time
Players with a shorter contact time for Long had a similar or shorter difference in peak push
between legs between conditions (Table 9-1, Figure 9-5). P2P time was significantly smaller for
2 of 4 players, while there was no significant difference for the remaining 2 players. Conversely,
players with a longer contact time for Long had a longer difference in peak push between legs
between conditions (Table 9-1, Figure 9-6). P2P time was significantly longer for 5 of 5 players.

Example Comparison
Example comparison of kinematics and force were made for two exemplary players. Player 3
had a significantly shorter total contact time and similar horizontal impulse generated for Long
compared to Short (Figure 9-5). Player 10 had a significantly longer total contact time and
greater horizontal impulse generated for Long compared to Short (Figure 9-6).
97

Figure 9-5: Median (line) and IQR (shading) front and back leg reaction forces for Player 3 for Short (blue) and
Long (red) conditions. RF curves have been time-scaled to median contact time for each condition. Player had a
significantly shorter contact time for Long compared to Short, and no significant difference in ∆Vh generated.
98

Figure 9-6: Median (line) and IQR (shading) front and back leg reaction forces for Player 10 for Short (blue) and
Long (red) conditions. RF curves have been time-scaled to median contact time for each condition. Player had a
significantly longer contact time for Long compared to Short, and greater ∆Vh generated.
99

Table 9-1: Jump In, Jump Out, and total contact times (∆t) and horizontal velocities (∆Vh), difference in start time
(∆start), and peak to peak time (P2P) for all individuals.

Discussion

In this study we investigated how performance of a 180° change in horizontal direction was
affected by short and long starting positions. The results of this within player analysis indicate
that when players initiate a change in direction from a further starting distance compared to a
shorter one they either (a) generate the same horizontal impulse in a shorter contact time or (b)
generate greater horizontal impulse in a longer contact time. When players completed the 180°
change in horizontal direction task in a shorter contact time (Long compared to Short) it was a
result of a shorter Jump In and not Jump Out interval. These players changed initiation technique
although initial velocities were similar, P2P time was shorter, and contribution to horizontal
impulse shifted from front leg to the back leg. When players completed the 180° change in
horizontal direction task in a longer contact time (Long compared to Short), it was the result of
longer Jump In and Jump Out intervals. In these cases, players did not change initiation
technique, initial velocity was greater, P2P time was longer, and contribution to horizontal
impulse did not change between legs. Coordination of initial leg configuration and impulse
distribution between legs are important to consider when determining how an individual can
improve performance time of a 180° change in horizontal direction.

All trials for a player were collected on the same day with sufficient rest between trials to
minimize any effect of fatigue or day-to-day variance in performance. Players were allowed to
practice and self-select their exact starting position relative to the target line in order to reduce
variability between trials. Any potential attenuation by the track flooring used to cover the force
plates is expected to be of similar magnitude between experimental conditions. The force-time
and magnitude characteristics observed in this study were consistent with those reported in
previous studies.
12,43,53
The study of elite athlete performance, by design, limits the sample size
100

and as a result, we chose to use a conservative within-player statistical method of comparison
where each player served as their own control. Under conditions when participation time isn’t as
limited, an increase in the number of trials per condition would strengthen the findings.

Players in this study took longer to complete the 180° change in horizontal direction when
initiating with greater horizontal momentum. When players had significantly greater horizontal
impulse generated for the Jump In (indicating a greater initial horizontal velocity), they had a
longer contact time for Long compared to Short conditions (Figures 9-2, 9-3). Increased initial
momentum can have a positive effect on an athlete’s ability to generate impulse
3,4,13–19
in that
active lengthening of muscle-tendon-units can lead to increased reaction force.
3,4,20–23
However,
players did not have greater horizontal impulse generated for the Jump Out, indicating that the
final horizontal velocity was similar regardless of initial momentum. It may be that the increased
initial momentum either exceeded the capacity of the individual to control the imposed load or
the performance enhancement associated with SSC dissipated too quickly, although additional
research is necessary to investigate these effects.
17,34–37

When players changed initiation technique between conditions, they decreased their total contact
time. Four of the eleven players initiated contact for Long with both feet at the same time
compared to initiating with the front leg only for Short (Figures 9-2, 9-5). This difference in
initiation technique resulted in a significantly shorter total contact time due to a shorter Jump In.
While placing the feet more anterior to the total body CM should result in increased horizontal
impulse generation, for these individuals the ability to use both legs together to coordinate
impulse generation may be the key to improving Jump In and subsequently overall performance
of a change in direction.
7–9,12
Horizontal impulse generation also shifted from the front leg to the
back leg for these players, allowing the back leg to have a greater role in slowing down the total
body CM to zero velocity and decrease the time between front leg Jump In and Jump Out push
(i.e. P2P time) (Figure 9-4). The remaining players had a longer contact time instead, and did not
have a difference in initiation technique used or contribution to impulse generation from each
leg. However, it is important to note that individuals with a shorter contact time for Long also
had a similar horizontal impulse generated during the Jump In (indicating a similar initial
horizontal velocity) and total horizontal impulse generated between conditions (Figure 9-3). This
suggests that differences in technique prior to final contact are important to consider as well.

Increased or decreased overall performance between conditions was a result of differences in
Jump In impulse generation. For players with decreased total contact time for Long, Jump In
contact time was also significantly shorter (Figure 9-3). These players had similar impulse
generated during the Jump In, suggesting that horizontal RF was increased during this interval.
As previously discussed, these individuals had a difference in initiation technique which may
explain the reduced contact time and increased RF despite similar initial momentum. Similarly,
for players with increased total contact time for the Long condition, Jump In contact time was
longer. While there were differences in Jump Out impulse generation as well for these players,
these differences were individual instead of group specific. Understanding these observed
differences between starting distances and between individuals emphasizes the need to consider
how best to facilitate improvement for their players.

