Senior Design Group P07108
Winter and Spring 2007
METEOR PROJECT: Gliding Instrumentation Platform Design
Tail Subsystem Design and Analysis : Ryan Weisman
METEOR PROJECT: Gliding Instrumentation Platform
Tail Design Synopsis:
The tail was designed to provide pitch and yaw stability and control through a
conventional vertical stabilizer design and an unconventional but effective horizontal stabilizer
design.
The vertical stabilizer is a two part design: (1) stationary forward part and (2) movable
horned rudder to provide directional control. The vertical stabilizer design provides inherent
directional stability through weathercock action, righting the glider when encountering a side
force. The rudder was designed in a horned fashion to minimize the amount of force needed to
move the rudder by using the air flowing around the vertical stabilizer to aid in pivoting the
rudder about its hingeline.
The horizontal stabilizer employs an all-moving design instead of the conventional
elevator and stationary horizontal stabilizer to control and maintain pitch. The horizontal
stabilizer consists of a left and right side mounted about the tail boom in order to provide
clearance for rudder deflection. The all-moving horizontal stabilizer has been used in the in the
past and diminishes the amount of force needed to move the horizontal stabilizer because it also
employs the air moving around the airfoil to pivot the stabilizer about its hingeline.
The unconventional aspect of the horizontal stabilizer is the trailing edge of the stabilizer
can be deflected 70 degrees above the horizontal. This extreme deflection provides for a “deepstall” or “dethermalizer” mode to control the forward momentum of the aircraft by stalling the
wing and not losing as yaw control. This deep-stall mode is useful for the initial roll out of the
vertical descent at launch from the weather balloon and in controlling the descent of the glider
for landing. This configuration has been used on small military Unmanned Aerial Vehicles in
order to land the UAV in the smallest area possible and in the smallest amount of time without
an extreme amount of damage to the aircraft. The horizontal stabilizer can then be brought
back into normal flight mode for pitch control (±25 degrees) and to increase forward momentum.
Rolling stability is ensured by proper balancing of the glider’s center of gravity and the mounting
of the wing above the fuselage of the glider.
The CAD drawing for the complete assembly is attached in Appendix A as High Altitude
Glider – Tail Assembly, A-1.
Tail Design Page -1-
METEOR PROJECT: Gliding Instrumentation Platform
All – Moving Horizontal Stabilizer
Operational Overview
The horizontal stabilizer for the tail was designed to be all-moving in order to provide
control of forward momentum via a deep-stall mode where the horizontal stabilizer’s trailing
edge is deflected upwards of -70 degrees about its y-axis, see figure T1. The control of forward
momentum results from stalling the main wing of glider and allowing the glider to first porpoise,
pendulum, then settle into a vertical descent with full yaw-control. Due to the design of the wing
being attached above the fuselage and center of gravity, roll stability is passively built into the
glider. Pitch stability is maintained through center of gravity positioning and deflection of the
all-moving horizontal stabilizer.
Figure T1: Tail Assembly
Vertical Tail
+Y
Horizontal Tail
(Left half)
+X
+Z
The horizontal stabilizer has two gliding modes: (1) Normal Flight, Figure T2, and (2)
Deep-stall, Figure T3. The in normal flight mode the entire horizontal stabilizer acts as an
elevator with a maximum deflection of ±25 degrees for operation assuming to take place from
approximately 65,000 feet until the deep-stall mode is entered for landing descent around
approximately 1,000 feet.
Figure T2: Normal Glide Mode(+25 degree deflection)
Tail Design Page -2-
Figure T3: Deep Stall Mode
METEOR PROJECT: Gliding Instrumentation Platform
The deep-stall mode is entered before the glider is released from the weather balloon after
the firing of the rocket and is used again in order to slow descent rate and prepare for parachute
deployment prior to landing. In deep-stall mode, the deflection of the horizontal stabilizer allows
for control of forward momentum via stalling the main wing of the glider in addition to allowing
the glider to exit its initial vertical drop from the balloon and glider parallel to the earth’s surface.
The deep-stall mode for pitch as well as forward momentum control was designed with help
from Pete Goldsmith, Steve Stricker, and Robert Vest.
Each half of the horizontal stabilizer has a 15 inch trailing edge span, 9 inch root chord, 6
inch tip chord and uses the NACA 0010 airfoil. The NACA 0010 airfoil provides the symmetry
needed for pitch control as well as being thin to keep weight minimal. The NACA 0010 has
been a highly researched airfoil and proven to be reliable.
