Cuboid Quasi-Steady Loads Report

Quasi Steady Air Loads Report: CUBOID
Sorin Pirau, Alexander Forbes, Brandon Liberi,
Vrishank Raghav, Narayanan Komerath
Experimental Aerodynamics and Concepts Group
Daniel Guggenheim School of Aerospace Engineering
Georgia Institute of Technology
Atlanta, Georgia USA 30332-0150
Contact: [email protected]
February 24, 2015
Report Number ADLP2015022401
February 24, 2015
1
Summary
The variation of quasi-steady air loads with attitude on a cuboid model is described. The loads are
ensemble-averaged with 1-degree resolution using the Continuous Rotation technique, with a stepper
motor rotating at 0.99 RPM above a 6-DOF load cell. The azimuthal variation is reduced to a Fourier
series. A truncated series of Fourier coefficients is listed. This is seen to represent the load variations
with adequate accuracy for use in dynamic simulation. Cases included those at zero pitch and at 10
degrees pitch.
2
Contents
1 Description
4
2 Model Geometry
6
3 Results-Fourier Coefficients
3.1 8.94 m/s (20 Mph), Yaw Rotation . . . . . . . . . . . . .
3.2 8.94 m/s (20 Mph), Pitch of -10 degrees, Yaw Rotation .
3.3 8.94 m/s (20 Mph), Pitch Rotation . . . . . . . . . . . .
3.4 13.41 m/s (30 Mph), Yaw Rotation . . . . . . . . . . . .
3.5 13.41 m/s (30 Mph), Pitch of -10 degrees, Yaw Rotation
3.6 13.41 m/s (30 Mph), Pitch Rotation . . . . . . . . . . .
3
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7
7
12
17
22
27
32
Chapter 1
Description
The main body of the CONEX is composed of wood, where the sides of the CONEX are connected
through 8 1/8 inch screws which are drilled flush against the surface. The CONEX has a metal support
in the center which attaches to a thin cylindrical rod of length 0.267 m (10.5in) and diameter of 0.0095
m (3/8 in). The metal support inside, ensures that the metal rod is flush to the surface of the wood
and there are no gaps between the rod and the CONEX to interact with the flow. It is to be noted that
the metal rod goes inside the CONEX, and thus only 0.219 m (8.625in) of the metal rod is exposed to
the airflow.
The cylindrical rod is used as a mounting strut for the model. A continuous rotation method is used
in order to obtain load data about the CONEX for incrimental changes in yaw. The model is rotated
at an RPM of 0.99 for 10 revolutions, after which the data obtained is phase averaged and ensemble
averaged to a resolution of 1 degree. After the data is averaged, Fast Fourier Transform can be used on
the data to estimate the coefficients of a trigonometric polynomial that interpolates each individual set
of data, Cx, Cy, Cz, CMx, CMy, CMz. Only the first 20 coefficients are used, thus during simulations,
it is more efficient to interpolate/calculate the load values from the Fourier coefficients than by looking
up and extracting the required values from a data set. This paper lists the coefficients for these Fourier
series representations so that they may be used instead of the actual data points. In order to interpolate
the data, a trigonometric polynomial of the form shown in Equation 1.1 was used.
y = a0 + b0 + a1 cos(2π(x/360)) + b1 sin(2π(x/360) + a2 cos(2π(2x/360)) + b2 sin(2π(2x/360)+
... + a2 0cos(2π(20x/360)) + b2 0sin(2π(20x/360) (1.1)
The conditions for which the CONEX was tested are listed before each data set and the geometric
dimensions of the CONEX are listed in Chapter 2 of this report.
The CONEX box was tested for three configurations at two different velocities/Reynolds numbers.
The first configuration is a 0 degree pitch yaw rotation, where at 0 degrees yaw the LxH (length times
height) side is facing the flow (the model is mounted on its LxW side, which is facing downward). The
second configuration is a -10 degree pitch yaw rotation, where again the LxH side is facing the flow.
For the last configuration, the CONEX was rotated and mounted on its WxH side, where at 0 degrees
yaw the LxW side is facing the flow. It is to be noted, that this is esentially a pitch rotation at 0 degree
yaw. The dimensions of Length, Width, and Height are given in the Model Geometry section.
