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Study of belly-flaps to enhance lift and pitching moment coefficient of a blended-wing-body airplane in landing and takeoff configuration
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Study of belly-flaps to enhance lift and pitching moment coefficient of a blended-wing-body airplane in landing and takeoff configuration
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Content
STUDY OF BELLY-FLAPS TO ENHANCE LIFT AND PITCHING MOMENT
COEFFICIENT OF A BLENDED-WING-BODY AIRPLANE IN LANDING AND
TAKEOFF CONFIGURATION
by
Yann Daniel Staelens
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
(AEROSPACE ENGINEERING)
December 2007
Copyright 2007 Yann Daniel Staelens
ii
Acknowledgements
I would like the time at first to thank all the people that helped and supported me
during these last five years to obtain my PhD degree, namely:
My parents and family who have always encouraged me and supported my decisions
even the day I decided to move 8000 miles away from home to Los Angeles to start
this program.
Professor Ron Blackwelder and Mark Page, my advisors, who were always there to
answer my many questions and guide me throughout this project as well as giving
me the chance to work on this novel research topic.
Ewald Schuster, the research lab technician of the Aerospace and Mechanical
Engineering Department, for his technical input and help to put the experimental
setup together.
My friends in particular Charlie and Stacey Radovich, Amy Tatum, Jeff Brown and
John Peros for being there when I needed them and considering me as part of their
family.
Finally I would like to thank Fay Collier from the National Aeronautics and Space
Administration (NASA) and David Peake from the National Institute of Aerospace
(NIA) for their financial contribution to this research project through the NASA
cooperative agreement NCC-1-02043.
Thanks to all of you, I would never have achieved this without your help.
iii
Table of Contents
Acknowledgements ii
List of Tables v
List of Figures vi
Abbreviations x
Abstract xvi
Introduction 1
Chapter 1 – Problem Statement 5
Chapter 2 – Proposed Study 8
Chapter 3 – Experimental Setup 11
3.1 Wind Tunnel Facility 11
3.2 Instrumentation and Experimental Apparatus 16
3.3 Model 19
Chapter 4 – Test Measurands 29
Chapter 5 – Experimental Data 31
5.1 Data Acquisition and Filtering 31
5.2 Moment Transfer 34
5.3 Correction Factors 35
5.3.1 Horizontal Buoyancy 35
5.3.2 Solid and Wake Blockage 37
Chapter 6 – Experimental Results 39
6.1 Phase One: location survey 39
6.2 Phase Two: shape survey 52
iv
Chapter 7 – Mathematical Simulation 63
7.1 Dynamics Equations 63
7.2 Flow Chart 67
7.3 Results 68
7.3.1 Landing simulation 70
7.3.2 Go-around simulation 74
7.3.3 Takeoff simulation 76
7.4 Experimental Flight 78
Conclusion 80
Bibliography 83
Appendices 85
Appendix A – Force-Balance Range Calculations 85
Appendix B – Trip-strip Calculations Using Braslow’s Method 86
Appendix C1 – Labview vi’s: Vi to measure dynamic pressure 87
and temperature
Appendix C2 – Labview vi’s: Digital data filter 89
Appendix D – Data Fit 90
Appendix E – Spring-Dashpot Constants 95
Appendix F – Additional landing simulation results 98
Appendix G – Additional go-around simulation results 99
Appendix H – Additional takeoff simulation results 100
v
List of Tables
Table 1 – AMTI’s FS6-500 force balance specifications (AMTI 2000) 18
Table 2 – Physical properties of the RPCure 300 Resin (3D Systems 2005) 21
Table 3 – Geometric characteristics of the model 22
Table 4 – Results of the FEM-analysis for the model 23
Table 5 – Parameters measured during the study 29
Table 6 – Results of horizontal buoyancy calculations 36
Table 7 – Correction factors for solid and wake blockage 38
Table 8 – Major variables considered in the simulation 69
Table 9 – Values used to determine the LFL for the three configurations of 72
the BWB-airplane.
Table D1 – Coefficients of the curve fit calculated by LINEST 91
vi
List of Figures
Figure 1 – Horton Ho-1 (1933). 1
Figure 2 – Horton Ho-229 (circa 1945). 2
Figure 3 – Horton Ho-18B “Amerika Bomber” (1945). 2
Figure 4 – Northrop N-1M (1940). 3
Figure 5 – Northrop Flying Wing XB-35 (1946). 3
Figure 6 – Northrop Stealth Bomber B-2 (1989). 4
Figure 7 – The NASA/Boeing BWB Concept, Commercial Transport 4
& Tanker (near future).
Figure 8 – CCP and ICR location with GOG (left) and in flight (right) 6
for a conventional airplane, a BWB airplane and the Space
Shuttle.
Figure 9 – Landing (top) and takeoff (bottom) analysis. 7
Figure 10 – Lockheed P-38 “Lightning’ with under-wing flaps for 9
dive recovery.
Figure 11 – Pressure field induced by the belly-flap (top) and photo of 10
the model in the wind tunnel (bottom).
Figure 12 – Wind tunnel facility. a) & b) overall view of the wind tunnel 11
and test section. c) moving ground plane mechanism.
d) moving ground plane controller.
Figure 13 – Boundary-layer survey at 30m/s. 12
Figure 14 – Traverse system with boundary-layer probe. 13
Figure 15 – Series of fine mesh screens upstream of the contraction. 13
Figure 16 – Normalized velocity profile in test section for a wind speed 14
of 30m/s.
vii
Figure 17 – Traverse system that is external to the wind tunnel test 15
section (left) and the pitot-tube inside the test section (right).
Figure 18 – CAD model view of the wind tunnel setup. 17
Figure 19 – AMTI’s FS6-500 force balance dimensions (AMTI 2000). 18
Figure 20 – Boeing BWB-450. 19
Figure 21 – Airfoil characteristics of the model. 20
Figure 22 – Airfoil characteristics along the span. 20
Figure 23 – Isometric and 3-view drawing of the model. 21
Figure 24 – Model during stereo lithography process at Swift Engineering, Inc. 21
Figure 25 – Total deflection of the model due to the applied loads. 23
Figure 26 – Von Mises stress of the model due to the applied loads. 24
Figure 27 – Span wise Reynolds number distribution. 24
Figure 28 – BWB wind tunnel model and Control surfaces. 25
Figure 29 – Boundary-layer detection setup. 26
Figure 30 – Power spectral density of the boundary-layer of the BWB model. 27
Figure 31 – Map of location of the different types of boundary-layers on 28
top-surface of the BWB-model.
Figure 32 – Belly-flaps used during the study. 28
Figure 33 – Independent variables studied during the tests. 30
Figure 34 – Equipment used to log the dynamic pressure and temperature 31
of the test section during the tests. Texas Instrument DAQ-card
(top left), 10Torr MKS Baratron Type 698A with Type 670
signal conditioner box (top right), thermocouple type J with
signal conditioner box (bottom).
Figure 35 – Sample of saved data from one channel of the force-balance 32
before and after applying the digital filter.
viii
Figure 36 – Graphic representation of the forces and moment transfer. 34
Figure 37 – Effect of the belly-flap for two deflections of the elevons, 40
δ
e
= 0
o
and δ
e
= -20
o
showing the lift, drag and pitching
moment coefficient curves.
Figure 38 – Effect of the belly-flap for different heights of the model in 43
the test section. The lift, drag and pitching moment coefficient
increment curves are shown.
Figure 39 – Effect of the belly-flap deflection angle, δ
bf
. The lift, drag and 45
pitching moment coefficient with and without belly-flap for
three angles of attack, α = 0
o
, α = 4
o
and α = 8
o
, are shown
for the wing being at H/2b
w
= 0.057.
Figure 40 – Effect of the belly-flap longitudinal rigging, x
bf
. The lift, drag 47
and pitching moment coefficient with and without belly-flap for
three angles of attack, α = 0
o
, α = 4
o
and α = 8
o
at H/2b
w
= 0.057.
Figure 41 – Effect of the belly-flap lateral rigging, y
bf
. The lift, drag and 48
pitching moment coefficient with and without belly-flap for three
angles of attack, α = 0
o
, α = 4
o
and α = 8
o
at H/2b
w
= 0.057.
Figure 42 – Effect of the belly-flap sweep angle, Λ
bf
. The lift, drag and 49
pitching moment coefficient with and without belly-flap for three
angles of attack, α = 0
o
, α = 4
o
and α = 8
o
at H/2b
w
= 0.057.
Figure 43 – Difference in increase in lift and pitching moment coefficient 51
with and without the use of a belly-flap.
Figure 44 – Effect of the belly-flap span, l
1
. The lift, drag and pitching 53
moment with and without belly-flap for three angles of attack,
α = 0
o
, α = 4
o
and α = 8
o
are shown.
Figure 45 – Lift, drag and pitching moment coefficient increment for 55
different type of belly-flaps for H/(2b
w
) = 0.115. Belly-flap
types #1 through #4.
Figure 46 – Lift, drag and pitching moment coefficient increment for 56
different type of belly-flaps for H/(2b
w
) = 0.115. Belly-flap
types #4 through #7.
ix
Figure 47 – Streamlines on the bottom surface of the BWB-model at an 58
angle of attack of 0
o
(left) and 8
o
(right) for three types of
belly-flaps; 47a - type #2, 47b - type #4 and 47c - type #7.
Figure 48 – Effect of the belly-flap type #7 for two deflections of the 60
elevons, δ
e
= 0
o
and δ
e
= 8
o
, for the lift, drag and pitching moment
coefficient curves.
Figure 49 – Effect of the belly-flap types #1 & #7 for different heights of 61
the model in the test section. Lift, drag and pitching moment
increment curves are shown.