101

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based model for simulating flight-phase dynamics. Biol Cybern. 2002;87(4):289-300.
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the reaction force. J Biomech. 2001;34(11):1471-1482. doi:10.1016/S0021-
9290(01)00110-5.
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106

Chapter 10: Multijoint Control of the Lower Extremities during a
180° Change in Direction

Introduction

When anticipating a need to change direction, athletes often reconfigure their bodies so that they
can effectively generate impulse in the desired direction.
1–4
If total body center of mass (CM)
position relative to the contact foot delays impulse generation in the desired direction, then time
to complete the task will increase.
5
As such, effective control of the CM relative to the feet when
in contact with the ground can be advantageous when performing quick changes in direction.

Initiation of a movement with momentum can facilitate increases in reaction force (RF)
generation, particularly in sport-specific contexts.
2,6,7
However, if the mechanical demand
imposed on the lower extremity exceeds the capacity of the individual to control the imposed
load, then a reduction in RF generation may occur or potential injury risk may increase.
8–10

Control of the lower extremity during foot contact involves coordinated multijoint control of the
ankle, knee and hip, which corresponds with activation of the lower extremity muscles.
1,11
The
mechanical demand imposed on the athlete is dependent on RF magnitude, orientation of the RF
relative to the lower extremity segments, and the adjacent net joint moments (NJM).
1,11
If RF
magnitude or RF-segment orientation is increased, their effect on mechanical demand at the
proximal joint will then increase. When the RF acting on the lower extremity is aligned with the
leg plane, the moments imposed by the net joint forces at the ankle, knee, and hip about the
segment CM tend to require NJMs that act about axes perpendicular to the leg.
1,3,12–14

Being able to change direction quickly, often referred to as agility, is an important aspect of
sports performance and has been investigated from training and injury prevention
perspectives.
15–19
Redirection on the court or in the field of play is often initiated with
momentum and in response to a stimulus such as an opponent’s movements. These changes in
direction or velocity of the total body CM involve strategic generation of horizontal impulse over
a short amount of time.
16–18
Work in long jump suggests that reducing leg yield (knee flexion
range and angular velocity) may result in increased reaction force magnitude over a similar
contact time, resulting in increased impulse generated, as seen in Chapter 8. Previous analysis of
180° changes in direction at the whole body level, as performed in basketball, revealed that
players take longer to change direction when they initiate contact with greater initial momentum,
resulting in increased RF and contact time, as seen in Chapter 9. Furthermore, changes in
direction were achieved more quickly when players altered how they utilized their legs to shift
impulse generation from the front to the back leg. However, the effect of differences in initial
momentum and configuration for a change in horizontal direction on lower extremity demand
have not been investigated.

In this study, we hypothesized that when an individual initiates a 180° change in horizontal
direction from a further compared to a closer starting distance, there would be greater
mechanical demand and work done by the lower extremity for both legs as a result of increased
RF magnitude and increased leg yield when reducing initial horizontal velocity to zero. It was
further hypothesized that the distribution of lower extremity mechanical demand would be the
107

same because of similar RF relative to leg orientation differences, regardless of differences in
initial configuration or initial momentum. We tested these hypotheses by comparing impulse
generation, RF-time characteristics, multijoint coordination, and lower extremity demand for
high school basketball players performing a series of 180° changes in horizontal direction
initiated from different distances.

Methods

Subjects
Nine skilled high school male basketball players between 15 and 18 years of age volunteered to
participate in this study. The mean (SD) height was 1.88 m (0.08) and the mean (SD) mass was
80.7 kg (9.4). All players provided informed consent in accordance with the Institutional Review
Board.

Tasks
Prior to collection, players warmed up and practiced the experimental tasks until they were
familiar with the experimental setup. Each player performed a series of 180° change in
horizontal direction movements initiated from either ~3 meters away (Short) from a target line or
~7 meters away (Long) from a target line in response to balls being dropped by their coach
(Figure 10-1). If two balls were dropped the player jumped straight up. If only the left ball was
dropped the player initiated the task. Players were instructed to move towards the target line and
back out through a set of timing gates 5 meters away from the target as quickly as possible. All
players performed 4 rounds of up to 8 trials, alternating rounds between starting at 3m versus
starting at 7m.

Data Collection
During the performance of each trial, sagittal and coronal plane kinematics were recorded using
high-speed cameras (240 Hz, Casio, Dover, NJ, USA). Vertical and horizontal ground reaction
forces for each leg were measured during the change in direction movement using dual force
plates (1200 Hz, Kistler, Amherst, NY, USA). Three-dimensional kinematics were recorded
using a retro reflective 16-camera motion capture system (100 Hz, Natural Point, Optitrak,
Corvallis, OR) and Acquire3D software (C-Motion, Germantown, MD). These sets of data were
synchronized at the time of initial plate contact.

Analysis
The RF-time characteristics of the change in direction movement were described using two
functional intervals (Jump In and Jump Out) as described in Chapter 9 (Figure 10-1). During the
Jump In interval, the mechanical objective is to slow the total body CM velocity to zero as
quickly as possible. During the Jump Out interval, the mechanical objective is to speed up the
total body CM as quickly as possible in the desired direction of movement from zero velocity.
Contact times were determined for each interval and in total for each leg from the force-time
curves during impulse generation. Horizontal impulse was calculated for each interval and in
total for each leg by integrating front and back leg reaction forces during foot contact. These
impulses were normalized by body mass to obtain change in horizontal velocity of the CM
(∆Vh).