4
Figure 1.1: CONEX model
5
Chapter 2
Model Geometry
Table 2.1: Experimental Velocities Tested
Experimental Velocities Tested
Velocity (mph) Velocity (m/s)
20
8.94
30
13.41
Table 2.2: Model Geometry
Model Geometry
CONEX Length (m)
CONEX Width (m)
CONEX Height (m)
Area Used for Coefficients (m2 )
Moment Arm Used for Coefficients (m)
Frequency (deg/s)
6
0.2334
0.169
0.173
0.03945
0.2334
5.94
Chapter 3
Results-Fourier Coefficients
3.1 8.94 m/s (20 Mph), Yaw Rotation
Table 3.1: Experimental Conditions
Experimental Conditions
Tempterature (F)
73.5
Pressure (inHg)
30.24
3
Density Calculated (kg/m ) 1.205
Density Used (kg/m3 )
1.205
Table 3.2: A-Fourier Coefficients
Number
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
CD
1.2334E+00
1.7948E-03
2.6571E-01
-3.6634E-03
-9.6961E-02
-2.4826E-04
2.4506E-02
-9.3983E-04
-1.1785E-02
-1.0810E-03
1.4320E-02
4.0361E-04
-7.2773E-03
1.0411E-03
5.6313E-03
1.1510E-04
-3.6744E-03
-1.9311E-03
3.5362E-03
-1.4666E-03
A-Fourier Coefficients
CY
CZ
CMX
-2.4927E-02 -1.8473E-01 4.0098E-03
1.4519E-02 -1.3917E-02 -6.9708E-02
-3.7055E-02 3.7029E-02 5.7320E-02
-1.1137E-02 -1.7006E-02 1.9612E-02
-2.2105E-02 -3.6111E-03 4.2128E-02
2.7207E-03 -6.7977E-04 -3.8477E-03
-1.3765E-02 2.4957E-03 2.3125E-02
-4.6265E-03 1.1701E-02 7.5894E-03
-1.9935E-02 6.7109E-03 3.4401E-02
8.0246E-04 2.8345E-03 -1.8717E-03
-1.5770E-02 6.7983E-03 2.6824E-02
-1.5479E-03 2.1754E-03 2.8135E-03
-6.2286E-03 -2.3094E-03 1.1662E-02
9.1885E-04 -3.1927E-04 -1.3465E-03
-4.1618E-03 -5.1823E-03 7.1073E-03
-1.7571E-03 2.2620E-04 2.9064E-03
1.9773E-03 -2.3812E-03 -3.4498E-03
7.7684E-05 -3.7135E-03 -4.1234E-04
2.5883E-03 -7.5755E-04 -5.0395E-03
3.9018E-04 -3.0302E-03 -7.2636E-04
7
CMY
2.1072E+00
1.2630E-03
4.7114E-01
-7.7226E-03
-1.7331E-01
8.8415E-04
4.4811E-02
1.5238E-03
-1.9004E-02
-1.4595E-03
2.8293E-02
-4.3080E-04
-1.3141E-02
1.4681E-03
1.0021E-02
8.4544E-04
-7.4426E-03
-3.0174E-03
5.8339E-03
-2.8907E-03
CMZ
-5.6931E-02
9.8569E-03
-1.3084E-02
-1.2522E-03
-8.4345E-03
5.2264E-05
4.9735E-03
1.9466E-04
-1.0341E-02
-1.4951E-04
6.9365E-03
4.4514E-04
-3.6517E-03
-1.4054E-04
4.8399E-03
2.8722E-04
-1.1726E-03
-1.9493E-04
2.8704E-03
4.1202E-04
Table 3.3: B-Fourier Coefficients
Number
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
CD
0
1.0166E-02
-3.5965E-02
-6.7164E-04
2.0469E-02
1.4306E-03
-9.7395E-03
-1.3775E-03
2.1452E-03
-4.4783E-05
-1.2108E-02
-3.7221E-04
2.4065E-03
-2.2767E-04
-6.9457E-03
-3.1205E-05
1.3694E-03
1.0543E-03
-6.1975E-03
2.6701E-04
B-Fourier Coefficients
CY
CZ
CMX
0
0
0
-5.1489E-04 2.9728E-02 -3.3102E-04
-3.8042E-01 6.5665E-02 6.6653E-01
5.7696E-03 -3.4591E-03 -1.0393E-02
-1.0008E-01 2.5301E-02 1.7256E-01
1.6159E-03 -7.6410E-03 -3.7782E-03
-4.1349E-02 9.7540E-03 7.2733E-02
-3.7203E-04 -1.2614E-05 1.5620E-03
-4.0864E-02 8.9582E-03 7.2053E-02
-1.4178E-03 -2.0393E-03 2.9681E-03