Figure 50 – Geometry of a BWB-airplane used in the simulation. 63
Figure 51 – Forces acting on a BWB-airplane considered in the simulation. 64
Figure 52 – Control law for the deflection of the belly-flap. 68
Figure 53 – Results of the landing simulation for a BWB-airplane. 71
Figure 54 – Results of the go-around simulation for a BWB-airplane. 75
Figure 55 – Results o the takeoff simulation for a BWB-airplane. 77
Figure 56 – Electric powered KillerBee1 equipped with a belly-flap. 78
Figure D1 – Curve-fit verification for the lift coefficient. 92
Figure D2 – Curve-fit verification for the drag coefficient. 93
Figure D3 – Curve-fit verification for the pitching moment coefficient. 94
Figure E1 – Free-body diagram used to model a landing gear. 95
Figure E2 – Time response of the main landing gear. 97
Figure E3 – Time response of the nose landing gear. 97
x
Abbreviations
W
AR geometric wing aspect ratio ( )
W W
S b
2
α or AOA angle of attack [deg]
α & dα/dt [deg/s]
δ
e
elevon deflection [deg]
δ
bf
hinge wise deflection of the spoiler [deg]
ε correction factor
ε
mg
non-linear spring constant for the main landing gear [lbs/ft
3
]
ε
ng
non-linear spring constant for the nose landing gear [lbs/ft
3
]
λ
3
body-shape factor
Λ
bf
sweep of the spoiler [deg]
θ pitch angle [deg]
θ
&
pitch rate [deg/s]
θ
& &
pitch acceleration [deg/s²]
γ or γ
climb
climb angle [deg]
γ
appr
approach angle [deg]
µ friction coefficient of the wheels of the main landing gear
Φ belly-flap porosity
A area [ft
2
]
BL boundary layer
b
w
half-wingspan of the model [ft]
xi
BWB Blended-Wing-Body
D
C drag coefficient
α &
D
C α & ∂ ∂
D
C [deg
-1
]
θ
&
D
C θ
&
∂ ∂
D
C [deg
-1
]
WT
D
C drag coefficient from wind tunnel tests
f
C friction coefficient
L
C lift coefficient
α &
L
C
α & ∂ ∂
L
C [deg
-1
]
θ
&
L
C θ
&
∂ ∂
L
C [deg
-1
]
WT
L
C lift coefficient from wind tunnel tests
m
C pitching moment coefficient
α &
m
C α & ∂ ∂
m
C [deg
-1
]
θ
&
m
C θ
&
∂ ∂
m
C [deg
-1
]
WT
m
C pitching moment coefficient from wind tunnel tests
c or mac mean aerodynamic chord [ft]
c chord [ft]
c
mg
linear dashpot constant for the main landing gear [lbs-s/ft]
c
ng
linear dashpot constant for the nose landing gear [lbs-s/ft]
CCP control’s center of percussion
xii
CG center of gravity
CL center line
D drag [lbs]
dp/dl static pressure gradient [lbs/ft
3
]
e elevon
FB
X
F force in the x-axis of the force-balance [lbs]
FB
Y
F force in the y-axis of the force-balance [lbs]
FRP floor of plane
0
g acceleration due to gravity [ft/s²]
GE ground effect
GOG gear on ground
h
DH
decision altitude for go-around [ft]
h
flare
flare altitude [ft]
h
GE
altitude when ground effects are considered [ft]
h
trim
trim altitude [ft]
H height of the model in the test section of the wind tunnel [ft]
T
i thrust angle [deg]
I
YY
moment of inertia in the y-direction [slug-ft²]
ICR instantaneous center of rotation
k
mg
linear spring constant for the main landing gear [lbs/ft]
k
ng
linear spring constant for the nose landing gear [lbs/ft]
l body length [ft]
xiii
l
1
spoiler span [ft]
l
2
spoiler height inboard [ft]
l
3
spoiler height outboard [ft]
L lift [lbs]
LE leading edge
LFL landing-field-length [ft]
LGW landing gross weight [lbs]
m pitching moment [lbs-ft]
M mach number
FB
Z
M moment in the z-axis of the force-balance [lbs]
max maximum value
m
u
mass of the airplane [slug]
n number of g’s
N
mg
reaction force of the main landing gear in the x-direction [lbs]
N
ng
reaction force of the nose landing gear in the x-direction [lbs]
q dynamic pressure [psf]
R rotation radius [ft]
Re Reynolds number
R
mg
reaction force of the main landing gear in the z-direction [lbs]
R
ng
reaction force of the nose landing gear in the z-direction [lbs]
mg
s stroke of the main landing gear [ft]
xiv
ng
s stroke of the nose landing gear [ft]
mg
s & stroke velocity of the main landing gear [ft]
ng
s & stroke velocity of the nose landing gear [ft]
W
S trapezoidal wing area [ft²]
SB solid blockage
t thickness [in]
T/W Thrust to weight ratio
T
max
maximum thrust available for climb [lbs]
T
net
thrust [lbs]
T
static
maximum static thrust [lbs]
TOFL takeoff-field-length [ft]
TOGW takeoff gross weight [lbs]
trim values for a trimmed airplane
V
appr
approach speed of the airplane [ft/s]
V
climb
climb speed of the airplane [ft/s]
V
local
velocity of the flow at one particular location of the test section
during a survey [ft/s]
V
ref
average velocity of the flow for a predefined reference area of the test
section [ft/s]
V
rot
rotation speed of the airplane [ft/s]
V
stall
stall speed of the airplane [ft/s]
V
takeoff
takeoff speed of the airplane [ft/s]
V
total
total speed of the airplane [ft/s]
xv
V
∞
wind speed [ft/s]
W weight of the airplane [lbs]
WB wake blockage
WL winglet
X length in the direction of the flow [ft]
X
B
axial reference axis in the earth coordinates
X
e
axial reference axis in the airplane coordinates
X
cg
axial position of the CG relative to the airplane’s datum [ft]
X
mg
axial position of the main gear relative to the airplane’s datum [ft]
X
ng
axial position of the nose gear relative to the airplane’s datum [ft]
X
bf
longitudinal rigging of the spoiler [ft]
X
T
axial position of the engine origin relative to the airplane’s datum [ft]
Y width [ft]
Y
bf
lateral rigging of the spoiler [ft]
Z height [ft]
Z
B
vertical reference axis in the airplane coordinates
Z
e
vertical reference axis in the earth coordinates
Z
cg
vertical position of the CG relative to the airplane’s datum [ft]
Z
mg
vertical position of the main gear relative to the airplane’s datum [ft]
Z
ng
vertical position of the nose gear relative to the airplane’s datum [ft]
Z
T
vertical position of the engine’s origin relative to the airplane’s
datum [ft]
xvi
Abstract
During the first century of flight few major changes have been made to the
configuration of subsonic airplanes. A distinct fuselage with wings, a tail, engines
and a landing gear persists as the dominant arrangement. During WWII some
companies developed tailless all-wing airplanes. However the concept failed to
advance till the late 80’s when the B-2, the only flying wing to enter production to
date, illustrated its benefits at least for a stealth platform. The advent of the Blended-
Wing-Body (BWB) addresses the historical shortcomings of all-wing designs,
specifically poor volume utility and excess wetted area as a result. The BWB is now
poised to become the new standard for large subsonic airplanes. Major aerospace
companies are studying the concept for next generation of passenger airplanes. But
there are still challenges. One is the BWB’s short control lever-arm pitch. This
affects rotation and go-around performances. This study presents a possible solution
by using a novel type of control surface, a belly-flap, on the under side of the wing to
enhance its lift and pitching moment coefficient during landing, go-around and
takeoff. Increases of up to 30% in lift-off C
L
and 8% in positive pitching moment
have been achieved during wind tunnel tests on a generic BWB-model with a belly-
flap. These aerodynamic improvements when used in a mathematical simulation of
landing, go-around and takeoff procedure were showing reduction in landing-field-
length by up to 22%, in takeoff-field-length by up to 8% and in loss in altitude
between initiation of rotation and actual rotation during go-around by up to 21.5%.
1
Introduction
During the year 1903, Wilbur and Orville Wright built Flyer 1, the first powered
aircraft, and with this ushered in the beginning of the aircraft industry. In one century
of flight, airplanes have evolved considerably. Fighters have become more reliable,
more powerful and more maneuverable. Commercial aircrafts have become more
efficient, more secure and more comfortable. But one thing that hasn’t changed
significantly over the years is the overall shape. An airplane is still configured with a
fuselage, wings, tail, engines and a landing gear.
In the early 1930’s the Horton brothers (Myhra 1998), Walter and Reimar, from
Germany developed a revolutionary design: a tailless, all-wing airplane in which the
pilot and engines were housed inside the wing. They gave birth to a whole line of all-
wing airplanes from the Horton Ho-1 to the Ho-229 jet fighter, and the “Amerika
Bomber” Horton Ho-18 concept (see Fig. 1-3).
Figure 1 - Horton Ho-1 (1933).
2
Figure 2 - Horton Ho-229 (circa 1945).
Figure 3 - Horton Ho-18B "Amerika Bomber" (1945).
In the mean time across the Atlantic the Northrop Corporation developed its own
version of an all-wing airplane, the N-1M (van der Linden 2002). Evolved versions
were built later like the XB-35 and YB-49 but the concept never really broke
through, even though it had proven its efficiency by reducing the airplane to a nearly
pure supporting surface in which every part contributes to weight-lifting ability (see
Fig. 4-5).
3
Figure 4 - Northrop N-1M (1940).
Figure 5 - Northrop Flying Wing XB-35 (1946).
In the late 80’s the Northrop Corporation brought the concept back to life with the
B-2, a bomber used by the Air Force (Air Force Technology 2006). To date the B-2
is the only significant flying wing to have entered production (see Fig. 6). Since then
companies like McDonnell Douglas (Liebeck, Page and Rawdon 1996) and now
Boeing through its Phantom Works division are studying a Blended-Wing-Body
(BWB) aircraft concept for commercial and military applications (see Fig. 7)
(Cawthon 2002).
4
Figure 6 - Northrop Stealth Bomber B-2 (1989).
Figure 7 - The NASA/Boeing BWB Concept, Commercial Transport & Tanker (near future).
This research contributes to the development of the BWB by investigating some
novel lift and pitch control effectors for takeoff and landing, a problem area for the
flying wing.
5
Chapter 1 – Problem Statement
The Blended-Wing-Body is a tailless, all wing airplane that houses the crew,
passengers and cargo entirely inside the wing. The BWB offers major advantages
compared to the traditional airplanes. For example, the drag is reduced by blending
the fuselage and the wing to increase the wetted aspect ratio while reducing the
structural aspect ratio. Fuel economy can be improved by 20% - 30% on flights at
high subsonic speeds (Liebeck, Page and Rawdon 1998).
One of the challenges encountered by the BWB design is related to short-coupled
controls. The BWB’s pitch controls, the elevons, have a short lever arm (l
pc
) to the
center of gravity (CG) compared to the elevator of a conventionally tailed airplane
(see fig.8). The BWB’s lever arm is 2 to 3 times smaller. This adversely affects flight
path control during rotation and landing flare since pitch changes are accompanied
by an unwanted initial plunging; i.e. a loss of lift leading to the plane flying at an
elevation below its intended trajectory. With gear-on-ground (GOG), the
instantaneous center of rotation (ICR), i.e. the fixed point around which the rest of
the plane moves when pitch controls are used, is where the main landing gear is in
contact with the runway which is aft of the CG. For this condition, the control’s
center of percussion (CCP), i.e. the effective point of action for the pitch control
force, is located closer to the CG for the BWB-airplane than that of a conventional
airplane. In flight the ICR is located far in front of the CG and the CCP is located
closer to the CG for the BWB compared to a conventional airplane (see Fig. 8). In
6
both GOG and in flight, an equivalent pitch change requires a larger down force
from the control surface on the BWB since the moment arm is smaller. The larger
down force is obtained by a greater negative deflection of the elevons which creates
a larger lift-loss, causing the BWB first to plunge downward before achieving the
desired angle of attack (AOA). Once at the desired AOA, the intended positive lift
change is realized.
Figure 8 - CCP and ICR location with GOG (left) and in flight (right) for a conventional
airplane, a BWB airplane and the Space Shuttle.
This phenomenon will introduce an unwanted “sagging” of the BWB’s flight path
during landing, go-around and takeoff. Compared to a conventional tailed airplane,
the pilot needs to initiate the flare and rotation earlier to reach the same end-state
(see Fig. 9). This effect is even more problematic during takeoff since ground effects
amplify the lift loss. A particular concern in the landing flare is gear-plunge. It’s
7
possible that a nose-up command will actually increase the sink-rate at the main
gear. This is a form of control reversal for the flare task, since the pilot is trying to
manage the impact at touchdown.
Figure 9 - Landing (top) and takeoff (bottom) analysis.
This behavior was physically seen on the Space Shuttle during landing approach.
Since the Shuttle has no horizontal tail its control surfaces for pitch, the elevons,
were positioned in a similar location as for the BWB-airplane so their ICR and CCP
are very similar which explains why the Shuttle has the same type of unwanted
sagging of the flight path during landing. (see Fig. 8).
8
Chapter 2 – Proposed Study
The present study contributes to the development of the BWB by investigating the
previous stated problem to determine if it can be solved or diminished by using
under-wing flaps or belly-flaps as pitch control effectors for landing, go-around and
takeoff.
An airplane for which under-wing flaps were used was the “Lockheed P-38
Lightning” (see Fig. 9). They were used for dive control (Anderson 2000). In a high-
speed descent the airplane had a strong tendency to nose over into a vertical dive
from which the pilot did not have the strength, or the elevator power to recover. This
phenomenon is known as “tuck-under”. Beyond a critical Mach number of the wing
(M = 0.65) a system of shock waves was formed on the upper surface of the inboard
wing section. The shock waves reacted with the boundary layer and caused flow
separation and loss of lift over that portion of the wing. This caused a loss of
downwash, which increased the angle of attack on the tail. This produced a larger
upward lift on the tail, which immediately put the airplane into a steeper dive which
further increased its velocity. Upon recommendation of Al Erickson, who was the
chief engineer responsible for the tests at the NACA Ames Aeronautical Laboratory
when investigating the problem, Lockheed installed flaps on the lower surface of the
wing at the 0.33c point. The action of the flap was to quickly restore the lift that the
wings had lost and restore flow over the tail to its normal condition.
