1. Blended Wing Body (BWB)
Aerodynamic Analysis and Redesign
16.100 Final Project
The report is the result of our work and the work breakdown is correct.
1. Overview

2. The purpose of this report is to analyze the aerodynamic performance of the Blended Wing Body (BWB)
at cruise, approach, and stall conditions, and to propose a redesign strategy that will increase the static
stability margin of the BWB to at least 5% at each operating condition. The redesign strategy will be
limited to the airfoil geometry of the BWB, with the use of AVL vortex lattice code and XFOIL subsonic
isolated airfoil code, written by Prof. M. Drela and Dr. H. Youngren. The basic geometry of the BWB is
summarized in Table 1.
Symbol Parameter Value
Sref Reference area (trapezoidal wing) 728.36 m2
Swet Wetted area 2909.72 m2
b Wing span 85.34 m
cmac Mean aerodynamic chord 9.37 m
Table 1: Geometric data for full-scale BWB
The following sections outline the analysis methodologies used for flight performance analysis at
operating conditions. Original BWB performance is compared critically with our redesign performance to
conclude stuff. Table 2 provides a list of the constants and parameters used in our flight performance
analysis.
Symbol Parameter
𝛼 Angle of Attack
c Chord length
Cm Moment Coefficient
Cd Drag Coefficient
Cl Lift Coefficient
D Drag
M Mach Number
xac Aerodynamic Center
Re Reynold’s Number
𝜌 Air Density
𝜐 Kinematic Viscosity
v velocity
xac Aerodynamic Center
xcp Center of Pressure
Table 2: Constants and parameters
2. Wind Tunnel Comparison

3. Aerodynamic data for a 1/47 scale model of the BWB is compared with AVL code of the BWB. Wind
tunnel tests were performed at velocities of 50 and 100 mph. Figure 1 shows the schematic of the wind
tunnel test apparatus. Flight performance between the simulation and wind tunnel tests are compared at
the freestream conditions in the Wright Brothers Wind Tunnel, summarized in Table 2.
2.1 Wind Tunnel Corrections
Figure 1: Wright Brother Wind Tunnel Test Setup
Velocity (v) Mach Number (M) Reynold’s Number (Re)
50 mph 0.128 270,143
100 mph 0.64 540,287
Table 3: Freestream Conditions in Wright Brother Wind Tunnel
where, assuming STP conditions for the Wright Brother Wind Tunnel,
𝑅𝑅 = 𝑅𝑅𝑅 /𝑅
𝜌 = 23.77𝑅10−4
𝑅𝑅𝑅𝑅𝑅/𝑅𝑅3
𝑅 = 𝑅 𝑅𝑅𝑅/47
𝜇 = 3.737𝑅10−7
𝑅𝑅. 𝑅/𝑅𝑅2
The wind tunnel data is corrected for contributions from the tunnel walls and mounting apparatus. The
dimensions of the mounting apparatus is summarized in Table 4.
Apparatus Shape Dimensions (w x h)
Walls Elliptical 10 ft x 7 ft

4. Cylindrical mount Cylindrical 0.115 ft x 0.41 ft
Pitch adjustment rod Elliptical Cross-Section 0.0656 ft x 0.0328 ft x 2.92 ft (l x w x h)
Flat plate sting Flat Plate 1.5 ft x 0.167 ft (l x h)
Table 4: Wind Tunnel Corrections
Wind Tunnel Walls
Modeling the BWB in the wind tunnel, to satisfy flow tangency along the walls, image vortices around
the wall are needed for the analysis. These image vortices generate an upwash that increases the effective
angle of attack of the BWB model. The increase in angle of attack leads to an increased coefficient of
induced drag because Cdi=CLαi . A formula to calculate the change in angle of attack is derived in the
notes and goes as follows:
Δαi=δ*(S/C)*CL where
where CL is the coefficient of lift, S is the reference area, C is the tunnel cross-sectional area, and δ is a
factor which depends on tunnel and model geometry. Equations are provided to calculate the δ. Once we
calculate Δαi , we can find the coefficient of drag of the wall (ΔCdwall=CL Δαi) and then calculate the drag
due to the wall.
Dwall = qinfSrefCdwall
Cylindrical Mount
The drag force due to the model’s cylindrical support is calculated with:
Dcyl = qinfdcylhcylCdcyl
where,
Cdcyl = 0.8 is approximated as the coefficient of drag on a cylinder, taken from Aerodynamic Drag by
Sighard Hoerner, at the appropriate Reynolds number.
hcyl & dcy represent the cylinder diameter and height.
Pitch Adjustment Rod
The drag due to the pitch adjustment is calculated using the drag coefficient, Cdrod = 0.35 given in
Aerodynamic Drag, by Sighard Hoerner. The drag coefficient is specified for an elliptical cross section
with a thickness ratio of t/c, where t is the thickness of the ellipse, and c is the chord length of the ellipse.
Therefore, the drag force is calculated with the equation
Drod = qinf hrod lrod Cdcyl
Where hrod &lrod are the height and length of the pitch adjustment.
Flat Plate Sting