-2.9582E-02 3.7834E-03 5.2768E-02
2.5948E-03 -2.4281E-04 -4.7133E-03
-6.1760E-03 1.7952E-03 1.0827E-02
-8.5556E-05 -4.5785E-04 3.4013E-04
-5.1981E-03 5.8534E-03 8.7060E-03
-1.7699E-03 4.1620E-03 3.1996E-03
3.2399E-03 1.2013E-03 -6.0315E-03
-2.7318E-03 3.8640E-03 4.6496E-03
2.4784E-03 -9.0964E-04 -4.2490E-03
2.0611E-04 6.0898E-04 -6.6437E-04
8
CMY
0
5.8608E-02
-5.3323E-02
5.4666E-04
4.2032E-02
-1.5896E-03
-1.6899E-02
-2.2016E-03
6.1854E-03
3.4538E-04
-2.2572E-02
-3.9077E-04
4.8283E-03
-9.0341E-04
-1.2541E-02
-4.1323E-04
3.4879E-03
2.3314E-03
-1.0243E-02
9.7105E-04
CMZ
0
3.1225E-03
-2.7804E-02
6.2557E-04
-5.9287E-02
-1.0510E-03
1.6354E-02
1.4929E-04
-2.2548E-02
-6.8410E-04
1.2042E-02
4.3305E-04
-5.7231E-03
9.8427E-05
5.4533E-03
-1.1109E-04
-1.1507E-03
-1.7483E-04
2.8053E-03
-7.6084E-06
9
10
11
3.2 8.94 m/s (20 Mph), Pitch of -10 degrees, Yaw Rotation
Table 3.4: Experimental Conditions
Experimental Conditions
Tempterature (F)
73.5
Pressure (inHg)
30.24
3
Density Calculated (kg/m ) 1.205
Density Used (kg/m3 )
1.205
Table 3.5: A-Fourier Coefficients
Number
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
CD
1.1959E+00
-3.2335E-02
2.4488E-01
3.5568E-03
-1.2107E-01
1.5366E-03
1.2933E-02
2.1959E-03
-1.5476E-02
-2.5613E-04
2.3910E-02
-1.0204E-03
-9.7052E-04
-7.9471E-04
9.1370E-03
1.1796E-03
-6.3087E-03
1.8672E-03
2.8484E-03
8.2245E-04
A-Fourier Coefficients
CY
CZ
CMX
1.3335E-02 -6.0590E-02 -1.5043E-01
6.8380E-03 8.9899E-02 2.7797E-02
-1.2317E-02 2.7540E-02 1.5678E-02
-1.5633E-02 1.5283E-01 2.0963E-02
-5.8565E-03 -1.0209E-02 1.2526E-02
3.2683E-03 1.7396E-02 -6.1038E-03
-5.3515E-03 -4.7716E-03 8.1964E-03
-4.2857E-03 -1.6258E-02 7.7470E-03
-7.9780E-03 4.1793E-03 1.3042E-02
3.2793E-03 -2.2723E-03 -6.1626E-03
-6.2624E-03 8.6319E-03 9.9421E-03
-1.5817E-03 4.9748E-03 3.1861E-03
-6.9526E-03 3.6594E-03 1.1975E-02
2.3400E-03 -5.1527E-03 -3.9156E-03
-4.5201E-03 -1.9482E-03 7.5790E-03
-1.6256E-03 -6.6296E-03 2.9359E-03
-3.7309E-03 4.2965E-03 6.6042E-03
1.6481E-03 2.8699E-03 -2.8866E-03
-1.4159E-03 1.2311E-03 2.4060E-03
-4.0201E-04 4.1427E-04 8.9481E-04
12
CMY
2.4158E+00
-3.3503E-01
4.3462E-01
2.6794E-02
-2.1055E-01
1.9297E-03
2.4089E-02
-5.6510E-03
-2.6709E-02
1.6302E-03
4.4491E-02
3.8301E-03
-2.1867E-03
-3.6111E-03
1.7341E-02
-1.4656E-03
-9.7980E-03
2.9034E-03
5.3217E-03
2.8142E-03
CMZ
-5.4645E-02
-7.0137E-03
-1.0670E-02
-1.5984E-03
-1.2244E-03
3.0160E-04
2.5355E-03
-2.1324E-04
-4.5470E-03
-5.9030E-04
2.6935E-03
4.2935E-05
-2.5130E-03
-3.2377E-04
2.2132E-03
1.2896E-04
-9.5432E-04
-4.6692E-05
9.9567E-04
1.4069E-04
Table 3.6: B-Fourier Coefficients
Number
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
CD
0
4.5830E-03
-2.3771E-02
-3.0425E-03
1.5214E-02
1.0393E-03
-4.4056E-03
4.4304E-04
2.5539E-03
1.8650E-03
-7.9803E-03
3.4548E-05
-5.1849E-04
1.4131E-04