9
Figure 10 - Lockheed P-38 "Lightning" with under-wing flaps for dive recovery.
Deploying a flap near the CG on the under surface of the airplane will increase the
static pressure ahead of the CG and decrease it aft, producing a nose-up couple (see
Fig. 11). The area of the flap is small compared to the wing area affected by the flap,
so the moment due to the flap’s drag should be relatively small. The resulting
moment and lift change will help to rotate the BWB during landing, go-around and
takeoff.
Since the flow around belly-flaps is separation dominated, an experimental approach
was adopted. In addition, since ground reflection effects are so critical, the tests were
performed in a wind tunnel with a moving ground plane (see Fig.11). The speed of
the ground plane matched the velocity of the air in the wind tunnel to properly model
the ground conditions. Further, different belly-flap geometries were studied to
determine the most effective shape and location. The difference between solid and
10
perforated belly-flaps was investigated as well as the use of end-plates on the belly-
flaps.
Figure 11 - Pressure field induced by the belly-flap (top) and photo of the model in the wind
tunnel (bottom).
All the experimental data was used as input with a home built mathematical model of
the longitudinal motion of the aircraft to create a non-linear simulation of the BWB’s
landing, go-around and takeoff dynamics. Ground reflection effects and the
interaction between landing gear and ground were incorporated in the model.
11
Chapter 3 – Experimental Setup
The tests were performed on a model of a generic BWB transport in the wind tunnel
facility located at the University of Southern California; 854 Downey Way, RRB
101; Los Angeles, CA 90089.
3.1 Wind Tunnel Facility
The wind tunnel is a closed return temperature-controlled airflow wind tunnel. Its
overall dimensions are 9ft wide, 18ft high and 63ft long. Its maximum operational
speed is 45m/s ( ≈ 100mph). It has a contraction ratio of 5.64:1. The test area is
39”9/16 high x 35”7/8 wide x 39”5/8 long and it has a rolling road of 32”1/4 long x
22” wide (see Fig. 12).
Figure 12 - Wind tunnel facility. a) & b) overall view of the wind tunnel and test section.
c) moving ground plane mechanism. d) moving ground plane controller.
12
The maximum speed of the moving ground plane is 35m/s ( ≈ 78mph) and is
synchronized with the wind speed. Suction is applied upstream of the rolling road to
remove the tunnel wall boundary-layer upstream of the moving ground plane. The
suction was supplied by an independent adjustable speed fan whose volume flow
was set by keeping the ratio between the pressure differences of the test section and
the suction device constant. At a wind speed of 30m/s, which is the speed used
during this study, three millimeters above the belt a wind speed of 97% of the free-
stream velocity is still measured (see Fig. 13) which is considered satisfactory for
this study. The measurements were performed at three different locations in a plane
perpendicular to the flow using a boundary-layer probe attached to a traverse system
powered by two stepper motors, one for the y-direction, perpendicular to the splitter
plate (i.e. parallel to the moving ground plane), and one for the z-direction,
perpendicular to the moving ground plane (see Fig. 13 & 14).
Figure 13 - Boundary-layer survey at 30m/s.
13
Figure 14 - Traverse system with boundary-layer probe.
A computer program using Labview routines monitored the free stream velocity and
kept it constant via a feedback routine. It also controlled the moving ground plane
speed and kept it within 1% of the free stream velocity. A stand-alone controller (see
Fig. 12d) was programmed to control the lateral position of the belt of the rolling
road (see Fig. 12c). To reduce the turbulences and guarantee a uniform velocity
distribution in the test section, a series of five mesh screens of size 20 (i.e. 20
openings per inch of screen) and a porosity level of 64% are installed upstream of the
contraction (see Fig. 15).
Figure 15 - Series of fine mesh screens upstream of the contraction.
14
The velocity distribution in the test section for speeds between 10 and 40 m/s was
uniform within 1%. Figure 16 shows a graph of this uniformity at the given test
speed of 30m/s. The velocity profile was obtained by measuring the dynamic
pressure at different locations in a plane perpendicular to the flow using a pitot-tube
attached to a traverse system driven by two stepper motors (see Fig. 17).
Figure 16 - Normalized velocity profile in test section for a wind speed of 30m/s.
The velocity deficit seen on the left of the graph is caused by the splitter plate’s
boundary layer. The magnitude of this deficit was significantly reduced by adding
boundary-layer suction on the plate through a vent located at the front of the splitter
plate. More details about the vent will be given in section 3.2 of this chapter. The
little increase in velocity before the drop due to the boundary layer is caused by the
presence of the slot in the splitter plate needed to take the measurements. Due to the
15
difference in pressure between both sides of the plate at this location the flow is
locally accelerated before going through the slot.
Figure 17 - Traverse system that is external to the wind tunnel test section (left)
and the pitot-tube inside the test section (right).
16
3.2 Instrumentation and Experimental Apparatus
A half model of the BWB was used and is shown schematically in the test section in
Fig. 18. A model support column (part #1) was designed so that vertical position and
angle-of-attack of the model could be changed easily and repeatably. A splitter plate
(part #6) was utilized to allow better control of the airflow over and around the
model. An adjustable flap (part #5) was installed at the end of the splitter plate to
maintain a zero pressure difference, measured using the two static pressure ports near
the fore section of the splitter plate, between both sides of the plate regardless the
flow obstruction introduced by the model. This ensured that the stagnation point was
located on the leading edge of the splitter plate and the flow was attached all along
the working surface of the plate. The pressure difference was measured using a 1Torr
MKS Baratron pressure meter.
A vent for side suction was located upstream of the model to reduce as much as
possible the boundary layer thickness on the splitter plate before the flow reaches the
model. It was covered by porous metal installed to be co-planar to the splitter plate’s
surface. The pressure difference across the porous plate was established by a small
exit type ramp on the backside of the splitter plate. The ramp’s height was chosen to
provide the appropriate amount of flow through the porous plate to remove the
boundary layer.
Some brush seals were used between the splitter plate and the belt and between the
upstream boundary layer suction device and the belt to prevent air leakage. For the
17
same reason, tape was used to cover the slot on the splitter plate and low stiffness
foam was used between the model and the splitter plate.
During the design some FEM-analysis was performed on the parts to make sure no
failure would occur and that the deformations due to the applied loads were
acceptable.
The model could be accessed via the tunnel door behind the splitter plate (near the
force balance) and also from a door on the model side of the wind tunnel.
Figure 18 - CAD model view of the wind tunnel setup.
18
The forces (lift and drag) and the moment (pitch) experienced by the model during
the tests were measured using an AMTI’s FS6-500 Fixator six component force
balance sensor connected to a MSA-6 strain gage amplifier manufactured by AMTI
(Advanced Mechanical Technology, Inc.). The dimensions of the force balance are
shown in Fig. 19 and its specifications are listed in Table 1. The force balance was
selected based on calculations available in Appendix A. AMTI’s NetForce data
acquisition software is used to save the measured quantities for further analysis.
Figure 19 - AMTI's FS6-500 force balance dimensions (AMTI 2000).
Table 1 - AMTI's FS6-500 force balance specifications (AMTI 2000)
Axis Origin (distances are from the geometric center of the device)
X
0
, in, (mm) 7.45E-03 (0.189)
Y
0
, in, (mm) 1.35E-02 (0.342)
Z
0
, in, (mm) 1.60E+00 (40.583)
Specifications
Fx, Fy capacity, lb, (N) 250 (1100)
Fz capacity, lb, (N) 500 (2200)
Mx, My capacity, in*lb, (Nm) 500 (56)
Mz capacity, in*lb, (Nm) 250 (28)
Fx, Fy sensitivity, µV/[V*lb], (µV/[V*N]) 6.0 (1.35)
Fz sensitivity, µV/[V*lb], (µV/[V*N]) 1.5 (0.34)
Mx, My sensitivity, µV/[V*in*lb], (µV/[V*Nm]) 7.5 (66)
Mz sensitivity, µV/[V*in*lb], (µV/[V*Nm]) 6.0 (50.4)
19
3.3 Model
The model is a 1/67
th
scale BWB commercial transport. The plan form and thickness
distribution are patterned after the Boeing BWB-450 described in Liebeck (2002)
(see Fig. 20 – 22). The thickness of the wing remains constant up to 20% span even
though the airfoil seems to become thicker as shown in Fig. 21. This is an artifact of
the chord decreasing continuously along the wingspan. It also explains why the t/c-
curve in Fig 22 doesn’t have its maximum at the centerline but at approximately
20%.
Figure 20 - Boeing BWB-450.
20
Figure 21 - Airfoil characteristics of the model.
Figure 22 - Airfoil characteristics along the span.
21
The model was designed with the help of the CAD package Solid Edge (see Fig. 23)
and constructed with a stereo lithography system at Swift Engineering, Inc. (see Fig.
24). It is made out of the RPCure 300 series, which is a three-epoxy resin. The
physical properties of the material can be found in Table 2.
Figure 23 - Isometric and 3-view drawing of the model.
Figure 24 - Model during stereo lithography process at Swift Engineering, Inc.
Table 2 - Physical properties of the RPCure 300 resin (3D Systems 2005)
Physical property RPCure 300
Density, lbm/in
3
, (g/cm
3
) 0.039 (1.1)
Flexural modulus, lbf/in
2
, (MPa) 406000 (2800)
Tensile modulus, lbf/in
2
, (MPa) 435000 (3000)
Tensile strength, lbf/in
2
, (MPa) 8700 (60)
Poisson’s ratio 0.3
22
The main geometric characteristics of the model are listed in Table 3.
Table 3 - Geometric characteristics of the model
Description Symbol Value
Half-span, ft b
w
1.767
Mean aerodynamic chord, ft mac 0.482
Trapezoidal wing area, ft
2
S
w
0.781
x-coordinate of the leading edge of the mac, ft x
LEmac
1.052
y-coordinate of the mac, ft y
mac
0.730
A complete FEM-analysis of the model was performed to make sure it would resist
the loads applied during the tests. The considered loads were the weight of the model
itself and a uniform pressure applied on the under-wing surface of the model
calculated by using equation 3.1 and the values listed in Table 4 for a full span
model.
a SurfaceAre
D L
pressure uniform
2 2
_
+
= (3.1)
The results of this analysis are listed in Table 4 as well and Fig. 25 & 26 are graphic
representations of it. The stressed (color scheme) and unstressed (blue wire frame)
cases of the model are represented on both figures. The winglets were removed from
the model during analysis for computational purposes. This was justified by the fact
that lift produced by the winglets is negligible compared to the lift produced by the
rest of the wing. From the results of the analysis a safety factor = 28.05 was found so
one could conclude that no reinforcements of any kind were needed to carry the
loads the model had to endure during testing. The maximum deflection of 0.187 in at
the wing tip due to the loads was within an acceptable range as well.
23
Table 4 - Results of the FEM-analysis for the model
Description Value
Max. Lift, lbs (cf. Appendix A: Force-balance Range) 27
Max. Drag, lbs (cf. Appendix A: Force-balance Range) 16
Body load (gravity), in/s
2
386.09
Surface Area (actual under wing surface), in
2
212.77
Uniform pressure, psi 0.1475
Max. Von Mises stress, psi 244
Max. deflection at the wing tip, in 0.187
Tensile strength of used material, psi 8700
Safety factor (= Max. Von Mises stress/ Tensile
strength of used material)
28.05
Figure 25 - Total deflection of the model due to the applied loads.
24
Figure 26 - Von Mises stress of the model due to the applied loads.
A semi span model is used to achieve the highest Reynolds numbers possible and is
warranted since the study was directed at pitch characteristics only. The Reynolds
number distribution along the span for a wind speed of 30m/s, which is the speed
used during the study, is shown in Fig. 27.
Figure 27 - Span wise Reynolds number distribution.