Calculations:
The all-moving horizontal tail design takes the place of the traditional elevator and nonmoving horizontal stabilizer to control pitch. The all-moving design is used to control pitch as a
normal elevator on a general aircraft would (between ±25 degrees) in addition to being able to be
deflected upwards of -70 degrees for control of momentum in the x-direction.
Aerodynamic Center and Hinge line:
Figure T4 shows the right half of the horizontal stabilizer drawn to a scale of 1:5. This
figure was used to calculate where the hinge line should be given the calculation of the
aerodynamic center, both the aerodynamic center and the hinge line were drawn in after the
calculations were conducted.[1] In addition, reference the CAD drawing entitled High Altitude
Glider – All Moving Horizontal Tail Assembly in Appendix A, as A-2.
The calculation for the aerodynamic center for the wing is important because at the
aerodynamic center of the wing, the lift and drag forces act and the pitching moment about the
aerodynamic center is independent of the angle of attack of the wing.[2]
Figure T4: Horizontal Stabilizer Right Half
Elevator Hinge
Line
Aerodynamic Center
Root(CR)
Tip(CT)
X
Y
Trailing Edge (length = b/2)
Tail Design Page -3-
METEOR PROJECT: Gliding Instrumentation Platform
For calculation of the aerodynamic center, equation 1 is used to find the mean
aerodynamic chord, MAC, length for the horizontal stabilizer and equation 2 is used to find the
X coordinate for the aerodynamic center.[3]
C C
2
MAC  (C R  CT  R T )
Eqn 1
3
C R  CT
3
* MAC
Eqn 2
4
From equations 1 and 2, the mean aerodynamic chord length is 7.6 inches and the x
coordinate of the aerodynamic center from the trailing edge is 5.7 inches. The y-coordinate of
the aerodynamic center from root cord is given in equation 3.[3]
b 1 C  2CT
YAC  * ( R
)
Eqn 3
2 3 C R  CT
The distance along the y-axis from the root chord to the aerodynamic center is found to
be 7.0 inches. From a conversation with Robert Vest of AAI Corporation the hingeline for an
all-moving horizontal tail must be in front of the aerodynamic center to maintain stability and
control of the aircraft and the hingeline tends to be approximately 20% of the MAC. Equation 4
gives the calculation of the X coordinate for the hingeline, the hingeline will be along the entire
span of the Y axis for the wing.[3]
X Hinge  0.8 * MAC
Eqn 4
The resulting x coordinate of the hingeline from the trailing edge of the wing is 6.0
inches.
X AC 
Horizontal Tail Volume Coefficient:
The tail volume coefficient is a normalized coefficient allowing for comparison of
different horizontal tail sizes to each other and to different applications. The coefficient reflects
the part of the tail’s contribution to the pitching moment normalized by the wing area and chord.
The range for gliders and general aircraft is approximately 0.5 to 0.7.[4],[5]. Equation 5 gives
the calculation for the horizontal tail volume coefficient. The taper ratio is the ratio of tip chord
to root chord and is given by equation 6.
l S
VH  T T Eqn 5
S w cw

ctip
Eqn 6
c root
Where the subscripts of “T” and “W” refer to tail and wing, the variable “S” refers to the
tail or wing’s planform area, “lT” refers to the distance from the glider’s center of gravity to the
horizontal tail’s aerodynamic center, and “c” refers to the MAC of the wing. Using the complete
horizontal tail of 30 inch span with a 6 inch tip chord, 9 inch root chord (taper ratio = 2/3),
distance from glider center of gravity to aerodynamic center of 52 inches, and rectangular wing
of 120 inch span and 12 inch chord the horizontal tail volume coefficient is 0.677. Thus the
values used for the tail design lie in the acceptable range.
Tail Design Page -4-
METEOR PROJECT: Gliding Instrumentation Platform
Vertical Stabilizer
Operational Overview:
The vertical stabilizer allows for directional control and stability by having a nonmovable vertical stabilizer and a moveable “horned” rudder that is able to move ±30 degrees
from center. See figure T5 for the moveable and non-movable parts and figure T6 for the
deflection of the rudder.
Figure T5: Vertical Stabilizer
Figure T6: Allowable Rudder Deflection
Moveable Rudder
(Direction Control)
Stationary
Stabilizer
Positive Rudder
Deflection Area
Negative Rudder
Deflection Area
From equations 1, 2, and 3, the MAC is 6.2 inches, the vertical distance from the root
chord to the aerodynamic center is 3.6 inches and the horizontal distance from the rudder trailing
edge to the aerodynamic center is 3.6 inches. Figure T6 displays left side of the rudder. The
airfoil used is the NACA 0010. In addition reference CAD drawing High Altitude Glider –
Vertical Stabilizer Assembly, in Appendix A, as A-3.