-3.5038E-03
-8.3822E-04
1.1935E-03
-1.4447E-04
-7.7921E-04
-9.0269E-04
B-Fourier Coefficients
CY
CZ
CMX
0
0
0
4.0249E-02 -3.3461E-02 -3.7389E-01
-3.5469E-01 8.5349E-02 6.2427E-01
-4.7066E-03 -8.0925E-03 1.3272E-02
-8.2722E-02 2.6771E-02 1.4868E-01
2.0883E-03 -1.1064E-02 -5.6368E-04
-4.0604E-02 1.1349E-02 7.2212E-02
2.3128E-03 1.0052E-03 -7.6547E-03
-4.1881E-02 1.1044E-02 7.3672E-02
3.6651E-03 2.2556E-04 -6.5818E-03
-3.0180E-02 6.0043E-03 5.3013E-02
2.1829E-03 -2.2245E-04 -1.8075E-03
-1.1002E-02 1.7792E-03 2.0187E-02
2.7325E-03 -2.9141E-03 -4.1403E-03
-1.8097E-02 6.0540E-03 3.1996E-02
1.3674E-03 -1.6076E-03 -3.2500E-03
-8.3591E-03 2.8114E-03 1.4936E-02
2.0660E-03 -1.3009E-03 -3.5333E-03
-5.9901E-03 3.3078E-03 1.0649E-02
1.2298E-03 8.3652E-04 -1.2292E-03
13
CMY
0
-3.5552E-02
-3.0006E-02
-4.5694E-03
2.8301E-02
2.3685E-04
-7.0999E-03
8.7364E-04
6.4694E-03
3.8976E-03
-1.3632E-02
-1.1462E-03
-3.7662E-04
-5.1752E-04
-5.8415E-03
-1.2491E-03
2.0943E-03
-1.3194E-04
-1.0108E-03
-2.0712E-03
CMZ
0
4.2238E-02
-2.3880E-02
-3.2764E-04
-5.8138E-02
-5.5812E-03
1.5810E-02
-3.2980E-04
-2.5856E-02
-2.7907E-03
1.1305E-02
5.1520E-04
-7.2169E-03
-1.2303E-03
5.8847E-03
-4.3129E-05
-3.3622E-03
-1.7888E-04
1.3831E-03
2.7936E-04
14
15
16
3.3 8.94 m/s (20 Mph), Pitch Rotation
Table 3.7: Experimental Conditions
Experimental Conditions
Tempterature (F)
73.5
Pressure (inHg)
30.24
3
Density Calculated (kg/m ) 1.205
Density Used (kg/m3 )
1.205
Table 3.8: A-Fourier Coefficients
Number
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
CD
1.2858E+00
-1.2375E-02
-3.4727E-02
-1.0506E-02
-5.8097E-02
1.8014E-03
7.2307E-03
1.1996E-03
3.2520E-02
-1.2746E-03
9.7587E-04
1.5420E-03
4.0949E-03
1.7073E-03
-2.1983E-03
-3.8462E-04
-4.3061E-03
-1.8957E-03
6.0926E-04
-1.3009E-03
A-Fourier Coefficients
CY
CZ
CMX
3.8363E-03 1.0317E+00 -1.5514E-01
1.3032E-03 1.1120E-03 -2.4959E-02
1.3339E-02 -1.0255E-02 -2.2953E-02
8.9459E-03 8.6599E-03 -1.6195E-02
-1.0767E-01 1.5677E-02 1.9039E-01
9.3981E-03 1.4203E-02 -1.7201E-02
-8.6840E-03 9.9867E-03 1.4434E-02
-9.2683E-04 4.5585E-03 1.4463E-03
-9.9494E-02 9.6215E-03 1.7523E-01
-7.6003E-03 9.6570E-04 1.3227E-02
9.1063E-04 -1.5109E-03 -1.9145E-03
4.0858E-04 -2.4588E-04 -8.1642E-04
-6.0000E-02 5.0208E-03 1.0661E-01
-1.9554E-03 -1.2459E-03 3.4756E-03
-7.7386E-03 -1.1624E-04 1.3593E-02
-4.5436E-03 -2.7813E-03 8.5960E-03
1.5736E-02 -9.6420E-03 -2.8213E-02
-3.2901E-03 -3.1300E-03 5.8085E-03
1.7793E-03 1.6333E-04 -2.9767E-03
-1.3144E-03 9.4963E-04 2.6183E-03
17
CMY
2.6097E+00
-1.2449E-01
-6.3997E-02
-1.8438E-02
-9.7854E-02
3.8655E-03
1.3227E-02
1.6064E-03
6.3015E-02
-2.9152E-03
4.1510E-04
3.0736E-03
1.0352E-02
3.5107E-03
-3.4863E-03
-1.1578E-03
-8.8902E-03
-3.7108E-03
1.1341E-03
-1.9759E-03
CMZ
-6.1625E-02
2.4198E-03
1.0893E-03
1.2598E-03
-1.9456E-02
-1.2027E-03
-1.1661E-03
-8.9205E-04