108

Figure 10-1: Example kinematic sequence and associated key events determined from RF-time data for the change
in direction movement for every 0.1 seconds elapsed (top) and associated vertical RFs (bottom) as determined from
Ramos 2017. The Jump In interval was defined from front leg initial contact to zero velocity (A to D). The Jump Out
interval was defined from zero velocity to front leg final contact (D to I).
109

A custom 32 marker set including anatomic and tracking retroreflective markers (1.2 cm
diameter, B&L Engineering) were applied to the player using an adhesive Velcro-system, skin
adhesive spray, and coban tape using the procedure described in Chapter 3 (Figure 10-2). The
marker set allowed for use of segment properties presented by deLeva.
20
All tracking markers
were placed in locations that allowed for natural kinematics used by the basketball players to
execute the change in direction movement.

Figure 10-2: Depiction of custom 32 marker set locations. Blue circles denote the 32 markers used during trials,
yellow markers denote the 4 additional markers added during calibration movements.

110

Kinematics and kinetics were synchronized at contact. Kinematic data (100 Hz) was interpolated
to match the kinetic data frequency (1200 Hz) using cubic spline function. The spline function
also automatically differentiated marker and segment center of mass position data to estimate
velocities and accelerations. Net joint forces (NJF) were calculated using ground reaction forces,
segment masses, segment endpoints, and segment center of mass acceleration.
20

Functional joint centers were calculated for the ankle, knee, and hip and used to define a leg
plane, similar to the arm plane defined by Russell et al 2015. Joint kinetics during the contact
phase of the change in direction movement were determined for both the front and back legs
using measured ground RF, 3D segment kinematics, and body segment parameters.
20
Resultant
net joint moments (NJM) calculated for the ankle, knee, and hip were then represented about the
axis perpendicular to the leg plane to determine how the NJMs were aligned with the leg plane.
Ankle plantar flexor, knee, and hip extensor NJMs are presented as positive values and
normalized to the player’s body mass. The knee, and hip NJMP for each leg were calculated as a
product of the NJM and their corresponding joint angular velocity. The NJM work done was
determined by integrating the NJMP during each time interval, and then normalized to the
player’s body mass. Greater leg yield was defined as a greater knee flexion angle and knee
flexion angular velocity as described in Muraki et al 2008.
21

Statistics
Within-player differences were determined using a subset of methods known as a two-state
linear model instead of Student’s T-test due to its limitations when it comes to non-normality,
incorrect assumptions of variance, and unequal sample sizes between conditions.
22
The
probability for each variable of any Short trial being less than any Long trial was calculated
within a player for each variable, where each player served as their own control (R, open-source,
Table 10-1). Assuming local independence (i.e. no order effect for trials within a condition), and
that movement conditions were independent (i.e. not directly tied to each other) for each
participant, p-values were calculated for each player using Cliff’s analog of the Wilcoxon-Mann-
Whitney test.
23,24
This method was chosen because it deals well with small numbers of trials per
condition. A modified, step-down Fisher-type method was then applied to control the familywise
error rate (α = 0.05) over multiple comparisons where the level of significance becomes α/k at
each k
th
iteration.
25–27
The current statistics provide more flexibility by allowing
heteroscedasticity across players and provides a conservative estimate of significant differences
between conditions.
28

Results

Players completed Long compared to Short trials in either (a) a significantly shorter time but the
same change in horizontal momentum (Players 1-4) or (b) a significantly longer time but with a
significantly larger change in horizontal momentum (Players 6-9), as previously studied in
Chapter 9 (p < 0.05) (Figure 10-3).

Kinematics
Players had less front leg yield but more back leg yield when they had a shorter contact time for
Long compared to Short (Table 10-1, Figure 10-4). Front leg knee flexion angular velocity and
range of motion during the Jump In were significantly smaller for 3 of 4 players with a
111

significantly shorter contact time between conditions. Back leg knee flexion angular velocity and
range of motion during the Jump In were significantly larger for 3 of 4 players between
conditions.

Players had more back leg hip yield when they had a longer contact time for Long (Table 10-1).
Back leg hip flexion angular velocity and range of motion during the Jump In were significantly
larger for 3 of 4 players with a significantly longer contact time between conditions.

Figure 10-3: Total contact time ( ∆t) and change in horizontal velocity ( ∆Vh) for Short (closed circle, blue) and
Long (open circle, red) trials for all players. All significant differences were denoted when tested at α = 0.05 level
when adjusted for multiple comparisons. * denotes significant difference in ∆t and ∆Vh. Individuals are sorted (1-9)
by increasing % difference between Long and Short total contact time.

Figure 10-4: Front leg median hip versus knee angle-angle diagrams for Short (blue) and Long (red). Players 1-4
have a significantly shorter total contact time between Long and Short, while Players 6-9 have a significantly longer
contact time. Individuals are sorted by increasing % difference between Long and Short total contact time.
112

Differences in both front and back leg extension were dependent on the individual and not the
group (Table 10-1, Figure 10-4). Front leg knee and hip angular velocities during the Jump Out
were significantly different for 2 and 4 players, respectively. Back leg knee and hip angular
velocities were significantly different for 2 and 2 players, respectively.

Net Joint Moments
Differences in both front and back leg NJMs during the Jump In were dependent on the
individual and not the group (Table 10-1, Figures 10-5, 10-6). Front leg lower extremity NJMs
during the Jump In were significantly different for only 3 of 9 players, while back leg lower
extremity NJMs were significantly different for only 4 players.