25
A photograph of the model is shown in Fig. 28. The control surfaces shown in the
figure are used during the tests to reproduce the trim conditions of the airplane
during takeoff, landing and cruise. They are maintained in place using tape and the
control surface brackets, which have a fixed and known angle. The number of
control surfaces is reduced relative to the Boeing BWB-450 to simplify model
changes during the tests.
Figure 28 - BWB wind tunnel model and Control surfaces.
The flow is tripped at the leading edge of the wing on the top and bottom surface
using a trip-strip (cf. Fig. 28) to insure a turbulent boundary layer over the wing is
present during the tests at all times. The location and diameter of the glass beads
composing the trip-strip were determined using the method described in Braslow &
Knox (1958). The details of these calculations can be found in Appendix B. The
efficiency of the trip-strip was verified by mapping the location of the laminar and
turbulent boundary layers as well as the transition region present over the model by
26
using a miniature pitot-tube connected to a stethoscope and microphone (see Fig.
29).
Figure 29 – Boundary layer detection setup.
In the laminar boundary layer, pressure fluctuations are almost non-existent whereas
in the turbulent flow, significant pressure fluctuations are present. When these
fluctuations were listened to with a stethoscope, their characteristic noise signature
was virtually non-existent in the laminar case, produced a cracking/popping noise
during transition and provided a loud continuous noise in the turbulent boundary
layer. The power spectral density of the noise signals for the three different type of
boundary layer can be seen in Fig. 30. It was established using Welch's averaged
modified periodogram method of spectral estimation with a sampling frequency of
48kHz (Welch 1967). The difference in location of the three types of boundary layer
with and without the trip-strip for an angle of attack of 0
o
and 8
o
can be seen in
Fig. 30.
27
Figure 30 - Power spectral density of the boundary layer of the BWB model.
28
Figure 31 - Map of location of the different types of Boundary-Layers on top-surface of the
BWB-model.
The belly-flaps were made of 0.02” thick brass or aluminum sheets and were
attached to the under side of the wing using aluminum tape so their location and
orientation could easily be changed. Figure 32 shows the seven types of solid and
porous belly-flaps used in the present study. Their dimensions, porosity and other
characteristics are given in Chapter 4 and Section 6.2.
Figure 32 - Belly-flaps used during the study.
29
Chapter 4 – Test Measurands
All the parameters that were varied (independent variables) are shown in Fig. 33.
They and the measured parameters (dependent variables) taken during the study are
listed in Table 5. The half-span of the model is b
w
and the values for the dependent
variables are estimates based on preliminary tests performed during the set-up of the
experiment.
Table 5 - Parameters measured during the study
Type of variable Parameter Range
Independent α (angle of attack)
0
o
up to 8
o
(increments of 2
o
)
H/(2b
w
)
(height of CG of model in tunnel)
0.057, 0.115, 0.230,
free-air
l
1
/b
w
(belly-flap span)
0.071 up to 0.284
(increments of 0.071)
l
2
/mac (belly-flap height inboard) 0.121 and 0.242
l
3
/mac (belly-flap height outboard) 0.121 and 0.242
x
bf
/(root chord)
(longitudinal rigging of belly-flap)
0.388, 0.466, 0.543,
0.631 and 0.670
y
bf
/b
w
(lateral rigging of belly-flap)
0.017, 0.034, 0.068,
0.137 and 0.205
Λ
bf
(sweep of belly-flap)
-60
o
up to 60
o
(by increments of 30
o
)
δ
bf
(hinge wise deflection of belly-flap)
0
o
up to 120
o
(by increments of 30
o
)
δ
e
(elevon deflection) 0
o
, -10
o
or -20
o
M
∞
(mach number)
0.09
(V
∞
≈ 30m/s ≈ 67 mph)
Φ (belly-flap porosity) 0%, 11.5% and 23%
Dependent C
L
(lift coefficient) ± 1.5
C
D
(drag coefficient) up to 0.3
C
m
(pitching moment coefficient) ± 0.6
30
Figure 33 are graphic representations of the different independent variables studied
during the tests.
Figure 33 - Independent variables studied during the tests.
31
Chapter 5 – Experimental Data
In this section details will be given about how the data was taken during the tests, the
type of equipment that was used as well as the calculations and corrections that were
performed on the data to obtain the results presented in chapter 6.
5.1 Data Acquisition and Filtering
As mentioned in section 3.1 the free stream velocity in the test section is monitored
by a computer using a Labview vi, a diagram of it is available in Appendix C1. The
dynamic pressure in the test section was measured using a 10Torr MKS Baratron
Type 698A with a Type 670 signal conditioner box which is connected to a SCB-68
Texas Instrument DAQ-card so the data can be saved for later use. The temperature
in the test section was measured using a thermocouple type J connected to the same
DAQ-card. Both quantities were sampled at a frequency of a 1000Hz. Figure 34
shows the different pieces of equipment just described.
Figure 34 - Equipment used to log the dynamic pressure and temperature of the test section
during the tests. Texas Instrument DAQ-card (top left), 10Torr MKS Baratron Type 698A with
Type 670 signal conditioner box (top right), thermocouple type J with signal
conditioner box (bottom).
32
The loads seen by the model during the tests were measured using AMTI’s six
component force-balance setup as described in details in section 3.2. After reaching
the desired speed of 30m/s data was taken over a period of 35 seconds at a sampling
rate of 200Hz. Figure 35 shows an example of the data recorded from one of the
channels of the force-balance using NetForce, AMTI’s data acquisition software.
Some high frequency noise from the surrounding environment is recorded at the
same time as the data (blue line). The electric motor driving the moving ground
plane and its controller were identified as being the main source of high frequency
noise. A low-pass Butterworth filter implemented in a Labview vi (diagram see
Appendix C2) is used to eliminate the high frequency noise from the data and so
obtain a cleaner signal (pink line) before being used for further analysis.
Figure 35 - Sample of saved data from one channel of the force-balance before and after
applying a digital filter.
33
A sanity check was performed to make sure filtering the signal wasn’t changing the
average value of the force by a significant amount. For the signal showed in figure
35 the average value of the force between 60 – 100 seconds is 3.0848N before
applying the filter (blue trace) and 3.0866N after applying the filter (pink trace).
A difference of 0.0018N exists between the two values which correspond to 0.06%
of the total value. The conclusion could be made that using a Butterworth filter
eliminates the high frequency noise picked up during the tests without changing the
average value of the signal.
34
5.2 Moment Transfer
Due to design constraints the force-balance couldn’t be attached to the model’s
center of pressure which is located at the quarter chord of the main aerodynamic
chord. A rotation of the forces as well as a transfer of the moment had to be
performed so that lift, drag and pitching moment could be calculated for each run.
Equations 5.1 through 5.3 were used to achieve those transformations. They were
established using Fig. 36.
Figure 36 - Graphic representation of the forces and moment transfer.
FB FB
y x
F F L α α cos sin + − =
(5.1)
FB FB
y x
F F D α α sin cos + =
(5.2)
FB FB
y z
F l M m
1
− =
(5.3)
F
xFB
, F
yFB
and M
zFB
are respectively the forces and the moment in the axis of the
force-balance seen by the model during the tests.
35
5.3 Correction Factors
When tests are performed on a model in a closed-loop wind tunnel the conditions are
not exactly the same as in free-air. No major difference is noticed by having the air
moving around the model instead of the other way around, but the longitudinal static
pressure gradient present in the test section and the closed boundaries create
additional forces that need to be counted for and subtracted from the measured
values to obtain the forces the model would undergo if it was in free-air.
Three corrections were considered during the present study: horizontal buoyancy,
solid blockage and wake blockage.
5.3.1 Horizontal Buoyancy
Most of closed wind tunnels have a change in static pressure along the axis of the
test section. This gradient is due to the thickening of the boundary layer as one
progress downstream which results into a reduction of the effective flow area. So
there is a tendency for the model to be pulled downstream which produces an
additional drag force. This additional drag force can be calculated using equation 5.4
(Rae & Pope 1984).
dl
dp
t D
B
3
3
4
λ
π
− = ∆
(5.4)
where λ
3
= body-shape factor for three dimensional bodies, t = body maximum
thickness, l = body length and =
dl
dp
static pressure gradient.
36
Table 6 shows the results of the horizontal buoyancy calculations for the model at
the test speed of 30m/s (q ≈ 520 Pa) for different heights in the test section and two
angles of attack. The values for t, l and λ
3
are respectively 0.2071ft, 2.161ft and 5.4
(Rae & Pope 1984).
Table 6 - Results of horizontal buoyancy calculations
H/2b
w
q (Pa) α (
o
) dp/dl (Pa/m) ∆D
B
(N)
0.057 526.4 0 -4.6937 0.0050
519.5 8 -7.0477 0.0075
0.115 522.2 0 -5.3920 0.0057
521.2 8 -7.2797 0.0078
free-air 514.1 0 -5.4486 0.0058
516.6 8 -7.0733 0.0075
From the values for ∆D
B
presented in table 6 the conclusion was made that the effect
of the horizontal buoyancy could be neglected since the values were within the
standard deviation of the measured drag of 0.05N.
A more detailed description of the horizontal buoyancy can be found in Rae & Pope
(1984).
37
5.3.2 Solid and Wake Blockage
When a model is placed in a test section it will reduce the area through which the air
must flow. The continuity equation for incompressible flow shows that the velocity
of the flow around the model will increase. This increase in velocity or dynamic
pressure is known as “solid blockage”.
Any body in a viscous flow field will have a wake behind it. The velocity of this
wake is lower than the free-stream velocity. So again by continuity the velocity
outside the wake needs to be higher than the free-stream velocity to guarantee that a
constant volume of flow still passes through the test section. By Bernoulli’s
equation, this higher velocity region will have a lowered pressure which grows on
the model and puts it in a pressure gradient which results in a local increase of
velocity around the model. This increase in velocity is known as “wake blockage”
Over the years different methods have been developed to determine the appropriate
corrections for solid and wake blockage depending on the size and shape of model
tested. Due to the unusual shape of the model used in the present study an
approximate blockage correction taken from Rae & Pope (1984) was adopted to
correct the dynamic pressure (Equations 5.5 & 5.6).
2
) 1 (
t measured corrected
q q ε + =
(5.5)
with
tion test
el
WB SB t
A
A
sec _
mod
4
1
= + = ε ε ε
(5.6)
where ε
SB
and ε
WB
are the solid and wake blockage correction factors respectively,
A
model
is the model frontal area and A
test_section
is the test section area.
38
Table 7 lists the values of the correction factors used on the data for the present study
at different angles of attack for a test section area of 1121.25 in
2
.
Table 7 - Correction factors for solid and wake blockage
α (
o
) A
model
(in
2
) ε
t
(1+ε
t
)
2
0 23.6 0.0053 1.0106
2 25.7 0.0057 1.0115
4 28.9 0.0064 1.0129
6 32.7 0.0073 1.0146
8 37.8 0.0084 1.0169
A more detailed description of the solid and wake blockage can be found in Rae &
Pope (1984).
39
Chapter 6 – Experimental Results
The tests were performed in two distinct phases. During phase one the attention was
focused to find the optimum location (longitudinal rigging, lateral rigging) for the
belly-flap. The sweep and deflection angle were also studied to determine their effect
on the aerodynamic coefficients. During the second phase of the study different
dimensions (span, in- and outboard height) and shapes (endplates and hole patterns)
for the belly-flap were studied in more details so that an optimum configuration
could be found.
6.1 Phase One: location survey
All the results presented in this section were obtained for a free stream velocity and a
moving ground plane speed of 30m/s. The model was placed in the test section at a
height equal to Gear-On-Ground (GOG) (H/2b
w
= 0.057) unless otherwise
mentioned. A solid rectangular shaped belly-flap with dimensions l
1
/b
w
= 0.142 and
l
2
/mac = l
3
/mac = 0.121 as seen in Fig. 32 type #1 was used for all the tests of phase
one.