-1.1945E-02
-1.0482E-03
-8.5301E-04
-8.6701E-04
3.2312E-03
-4.7485E-04
-4.3825E-04
-2.3706E-04
4.6691E-03
1.8545E-04
-2.4437E-04
-1.6098E-05
Table 3.9: B-Fourier Coefficients
Number
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
CD
0
2.0377E-03
6.5687E-04
9.8286E-04
2.2948E-02
2.6742E-03
-2.0829E-03
-9.8990E-04
-2.4098E-02
8.8920E-04
1.6345E-03
-9.5457E-04
-1.6965E-02
-2.3616E-03
-1.5087E-03
-1.9376E-03
-2.7893E-03
-8.0042E-05
1.5206E-03
2.3110E-03
B-Fourier Coefficients
CY
CZ
CMX
0
0
0
3.6316E-02 -1.5994E-02 -1.7077E-01
7.5277E-02 -1.2091E-02 -1.3529E-01
3.2735E-02 -7.8788E-03 -5.9487E-02
-2.6594E-01 3.0556E-02 4.7390E-01
-5.1982E-03 -5.2354E-03 8.7552E-03
-1.1324E-02 -4.6847E-03 2.0420E-02
1.5604E-03 -3.0194E-03 -3.4522E-03
-1.0807E-01 1.1883E-02 1.9547E-01
3.8493E-04 1.3270E-03 -9.3998E-05
-1.0345E-02 2.9597E-03 1.8840E-02
-1.8685E-03 -2.9383E-03 3.6644E-03
-3.9937E-02 3.4613E-03 7.2197E-02
-1.7634E-03 1.7334E-03 2.8252E-03
-4.2188E-03 4.5426E-04 7.7115E-03
-3.0793E-03 9.3554E-04 5.5930E-03
1.1634E-02 6.8861E-03 -2.1234E-02
4.4507E-04 4.5594E-03 -6.3242E-04
1.0149E-02 2.3722E-03 -1.7997E-02
1.4118E-04 1.5873E-03 -1.5514E-04
18
CMY
0
2.4391E-02
-8.4108E-04
7.3947E-04
4.9556E-02
4.9301E-03
-2.9055E-03
-1.8982E-03
-4.0382E-02
2.3566E-03
3.9290E-03
-2.0258E-03
-3.0221E-02
-5.3055E-03
-3.3178E-03
-3.3474E-03
-5.1110E-03
8.0329E-04
2.3182E-03
4.0786E-03
CMZ
0
1.8939E-02
3.3471E-03
5.5412E-04
-6.2443E-02
-2.0348E-03
-1.9542E-03
-1.0205E-03
-1.1476E-02
-6.6028E-04
-1.1061E-03
-1.0941E-03
2.3349E-03
-7.8150E-07
1.6368E-04
5.1122E-06
1.4068E-03
-1.0543E-04
2.1628E-04
-1.5406E-04
19
20
21
3.4 13.41 m/s (30 Mph), Yaw Rotation
Table 3.10: Experimental Conditions
Experimental Conditions
Tempterature (F)
73.5
Pressure (inHg)
30.24
3
Density Calculated (kg/m ) 1.205
Density Used (kg/m3 )
1.205
Table 3.11: A-Fourier Coefficients
Number
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
CD
1.1357E+00
1.0307E-03
2.7053E-01
-3.9893E-03
-1.0286E-01
-1.7095E-03
2.6723E-02
-1.5736E-03
-1.2092E-02
-1.5011E-03
1.6272E-02
5.8210E-04
-8.2554E-03
1.4535E-03
8.1760E-03
1.1982E-03
-3.9560E-03
-1.1902E-03
6.5229E-03
-1.4050E-03
A-Fourier Coefficients
CY
CZ
CMX
5.9574E-03 -5.4652E-01 5.1737E-02
1.0162E-02 -5.2586E-03 -3.8274E-02
-1.9711E-02 2.1933E-02 2.8305E-02
-1.1643E-02 -1.9014E-02 2.0347E-02
-1.0901E-02 -2.2380E-02 2.0509E-02
2.0992E-03 -8.7467E-04 -2.8747E-03
-7.2309E-03 2.1449E-04 1.2485E-02
-3.9541E-03 1.0943E-02 6.7480E-03
-1.0280E-02 3.8301E-03 1.7462E-02
1.4267E-03 4.3933E-03 -2.9962E-03
-7.5559E-03 4.3424E-03 1.3386E-02
-1.6757E-03 3.4551E-03 2.5664E-03
-3.7723E-03 -6.8519E-03 6.3359E-03
5.7856E-04 1.2849E-03 -4.7968E-04
-1.9360E-03 -9.3530E-03 3.7384E-03
-1.4665E-03 -1.9047E-03 3.0283E-03
1.3466E-03 -4.8261E-03 -2.3602E-03
1.3305E-03 -4.0077E-03 -2.4617E-03