Differences in front leg NJMs during the Jump Out were dependent on the individual and not
group (Table 10-1, Figures 10-5, 10-6). Front leg lower extremity NJMs during the Jump Out
were significantly different for only 2 players.

Players had larger back leg NJMs when they had a longer contact time for Long (Table 10-1,
Figures 10-5, 10-6). Back leg ankle, knee, and hip NJMs were significantly larger during the
Jump Out for 3 of 4 players with a significantly longer contact time between conditions.

Work
Less negative work was done by the front leg during the Jump In when players had a shorter
contact time for Long (Figures 10-7, 10-9). Front leg total work was significantly smaller for 4 of
4 players with a significantly shorter total contact time between conditions as a result of
significantly smaller front leg knee (n = 4/4) and hip (n = 3/4) work. In comparison, there were
no significant differences in front leg work for 4 of 4 players with a significantly longer total
contact time between conditions, despite having a significantly longer Jump In contact time
(Figures 10-8, 10-9).

More negative work was done by the back leg during the Jump In for all players for Long,
regardless of differences in contact time (Figures 10-7 to 10-9). Back leg total work was
significantly larger for 6 of 9 players as a result of significantly larger back leg knee (n = 5/6)
and / or hip (n = 3/6) work.

Work done by the front leg during the Jump Out was similar for Long compared to Short
(Figures 10-7 to 10-9). Front leg total work was significantly different for only 2 of 9 players.

More positive work was done by the back leg during the Jump Out when players had a
significantly longer contact time for Long (Figures 10-8, 10-9). Back leg total work was
significantly larger for 4 of 4 players with a significantly longer contact time between conditions
as a result of larger knee (n = 2/4) and hip (n = 3/4) work. In comparison, back leg total work
was only significantly larger for 1 of 4 players with a significantly shorter contact time between
conditions.

113

Figure 10-5: Median (line) and IQR (shading) front and back leg resultant reaction force and ankle, knee, and hip
NJM about the axis perpendicular to the leg plane for Player 3 for Short (blue) and Long (red). Example kinematic
images with front (yellow) and back (green) force vectors overlaid are above for select key events. Player had a
significantly shorter contact time for Long compared to Short.
114

Figure 10-6: Median (line) and IQR (shading) front and back leg resultant reaction force and ankle, knee, and hip
NJM about the axis perpendicular to the leg plane for Player 8 for Short (blue) and Long (red). Example kinematic
images with front (yellow) and back (green) force vectors overlaid are above for select key events. Player had a
significantly longer contact time for Long compared to Short.

115

Figure 10-7: Median (line) and IQR (shading) net joint moment (NJM), joint angular velocity (JAV), and net joint
moment power (NJMP) for back leg knee, back leg hip, front leg knee, and front leg hip for Player 3 for Short (blue)
and Long (red). Player had a significantly shorter contact time for Long compared to Short.

Figure 10-8: Median (line) and IQR (shading) net joint moment (NJM), joint angular velocity (JAV), and net joint
moment power (NJMP) for back leg knee, back leg hip, front leg knee, and front leg hip for Player 8 for Short (blue)
and Long (red). Player had a significantly longer contact time for Long compared to Short.
116

Figure 10-9: 20% trimmed mean (IQR) of the normalized knee and hip work for the front and back legs for the
Jump In and Jump Out for each player. All significant differences were denoted when tested at α = 0.05 level when
adjusted for multiple comparison. * total, † knee, and ‡ hip significant difference between conditions. Individuals
(P1-9) are sorted by increasing % difference between Long and Short total contact time.

Discussion

In this study we investigated how performance and control of the lower extremities during a 180°
change in horizontal direction was affected by short and long starting distances. The results of
this within player analysis indicate that when players had a shorter contact time when initiating
from a further distance (Long), their front leg yield was smaller but back leg yield was greater.
Players with similar initial momentum but shorter contact time had less front leg yield but more
back leg yield for Long compared to Short starting distances as a result of a more flexed initial
knee angle and differences in initiation technique. In comparison, players with greater initial
momentum and longer contact time had similar front and back leg yield between conditions but
had greater back leg hip yield. Mechanical demand imposed on the lower extremities (NJMs)
was comparable for both groups of players between conditions, and differences occurred on the
individual and not the group level. This demand was primarily aligned with the axis
perpendicular to the leg plane for all players for the entire duration of both the Jump In and Jump
Out, suggesting that control of the RF relative to the leg may be a priority. While players in
general had increased work done by the back leg for the Jump In, players with a shorter total
contact time had decreased work by the front leg instead as a result of the smaller leg yield and
contact time. This suggests that work done during the Jump In shifted from the front to the back
leg similar to how impulse generation had been shown to shift to the back leg in previous work.
Coordination of initial leg configuration, impulse distribution, and demand between legs are
important to consider when determining how an individual can improve performance for a
change in horizontal direction.

117

All trials for a player were collected on the same day with sufficient rest between trials to
minimize any effect of fatigue or day-to-day variance in performance. Players were allowed to
practice and self-select their exact starting position relative to the target line in order to reduce
variability between trials. Any potential attenuation by the track flooring used to cover the force
plates is expected to be of similar magnitude between experimental conditions. The force-time
and magnitude characteristics observed in this study were consistent with those reported in
previous studies.
5,19,29
In this initial exploratory study involving competitive athletes, we chose to
use a conservative within-player statistical method of comparison where each player served as
their own control. Under conditions when participation time isn’t as limited, an increase in the
number of trials per condition would strengthen the findings.