5. Modeling the flat plate sting as a flat plate, and using the Blasius solution for the coefficient of drag over
a flat plate at turbulent conditions (Re > 500,000). The coefficient of drag from turbulent boundary layer
theory is
𝑅 𝑅 = 2(.0740)(𝑅𝑅𝑅(𝑅𝑅 𝑅𝑅𝑅𝑅𝑅))−2.58
where the factor of 2 comes from the total drag from both sides of the plate. The drag can then be
calculated from the dynamic pressure head and freestream conditions in the wind tunnel.
Component Drag Value (N)
Cylinder mount 4.2019
Pitch Adjustment rod 7.4684
Flate Plate Sting 1.6759
Wind Tunnel Walls (depends on 𝑅 𝑅) 0.0248 - 1.0774
Table 5: Drag values in 100 mph wind tunnel
Finally, each drag component is subtracted from the experimentally measured value for drag in order to
obtain the drag on the BWB model alone.
Dtotal = Dbwb – Drod – Dcyl – Dplate - Dwall
2.2 Profile Drag Correction
Our analysis uses AVL to simulate the BWB performance, but requires a parabolic profile drag model to
predict profile drag. The drag profile for the BWB airfoil cross-sections are evaluated from XFOIL, and
inputted into AVL.
2.3 Analysis Comparison
Coefficient of Lift vs Angle of Attack
After correcting the wind tunnel lift values with contributions from the wall, the AVL simulation is
compared against wind tunnel data for freestream conditions in the Wright Brother’s Wind Tunnel for
both 50 mph and 100 mph tests. The AVL simulation matches the 100 mph wind tunnel data more
accurately likely because of the higher Reynold’s freestream conditions. The deviation between AVL and
wind tunnel data at higher angle of attacks is likely due to flow separation, which is not captured by the
AVL code. As AVl will be simulating actual flight conditions of higher Reynold’s numbers, further flight
performance analysis is compared for 100 mph wind tunnel data.

6. Figure 2: Coefficient of Lift against angle of attack at: (left) 50 mph (right) 100mph
Coefficient of Lift vs Coefficient of Drag
The coefficient of drag is determined by correcting the AVL analysis with profile drag contributions, and
the wind tunnel data with contributions from the wall and mounts described in section 1. Figure 3 shows
that the AVL simulation provides a good estimation of the drag experienced by the airfoil, with a higher
drag coefficient of about .03 over relevant lift coefficients. The addition of the profile drag characteristics
of the airfoil results in a better match in the general shape of the characteristics, which may differ slightly
due to measurement errors. AVL analysis will be used for determining coefficient of drag at operating
conditions, with profile drag characteristics at each Reynold’s number determined through XFOIL and
added into the AVL simulation.
Figure 3: Coefficient of Lift vs Drag data at 100 mph
Moment about Aerodynamic Center
The aerodynamic center is fixed as the aerodynamic center of the BWB at zero lift. The moment
coefficient for AVL is defined at the nose, and the moment coefficient for wind tunnel data is defined at
the cylindrical mount. In the wind tunnel data, the mounting apparatus is assumed to have no effect on the
moment calculated on the wing; any moment the mounts may experience is assumed to be absorbed
completely by the fixed end of the mount attached to the floor. The translation of the moment coefficient
to a different reference point is done using the following equation

7. 𝑅 𝑅(𝑅1) = 𝑅 𝑅(𝑅0) + ((𝑅1 − 𝑅0)/𝑅 𝑅𝑅𝑅)𝑅 𝑅
After solving for the aerodynamic center at 100 mph free stream conditions, the coefficient of moment is
taken about xac = 25.28 m. Figure 4 shows the moment coefficient as a function of the lift coefficient. The
AVL data differs greatly from wind tunnel data. For further comparison of the moment coefficient values,
the center of pressure and aerodynamic center, both of which are a function of the moment and lift
coefficient distribution, are plotted against angle of attack in Figure 5. The wind tunnel data suggests that
the BWB would be stable across a wide range of angle of attacks. For our analysis we choose to use AVL,
which indicates a greater requirement for stability, and attribute the difference in the comparison to errors
in the wind tunnel moment coefficient measurements.
Figure 4: Moment Coefficient about aerodynamic center vs coefficient of lift at 100 mph
Figure 5: Center of Pressure and Aerodynamic Center vs. Angle of Attack at 100 mph
3. Cruise analysis: Nominal Geometry
Wave Drag Calculation