2.7833E-03 -7.4294E-04 -4.1261E-03
-1.9387E-04 -4.0753E-03 -7.3244E-05
22
CMY
2.1216E+00
-1.6008E-04
4.7572E-01
-8.5961E-03
-1.8334E-01
-1.5927E-03
4.8976E-02
2.2386E-04
-1.9199E-02
-1.9753E-03
3.1530E-02
1.4059E-05
-1.4988E-02
2.4010E-03
1.4643E-02
2.5715E-03
-8.0233E-03
-1.5811E-03
1.0766E-02
-2.6242E-03
CMZ
-4.8622E-02
9.2847E-03
-1.2076E-02
-1.7450E-03
-2.0948E-03
1.4989E-04
2.0884E-03
4.0310E-05
-5.4779E-03
-2.1394E-04
3.3639E-03
2.4851E-04
-1.9781E-03
-1.5804E-04
2.4792E-03
8.9202E-05
-7.5822E-04
-9.8362E-05
1.3408E-03
2.6299E-04
Table 3.12: B-Fourier Coefficients
Number
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
CD
0
7.7706E-03
-1.5751E-02
4.3254E-05
9.7216E-03
2.1967E-03
-5.3909E-03
-7.2485E-04
3.3976E-04
5.9766E-04
-6.9340E-03
-7.1526E-04
6.0739E-04
1.2458E-04
-3.4047E-03
3.6996E-04
6.6293E-04
4.9796E-04
-3.5910E-03
5.3891E-04
B-Fourier Coefficients
CY
CZ
CMX
0
0
0
3.8219E-04 6.2655E-02 -4.8447E-03
-3.8763E-01 2.9505E-02 6.7408E-01
5.2288E-03 5.8770E-03 -9.1197E-03
-9.9011E-02 1.8477E-02 1.6849E-01
2.0297E-03 -1.1013E-03 -3.7211E-03
-4.2002E-02 7.3006E-03 7.4504E-02
-2.0978E-03 6.2488E-03 3.5118E-03
-4.4850E-02 8.7881E-03 7.8132E-02
-3.9475E-04 2.6440E-03 8.1650E-04
-3.3024E-02 2.6049E-03 5.7813E-02
1.8966E-03 4.1330E-03 -4.4820E-03
-6.5957E-03 2.6414E-03 1.1881E-02
1.3286E-03 3.1794E-04 -2.5222E-03
-6.0609E-03 5.4757E-03 1.0481E-02
-9.6953E-04 3.2682E-03 1.8096E-03
5.6757E-03 2.2506E-03 -1.0407E-02
-2.1358E-03 1.1047E-03 2.9651E-03
3.7421E-03 2.3746E-04 -6.6274E-03
1.0033E-03 -1.6004E-03 -1.4766E-03
23
CMY
0
2.5927E-02
-2.1013E-02
8.1246E-04
2.0200E-02
-5.3196E-04
-9.8652E-03
-7.7569E-04
3.0132E-03
9.0799E-04
-1.2808E-02
-1.5439E-03
1.3064E-03
-4.1922E-04
-6.6142E-03
5.8377E-04
1.3300E-03
1.2742E-03
-6.3280E-03
1.1069E-03
CMZ
0
3.2468E-03
-2.9063E-02
6.2709E-04
-6.0394E-02
-1.0782E-03
1.6729E-02
-6.1800E-06
-2.5019E-02
-9.6998E-04
1.3528E-02
2.5798E-04
-6.7153E-03
1.3441E-04
6.6708E-03
-5.5667E-05
-1.6202E-03
-3.0903E-04
3.7742E-03
-9.6687E-05
24
25
26
3.5 13.41 m/s (30 Mph), Pitch of -10 degrees, Yaw Rotation
Table 3.13: Experimental Conditions
Experimental Conditions
Tempterature (F)
73.5
Pressure (inHg)
30.24
3
Density Calculated (kg/m ) 1.205
Density Used (kg/m3 )
1.205
Table 3.14: A-Fourier Coefficients
Number
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
CD
1.1729E+00
-5.7610E-03
2.5438E-01
4.7111E-03
-1.2895E-01
2.0294E-03
1.5300E-02
2.0566E-03
-1.6112E-02
-1.2464E-03
2.5530E-02
-1.4723E-03
-2.4460E-04
-2.0756E-03
1.1143E-02
5.4795E-04
-6.6470E-03
1.2831E-03
2.7297E-03
9.4569E-04
A-Fourier Coefficients
CY
CZ
CMX
4.0327E-02 -3.4321E-02 -1.2035E-01
4.9134E-03 1.0624E-01 8.6384E-03
-6.6592E-04 1.7152E-02 -8.7197E-03
-1.6732E-02 1.6099E-01 2.2777E-02
8.5398E-04 -1.3447E-02 1.2083E-03
2.1184E-03 1.9935E-02 -4.3511E-03