When players had a shorter total contact time for Long compared to Short, they had decreased
leg yield and negative work done by the front leg. Front leg knee flexion angular velocity and
range of motion were significantly smaller when players completed the change in direction in a
shorter total contact time between conditions. During this interval, less negative work was done
by the front leg at the knee and hip as a result of both shorter Jump In contact time and smaller
joint flexion angular velocity. Previous work in long jump suggests that reducing leg yield may
result in increased reaction force magnitude over a similar contact time, as seen in Chapter 8. It
is important to note, however, that initial configuration between conditions was different for
these individuals as initial knee angle was typically more flexed for Long compared to Short as a
result of initiating with both legs at the same time. Furthermore, these players had both increased
back leg yield and negative work, suggesting that work done during the Jump In shifted from the
front to the back leg similar to how impulse generation had been shown to shift to the back leg in
Chapter 9. This suggests that differences in Jump In and overall performance of a change in
horizontal direction may depend on coordination between legs and shifting impulse generation
away from the back leg. For select individuals, this may have been achieved by initiating contact
with both legs at the same time rather than one leg at a time, allowing the legs to coordinate
impulse generation together.

Lower extremity mechanical demand during the entire contact phase was mostly aligned with the
axis perpendicular to the leg plane for all individual, similar to results found in other tasks.
12–14

Regardless of initial momentum or configuration, NJMs at the ankle, knee, and hip were aligned
with the axis perpendicular to the leg plane to within less than 10°. This suggests that
maintaining the reaction force in-line with the leg plane may be a control priority during both the
Jump In and Jump Out, regardless of initial momentum or configuration, and that the ability to
control the imposed mechanical demand during both intervals is key to improving performance.
The imposed moments were mostly joint extensors across the lower extremity, similar to tasks
with periods of high loading where the athlete must be able to control the imposed mechanical
demand by using effective muscle activation and common impedance-like control strategies.
1,11

This suggests that each player may have used their ankle, knee, and hip NJMs across both legs to
help stabilize the lower extremity to stabilize the leg, resist joint flexion, and perhaps reduce leg
yield.

Differences in mechanical demand between conditions during both the Jump In and Jump Out
was typically player-specific and not reflective of the group. Front leg NJMs during the Jump In
were significantly different for only three players, while back leg NJMs were significantly
118

different for only four players. Similarly, front leg NJMs during the Jump Out were significantly
different for only two players. However, it is important to note that Jump Out back leg ankle,
knee, and hip moments were significantly larger when players had both greater initial momentum
and longer contact time, resulting in increased work done by the back leg. While contact time
during this interval was longer, there was no increase in horizontal impulse generated, however,
suggesting a reduction in RF over a longer contact time. A sudden reduction in muscle force and
subsequently reaction force generation may occur if the mechanical demand imposed on the
lower extremity during active lengthening of the muscle tendon units involved exceeds the
capacity of the individual to control the imposed load, although this phenomena needs to be
investigated further for these individuals.
8–10
These between-player differences in control
requirements emphasize the need consider that the mechanical demand imposed on an individual
athlete may be different when preparing athletes for play.

Table 10-1: 20% trimmed mean (IQR) of net joint moment (NJM), joint angular velocity (JAV), and net joint
moment power (NJMP) for front and back knee and hip joints during the Jump In and Jump Out intervals.

119

References
1. McNitt-Gray JL, Hester DME, Mathiyakom W, Munkasy B a. Mechanical demand and
multijoint control during landing depend on orientation of the body segments relative to
the reaction force. J Biomech. 2001;34(11):1471-1482. doi:10.1016/S0021-
9290(01)00110-5.
2. Mathiyakom W, McNitt-Gray JL, Wilcox R. Lower extremity control and dynamics
during backward angular impulse generation in backward translating tasks. Exp Brain Res.
2006;169(3):377-388. doi:10.1007/s00221-005-0150-7.
3. Mathiyakom W, McNitt-Gray JL, Wilcox R. Lower extremity control and dynamics
during backward angular impulse generation in forward translating tasks. J Biomech.
2006;39(6):990-1000. doi:10.1016/j.jbiomech.2005.02.022.
4. Mathiyakom W, McNitt-Gray JL, Wilcox RR. Regulation of angular impulse during two
forward translating tasks. J Appl Biomech. 2007;23(2):149-161.
5. Costa K. Control and Dynamics during Horizontal Impulse Generation. 2004.
6. Dapena J, Chung C. Vertical And Radial Motions Of The Body During The Take Off
Phase Of High Jumping. Med Sci Sport. 1988;20:290-302.
7. Bobbert MF, Gerritsen KG, Litjens MC, Van Soest a J. Why is countermovement jump
height greater than squat jump height? Med Sci Sports Exerc. 1996;28(11):1402-1412.
doi:10.1097/00005768-199611000-00009.
8. Moran K a., Wallace ES. Eccentric loading and range of knee joint motion effects on
performance enhancement in vertical jumping. Hum Mov Sci. 2007;26(6):824-840.
doi:10.1016/j.humov.2007.05.001.
9. Flitney FW, Hirst DG. Cross-bridge detachment and sarcomere “give” during stretch of
active frog’s muscle. J Physiol. 1978;276:449-465. doi:10.1113/jphysiol.1978.sp012246.
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1972;225(1):237-253. doi:10.1113/jphysiol.1972.sp009935.
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doi:10.1109/TAC.1984.1103644.
12. Russell IM, Raina S, Requejo PS, Wilcox RR, Mulroy S, McNitt-Gray JL. Modifications
in Wheelchair Propulsion Technique with Speed. Front Bioeng Biotechnol.
2015;3(October):1-11. doi:10.3389/fbioe.2015.00171.
13. Peterson T. Lower Extremity Control and Dynamics during the Golf Swing. 2017.
120