The graphs of Fig. 37 show the lift, drag and pitching moment coefficient curves for
a particular location of this type of belly-flap. It was placed at 63% of the model’s
center line chord with no sweep and a deflection of δ
bf
= 90
o
. The inboard edge of
the belly-flap was on the wing’s centerline so there was no gap between the splitter
40
plate and the belly-flap. Two deflections of all the elevons were considered; namely
0
o
and -20
o
.
Figure 37 - Effect of the belly-flap for two deflections of the elevons, δ
e
= 0
o
and δ
e
= -20
o
showing the lift, drag and pitching moment coefficient curves.
41
The problem stated in chapter 1 is shown on the top graph of Fig. 37. When the
elevons are deployed to rotate the airplane and no belly-flap is used (dashed lines) a
drop of 0.6 in C
L
is seen at all angles of attack which will cause a severe problem for
control during landing and a delay in takeoff. A major advantage of the belly-flap
over the elevon effectors can be seen on these graphs; namely the creation of
enhanced pitching moment with belly-flaps does not come with as large of lift loss as
in the case of flying wings that use trailing edge devices to create a pitching moment.
For context, a C
L
increase of 0.4 due to the belly flap represents 35% of the lift-off
C
L
at zero angle of attack. A C
D
increase of 0.04 represents 10% of the lift-off C
D
. A
belly-flap moment of +0.05 is equivalent to 10% of the total control power available
from all the elevons combined. The objective is to determine a belly-flap
configuration that preserves the lift gain up to lift-off conditions.
An uncertainty of about 10% of maximum C
m
was seen on the values for C
m
for a
particular test but the uncertainty on the increase in C
m
due to the use of a belly-flap
was about 2%. This shift in C
m
values is due to a change in friction between the
splitter plate and the model every time the model is taken out of the test section for a
change in configuration. For this reason before each test the data is taken without the
belly-flap and than with the belly-flap so the values obtained for a certain
configuration can be compared at the end.
The C
D0
values are higher than one would expect for a BWB-configuration. This can
be explained by the low Reynolds number during the tests. At the center line of the
model, the Reynolds number is Re ≈ 1,350,000 compared to the Reynolds number
42
for a full size BWB at center line of Re ≈ 316,000,000. Using the equation for skin
friction coefficient (C
f
) for a turbulent flow (Eq. 6.1) given in Raymer (1999) with
M = 0.09 one can calculate that the C
f
of the model is 2.68 times the C
f
of the
full-size BWB. This would explain why the C
D0
value reported here is roughly a
factor of three greater than the assumed value of the C
D0
of the full scale BWB.
()()
65 . 0
2
58 . 2
10
144 . 0 1 Re log
455 . 0
M
C
f
+
=
(6.1)
Figure 38 shows the incremental change in lift, drag and pitching moment coefficient
due to a particular type and location of belly-flap for different heights of the model in
the test section, going from GOG, H/2b
w
= 0.057, to the height at the centerline of
the test section which is considered in this study as free-air since this is the location
where the reflections of ceiling and floor are reduced to their minimum. The same
type of belly-flap was used as described in the previous paragraph. The longitudinal
and lateral rigging of the belly-flap were respectively 63% of the center line chord
and 0% of the span. The belly-flap had no sweep angle and the elevons were set at
zero degrees. The effects of the belly-flap decreases as the model is placed further
above the moving ground plane; that is, the belly-flaps are more efficient when they
are in close proximity to the ground. The large increase in C
m
at high AOA seen at
height equal to gear on ground is explained by the fact that at this particular
condition the distance between the trailing edge of the wing and the ground is
reduced to a minimum which will cause the flow to exert a larger force on the front
of the model and so create a larger moment.
43
Figure 38 - Effect of the belly-flap for different heights of the model in the test section. The lift,
drag and pitching moment coefficient increment curves are shown.
44
Figure 39 shows the effect of the belly-flap deflection angle on the lift, drag and
pitching moment coefficient for three different angles of attack, namely α = 0
o
,
α = 4
o
and α = 8
o
. Again the longitudinal and lateral rigging of the belly-flap were
respectively 63% of the center line chord and 0% of the span. The belly-flap had no
sweep angle and the elevons were set at zero degrees. The model was placed at a
height in the test section equal to H/2b
W
= 0.057. The data show a monotonic
increase in effectiveness for the belly flap as its deflection angle increases from zero
to 90
o
. This confirms that a belly-flap deflection of 90
o
should be selected to obtain
the highest increase in lift and a good increase in favorable pitching moment for
rotation.
45
Figure 39 - Effect of the belly-flap deflection angle, δ
bf
. The lift, drag and pitching moment
coefficient with and without belly-flap for three angles of attack,
α = 0
o
, α = 4
o
and α = 8
o
, are shown for the wing being at H/2b
w
= 0.057.
46
Figures 40 and 41 show respectively the effects of the longitudinal and lateral
rigging of the belly-flap on the lift, drag and pitching moment curves at
H/2b
w
= 0.057. For the longitudinal rigging survey the belly-flap had a lateral rigging
of 0% of the span, for the lateral rigging survey it had a longitudinal rigging of 63%
of the center line chord. For both surveys the belly-flap had no sweep angle, had a
deflection of δ
bf
= 90
o
and the elevons were set to zero deflection. The longitudinal
location of the belly flap had the most effect on the moment coefficient. The belly
flap increased the C
m
by maximum of about 0.10 at all angles of attack, but the
location of the maximum increase changed strongly with the longitudinal location of
the belly flap. At an AOA of 0
o
, the maximum occurred when the belly flap was at
45% of the center line chord. But at an AOA of 0
o
, the maximum increase occurred
when the belly flap was at 65% of the center line chord. The lift coefficient showed
the most consistent improvement when the belly flaps was near 65% of the center
line chord; thus that location was chosen as the optimum location of the belly flap.
The lateral rigging tests in Fig. 41 showed that no gap should be left between the
center line and the inboard edge of the belly-flap. The further the inboard edge is
placed off the center line the less lift is created by the belly-flap. On the other hand
the pitching moment increases when increasing the gap between inboard edge and
center line which can be explained by the fact that the line of action of the pitching
moment isn’t perpendicular to the center line of the plane. So moving the belly-flap
outboard increases the lever arm of the force that induces the positive pitching
moment.
47
Figure 40 - Effect of the belly-flap longitudinal rigging, x
bf
. The lift, drag and pitching moment
coefficient with and without belly-flap for three angles of attack,
α = 0
o
, α = 4
o
and α = 8
o
at H/2b
w
= 0.057.
48
Figure 41 - Effect of the belly-flap lateral rigging, y
bf
. The lift, drag and pitching moment
coefficient with and without belly-flap for three angles of attack,
α = 0
o
, α = 4
o
and α = 8
o
at H/2b
w
= 0.057.
49
Figure 42 - Effect of the belly-flap sweep angle, Λ
bf
. The lift, drag and pitching moment
coefficient with and without belly-flap for three angles of attack,
α = 0
o
, α = 4
o
and α = 8
o
at H/2b
w
= 0.057.
50
Figure 42 pictures the effect of the belly-flaps sweep angle on the lift, drag and
pitching moment coefficient. A longitudinal rigging of 63% of center line chord and
a lateral rigging of 0% of span were used to allow for a fair comparison with the
previous tests. Adding a negative sweep angle to the belly-flap had a slight
improvement to its performance. But the effect was small enough that it was
concluded there was no significant improvement on the lift and pitching moment
compared to a belly-flap with no sweep angle.
The results of the test performed during this phase led to two major conclusions. The
first being that the most efficient location for the belly-flap is when the belly-flap has
a longitudinal rigging of 63% of the centerline chord, a lateral rigging of 0% of the
span, no sweep angle and a deflection angle of 90
o
. This location is used for all the
subsequent tests.
The second conclusion that could be made is the belly-flap is mainly a lift enhancing
device as can be seen from Fig. 43. The increase in lift due to the belly-flap with and
without the elevons deflected (respectively ∆C
Lbf
and ∆C
Lbfe
) are comparable.
However the increase in positive pitching moment due to the belly-flap with the
elevons deflected (∆C
mbfe
) is negligible compared to the increase when the elevons
are not deflected (∆C
mbf
). So the objective of the remaining tests will be to find a
type of belly-flap that maximizes the lift gain at all angles of attack. This search will
help overcome the large lift loss (∆C
Le
) introduced when a flying wing uses only
trailing edge devices, i.e. elevons, to create a pitching moment.
51
Figure 43 - Difference in increase in lift and pitching moment coefficient with and without the
use of a belly-flap
52
6.2 Phase Two: shape survey
As mentioned in the previous section attention was focused during this phase to find
a shape for the belly-flap that maximizes the lift gain for the whole range of angle of
attack. The tests were performed at a free-stream velocity and a moving ground
plane speed of 30m/s. The optimum location of the belly-flap determined during
phase one was used for all the tests during this phase; namely a longitudinal rigging
of 63% of the center line chord, a lateral rigging of 0% of the span, no sweep angle
and a deflection angle of 90
o
. All the elevons had a deflection of 0
o
unless otherwise
mentioned.
At first belly-flaps with end plates were tested but no benefits compared to a straight
belly-flap were seen. Belly-flaps with end plates would also be more difficult to
incorporate in the design of a BWB-airplane since they would pose a storage
problem. Next attention was focused on the actual dimensions of the belly-flap
starting with the span. Figure 44 shows the effect of the belly-flap span on the lift,
drag and pitching moment coefficient for three different angles of attack; namely
α = 0
o
, α = 4
o
and α = 8
o
. The belly-flap had a height of l
2
/mac = l
3
/mac = 0.121 and
the model was placed at a distance above the ground of H/2b
w
= 0.057. Increasing
the span of the belly-flap results in increasing the lift and pitching moment in a
continuous matter up to a length of 22% of the half-wing span. At larger spans, the
increase in lift flattens out and even starts to decrease at higher angle of attack. This
effect may be explained due to that at higher angle of attack with a long belly-flap
the wing is being overloaded and a stall region is being created on the outer wing
53
starting at approximately 60% of the wingspan. A belly-flap span of 14% of the half-
wing span was chosen for the remaining of the tests since it corresponds to the value
when the increase in lift starts to flattens out at higher angle of attack.
Figure 44 - Effect of the belly-flap span, l
1
. The lift, drag and pitching moment with and without
belly-flap for three angles of attack, α = 0
o
, α = 4
o
and α = 8
o
are shown.
54
The graphs in figures 45 and 46 show the lift, drag and pitching moment coefficient
increment due to the different types (#1-7) of belly-flaps shown in Fig. 32. Types #3
through #5 have a total porosity of 11.5% where types #6 & #7 have a total porosity
of 23% (dashed lines). Doubling the height (l
2
& l
3
) of the basic un-perforated belly-
flap (i.e. type #2) more than triples the lift gain at low angles of attack over type #1.
The gain in C
L
increases by a higher percentage at higher angles of attack. Compared
to the type #1 belly-flap, the pitching moment gain is increased by roughly a factor
of 1.6 over the whole range of angle of attack and the drag increase is doubled.
Adding perforations to the belly-flaps generally amplifies the increase in lift gain. It
slightly reduces the drag increase compared to a plain belly-flap and reduces the
pitching moment gain to the value obtained with a belly-flap of half the height. The
location of the porous region is of interest because it changes the results. Comparing
belly-flaps porosity of 11.5% (i.e. types #3, 4 and 5) indicates that the best lift
increase is provided with the porous region uniformly spaced over the flap (i.e. #4).
However the largest increase in pitching moment is obtained with the slit near the
wing’s surface (i.e. #3) which is explained by the fact that it can almost be
considered as a plain belly-flap since the slit is located in and near the boundary
layer of the under-wing. Increasing the porosity to 23%, i.e. types #6 & #7, both
reduce the increase in the pitching moment but type #7 increases the lift slightly
above the best 11.5% porous belly-flap. Note that all of the larger area belly flaps, #2
through #7, essentially double the drag coefficient.
55
The decrease in pitching moment gain for the porous flaps can be explained by the
fact that the pressure difference between the two sides of the belly-flap is reduced
when perforations are added. This produces a smaller pressure on the wing surface
fore and aft of the flap, and thus creates a smaller positive pitching moment.