1.2825E-03 -6.4902E-03 -3.2253E-03
-5.4182E-03 -1.9985E-02 1.2144E-02
-9.6181E-04 1.2012E-03 1.5488E-03
1.2648E-03 -1.8931E-03 -2.8255E-03
5.4377E-04 5.5348E-03 -2.0589E-03
-2.9508E-03 6.5471E-03 4.9007E-03
-2.7721E-03 1.9111E-03 4.4370E-03
1.9095E-03 -3.4597E-03 -2.4132E-03
-3.1585E-04 -2.9944E-03 -3.5744E-04
-5.6386E-04 -6.6915E-03 2.0325E-03
-2.9570E-04 2.5251E-03 1.4506E-03
4.4861E-04 2.8602E-03 -1.2346E-03
5.7656E-04 -7.8072E-04 -1.0754E-03
-8.3263E-04 7.4981E-04 1.0343E-03
27
CMY
2.2604E+00
-1.2123E-01
4.4899E-01
2.9128E-02
-2.2473E-01
2.0095E-03
2.7881E-02
-6.7094E-03
-2.8606E-02
3.4070E-04
4.6309E-02
3.5399E-03
-1.6240E-03
-5.7244E-03
2.0538E-02
-2.6856E-03
-1.0676E-02
1.7134E-03
5.0865E-03
3.1254E-03
CMZ
-4.0896E-02
-8.1514E-03
-1.0089E-02
-1.5192E-03
3.5238E-03
7.3704E-04
8.5544E-04
-2.8989E-04
-7.8758E-04
-1.0250E-04
5.9250E-04
-1.5373E-05
-6.6630E-04
-7.4729E-05
3.8702E-04
1.8337E-04
1.6551E-04
-3.6788E-05
3.4704E-04
1.3454E-04
Table 3.15: B-Fourier Coefficients
Number
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
CD
0
4.8042E-03
-1.1945E-02
-2.0042E-03
6.1005E-03
8.2401E-04
-1.3304E-03
2.1007E-04
1.3174E-03
2.3608E-03
-2.2241E-03
-5.0603E-04
-3.2228E-04
3.5512E-04
-1.7159E-03
-3.2315E-04
-8.0839E-04
5.5519E-04
1.9702E-06
5.2110E-05
B-Fourier Coefficients
CY
CZ
CMX
0
0
0
1.3407E-02 -4.9746E-03 -1.5696E-01
-3.7218E-01 9.1314E-02 6.5625E-01
-4.9518E-03 -4.0164E-04 1.4593E-02
-8.2519E-02 2.6381E-02 1.4797E-01
3.8371E-03 -8.4998E-03 -2.1429E-03
-4.2620E-02 1.0467E-02 7.6557E-02
3.1393E-03 -6.0491E-05 -9.0947E-03
-4.4489E-02 1.1411E-02 7.8325E-02
3.8949E-03 -1.4517E-04 -7.2803E-03
-3.3214E-02 9.0203E-03 5.8318E-02
6.6713E-04 -1.0270E-03 9.3319E-05
-1.1918E-02 4.7987E-03 2.2486E-02
3.5109E-03 -5.1260E-03 -6.2613E-03
-2.0764E-02 7.0703E-03 3.8242E-02
2.6993E-03 -3.0683E-03 -4.4655E-03
-1.0800E-02 4.4193E-03 1.9843E-02
3.6287E-03 -5.2921E-04 -6.4487E-03
-7.2435E-03 3.0774E-03 1.2456E-02
1.5227E-03 1.3477E-03 -1.5768E-03
28
CMY
0
-1.6353E-02
-9.2976E-03
-1.8265E-03
1.1553E-02
-1.1152E-04
-1.7031E-03
-6.8336E-04
3.8274E-03
4.4218E-03
-3.0481E-03
-1.3115E-03
5.0876E-05
-8.7440E-04
-2.1329E-03
-1.0412E-03
-8.9597E-04
5.9087E-04
6.0140E-04
-1.6907E-04
CMZ
0
4.0743E-02
-2.5624E-02
-7.8144E-04
-6.0117E-02
-5.6386E-03
1.6145E-02
-2.4479E-04
-2.7887E-02
-2.6327E-03
1.1496E-02
6.7350E-04
-8.0148E-03
-1.0585E-03
6.0590E-03
1.9206E-04
-3.7185E-03
-6.7584E-05
1.4551E-03
3.6493E-04
29
30
31
3.6 13.41 m/s (30 Mph), Pitch Rotation
Table 3.16: Experimental Conditions
Experimental Conditions
Tempterature (F)
73.5
Pressure (inHg)
30.24
3
Density Calculated (kg/m ) 1.205
Density Used (kg/m3 )
1.205
Table 3.17: A-Fourier Coefficients
Number
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
CD
1.3271E+00
-2.8727E-03
-3.4831E-02
-1.2105E-02
-5.7338E-02
8.5168E-05
5.4982E-03