8. Wave drag becomes important as the mach number approaches 1, because even if the flow overall isn’t
sonic, locally the flow can become sonic, leading to a sharp rise in coefficient of drag at that location. At
cruise, the operating mach number is 0.8 and therefore must take into account the wave drag. Reading
through chapter 9 of Commercial Airplane Design Principles, a method for estimating wave drag is
explained. This method explains that wave drag is affected by the thickness to chord ratio of the airfoil
section, the coefficient of lift, and the sweepback angle. The idea of this method is to find the critical
mach number, which is the lowest mach number at which flow locally becomes sonic, and then use this to
determine a coefficient of wave drag. We can find the critical mach number though the Korn Equation
Method which goes as follows:
where Λc/2 is the sweepback angle,(t/c) is the thickness to chord ratio, and k is a coefficient relating to
drag divergence number and that can describe an airfoil’s merit. The thickness to chord ratio was
determined by loading the airfoil geometry into xfoil and recording the data from there. The sweep angle
for a specific section was calculated by the using the geometry specified in the .avl file. An ideal airfoil
would have k=1, but typical values of k fall within 0.87 for conventional airfoils to 0.95 for supercritical
airfoils. Since we can’t calculate the exact k values for our airfoil sections, because they rely on
experimental data, we carried on in our analysis using k=0.87 for the worst case scenario of wave drag.
The result is that we might be overestimating for wave drag.
To calculate the coefficient of wave drag, Lock’s fourth power rule is used, which goes as follows:
Cdw=20*(M - Mcr)4
The wave drag coefficient is calculated for each airfoil section and then is added to the profile drag in the
.avl file. What was found was that the wave drag for the first 5 sections was an order of magnitude greater
than the profile drag. This seems odd because one would expect that a larger sweep angle would reduce
the wave drag since wave drag depends on the normal mach number which becomes smaller as the sweep
angle increases. Results do get better as we increase k, but we don’t know what the k values should be for
the airfoil sections so we decided to carry on the analysis assuming worst case wave drag.
sweep angle: [57.7, 60.6, 49.98, 45, 42.6, 40.2, 39.9, 39.7, 37, 37.2, 37, 37, 37, 37]
C_wd:[0.013, 0.063, 0.0148, 0.0176, 0.02*, 0.0025, 0.0011, 0.0002, 0, 0, 0.0002, 0.0002, 0.0002, 0.0002]
*an order of magnitude higher than profile drag
AVL Analysis
At cruise, the lift of the aircraft needs to equal its weight. Using this principle, we can determine/solve for
the coefficient of lift we want in our AVL analysis to be. When tell AVL to what angle of attack the BWB
needs to be at to achieve this coefficient of lift.. AVL will then run an analysis at this angle of attack. The
AVL analysis needs certain inputs to run the case at appropriate conditions. Such inputs include air
density, mach number, and velocity. Given and using that cruise is at 35,000 ft., we can determine the
freestream conditions.

9. Cruise
Mach Number 0.8
Air Density (kg/m^3) 0.38
Velocity (m/s) 237
Desired CL 0.457
Table 6: Flight Conditions at Cruise
We ran this case and got the following results:
- Estimated Drag: D= ½ ρ v2
Sref CD= 443481 N
- Estimated Lift-to-drag ratio : CL/CD=.4570/.05705= 8.01
- xcp/cmac = 2.88
- xac/cmac = 2.66
- stability margin = 2.66 - 2.88= -0.22
- center of pressure lies behind aerodynamic center so design is unstable
- Lift Distribution Plot (coefficients vs spanwise location)
Figure 6: Lift Distribution plot for Nominal Geometry at Cruise

10. 4. Approach and Stall Analysis
Approach Analysis
First approach conditions without flaps is considered, at full payload and 25% fuel remaining. Assuming
approach and stall are performed at STP, AVL simulations of the BWB without flaps is run at Mach
0.2328 (77.17 m/s), the given approach speed. The required coefficient of lift for approach is calculated to
be 1.088 at the aircraft weight of 294,746 kg. The required angle of attack is evaluated through AVL to be
7.38 degrees. Figure 7 shows the lift distribution at approach conditions. As the sectional lift coefficient
does not increase above 1.0, the use of slats is not needed for approach. The design with no flaps is
statically unstable during approach.
Figure 7: Lift Distribution plot for Nominal Geometry at Approach
- Estimated Drag: D= ½ ρ v2
Sref CD= 320628 N
- Estimated Lift-to-drag ratio : CL/CD=1.0887/.12069= 9.02
- xcp/cmac = 2.79
- xac/cmac = 2.73
- stability margin = 2.73 - 2.79= -0.06
Stall Analysis
The approach speed is required to be 1.3x the stall speed. The stall speed is thus calculated to be 0.179
Mach (59.36 m/s). The required coefficient of lift is calculated to be 1.835, and the airfoil must be under