Figure 45 - Lift, drag and pitching moment coefficient increment for different type of belly-flaps
for H/(2b
w
) = 0.115. Belly-flap types #1 through #4.
56
Figure 46 - Lift, drag and pitching moment coefficient increment for different type of belly-flaps
for H/(2b
w
) = 0.115. Belly-flap types #4 through #7.
57
The increase in lift gain with the perforations can be explained by the shape of the
streamlines around the belly-flap as seen in Fig. 47. The surface shear stress and
streamlines were estimated using an oil-dot technique. Oil-dots, which are a mix of
3 in 1 oil and phosphorescent dye (DayGlo AX-13 pigments), were placed on the
surface of the model before turning the wind tunnel on. When the tunnel was brought
up to speed, the surface shear stress due to the flow over the model spread the oil-
dots along the local direction of the flow. This process continued until the viscous
stress hindered further spreading of the oil leaving a permanent record of the local
flow direction. After the tunnel was shut down the model was removed and the
footprint of the streamlines near the surface was captured using black lights and a
camera. The results for three types of belly-flaps, i.e. #2, 4 & 7, are shown in Fig. 47.
The oil-dot patterns in Fig. 47a show that with no perforations in the belly-flap, a
strong region of reverse flow around the belly-flap is present at both angles of attack,
α = 0
o
or 8
o
. When perforations are added, less flow recirculation is present (see
Fig. 47b) behind the perforated belly-flap compared to a plain belly-flap (Fig. 47a).
When a porous screen with 23% porosity was used, no evidence of reverse flow was
present behind the belly-flap at either α = 0
o
or 8
o
(see Fig. 47c). This indicates that
the flow separation is less vigorous under these conditions and hence provides an
indication of why the lift gain is increased and the drag is reduced.
58
Figure 47 - Streamlines on the bottom surface of the BWB-model at an angle of attack of 0
o
(left) and 8
o
(right) for three types of belly-flaps; 47a - type #2, 47b - type #4 and 47c - type #7.
59
During the final stage of this second phase, additional tests were performed with one
particular type of belly-flap, namely type #7 of Fig. 32 to determine its performance
with the elevons deflected. The reason behind the selection of this particular belly-
flap was its higher lift gain compared to any other belly-flap. As mentioned at the
end of the previous section, the lift gain has a greater figure of merit than the
pitching moment gain since it will help overcome the large lift loss introduced by the
use of trailing edge devices to create the desired pitch attitude. For the tests, the
model was placed at a height above the moving ground plane of H/(2b
w
) = 0.115 and
the elevons were deflected at 0
o
and -20
o
. The results for the lift, drag and pitching
moment coefficient are shown in Fig. 48. The dashed lines show the effect of the
elevon deployment without any belly-flaps. (The slight difference for no belly flap
between these results and those in Fig. 37 are due to the slight difference in elevation
above the ground plane.) As expected, elevon deployment greatly increases the
pitching moment coefficient but with a deleterious effect of a large loss in the lift
coefficient. The drag coefficient is largely unchanged. The major advantage of the
belly-flaps over elevon deflection alone can be seen when the belly-flaps are
deployed along with the elevons. In this case, the increased pitching moment is
preserved but the belly-flaps significantly reduce the large lift loss due to the elevons
alone.
60
Figure 48 - Effect of the belly-flap type #7 for two deflections of the elevons, δ
e
= 0
o
and δ
e
= 8
o
,
for the lift, drag and pitching moment coefficient curves.
61
Figure 49 - Effect of the belly-flap types #1 & #7 for different heights of the model in the test
section. Lift, drag and pitching moment increment curves are shown.
62
Figure 49 shows the change in lift, drag and pitching moment coefficient due to two
types of belly-flaps (types #1 & #7) for different heights of the model in the test
section, going from H/(2b
w
) = 0.115 to free-air. The elevons had 0
o
deflection during
these tests. The effects of both type of belly-flap decrease as the model moves away
from the ground which confirms again that they are more efficient in close proximity
of the ground. The larger increase in lift coefficient seen earlier for the larger belly-
flap, type #7, was more persistent at the higher elevations compared to type #1 or the
other ones.
63
Chapter 7 – Mathematical Simulation
The mathematical simulation is a 3-DOF (degrees of freedom) pitch simulation
which neglects all lateral effects. This simulation, combined with the wind tunnel
data presented in chapter 6, allows the creation of a flight path control model for a
BWB-airplane to analyze its behavior with and without belly-flaps during all the
stages of its flight: takeoff, cruise, landing and go-around. The simulation helps to
prove that the increase in trimmed C
Lmax
seen during the wind tunnel tests on a
BWB-model with a belly-flap compared to a BWB-model with no belly-flap will
improve the landing field length (LFL) and takeoff field length (TOFL) as well as
reduce the flight path lagging pitch in go-around.
7.1 Dynamics Equations
Figures 50 & 51 show the reference system, the geometric dimensions and the forces
seen by the airplane considered in the simulation.
Figure 50 - Geometry of a BWB-airplane used in the simulation.
64
Figure 51 – Forces acting on a BWB-airplane considered in the simulation.
Using the two schematics presented above one can write the following equilibrium
equations in the earth axis
Forces in the x-direction
x u X
a m F
e
− =
∑
(7.1)
( ) 0 cos cos sin = + + + + − +
x u ng mg T net W D W L
a m N N i T qS C qS C θ γ γ (7.2)
Forces in the z-direction
( )
0
g a m F
z u Z
e
+ =
∑
(7.3)
()() 0 sin sin cos
0
= + − + + + + − g a m R R i T qS C qS C
z u ng mg T net W D W L
θ γ γ (7.4)
Moment with respect to the CG
0 =
∑
e
YY
M (7.5)
()()
() ( ) []
() ( )
() ( )
() ( )
() ( ) 0 cos sin
sin cos
sin cos
sin cos
cos sin
cos sin sin cos
= − + + − − +
+ + + − +
− − + + −
+ + + − −
− + − −
⎥
⎦
⎤
⎢
⎣
⎡
− + + +
θ θ θ
θ θ
θ θ
θ θ
α α α α
& &
YY cg ng ng ng ng cg ng
cg mg ng ng ng cg ng
cg mg mg cg mg mg mg
cg mg mg mg cg mg mg
cg T T cg T T net
W
cg
D L
cg
D L m
I z s z N x x N
z s z R x x R
x x N z s z N
z s z R x x R
z z i x x i T
c qS
c
z
C C
c
x
C C C
(7.6)
65
A non-linear AERO model is considered in the simulation. This gives the following
equations for lift, drag and pitching moment coefficient.
Lift coefficient
∞ ∞
+ + =
V
c
C
V
c
C C C
L L L L
WT
2 2
α θ
α θ
&
&
& &
(7.7)
Drag coefficient
∞ ∞
+ + =
V
c
C
V
c
C C C
D D D D
WT
2 2
α θ
α θ
&
&
& &
(7.8)
Moment coefficient
∞ ∞
+ + =
V
c
C
V
c
C C C
m m m m
WT
2 2
α θ
α θ
&
&
& &
(7.9)
The first term on the right hand side of each equation is obtained after performing a
data fit on the wind tunnel data presented in section 6.2 using the LINEST function
of Excel with 4 independent variables (angle of attack, height above the ground,
belly-flap deflection and elevon deflection) and 12 additional curve-fit variables
which are a combination of the 4 independent variables. The details of this data fit
are available in Appendix D: LINEST Data fit. The remaining coefficients
θ
&
L
C
,
α &
L
C
,
θ
&
D
C
,
α &
D
C
,
θ
&
m
C
and
α &
m
C
where obtained from Liebeck, Page and Rawdon
(1996).
66
A non-linear spring-dashpot approximation was used to model the landing gear
system which gives the following equations for the reaction forces between airplane
and ground.
Normal reaction forces
mg mg mg mg mg mg mg
s c s s k R & − − − =
3
ε (7.10)
ng ng ng ng ng ng ng
s c s s k R & − − − =
3
ε (7.11)
Tangential reaction forces
mg mg mg
R j N = (certain percentage of the normal force) (7.12)
ng ng ng
R j N = (certain percentage of the normal force) (7.13)
mg
s ,
mg
s &
,
ng
s and
ng
s &
are respectively the stroke and stroke velocity of the main and
nose landing gear.
mg
k ,
mg
ε ,
mg
c ,
ng
k ,
ng
ε and
ng
c are the spring and dashpot
constants for the main and nose landing gear. The details of how these constants
were determined are available in Appendix E: Spring-Dashpot constants.
mg
j and
ng
j represent the percentage of the normal force that is considered to calculate the
tangential force. There value is between 0 and 0.03 depending on the segment of the
flight.
67
7.2 Flow Chart
68
7.3 Results
The simulation allowed for a fair comparison of the landing field length (LFL),
takeoff field length (TOFL) and the flight path lagging pitch in a go-around for three
different configurations of a generic BWB-450 airplane while respecting the FAR
rules. The three configurations considered are a BWB-airplane with no belly-flap
(case #1), a BWB-airplane with a belly-flap fixed at 90
o
(case #2) and finally a
BWB-airplane with a dynamically controlled belly-flap (case #3). The control law
for the latter case was established by deflecting the belly-flap (δ
bf
) by a given amount
with respect to the elevon deflection (δ
e
). The value by which the belly-flap is
deflected follows the graph presented in Fig. 52. The same type of control law is
used for the landing, takeoff and go-around simulations for the three different
configurations of the airplane. The only difference between them is the value of
δ
etrim
, which is the deflection of the elevons in trimmed conditions for each particular
simulation.
Figure 52 - Control law for the deflection of the belly-flap
69
Table 8 lists the major variables considered in the simulation.
Table 8 - Major variables considered in the simulation
Value
Description
Symbol
[units] Case #1 Case #2 Case #3
Wingspan b
w
[ft] 239.2
(1)
Reference area S
w
[ft] 7180.7
(1)
Mean aerodynamic
chord
Mac or c [ft] 32.695
(1)
Takeoff gross weight TOGW [lbs] 500,000
(1)
Landing gross weight LGW [lbs] 325,000
(1)
Thrust to weight ratio T/W 0.28
(1)
Max static thrust T
static
[lbs] T/W*TOGW
(2)
Max thrust for climb T
max
[lbs] 0.85* T
static
(2)
Trim altitude h
trim
[ft] 500
Flare altitude h
flare
[ft] 50
(2)
Decision altitude for
go-around
h
DH
[ft] 50
(2)
Altitude when ground
effects are considered
h
GE
[ft] Wingspan
(3)
Approach angle γ
appr
[
o
] -3
(2)
Climb angle γ
climb
[
o
] Max available
Max Lift coefficient C
Lmax
1.7 1.912 1.912
Approach speed V
appr
[ft/s] 1.3*V
stall
+5knots
(2)
Climb speed V
climb
[ft/s] 1.2*V
stall
+10knots
(2)
Lift-off speed V
lift-off
[ft/s] 1.1*V
stall
(2)
Rotation speed V
rot
[ft/s] 0.95*V
stall
0.94*V
stall
0.963*V
stall
(1) Liebeck (2002)
(2) Typical value from FAR part 25 transport
(3) Corning (1986)
70
7.3.1 Landing simulation
The trim values for the descent during the landing simulation were determined at an
altitude of 500 ft, for an approach speed equal to 1.3*V
stall
+ 5knots and an approach
angle of -3
o
. The simulation stops 15 seconds after the airplane’s CG passes the
altitude of 70ft extending above the runway. This 70ft distance consisted of the 50ft
required by the FAR when the landing gear of the airplane is extended plus the
distance of 20ft between the CG and the lower most section of the landing gear of
the airplane used in the simulation. No brakes are applied to slow down the airplane
after the main gear touches the ground. The only force decelerating the airplane once
on the ground is the rolling friction of the wheels, which is expressed as a friction
coefficient µ times the normal force on the wheels. A µ value of 0.03 is used in the
simulation which corresponds to the rolling resistance on a hard runway.