14. Zaferiou A. Control and Dynamics of Turning Tasks with Different Rotation and
Translation Requirements. 2015.
15. Spittle M. Motor Learning and Skill Acquisition: Applications for Physical Education and
Sport. Palgrave-MacMillan; 2013.
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Sports Sci. 2006;24(9):919-932. doi:10.1080/02640410500457109.
17. Scanlan A, Humphries B, Tucker PS, Dalbo V. The influence of physical and cognitive
factors on reactive agility performance in men basketball players. J Sports Sci.
2014;32(4):367-374. doi:10.1080/02640414.2013.825730.
18. Young W, Rogers N. Effects of small-sided game and change-of-direction training on
reactive agility and change-of-direction speed. J Sports Sci. 2014;32(4):307-314.
doi:10.1080/02640414.2013.823230.
19. James CR, Sizer PS, Starch DW, Lockhart TE, Slauterbeck J. Gender differences among
sagittal plane knee kinematic and ground reaction force characteristics during a rapid
sprint and cut maneuver. Res Q Exerc Sport. 2004;75(1):31-38.
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21. Muraki Y, Ae M, Koyama H, Yokozawa T. Joint Torque and Power of the Takeoff Leg in
the Long Jump. Int J Sport Heal Sci. 2008;6:21-32. doi:10.5432/ijshs.6.21.
22. Wilcox RR. Modern Statistics for the Social and Behavioral Sciences: A Practical
Introduction. Boca Raton, FL: CRC Press Taylor & Francis Group; 2012.
23. Cliff N. Ordinal Methods for Behavioral Data Analysis. Mahwah, NJ: Lawrence Erlbaum
Associates, Inc; 1996.
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28. Crowder M, Hand D. Analysis of Repeated Measures. Vol 1st ed. New York, NY:
Chapman & Hall/CRC; 1990.
29. McNitt-Gray JL, Sand K, Ramos C, Peterson T, Held L, Brown K. Using technology and
engineering to facilitate skill acquisition and improvements in performance. Proc Inst
Mech Eng Part P J Sport Eng Technol. 2015;229(2):103-115.
doi:10.1177/1754337114565381.

122

Chapter 11: Discussion

To succeed in athletic environments, athletes must regulate linear and angular momentum of
their body by generating linear and angular impulse during contact with the ground. Effective
impulse generation often requires the individual to re-configure their body so that they can
generate the impulse needed to move in a desired direction. This can be accomplished by
repositioning the feet relative to the total body CM and taking advantage of initial momentum to
increase RF and / or contact time, resulting in increased impulse generated.
1–8
To maximize the
horizontal impulse in the shortest amount of time, the athlete must strategically configure their
body segments so that the net joint moments (NJM) generated by muscles crossing the ankle,
knee, and hip can effectively generate the required reaction forces in relation to the CM
trajectory. Studying how individuals accomplish these mechanical objectives under varying
initial momentum and configuration conditions advances our understanding of the control
structure and its benefits specific to an individual.
9–12
By determining what problems the athlete
needs to solve and designing experiments to investigate how and why they move, we can
determine solutions to help facilitate skill acquisition. The goal of these studies was to determine
how elite-level athletes effectively regulate impulse generation to satisfy the mechanical
objectives of a task under contextually relevant training conditions and how this information
could be used to improve performance (Figure 11-1).

Figure 11-1: Outline of series of studies conducted exploring multijoint coordination and control under different
initial momentum and configuration setups.

For all studies, subjects were given sufficient time to warm-up and adequate rest between trials
so as to minimize any effect of fatigue or day-to-day variance in performance. Subjects were
allowed to self-select starting positions and / or execution of tasks in order to reduce variability
between trials. Any potential attenuation by flooring used to cover the force plates was of similar
magnitude between experimental conditions. The study of elite athlete performance, by design,
limits the sample size and as a result, we chose to use a conservative within-player statistical
method of comparison where each subject served as their own control. Under conditions when
participation time isn’t as limited, an increase in the number of trials would strengthen findings.
123

In Specific Aim 1 (Chapter 4), we determined how augmented feedback on quick first step
performance affects improvement in lead leg impulse generation and overall task performance
for elite-level college volleyball players. Within player analysis of participants in this study
indicated that players improved both lead leg and overall impulse generation more often when
given augmented feedback in the form of force-time curves overlaid onto video compared to
being given performance time only. All seven players receiving augmented feedback had a
significant reduction in total contact time, with six of the players demonstrating significant
improvement in multiple aspects of lead leg impulse generation. In comparison, only three of six
time-only feedback players had significant improvement in total contact time and lead leg
impulse generation, with the remaining three players showing no improvement in either. In
particular, augmented feedback resulted in more consistent improvement in quick first step
performance with players improving their ability to generate horizontal impulse after only 21
performance trials. This suggests that allowing elite-level athletes to observe their own
movements, focusing on successful performance of those movements, directing attention towards
improvement using an external focus, and giving them control over the learning process can
substantially increase the chance and degree to which they improve their movement
performance. Taking these factors into consideration when coaching or trying to facilitate
improvement is essential for maximizing athletic performance.

In Specific Aim 2 (Chapter 5), we determined how differences in individual knee-hip
coordination affect impulse generation and muscle activation during the takeoff phase of
backwards and reverse somersaults performed by national and Olympic level divers. The results
of this within subject analysis indicated that regulation of angular impulse involves coordination
between multiple subsystems, which can be accomplished via at least two different coordination
strategies. Either a more hip dominated or evenly distributed knee-hip extension can be used to
satisfy the same linear and angular impulse requirements of backwards-rotating tasks. Associated
differences in lower extremity extension strategy correspond with selective activation of bi-
articular muscles crossing the knee and hip (semimembranosus and biceps femoris muscles).
These differences in selective activation were consistent within individual even across tasks with
similar mechanical objectives when comparing the backwards to the reverse somersault.
However, there was no observed advantage in impulse generation between coordination
strategies. Understanding and studying the ability of the individual to execute their respective
power generation strategy is key to determining how best to modify technique and facilitate skill
improvement.