Figure T6: Vertical Stabilizer
Vertical
Stabilizer
Aerodynamic
Center
Rudder
Area
Rudder
Hingeline
As shown in Figure T6, the rudder hingeline is typically set behind the aerodynamic
center. The rudder area in front of the hingeline, from the horn design, allows less force to be
exerted in moving the rudder by employing the air flowing around the vertical stabilizer.
Tail Design Page -5-
METEOR PROJECT: Gliding Instrumentation Platform
Vertical Tail Volume Coefficient:
Equation 7 calculates the vertical tail volume by use of the vertical tail’s planform area,
horizontal distance from aircraft center of gravity to aerodynamic center, and the planform area
of the wing and the wingspan.
VV 
lV SV
S w bw
Eqn 7
From equation 6, the taper ratio of the vertical tail is 0.5, due to a 8 inch root and 4 inch
tip. The distance between center of gravity and aerodynamic center is set at 48 inches, the
planform area is 48 square inches, the resulting vertical tail volume coefficient is 0.013. The
typical range is 0.02 to 0.04.[4],[5] However, due to the horned rudder design and the control
authority available this volume coefficient is acceptable.
Rudder Area and Blanketing:
The rudder area aft of the rudder hingeline is calculated to be 24 square inches and the
rudder area forward of the hingeline is calculated to be 3 square inches. This results in the ratio
of Forward Area to Aft Area of 11.1%, from the analysis conducted by Ron Ellis and Mike
Whaley this results in a significant reduction in torque needed for rudder deflection.[6]
Daniel P. Raymer states that a minimum of 1/3 of the area must remain unblanketed by
the deflection of the horizontal stabilizer in order to maintain proper yaw control authority. The
leading edge of the horizontal stabilizer is positioned to be even with the leading edge of the tip
chord on the vertical stabilizer, when the horizontal stabilizer is deflected in deep stall mode to
70 degrees about the Y-axis, this leads to the blanketing of approximately 3 inches of the
rudder. This leaves approximately 89% of the rudder unblanketed and able to maintain full yaw
control with the deep stall deflection of the horizontal stabilizer.
Tail Design Page -6-
METEOR PROJECT: Gliding Instrumentation Platform
Flight Dynamics Calculations [5],[8],[12]
Lift Coefficient:
The chosen airfoil to be used throughout the tail is the NACA 0010 because it is a
symmetric airfoil allowing for equal control in both positive and negative deflections in addition
to be a smaller airfoil that will conserve weight but is still robust enough to survive all applied
forces. XFLR 5 was used to run batch analysis and produce inviscid solutions for the airfoil’s
lift, drag, moment, and pressure coefficients throughout given ranges of angle of attack. See
Appendix B for sample data table produced for one simulation of the airfoil for a given
Reynolds’ Number. The coefficient of lift for an airfoil (infinite wing) was found to be 0.1/deg
or 5.73/rad.
The coefficient of lift for a finite wing is calculated using equation 8 that employs
equation 9 for calculation of the aspect ratio of the wing, the elliptical wing factor, e, is assumed
to be 1 because the factor produces only very small changes in the prediction of the finite wing
lift coefficient.
C l
C L 
Eqn 8
C l
1
eAR
b2
AR 
Eqn 9
MAC * b
Where Cl is the lift coefficient for an airfoil (infinite wing), “b” is the wingspan, and
“MAC” is the mean aerodynamic chord of the wing. From equation 8 the coefficient of lift for a
finite wing of the horizontal stabilizer with aspect ratio of 3.95 is 3.92/rad and the coefficient of
lift for a finite wing of the vertical stabilizer with aspect ratio of 2.57 is 3.35/rad.
Control Authority for Elevator and Rudder:
From [5], the ratios of control surface chord to the chord of the wing used are comparable
to the values specified, which are averages of what are used in aerodynamic design. For the
elevator the ratio is 1 and is greater than the specified value for a sailplane, 0.43. The rudder ratio
is 3/8, 0.375, and is slightly smaller than the ratio given for the sailplane for the sailplane, 0.40.
The moment about the center of gravity imposed by the deflection of the elevator is given
by equation 10, where a positive elevator deflection has the trailing edge being deflected upward.