11. the maximum sectional coefficient of lift at 1.6 with slats. The sectional lift coefficient peaks at 1.6, thus
the BWB can operate at stall conditions only with the use of slats with no flaps. The stall angle of attack
for these conditions is found at around 14 degrees, with a coefficient of lift of 1.835. The design with no
flaps is statically unstable during stall.
Figure 8: Lift Distribution plot for Nominal Geometry at Stall
- Estimated Drag: D= ½ ρ v2
Sref CD= 1,335,154N
- Estimated Lift-to-drag ratio : CL/CD=1.8347/.84935= 2.16
- xcp/cmac = 2.99
- xac/cmac = 2.73
- stability margin = 2.73 - 2.99= -0.26
The use of flaperons will change the lift distribution of the wing, but as the sectional coefficients can be
handled by the wing, they are not needed in this design. Use of flaps changing the lift distribution may
affect the stability margin, but flaps are kept at 0 degrees in order to compare similar geometries with the
redesign.
5. Redesign Strategy
A blended wing body (BWB) is a flying-wing configuration with a wide lift producing center
body blending to conventional outer wings. As it lacks a typical rear empennage section it is inherently

12. unstable. As shown in the analysis section the center of pressure lies behind the aerodynamic center.
Hence a redesign is required to mimic “tail-like” effect especially at approach and cruise conditions.
Possible Redesign Approaches:
1. Sweep
On increasing the sweep angle of the wing a larger portion of the wing roots would fall behind the
line of the center of pressure (cop). Hence this would add to the lift contribution behind the cop and in
essence cause the cop to move forward.
2. Reflexed Airfoil Section
A reflex is an opposite curvature added near the trailing edge at around 70% of the chord. This
essentially creates a negative lift that applies a restoring force similar to a horizontal tail to keep the BWB
from pitching too far up or down. The effect is achieved thanks to a positive pitching moment associated
with reflexed airfoils.
3. Twist
Wing twist is a feature to adjust lift distribution along the wing. Applying a negative wing twist
at the tip causes the effective angle of attack to be lower than that at the root.
We wanted to change the wing such that we do not change the reference parameters such as area and
mean aerodynamic chord because this would interfere with the calculation of other important parameters.
We also thought that it would be easier if we did not have to re-calculate them every time we made a
change to the BWB geometry.
Final Design modification
The wing planform is kept the same so that we do not change the reference area and chord. This would
also minimize the effort going into calculating wave drag for the new design.
Sectional airfoils of the base BWB design are replaced with one reflexed airfoil starting at span location
of 60 ft onwards with a similar t/c ratio. The airfoil chosen is one that is thinner than each section of the
original design so as to keep the profile and wave drag down. Having the same airfoil for the outer part of
the wing (9 sections) also makes it easier to modify profile drag correction between cases. The airfoil
chosen specifically is the MH61 airfoil by Martin Hepperle for its high positive pitching moment.
An increasing geometric twist is applied starting from span of 60ft at each section. The increment in the
twist is chosen in order to have a smooth transitioning wing surface and to avoid abrupt changes in the
geometry. If we look at the outer section of the wing as a whole, from 50ft to the wing tip, there’s an
additional 2.7 degree washout to the original design.
Changing the airfoil alone puts our design at approximately the stability requirement. We then decided it
would be simplest to apply additional washout for the extra stability margin. In the AVL geometry file
every airfoil at 60ft onwards is replaced with orig6foilmod_mod.dat. This is the new MH61 airfoil.
6. Analysis of Redesigned Geometry: Approach, Stall and Cruise
Cruise Analysis
From the parameters defined at cruise condition:
L = MTOW = 3555000N