In Specific Aim 3 (Chapter 6), we determined how vertical jump performance in skilled players
was affected by the timing of vertical jump initiation. The results of this within player analysis
indicated that players were able to generate greater change in vertical velocity when initiating a
VBJ immediately as compared to with a delay. However, the resulting jump height increase
during the Immediate VBJ was minimal for most players. The magnitude of these differences
between conditions varied across individuals. Mechanical loading of lead and lag legs during the
impact phase were comparable between VBJ conditions. In these cases, the timing of the VBJ
may be more important for some players than the increased jump height when it comes to
jumping performance. The implications for performance in competitive volleyball context are
important to consider when determining whether to use an immediate or delayed VBJ.

124

In Specific Aim 4 (Chapters 7 and 8) we determined how differences in initial leg angle and leg
yield affect linear impulse generation during the takeoff phase of a long jump performed by
national and Olympic level long jumpers. The results of this within-jumper analysis indicate that
when jumpers initiate the takeoff with larger leg angles, some are able to generate greater
increases in CM vertical velocity. Increases in CM velocity typically occurred at the expense of
greater decreases in CM horizontal velocity at the group level. These greater changes in CM
velocity during the take-off phase corresponded with increases in impulse generation resulting
from increased contact time or average reaction force during either the impact or post-impact
interval, depending on the individual. However, the conclusions at the group level do not
necessarily reflect the findings on the individual level, with eight jumpers having a significant
correlation between larger initial leg angle and increase in CM vertical velocity, for example,
while the remaining three jumpers did not. Furthermore, when jumpers had reduced leg yield and
shank rotation, all but one generated more vertical velocity during the takeoff phase. The ability
to both maintain a more rigid knee and reduce shank rotation may improve the chances of being
able to increase impulse generation during the post-impact of the long jump. An exemplar
jumper displayed more evenly distributed demand between the knee and the hip during the
impact interval, which may allow her to sustain and increase her RF through the end of the
impact interval and into the post-impact interval. Net joint moments during transition and the
post-impact intervals were similar between trials for this jumper. Initial leg configuration at
contact and individual specific impulse generation strategies are important to consider when
determining how an athlete with initial momentum can increase impulse generation to jump for
distance. Understanding how each individual jumper is able to regulate and increase impulse
generation during the takeoff is essential for determining how best to improve jump distance
performance.

Finally, in Specific Aim 5 (Chapters 9 and 10) we determined how differences in initial
momentum affect linear impulse generation and the mechanical demand imposed on the front
and back legs during a 180° change in horizontal direction performed by competitive high school
basketball players. The results of this within player analysis indicate that when players initiate a
change in direction from a further starting distance compared to a shorter one they either (a)
generate the same horizontal impulse in a shorter contact time or (b) generate greater horizontal
impulse in a longer contact time. When players completed the 180° change in horizontal
direction task in a shorter contact time (Long compared to Short) it was a result of a shorter Jump
In and not Jump Out interval. These players changed initiation technique although initial
velocities were similar, P2P time was shorter, and contribution to horizontal impulse shifted
from front leg to the back leg. When players completed the 180° change in horizontal direction
task in a longer contact time (Long compared to Short), it was the result of longer Jump In and
Jump Out intervals. In these cases, players did not change initiation technique, initial velocity
was greater, P2P time was longer, and contribution to horizontal impulse did not change between
legs. Furthermore, when players had a shorter contact time when initiating from a further
distance (Long), their front leg yield was smaller but back leg yield was greater. Players with
similar initial momentum but shorter contact time had less front leg yield but more back leg yield
for Long compared to Short starting distances as a result of a more flexed initial knee angle and
differences in initiation technique. In comparison, players with greater initial momentum and
longer contact time had similar front and back leg yield between conditions but had greater back
leg hip yield. Mechanical demand imposed on the lower extremities (NJMs) was comparable for
125

both groups of players between conditions, and differences occurred on the individual and not
the group level. This demand was primarily aligned with the axis perpendicular to the leg plane
for all players for the entire duration of both the Jump In and Jump Out, suggesting that control
of the RF relative to the leg may be a priority. While players in general had increased work done
by the back leg for the Jump In, players with a shorter total contact time had decreased work by
the front leg instead as a result of the smaller leg yield and contact time. This suggests that work
done during the Jump In shifted from the front to the back leg similar to how impulse generation
had been shown to shift to the back leg. Coordination of initial leg configuration, impulse
distribution, and demand between legs are important to consider when determining how an
individual can improve performance for a change in horizontal direction.

Studying how individuals satisfy mechanical objectives under various initial configuration and
momentum conditions advances our understanding of lower extremity control and dynamics and
its benefits specific to the individual. In particular, improvements in impulse generation can be
facilitated by studying and providing feedback focused on the individual level. Determining how
to best facilitate individual-specific improvement requires investigating and understanding that
particular athlete’s power generation and multi-joint coordination strategy, while assessing their
performance in the context of the performance objective. In the case of impulse generation using
only one leg, initiating contact at a greater leg angle and reducing leg yield during contact can
enhance impulse generation by increasing RF magnitude or extending contact time. In the case
of impulse generation using two legs, allowing both legs to coordinate impulse generation
together to change total body CM direction is essential for improving overall performance. In
both cases, however, the mechanical demand was unique to the individual and must be
considered when trying to introduce changes in technique to help improve impulse generation.
Personalizing training and feedback on the individual level is essential to facilitating skill
acquisition and maximizing both impulse generation and athletic performance.