Cme  VHC L t Eqn 10
Where V is the tail volume coefficient,  is the ratio of the wind vector seen by the tail to
that seen by the wing, Cl is the slope of the lift coefficient versus angle of attack for the
horizontal wing,  is the flap effectiveness parameter for the horizontal tail given by equation 11,
and  is the ratio of tail and wing dynamic pressures given by equation 12.
Tail Design Page -7-
METEOR PROJECT: Gliding Instrumentation Platform
 Control Surface Area 
 Eqn 11 Where the area ratio is used to look up the function from
Planform Area


  func
Figure 2.21 in [8] or Figure 1.7.3 in [12]
1
VT
1
2

Eqn 12 From [8] with assumption Vt  Vw,  
where  is the angle between
2
1
cos
(ε
)
VW
2
the tail wind vector and the wing wind vector
Assuming a small angle between the wind vector of the wing and the wind vector of the
tail, a Horizontal tail volume coefficient of 0.625, coefficient of lift of 3.92/rad, and a flap
effectiveness parameter of 1 for an all moving elevator. The elevator control authority is found
to be -2.205/rad = -0.385/deg. This is acceptable because this generates a restoring moment to
counteract the pitch instability of the wing.
The moment about the center of gravity imposed by the rudder deflection is given by
equation 11, where a positive rudder deflection is the trailing edge moving toward the port side
of the glider.
Cnr  V VV C L V  Eqn 13
Assuming that the velocity vector seen by the tail is the same as that seen by the wing,
the flap effectiveness parameter of the vertical tail being 0.7, the vertical tail volume coefficient
being 0.013, and the slope of the coefficient of lift for the vertical tail being 3.35 per radian, the
rudder control effectiveness becomes -0.0305/rad=-0.532x10-3/deg. This provides a weathercock
stability assuring an opposite restoring moment than the one imposed via the wind gust.
Tail Design Page -8-
METEOR PROJECT: Gliding Instrumentation Platform
Control Algorithm
The control algorithm written for longitudinal and lateral-directional control is given in
the document entitled “High Altitude Glider Control Information Packet” where an outline of the
controller algorithm is given along with pseudo Matlab code for the decision making processes.
Tail Design Page -9-
METEOR PROJECT: Gliding Instrumentation Platform
Tail Sizing and Analysis References
[1] Art Roach. Establishing the MAC - Mean Aerodynamic Chord on any Platform.
<http://www.palosrc.com/newsletter/articles/wing_mac.pdf>
[2] John Anderson Jr. Fundamentals of Aerodynamics. 4th Ed. McGraw-Hill. New York, NY.
2007.
[3] Robert Vest. AAI Corporation Aerodynamicist. Phone Conversation February 8, 2007.
[4] John Anderson Jr. Aircraft Performance and Design. McGraw-Hill. New York, NY. 1999.
[5] Daniel P. Raymer. Aircraft Design: A Conceptual Approach. 4th Ed. AIAA Education
Series. Reston, VA. 2006.
[6] Ron Ellis with Mike Whaley. The Great Rudder Experiment.
<http://www.mindspring.com/~rellis2/rcpattrn/rudder.htm>
[7] Steve Stricker. AAI Corporation Special Projects Manager and Acting Director of
Engineering Support. Phone Conversations December 2006 – Present.
[8] Robert C. Nelson Flight Stability and Automatic Control. 2nd Ed. McGraw-Hill. New York,
NY. 1998.
[9] Joseph E. Shigley. Mechanical Engineering Design. 7th Ed. McGraw-Hill. New York, NY.
2004.
[10] Peter Goldsmith. Horizon Hobby Field Marketing Manager. Phone Conversation.
December 2006 – Present.
[11] Warren F. Phillips. Mechanics of Flight. John Wiley and Sons. Hoboken, NJ. 2004.