13. 𝜌 = 0.380 kg/m3
v = 273m/s
S_ref = 728.4m2
We calculated the necessary CL = 0.457. We then ran the new geometry at this CL and got the following
results:
- D = 783000N
- Lift-to-drag ratio : 4.54.
This poor performance figure could have been due to over estimation of wave drag. The wave
drag we estimated is about an order of magnitude greater than the profile drag and induced drag
combined, so it directly affects our performance figure. Luckily it does not affect the calculation
of the stability margin.
- Location of the aerodynamic center and the center of pressure
Figure 9: cp and ac location at cruise for redesigned BWB over a range of AOA
- xcp/cmac = 2.64
- xac/cmac = 2.82
- stability margin = 2.82 - 2.64 = 0.18
We ran the geometry over a range of angle of attack and found that it is stable at cruise.
- Lift distribution plot

14. Figure 10: Lift Distribution for Redesigned BWB at cruise
As seen by the plot the redesigned BWB is stable for a wide range of lift coefficients and angle of attacks
unlike the baseline design which wasn't statically stable for most of the range of angle of attack. In
general, these results indicate that the main goal of the redesign, to increase static stability, has been
achieved. There are more values of for which the BWB is stable in the redesign than in the baseline. One
downsize of the redesign is however, the increase of induced drag at cruise because of the greater angle of
attack needed to maintain enough lift. Hence, we tried to cancel this effect by reducing the profile drag
with a thinner airfoil.
Approach Analysis
We again consider approach without flaperon deflection. The same required Cl = 1.088 applies because
the planform stays the same. The required angle of attack is evaluated through AVL to be 8.76 degrees.
We see that the sectional lift coefficient does not increase above 1.0, so the use of slats is also not needed.
- D = 759000N
- L/D = 4.038
- xcp/cmac = 2.69

15. - xac/cmac = 2.75
- Stability margin = 2.75 - 2.69 = 0.06
- Lift distribution plot
Figure 11: Lift Distribution for Redesigned BWB at approach
Stall Analysis
The stall speed is still 0.179 Mach (59.36 m/s). The required coefficient of lift is also 1.835, which is
greater than the maximum sectional coefficient of lift at 1.6 with slats.
- D = 1,689,838N
- L/D = 1.7
- xcp/cmac = 2.95
- xac/cmac = 2.75
- Stability margin = 2.75-2.95 = -.2
- Lift distribution plot

16. Figure 12: Lift Distribution for Redesigned BWB at stall
7. Review of proposed design strategy
Our proposed design works in the sense that additional stability margin is introduced into the design at the
cost of increased induced drag. The design seems to be stable cruise and approach. At stall it is unstable,
which should make sense because the angle of attack is considerably large and the flow is not well
understood at this range. We stayed away from changing the reference area and chord to keep the
calculation effort down which might have placed a limit on what we could do to make the design better.
Another design to start with would be to increase the chord length and area so that the same lift is
generated at a smaller angle of attack, reducing induced drag. We have no idea how that is going to affect
the profile drag however, so detailed calculation is needed to evaluate the feasibility of such a design.
8. Conclusion
In the analysis phase it was determined that the geometry of the Blended Wing Body aircraft did not meet
the requirements of this project. According to the simulations, it was not stable at cruise conditions. The
goal of the redesign phase was to change the geometry of the aircraft to increase stability at cruise
conditions. After running a series of simulations using AVL, it was determined that adding a reflex to the
shape of all the airfoils could cause a significant improvement in the stability of the aircraft. New
reflexed airfoil sections were then added which brought the stability margin close to the requirement.

17. Finally additional washout was applied resulting in the overall static stability margin to be 18%. The
redesigned geometry was statically stable with a reasonable margin of stability.
9. Work Breakdown
Eric Tu
- Flat Plate Sting Drag Correction
- Wind Tunnel Analysis
- Basis for Aerodynamic, Pressure Center Calculations.
- Original BWB Approach and Stall Analysis
- Profile Drag Correction
- 40 hours
Nhat Cao
- BWB Geometry Redesign and Testing
- Redesigned BWB Cruise, Approach and Stall Analysis
- Profile Drag Correction
- Help with Xfoil and AVL
- Proposal for another design
- 30 hours
Joel Argueta
- Wind Tunnel Wall Drag Correction
- Wave Drag Calculation for Cruise
- Cruise Analysis: Nominal Geometry
- 20 hours
Ishaan Prakash
- Wind tunnel Cylindrical mount and pitch rod drag calculation
- Total drag estimation for wind tunnel BWB model
- BWB redesign strategy
- 35 hours
10. Bibliography
[1] S.F. Hoerner. Fluid Dynamic Drag. Hoerner Fluid Dynamics, 1965. 2nd ed.
[2] Sforza, Pasquale M. Commercial Airplane Design Principles. Elsevier Inc, 2014. 1st ed.
[3] Hepperle, Martin. Basic Design of Flying Wing Models. 2002.