1.1758E-03
3.2886E-02
-1.2079E-03
1.7809E-03
2.2472E-03
4.2433E-03
1.0486E-03
6.4935E-04
-1.6466E-03
-1.0172E-03
3.7336E-04
-3.8928E-04
-7.7152E-04
A-Fourier Coefficients
CY
CZ
CMX
7.7985E-02 8.4563E-01 -1.8128E-01
5.7706E-03 4.2186E-03 -2.0420E-02
1.3095E-02 -1.2454E-02 -2.1799E-02
6.5662E-03 8.9888E-03 -1.2573E-02
-1.0710E-01 1.2040E-02 1.8968E-01
-2.5455E-03 1.2260E-02 3.6618E-03
-1.0442E-02 3.4185E-03 1.7460E-02
-1.6532E-03 4.5362E-03 2.3561E-03
-1.0234E-01 1.0672E-02 1.8190E-01
3.0533E-03 -2.5196E-03 -5.6166E-03
3.5413E-04 -1.3661E-03 -7.7280E-04
-2.0994E-03 -5.4418E-04 2.5496E-03
-4.0547E-02 2.7438E-03 7.3784E-02
-7.2851E-03 -1.9486E-03 1.2906E-02
-3.5760E-03 -3.4605E-04 7.2489E-03
2.1862E-04 -4.0409E-03 1.0906E-03
7.4712E-03 -5.5476E-03 -1.2960E-02
1.2151E-03 -3.1113E-03 -1.7694E-03
-1.7756E-03 1.5960E-03 3.0729E-03
-3.4228E-03 1.2243E-03 6.0339E-03
32
CMY
2.5206E+00
-4.7343E-02
-6.4590E-02
-2.1437E-02
-9.8125E-02
2.0682E-03
1.1272E-02
2.0320E-03
6.4304E-02
-2.8417E-03
2.9999E-03
3.8357E-03
9.5275E-03
2.1456E-03
1.5924E-03
-3.1383E-03
-2.6538E-03
6.5924E-04
-3.4027E-04
-8.1854E-04
CMZ
-5.7118E-02
2.3643E-03
7.6186E-04
1.1123E-03
-1.8767E-02
-1.2304E-03
-1.4529E-03
-9.9164E-04
-1.1860E-02
-8.7077E-04
-8.3370E-04
-7.3888E-04
3.5357E-03
-3.8932E-04
-3.7795E-04
-5.6930E-05
4.4261E-03
6.6736E-05
-1.8216E-04
-3.6121E-05
Table 3.18: B-Fourier Coefficients
Number
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
CD
0
-1.9748E-03
2.9315E-03
2.3573E-03
2.1361E-02
2.4147E-03
-3.1912E-03
-2.2561E-03
-2.0610E-02
3.7741E-04
1.2673E-03
-5.0190E-04
-1.2719E-02
-1.3907E-03
-1.1486E-03
-1.0448E-04
-4.7151E-03
5.4681E-05
8.4419E-04
1.2673E-03
B-Fourier Coefficients
CY
CZ
CMX
0
0
0
2.8050E-02 1.2162E-03 -1.0057E-01
9.1972E-02 -8.1647E-03 -1.6623E-01
3.8202E-02 -4.8104E-03 -6.9366E-02
-2.3987E-01 2.6895E-02 4.3012E-01
-5.8587E-03 -3.4742E-03 1.0143E-02
-1.8352E-02 -3.1995E-03 3.2763E-02
3.3677E-03 -1.7226E-03 -6.7089E-03
-1.2750E-01 1.6449E-02 2.3089E-01
-6.7777E-04 4.5400E-03 1.4113E-03
-5.6691E-03 2.5079E-03 1.0080E-02
-3.7629E-03 6.8924E-04 6.6539E-03
-3.1352E-02 6.3396E-03 5.7028E-02
3.8839E-03 1.9824E-03 -6.4251E-03
-3.6228E-03 9.2829E-04 6.5721E-03
-3.8785E-03 2.4153E-03 6.7805E-03
1.2614E-02 7.0423E-03 -2.3672E-02
-6.5533E-03 3.8627E-03 1.0722E-02
2.6235E-03 1.6964E-03 -3.5683E-03
4.2807E-03 1.7736E-03 -6.6938E-03
33
CMY
0
2.7185E-03
7.5206E-04
2.2212E-03
4.3955E-02
3.0833E-03
-6.2184E-03
-4.0809E-03
-3.5506E-02
2.0225E-03
2.7132E-03
-1.2561E-03
-2.3129E-02
-3.4078E-03
-2.7434E-03
-1.0555E-04
-9.8005E-03
5.3926E-04
1.3885E-03
1.8664E-03
CMZ
0
1.8194E-02
3.8215E-03
7.8913E-04
-6.1801E-02
-2.0308E-03
-2.0043E-03
-1.0877E-03
-1.2322E-02
-1.0124E-03
-1.1559E-03
-8.5363E-04
2.5851E-03
-1.2531E-04
2.3296E-04
5.6670E-05
1.6203E-03
-1.5508E-04
2.5657E-05
-9.3929E-05
34
35
36