References
METEOR PROJECT: Gliding Instrumentation Platform
Appendix A: Referenced CAD Drawings for High Altitude Glider
A-1
Tail Assembly
A-2
All-Moving Horizontal Stabilizer
A-3
Vertical Stabilizer Assembly
Appendix A : CAD Drawings
METEOR PROJECT: Gliding Instrumentation Platform
Appendix B: NACA 0010 Coefficient Solutions from XFLR 5
XFLR5_v2.01
Calculated polar for: NACA 0010
Reynolds number fixed
Mach number fixed
xtrf = 1.000 (top)
1.000 (bottom)
Mach = 0.000 Re = 0.250 e 6 Ncrit = 9.000
alpha
CL
CD
CDp
CM
Top Xtr
Bot Xtr
Cpmin
Chinge
----------------------------------------------------------------31.5
-1.2075 0.38715 0.38405
0.1952
1
0.0089
-2.0973
0
-31
-1.1935 0.38203
0.3789
0.1892
1
0.0091
-2.1597
0
-25
-1.0206 0.31643 0.31307
0.1271
1
0.0149
-2.0385
0
-20.5
-0.8803 0.25925 0.25581
0.0821
1
0.0223
-2.1614
0
-20
-0.8602 0.25219 0.24874
0.081
1
0.0229
-1.9364
0
-19.5
-0.8433 0.24614 0.24267
0.0774
1
0.0242
-1.8581
0
-19
-0.8329 0.23844 0.23499
0.0694
1
0.0264
-2.1166
0
-18.5
-0.8136 0.23124 0.22777
0.0678
1
0.027
-1.9809
0
-18
-0.7968 0.22501 0.22153
0.0646
1
0.0283
-1.9027
0
-17.5
-0.7848 0.21702 0.21356
0.0587
1
0.0306
-2.025
0
-17
-0.7712 0.20917 0.20572
0.0549
1
0.0314
-2.0361
0
-16.5
-0.7544 0.20298 0.19951
0.0525
1
0.033
-1.9255
0
-16
-0.7574
0.193 0.18958
0.0427
1
0.0357
-2.2683
0
-15.5
-0.7305 0.18754 0.18408
0.0444
1
0.0373
-1.9452
0
-15
-0.7266 0.17866 0.17523
0.0382
1
0.0405
-2.1063
0
-14.5
-0.7159 0.17042
0.167
0.0353
1
0.0416
-2.1148
0
-14
-0.7023 0.16368 0.16025
0.0332
1
0.0439
-2.0482
0
-13.5
-0.712 0.15137 0.14799
0.0252
1
0.0466
-2.3404
0
-13
-0.6943 0.14599
0.1426
0.0253
1
0.0486
-2.1655
0
-12.5
-0.7174 0.13047 0.12715
0.0147
1
0.0523
-2.5763
0
-12
-0.6933 0.12747 0.12412
0.0172
1
0.0552
-2.2725
0
-11.5
-0.7248 0.11036
0.1071
0.0059
1
0.0586
-2.6894
0
-11
-0.7156 0.10406
0.1008
0.0054
1
0.0602
-2.5639
0
-10.5
-0.7424 0.08827 0.08509
-0.0048
1
0.0615
-2.8413
0
-10
-0.9905 0.03561 0.02948
-0.0173
1
0.0302
-5.5877
0
-9.5
-0.9654 0.03026 0.02338
-0.0141
1
0.0315
-5.373
0
-9
-0.9259 0.02716 0.02004
-0.0123
1
0.0335
-5.0235
0
-8.5
-0.8852 0.02415 0.01661
-0.0102
1
0.0366
-4.7048
0
-8
-0.841 0.02204 0.01424
-0.0085
1
0.0404
-4.3345
0
-7.5
-0.7969 0.01988 0.01204
-0.0067
1
0.0449
-3.9593
0
-7
-0.7527 0.01819 0.01025
-0.0048
1
0.0515
-3.5906
0
-6.5
-0.7103
0.0165 0.00861
-0.0026
1
0.0598
-3.2686
0
-6
-0.6677 0.01512 0.00726
-0.0003
1
0.0726
-2.9453
0
-5.5
-0.6251 0.01384
0.0061
0.002
1
0.0946
-2.6246
0
-5
-0.5826 0.01256
0.0051
0.0042
1
0.1407
-2.3346
0
-4.5
-0.54 0.01136 0.00437
0.0062
1
0.2322
-2.0492
0
-4
-0.4962 0.01042 0.00389
0.0081
1
0.3398
-1.7752
0
-3
-0.4051 0.00916 0.00341
0.0116
1
0.5401
-1.2922
0
-2.5
-0.3581 0.00875 0.00336
0.0133
1
0.6331
-1.0841
0
-2
-0.3104 0.00847 0.00344
0.0151
1
0.7223
-0.9011
0
-1.5
-0.2577 0.00838 0.00366
0.0159
0.9979
0.8065
-0.7377
0
-1