Future work to consider involves bridging the gap between studying the biomechanics of athletes
and providing feedback to facilitate skill acquisition. Additional investigation with athletes
experimenting in realistic scenarios and using technology to better assess these tradeoffs may
help coaches determine which solutions are best for each individual athlete
13
. Sensor technology
may be useful in simultaneously determining coordination strategies used on the individual level,
while providing real-time information to coaches to help deliver augmented feedback in
practice
13
. Further investigation is required into the effect of initial momentum and segment
configuration on both leg yield and imposed demand, particularly as it relates to trying to
introducing technical changes for an athlete. By exploring how changes in individual movement
techniques affect changes in leg yield, impulse regulation, and mechanical demand, we can
further determine how best to expedite skill acquisition and maximize impulse generation and
athletic performance.

126

References
1. Requejo PS, McNitt-Gray JL, Flashner H. An approach for developing an experimentally
based model for simulating flight-phase dynamics. Biol Cybern. 2002;87(4):289-300.
doi:10.1007/s00422-002-0339-9.
2. Hodgins JK, Raibert MH. Biped Gymnastics. Int J Rob Res. 1990;9(2):115-128.
3. McMahon T a., Cheng GC. The mechanics of running: How does stiffness couple with
speed? J Biomech. 1990;23(SUPPL. 1):65-78. doi:10.1016/0021-9290(90)90042-2.
4. Seyfarth a., Friedrichs a., Wank V, Blickhan R. Dyanamics of the Long Jump. J Biomech.
1999;32:1259-1267.
5. Ridderikhoff A, Batelaan JH, Bobbert MF. Jumping for distance: control of the external
force in squat jumps. Med Sci Sport Exerc. 1999;31(8):1196-1204.
doi:10.1097/00005768-199908000-00018.
6. Kraan G a., Van Veen J, Snijders CJ, Storm J. Starting from standing; Why step
backwards? J Biomech. 2001;34(2):211-215. doi:10.1016/S0021-9290(00)00178-0.
7. Costa K. Control and Dynamics during Horizontal Impulse Generation. 2004.
8. Raibert MH. Running With Symmetry. Int J Rob Res. 1986;5(4):3-19.
doi:10.1177/027836498600500401.
9. McNitt-Gray JL, Hester DME, Mathiyakom W, Munkasy B a. Mechanical demand and
multijoint control during landing depend on orientation of the body segments relative to
the reaction force. J Biomech. 2001;34(11):1471-1482. doi:10.1016/S0021-
9290(01)00110-5.
10. Mathiyakom W, McNitt-Gray JL, Wilcox R. Lower extremity control and dynamics
during backward angular impulse generation in backward translating tasks. Exp Brain Res.
2006;169(3):377-388. doi:10.1007/s00221-005-0150-7.
11. Mathiyakom W, McNitt-Gray JL, Wilcox R. Lower extremity control and dynamics
during backward angular impulse generation in forward translating tasks. J Biomech.
2006;39(6):990-1000. doi:10.1016/j.jbiomech.2005.02.022.
12. Mathiyakom W, McNitt-Gray JL, Wilcox RR. Regulation of angular impulse during two
forward translating tasks. J Appl Biomech. 2007;23(2):149-161.
13. McNitt-Gray JL, Sand K, Ramos C, Peterson T, Held L, Brown K. Using technology and
engineering to facilitate skill acquisition and improvements in performance. Proc Inst
Mech Eng Part P J Sport Eng Technol. 2015;229(2):103-115.
doi:10.1177/1754337114565381.
127

Appendix A: Force Plate Documentation

Force, moment, and center of pressure calculations based on manufacturer documentation.
1

128

129

130

131

References
1. Vaughan CL. Kistler Force Plate Formulae.; 1999.

Abstract (if available)

Abstract To succeed in athletic environments, athletes must regulate linear and angular momentum of their body by generating linear and angular impulse during contact with the ground. Effective impulse generation often requires the individual to re-configure their body so that they can generate the impulse needed to move in a desired direction. This can be accomplished by repositioning the feet relative to the total body CM and taking advantage of initial momentum to increase RF and / or contact time, resulting in increased impulse generated. To maximize the horizontal impulse in the shortest amount of time, the athlete must strategically configure their body segments so that the net joint moments (NJM) generated by muscles crossing the ankle, knee, and hip can effectively generate the required reaction forces in relation to the CM trajectory. Studying how individuals accomplish these mechanical objectives under varying initial momentum and configuration conditions advances our understanding of the control structure and its benefits specific to an individual. By determining what problems the athlete needs to solve and designing experiments to investigate how and why they move, we can determine solutions to help facilitate skill acquisition. The goal of these studies was to determine how elite-level athletes effectively regulate impulse generation to satisfy the mechanical objectives of a task under contextually relevant training conditions and how this information could be used to improve performance.

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Asset Metadata

Creator Ramos, Christopher Daniel (author)

Core Title Regulation of linear and angular impulse generation: implications for athletic performance

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Biomedical Engineering

Publication Date 12/11/2017

Defense Date 08/31/2017

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag biomechanics,Engineering,impulse,OAI-PMH Harvest,performance,Sports

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor McNitt-Gray, Jill (committee chair), D'Argenio, David (committee member), Requejo, Philip (committee member), Wilcox, Rand (committee member)

Creator Email chrisdramos7@gmail.com,rchristo@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c40-461915

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