Figure 53 shows the results of the landing simulation for the three considered
configurations of the BWB-airplane; namely the BWB-airplane with no belly-flap
(case #1: blue line), the BWB-airplane with fixed belly-flap at 90
o
(case #2: green
line) and the BWB-airplane with controlled belly-flap (case #3: red line).
71
Figure 53 - Results of the landing simulation for a BWB-airplane
Time zero of graphs b, c and d corresponds to when the airplane’s CG crosses the
altitude of 70ft mentioned in the previous paragraph which defines the beginning of
the landing field length (LFL); i.e. X = 0ft. The Federal Air Regulation defines the
LFL as the horizontal distance for the aircraft to clear a 50 foot obstacle and then
come to a complete stop. So it can be separated into two parts, the descent from the
50 foot altitude to when the pilot applies the brakes (= S
50
) and the deceleration
distance to a complete stop (= S
G
). Using this definition Eq. 7.14 can be derived to
calculate the LFL.
G
S S LFL + =
50
(7.14)
72
No thrust reversal was assumed in any of the simulations. Thus the deceleration
distance on the ground (= S
G
) can be calculated with (Corning 1986)
a
V
S
TD
G
2
2
−
=
(7.15)
where V
TD
= velocity at touchdown right before the brakes would be applied
-a = average deceleration in ft/s
2
= µ
brakes
g
o
µ
brakes
= ground rolling resistance with brakes on
g
o
= acceleration due to gravity = 32.174 ft/s
2
When analyzing the graphs of Fig. 53 the values of all the variables could be
determined for the three different configuration of the airplane and the corresponding
LFL was calculated. A ground rolling resistance with µ
brakes
= 0.4 was used during
the calculation which corresponds to the value for dry conditions on a hard runway
(Raymer 1999). A delay of one second between the time the front gear touches the
ground and when the pilot applies the brakes was considered to determine V
TD
. The
landing field results are listed in Table 9.
Table 9 - Values used to determine the LFL for the three configuration of the BWB-airplane
Variable Case #1 Case #2 Case #3
V
TD
(ft/s) 209.96 198.08 163.91
-a (ft/s
2
) 12.87 12.87 12.87
S
50
(ft) 1790.81 1814.53 1756.24
S
G
(ft) 3425.37 3048.71 2087.59
LFL 5216.18 4863.24 3843.83
73
From the results one can conclude the following, using a fixed belly-flap deflected at
90
o
during landing reduces the LFL by about 7%. When using a controlled belly-flap
on the other hand the decrease in LFL can be improved up to 23%. The improvement
in LFL is due to the 12.5% increase in C
Lmax
due to the belly flap. This leads to a
decrease of about 6% in V
stall
of a BWB-airplane with a belly-flap compared to a
BWB-airplane with no belly-flap (see table 8). The lower stall speed allows for a
slower approach speed (see graph (d) of Fig. 53) which reduces the LFL. A
beneficial side effect is a softer landing. A decrease of 7.5% in the peak deceleration
(i.e. the g’s shown in graph (b) of Fig. 53) is achieved at touch down when using a
belly-flap. The slower approach speed will also help increase the life span of the
landing gear’s braking systems since less energy will be required to bring the plane
to a stop. Graph (c) of Fig. 53 shows the change in belly-flap angle during the
landing procedure of a BWB-airplane. Additional graphs of the landing simulation
are available in Appendix F.
74
7.3.2 Go-around simulation
As for the landing simulation, the trim values for the descent part of the go-around
simulation were determined at an altitude of 500 ft, for an approach speed equal to
1.3*V
stall
+ 5knots and an approach angle of -3
o
. The go-around procedure is started
when the CG of the airplane crosses the decision height of 50ft. At this point the time
is set to 0 sec and the distance covered by the airplane over the runway is set to
0ft. The maximum climb thrust available is used to regain altitude and reach the 70ft
clearance altitude of the airplane’s CG as soon as possible. The simulation ends 6
seconds after the go-around maneuver is initiated. No restriction was set to limit the
climb angle of the airplane once the go-around was started. Figure 54 shows the
results of the go-around simulation for the three considered configuration of the
BWB-airplane. The same color code as the landing simulation is used for the graphs.
The negative side of the x-axis represents what is happening before the airplane
reaches the decision height of 50ft. When analyzing the graphs the following
conclusions can be made. When the pilot starts the go-around when reaching the
decision height it will take the BWB-airplane a little over 2 seconds to have enough
nose up attitude to regain altitude (see Fig. 54b) and around 6 seconds to reach the
clearance altitude of 70ft regardless if a belly-flap is used or not (seen by combining
54a and 54b). The advantage of using a controlled belly-flap over no belly-flap or a
fixed belly-flap can be seen in graph (a) of Fig.54. The additional loss in altitude,
after the go-around is started, is decreased by 21.57% when using a controlled belly-
flap. The change in altitude is -12.65ft for a controlled belly-flap compared to
75
-16.13ft or -16.15ft for no belly-flap or a fixed belly-flap. The distance covered by
the airplane when it reaches the clearance altitude of 70ft is substantially decreased
as well when using a controlled belly-flap, 1065ft for no belly-flap and 867ft with a
controlled belly-flap. This represents a decrease in field length of about 18.59%. All
these benefits are again the result of the increase in C
Lmax
and so the decrease in
approach speed (see graph (d) of Fig.54) for the BWB-airplane when a controlled
belly-flap is used. Graph (c) of Fig. 54 shows the change in belly-flap angle used
during the go-around procedure to obtain these results. Additional graphs of the go-
around simulation are available in Appendix G.
Figure 54 - Results of the go-around simulation for a BWB-airplane
76
7.3.3 Takeoff simulation
The trim values for the takeoff simulation were determined for an altitude of 500ft
using a climb speed of 1.2*V
stall
+ 10knots and a thrust equal to the maximum thrust
for climb available (see Table 8). The simulation stops when the airplane’s CG has
reached the obstacle clearance altitude of 70ft defined in section 7.3.1. To allow for a
fare comparison of the results the rotation speed, i.e. the speed at which the pilot
starts to pull up the nose of the airplane, was selected so that a lift-off speed, speed at
which the main gear gets off the ground, of 1.1*V
stall
was reached for all three
configurations of the BWB-airplane while making sure meeting the FAR Part 25
requirements. The FAR requires that the lift-off speed (V
LO
) is equal or greater than
1.1*V
MU
which is the ground-angle-limited “minimum unstick” lift-off speed. For
the BWB-450 the ground-angle-limit is about 12
o
which means C
Lmax
can be reached
during takeoff. So C
LVMU
≈ C
Lmax
therefore V
MU
≈ V
stall
and so justifies the choice of
1.1* V
stall
for the lift-off speed. No maximum value was set to limit the climb angle
of the airplane during the takeoff procedure.
Figure 55 shows the results of the takeoff simulation. The same color code as in the
landing simulation and the go-around simulation is used to differentiate the three
configurations of the BWB-airplane. When analyzing the graphs the following
conclusions can be made. The BWB-airplane will reach the obstacle clearance
altitude of 70ft defined in section 7.3.1 in a little less than 35 seconds when no belly-
flap or a fixed belly-flap is used. A controlled belly-flap will reduce this time by
little over a second. The takeoff field length (TOFL
50
), distance needed to reach the
77
obstacle clearance altitude with all engines operational, changes from 3974ft when
no belly-flap is used to 3923ft for a fixed belly-flap and 3672ft for a controlled belly-
flap. This represents a decrease in TOFL
50
of 1.28% for the fixed belly-flap and
7.60% for the controlled belly-flap compared to a no belly-flap configuration. This
decrease in TOFL
50
can be credited again to the increase in C
Lmax
when a belly-flap
is used since this reduces the stall speed and hence the minimum speed at which the
airplane can takeoff when following FAR rules. Graph (c) of Fig. 55 shows the
change in belly-flap angle used during the takeoff to obtain these results. Additional
graphs of the takeoff simulation are available in Appendix H.
Figure 55 - Results of the takeoff simulation for a BWB-airplane
78
7.4 Experimental Flight
To verify the results obtained by the computer simulation, flight tests were
performed at El Mirage, CA using a BWB radio controlled model airplane equipped
with a belly-flap. The model used was an electric powered KillerBee1 UAS
(Unmanned Aircraft System) designed by Swift Engineering, Inc. KB1 has a
wingspan of 5ft, an aspect ratio of 12.5 and a main aerodynamic chord of 0.4ft.
Figure 56 shows some pictures of the KB1 with the belly-flap deployed on the
under-wing.
Figure 56 - Electric powered KillerBee1 equipped with a belly-flap
The belly-flap was located at 60% of the centerline chord. It had a span equivalent to
14% of the total span of the model and a height equal to 3.3% of the total span.
These values correspond to the type of belly-flaps as well as the locations tested on
79
the model during the wind tunnel experiment stage of this study. The belly-flap was
connected to a servo so it could be deployed during the flight by the pilot. Data
during the flight was recorded using a telemetry system from EagleTree Systems.
Unfortunately due to radio interferences and windy conditions at the test site no
reliable data could be recorded. An increase in altitude of about a 100ft and a
decrease in speed of about 10ft/s were however noticed by the pilot every time the
belly-flap was deployed to an angle of 90
o
. Some additional flight tests with a more
sophisticated telemetry system would be needed to verify that the results obtained
during the wind tunnel tests and the computer simulation can be reproduced with an
actual flying model.
80
Conclusions
A new control surface consisting of a flap located near the mid-section on the lower
surface of the wing, called a belly-flap, was studied to determine if it can be used in
combination with trailing edge devices to overcome the large lift loss undergone by a
BWB type aircraft when it is using those trailing edge devices to create a pitching
moment. The study was performed using two distinct methods; namely experimental
tests in a wind tunnel and a mathematical simulation using the experimental data.
The wind tunnel tests were performed on a generic BWB-450 model. Various types
of belly-flaps as well as locations were studied during those tests. Their behavior was
studied at conditions near takeoff and landing; i.e. at high angles of attack and
heights near the ground. Results found that the optimal belly-flap has no sweep, a
longitudinal rigging of about 60-65% of the root chord and no gap left between the
inboard of its edge and the center line of the BWB. The belly-flap is the most
effective when it is totally deployed to a deflection angle of 90
o
, has a total span of
about 20% of the wing span and a height of about 20-25% of the main aerodynamic
chord. Significant advantages were found for a porous belly-flap with a porosity of
20-25%, which reduced the vigorous flow separation behind the belly flap during
deployment. With these characteristics, an absolute increase of 20% to 30% of lift-
off C
L
was realized at low angles of attack. At higher angle-of-attack, increases up to
12% in lift-off C
L
were reached when the described belly-flap was used. The
81
favorable pitching moment at high angle-of-attack is equivalent to 4-8% of that
available from the elevons.
During the second part of the study; namely the mathematical simulation, these
experimental results were incorporated as the aerodynamic input for a dynamic flight
path model of a BWB-airplane developed for this research. This model showed that
the increase in C
Lmax
seen during the wind tunnel tests due to the use of a belly-flap,
would definitely improve the LFL, TOFL
50
and pitch lagging during go-around. In
addition, the model provided a platform to develop a control law that could be used
for this new type of control surface. For example on the one hand, if the belly flap
were statically deployed to an angle of 90
o
during approach and left there for the
remainder of the flight, a reduction of about 7% in LFL can be expected. On the
other hand, by using a dynamically controlled belly-flap over a fixed belly-flap
during final approach, the LFL decreases by up to 26%. During go-around the same
kind of dynamically controlled belly-flap will reduce the loss in altitude between
when the pilot initiates the go-around and when the airplane starts to regain altitude
by 21.5%. Finally the use of the belly-flap during takeoff will reduce the TOFL
50
by
about 8%.