-0.1764
0.0084 0.00386
0.0114
0.9831
0.8778
-0.5708
0
-0.5
-0.0916
0.0085 0.00401
0.0064
0.9682
0.9247
-0.4429
0
0
0 0.00856 0.00406
0
0.9515
0.9515
-0.3445
0
0.5
0.0916
0.0085 0.00401
-0.0064
0.9247
0.9682
-0.4429
0
Appendix B: Sample Airfoil Coefficient Solutions
METEOR PROJECT: Gliding Instrumentation Platform
1
1.5
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
7
7.5
8
8.5
9
9.5
10
10.5
11
11.5
12
12.5
14
14.5
15
15.5
16
16.5
17
17.5
18
18.5
19
19.5
20
20.5
21
21.5
22
22.5
23
23.5
24
24.5
25
25.5
0.1764
0.2577
0.3104
0.3581
0.4051
0.4511
0.4961
0.5399
0.5826
0.6251
0.6676
0.7103
0.7527
0.7969
0.8411
0.8853
0.9259
0.9655
0.9906
0.9964
0.9785
0.925
0.8706
0.8314
0.5098
0.5187
0.5114
0.515
0.536
0.5212
0.5348
0.5329
0.541
0.5593
0.5531
0.5612
0.5743
0.5753
0.5832
0.5937
0.599
0.6051
0.6129
0.6216
0.6291
0.6341
0.6413
0.6487
0.0084
0.00838
0.00847
0.00874
0.00916
0.00972
0.01042
0.01136
0.01256
0.01384
0.01512
0.0165
0.01819
0.01988
0.02204
0.02415
0.02716
0.03026
0.03562
0.04209
0.05003
0.05977
0.07457
0.09186
0.14356
0.14802
0.15437
0.15957
0.16503
0.17089
0.17549
0.18173
0.18684
0.1927
0.1983
0.20359
0.20889
0.21502
0.22053
0.22576
0.23198
0.23807
0.24368
0.2491
0.25538
0.26168
0.26749
0.27306
0.00386
0.00366
0.00344
0.00336
0.00341
0.00359
0.00389
0.00437
0.0051
0.0061
0.00726
0.00861
0.01025
0.01204
0.01424
0.01661
0.02004
0.02338
0.02949
0.0369
0.04561
0.05592
0.0711
0.08852
0.14036
0.14484
0.15119
0.1564
0.16187
0.16772
0.17235
0.17859
0.18371
0.18959
0.19519
0.2005
0.20583
0.21196
0.21748
0.22274
0.22897
0.23508
0.24072
0.24616
0.25246
0.25878
0.26461
0.27021
-0.0114
-0.0159
-0.0151
-0.0133
-0.0116
-0.0099
-0.0081
-0.0062
-0.0042
-0.002
0.0003
0.0026
0.0048
0.0067
0.0085
0.0102
0.0123
0.0141
0.0173
0.0215
0.0259
0.0277
0.0172
0.0045
-0.0101
-0.0109
-0.0143
-0.0165
-0.016
-0.0216
-0.0225
-0.0263
-0.0285
-0.0286
-0.0336
-0.036
-0.0371
-0.041
-0.0435
-0.0453
-0.0482
-0.0513
-0.0538
-0.0559
-0.0583
-0.0616
-0.0642
-0.0667
0.8778
0.8065
0.7223
0.6331
0.5402
0.443
0.3398
0.2323
0.1408
0.0946
0.0726
0.0598
0.0515
0.0449
0.0404
0.0366
0.0335
0.0315
0.0302
0.0289
0.0285
0.0292
0.0299
0.0307
0.0501
0.0469
0.0451
0.0421
0.0407
0.0381
0.036
0.034
0.0319
0.0309
0.0292
0.0275
0.0265
0.0253
0.0234
0.0225
0.022
0.0206
0.0195
0.0187
0.0184
0.0171
0.016
0.0153
0.9831
0.9979
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
Appendix B: Sample Airfoil Coefficient Solutions
-0.5708
-0.7377
-0.9011
-1.084
-1.2921
-1.5223
-1.7751
-2.0491
-2.3345
-2.6245
-2.9452
-3.2686
-3.5906
-3.9593
-4.3346
-4.705
-5.0237
-5.3733
-5.5879
-5.6481
-5.564
-5.2735
-4.9148
-4.5714
-1.5562
-1.6275
-1.4831
-1.4555
-1.6168
-1.3295
-1.4501
-1.3046
-1.3251
-1.4957
-1.2453
-1.2466
-1.3561
-1.1724
-1.1841
-1.2783
-1.2145
-1.1456
-1.1518
-1.2064
-1.2046
-1.0733
-1.0851
-1.1368
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0