All these results are encouraging enough for belly-flaps to be considered as a
possible solution to the lag in flight path control during rotation of a BWB-airplane
and start developing a more detailed design of the belly-flap. Additional
development would be required to determine the optimal control law for this type of
device during each segment of the flight. Some effort should also be spent to study
82
the effect of the belly-flap on the lateral stability of the airplane. Additional uses of
the belly flap could be explored such as their use in flight to increase the lift and drag
simultaneously, their possible incorporation into the wheel well doors, etc. Finally all
these theoretical improvements should be verified during actual flight tests of a
BWB-type model airplane equipped with a controllable belly-flap.
83
Bibliography
3D Systems, ”Products and Materials,” 3D Systems, Inc. [online],
URL: http://www.3dsystems.com, 2005.
Air Force Technology, “B-2 Spirit Stealth Bomber, USA,” SPG Media Limited
[online database], URL: http://www.airforce-technology .com/projects/b2/,
November 2006.
AMTI, “Dynamometer Instructions, Model FS6-500, Serial Number m4039.1,”
Advanced Mechanical Technology, Inc., Waterton, Massachusetts, August 2000.
Anderson Jr., J. D., “Introduction to Fligth, 4
th
Ed.,” McGraw-Hill, Boston, 2000.
Braslow, A.L., Knox, E.C., “Simplified Method for Determination of Critical Height
of Distributed Roughness Particles for Boundary-Layer Transition at Mach Numbers
from 0 to 5,” Technical Note 4363 Langley Aeronautical Laboratory, Langley Field,
Virginia, September 1958.
Cawthon, B., “The Phantom Works: Where dreams take flight,” Promotex Online
[online article], URL: http://www.promotex.ca/articles/cawthon/2002/11-01-
2002_article.html, January 2002.
Corning,G., “Supersonic and Subsonic CTOL and VTOL, Airplane Design, 4
th
Edition” College Park, Maryland, 1986.
Liebeck, R. H., Page, M. A., and Rawdon, B. K., “Blended-Wing-Body Technology
Readiness Program,” NASA Contract NAS1-20275, McDonnell Douglas Aerospace,
Long Beach, California, USA, January 1996.
Liebeck, R. H., Page, M. A., and Rawdon, B. K., “Blended-Wing-Body Subsonic
Commercial Transport,” AIAA Paper 98-0438, January 1998.
Liebeck, R. H., 2002 Wright Brothers Lecture “Design of the Blended-Wing-Body
Subsonic Transport,” AIAA Paper 2002-0002, January 2002.
Myhra, D., “The Horton Brothers and their All-wing Aircraft,” Shiffer Publishing
Ltd, Atglen, Pennsylvania, 1998.
Page, M. A. and Rawdon, B. K., “Formal inquiry regarding transport category
landing gear”, Los Angeles, March 2007.
84
Rae Jr., W. H., Pope, A., “Low-Speed Wind Tunnel Testing, 2
nd
Ed.,” John Wiley &
Sons, Inc., New York, 1984.
Raymer, D. P., Aircraft Design: A Conceptual Approach, 3
rd
ed., AIAA Education
Series, AIAA, Reston, VA, 1999.
van der Linden, F. R., “Northrop N1-M,” National Air and Space Museum,
Smithsonian Institution [online database], URL:
http://www.nasm.si.edu/research/aero/aircraft/northN1M.htm, August 2002.
Welch, P. D., "The Use of Fast Fourier Transform for the Estimation of Power
Spectra: A Method Based on Time Averaging Over Short, Modified Periodograms,"
IEEE Trans. Audio Electroacoustics, Vol. AU-15, pp. 70-73, June 1967.
85
Appendices
Appendix A – Force-Balance Range Calculations
86
Appendix B – Trip-strip Calculations Using Braslow’s Method
87
Appendix C1 – Labview vi’s: Vi to measure dynamic pressure and temperature
88
89
Appendix C2 – Labview vi’s: Digital Data Filter
90
Appendix D – Data fit
A data fit was performed on the wind tunnel data so it could be used as input for the
non-linear aerodynamic model of the computer simulation. To obtain this curve fit
for the lift, drag and pitching moment coefficients the LINEST function of Excel was
used. The “LINEST” function of Excel calculates the coefficients of independent and
additional curve-fit variables to create a polynomial curve-fit of the input data.
Equations D1 through D3 are the polynomials used in the simulation and Table D1
lists the values of the coefficients for the lift, drag and pitching moment coefficient.
() ()
() ()
w
e bf
w
e
w
bf
w
bf
w
e bf
w
bf
w
w
e
w
bf
e bf
w
e bf
w
L
b H
a
b H
a
b H
a
b H
a
b H
a
b H
a
b H
a
b H
a
b H
a
a a
b H
a a a
b
H
a a a C
WT
2
2 2
2
2
2 2
2 2
2 2
16
2
15
2
14 13
12
2
11
2
10 9 8
7 6 5 4 3 2 1 0
δ αδ
δ
αδ αδ
δ δ δ
α δ
δ
αδ αδ
α
δ δ α
+ + +
+ + + + +
+ + + + + + + + =
(D1)
() ()
() ()
w
e bf
w
e
w
bf
w
bf
w
e bf
w
bf
w
w
e
w
bf
e bf
w
e bf
w
D
b H
a
b H
a
b H
a
b H
a
b H
a
b H
a
b H
a
b H
a
b H
a
a a
b H
a a a
b
H
a a a C
WT
2
2 2
2
2
2 2
2 2
2 2
16
2
15
2
14 13
12
2
11
2
10 9 8
7 6 5 4 3 2 1 0
δ αδ
δ
αδ αδ
δ δ δ
α δ
δ
αδ αδ
α
δ δ α
+ + +
+ + + + +
+ + + + + + + + =
(D2)
() () ()
() ()
w
e bf
w
e
w
bf
w
bf
e bf
w
bf
w
w
e
w
e bf
w
e bf
w
m
b H
a
b H
a
b H
a
b H
a
a
b H
a
b H
a
b H
a
b H
a
a a
b H
a a a
b
H
a a a C
WT
2
2 2
2
2 2
2
2
2 2
16
2
15
2
14 13
5 . 0
12
2
5 . 0
11
2
10 9
3
8
7 6 5 4 3 2 1 0
δ αδ
δ
αδ αδ
δ δ
δ
α δ α
αδ αδ
α
δ δ α
+ + +
+ + + + +
+ + + + + + + + =
(D3)
91
Table D1 – Coefficients of the curve fit calculated by LINEST
Coefficients C
L
C
D
C
m
a
0
0.088138 0.012910 -0.041830
a
1
5.795494 0.214666 -0.670918
a
2
0.010852 0.021121 -0.040100
a
3
0.121734 0.020926 0.003348
a
4
2.016637 -0.068959 -1.031239
a
5
-0.020298 0.055524 0.093076
a
6
-0.198065 0.110559 0.023427
a
7
-0.323129 1.436832 -1.562082
a
8
-0.004181 0.004360 0.003156
a
9
-0.001112 -0.000502 0.031372
a
10
0.014992 -0.005446 -0.034477
a
11
0.001253 -0.000439 0.000422
a
12
-0.017522 -0.002280 0.008641
a
13
0.001279 -0.060239 0.054434
a
14
-0.008004 0.005589 -0.005224
a
15
0.001061 0.000149 -0.006184
a
16
-0.106082 -0.031272 0.107482
To confirm the actual fit of the polynomials with the wind tunnel data both where
plotted on a same graph for different values of the independent variables (angle of
attack, height above the ground, belly-flap deflection and elevon deflection).
Figures D1 through D3 show some examples of these comparisons for the lift, drag
and pitching moment respectively. The solid lines represent the polynomial fit to the
data and the symbols are the corresponding wind tunnel data for that particular case.
One can conclude from the plots that the curve-fit is satisfactory for our study.
92
Figure D1 – Curve-fit verification for the lift coefficient.
93
Figure D2 – Curve-fit verification for the drag coefficient.
94
Figure D3 – Curve-fit verification for the pitching moment coefficient.
95
Appendix E – Spring-Dashpot Constants
To establish the equations that allow determining the constants for the
non-linear spring and dashpot the following free-body diagram was used
Figure E1 – Free-body diagram used to model a landing gear.
) (
3
t F s ks s c s m = + + + ε & & & (E1)
Two different motion cases were considered to determine the two spring constants.
Case 1 – Airplane static on the runway:
0
) ( mg t F = ,
1
s s = , 0 = s & , 0 = s & &
(E1)
1
3
1 0
s
s mg
k
ε − −
= (E2)
Case 2 – Full stroke reached for a hard landing:
0
) ( mg t F = ,
2
s s = , 0 = s & ,
0
67 . 1 g s = & & (Page and Rawdon 2007)
(E1) & (E2)
( )
()
1
3
2 2
3
1
0 2 1
67 . 2
s s s s
mg s s
−
−
= ε (E3)
96
The same equations E2 and E3 as well as the same values for the static stroke
(s
1
= 16.5 in) and the full stroke (s
2
= 23 in) (Page and Rawdon 2007) were used to
calculate the non-linear spring constants of the main and nose landing gear. The
weight seen by each gear on the other hand was different. The main landing gear is
considered to take 85% of the landing gross weight of the airplane
(= 325000 lbs) where as the nose gear is absorbing the remaining 15%. The obtained
values used in the simulation are for the main gear
k
mg
= 6,000 ε
mg
= 100,000
and for the nose gear
k
ng
= 1,040 ε
ng
= 18,000
The constants for the dashpots were chosen so that the system is close to be critically
damped.
c
mg
= 75,000 c
ng
= 15,000
Figures E2 & E3 show the time responses of the spring-dashpot system used to
model the main and nose landing gear when the only force acting on the airplane is
gravity.
97
Figure E2 – Time response of the main landing gear.
Figure E3 – Time response of the nose landing gear.
98
Appendix F – Additional landing simulation results
99
Appendix G – Additional go-around simulation results
100
Appendix H – Additional takeoff simulation results
Abstract (if available)
Abstract
During the first century of flight few major changes have been made to the configuration of subsonic airplanes. A distinct fuselage with wings, a tail, engines and a landing gear persists as the dominant arrangement. During WWII some companies developed tailless all-wing airplanes. However the concept failed to advance till the late 80's when the B-2, the only flying wing to enter production to date, illustrated its benefits at least for a stealth platform. The advent of the Blended-Wing-Body (BWB) addresses the historical shortcomings of all-wing designs, specifically poor volume utility and excess wetted area as a result. The BWB is now poised to become the new standard for large subsonic airplanes. Major aerospace companies are studying the concept for next generation of passenger airplanes. But there are still challenges. One is the BWB's short control lever-arm pitch. This affects rotation and go-around performances. This study presents a possible solution by using a novel type of control surface, a belly-flap, on the under side of the wing to enhance its lift and pitching moment coefficient during landing, go-around and takeoff. Increases of up to 30% in lift-off CL and 8% in positive pitching moment have been achieved during wind tunnel tests on a generic BWB-model with a belly-flap. These aerodynamic improvements when used in a mathematical simulation of landing, go-around and takeoff procedure were showing reduction in landing-field-length by up to 22%, in takeoff-field-length by up to 8% and in loss in altitude between initiation of rotation and actual rotation during go-around by up to 21.5%.
Linked assets
University of Southern California Dissertations and Theses
Asset Metadata
Creator
Staelens, Yann Daniel (author)
Core Title
Study of belly-flaps to enhance lift and pitching moment coefficient of a blended-wing-body airplane in landing and takeoff configuration
School
Andrew and Erna Viterbi School of Engineering
Degree
Doctor of Philosophy
Degree Program
Aerospace Engineering
Publication Date
10/31/2007
Defense Date
10/22/2007
Publisher
University of Southern California
(original),
University of Southern California. Libraries
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Tag
all-wing airplane,belly-flap,blended-wing-body,Landing,lift enhancing device,OAI-PMH Harvest,takeoff
Language
English
Advisor
Blackwelder, Ron (
committee chair
), Browand, Frederick (
committee member
), Ioannou, Petros A. (
committee member
), Page, Mark (
committee member
), Shiflett, Geoffrey R. (
committee member
)
Creator Email
staelens@usc.edu
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Tags
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