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Pioneer -- Nonlinear Model

Graduate Research done by Jeff Scott
Advisor: Prof. Michael Selig
Applied Aerodynamics Group
Department of Aeronautical and Astronautical Engineering
University of Illinois at Urbana-Champaign, Urbana, Illinois 61801

Last updated April 10, 2000

The nonlinear aerodynamics model uses tables of aerodynamic coefficients to approximate actual aircraft behavior. The data input into the simulator is listed in the following tables:

Geometry
Variable Variable
in Code 		Description Units Value(s) Source Notes
b bw wingspan ft 16.9 Bray pg 33
cbar wing mean aerodynamic chord ft 1.80 Bray pg 33
S Sw wing surface area ft2 30.42 Bray pg 33

Control Surface Geometry
Variable Variable
in Code 		Description Units Value(s) Source Notes
emax demax maximum elevator deflection deg +20 Bray pg 31
emin demin minimum elevator deflection deg -20 Bray pg 31
amax damax maximum aileron deflection deg +20 Bray pg 31
amin damin minimum aileron deflection deg -20 Bray pg 31
rmax drmax maximum rudder deflection deg +20 Bray pg 31
rmin drmin minimum rudder deflection deg -20 Bray pg 31

Mass Data
Variable Variable
in Code 		Description Units Value(s) Source Notes
GTOW Weight gross takeoff weight lb 420 Bray pg 33 converted to Mass
[slug/ft3] in code
Ixx I_xx roll inertia slug ft2 34.832 IAI (manufacturer)
MSS notes
Iyy I_yy pitch inertia slug ft2 67.08 IAI (manufacturer)
MSS notes
Izz I_zz yaw inertia slug ft2 82.22 IAI (manufacturer)
MSS notes
Ixz I_xz lateral cross inertia slug ft2 -4.902 IAI (manufacturer)
MSS notes

Propulsion Data
Variable Variable
in Code 		Description Units Value(s) Source Notes
Tmax simpleSingleMaxThrust maximum thrust lb 150 - approximated from
max power of 27 hp

Aerodynamic Data
Variable Variable
in Code 		Description Units Value(s) Source Notes
CD CDfa drag coefficient vs. angle of attack - 
 alpha    CD   
  -8    0.0734
  -7    0.0674
  -6    0.0629
  -5    0.0597
  -4    0.0576
  -3    0.0568
  -2    0.0569
  -1    0.0580
   0    0.0601
   1    0.0630
   2    0.0668
   3    0.0713
   4    0.0767
   5    0.0830
   6    0.0900
   7    0.0980
   8    0.1069
   9    0.1167
  10    0.1276
  11    0.1397
  12    0.1530
  13    0.1676
  14    0.1837
  15    0.2014
  16    0.2209
  17    0.2423
 Bray pg 50
Table 4.7 		in deg
CD CDfade change in drag due to elevator - 
 alpha   e=-20  e=-15  e=-10   e=-5    e=5   e=10   e=15   e=20  
  -7     0.0231   0.0178   0.0111   0.0058  -0.0028  -0.0053  -0.0063  -0.0029
  -6     0.0209   0.0155   0.0095   0.0050  -0.0021  -0.0037  -0.0043  -0.0007
  -5     0.0187   0.0135   0.0081   0.0043  -0.0015  -0.0024  -0.0025   0.0012
  -4     0.0166   0.0117   0.0069   0.0037  -0.0010  -0.0014  -0.0010   0.0028
  -3     0.0147   0.0101   0.0057   0.0031  -0.0006  -0.0005   0.0002   0.0042
  -2     0.0129   0.0086   0.0047   0.0025  -0.0003   0.0002   0.0013   0.0053
  -1     0.0113   0.0073   0.0038   0.0020   0.0000   0.0008   0.0022   0.0064
   0     0.0098   0.0061   0.0030   0.0016   0.0003   0.0013   0.0031   0.0074
   1     0.0086   0.0050   0.0022   0.0011   0.0005   0.0018   0.0039   0.0082
   2     0.0074   0.0040   0.0015   0.0007   0.0007   0.0022   0.0046   0.0091
   3     0.0063   0.0030   0.0008   0.0003   0.0010   0.0026   0.0053   0.0099
   4     0.0053   0.0020   0.0001  -0.0001   0.0012   0.0030   0.0060   0.0108
   5     0.0043   0.0010  -0.0006  -0.0005   0.0014   0.0034   0.0068   0.0117
   6     0.0031   0.0000  -0.0013  -0.0009   0.0016   0.0039   0.0076   0.0126
   7     0.0017  -0.0010  -0.0020  -0.0013   0.0018   0.0044   0.0084   0.0136
   8     0.0001  -0.0020  -0.0027  -0.0018   0.0020   0.0050   0.0093   0.0147
   9    -0.0020  -0.0031  -0.0035  -0.0022   0.0023   0.0056   0.0102   0.0158
  10    -0.0046  -0.0042  -0.0042  -0.0027   0.0025   0.0063   0.0112   0.0170
  11    -0.0079  -0.0054  -0.0050  -0.0032   0.0028   0.0070   0.0122   0.0182
  12    -0.0120  -0.0067  -0.0058  -0.0037   0.0031   0.0078   0.0133   0.0195
  13    -0.0171  -0.0080  -0.0067  -0.0043   0.0035   0.0086   0.0144   0.0209
  14    -0.0234  -0.0094  -0.0075  -0.0048   0.0038   0.0095   0.0155   0.0222
  15    -0.0311  -0.0109  -0.0084  -0.0054   0.0041   0.0103   0.0167   0.0236
  16    -0.0403  -0.0125  -0.0093  -0.0060   0.0045   0.0111   0.0177   0.0250
  17    -0.0543  -0.0141  -0.0102  -0.0066   0.0048   0.0119   0.0188   0.0263
 Bray pg 45
Table 4.6 		in deg
e in deg

e positive down

CL CLfa lift coefficient vs. angle of attack - 
 alpha     CL  
  -8    -0.384
  -7    -0.294
  -6    -0.202
  -5    -0.107
  -4    -0.010
  -3     0.088
  -2     0.187
  -1     0.286
   0     0.385
   1     0.483
   2     0.580
   3     0.674
   4     0.766
   5     0.855
   6     0.940
   7     1.022
   8     1.098
   9     1.170
  10     1.235
  11     1.295
  12     1.347
  13     1.392
  14     1.430
  15     1.458
  16     1.478
  17     1.488
 Bray pg 50
Table 4.7 		in deg
CL CL_adot lift due to angle of attack rate 1/rad 2.42 Bray pg 33
CLq CL_q lift due to pitch rate 1/rad 8.05 Bray pg 33
CL CLfade change in lift due to elevator - 
 alpha  e=-20  e=-15  e=-10   e=-5   e=5   e=10  e=15  e=20 
  -7    -0.088   -0.075   -0.057   -0.036   0.025   0.058   0.093   0.100
  -6    -0.093   -0.079   -0.061   -0.038   0.026   0.059   0.093   0.101
  -5    -0.098   -0.083   -0.064   -0.040   0.027   0.060   0.094   0.101
  -4    -0.103   -0.087   -0.067   -0.041   0.027   0.061   0.095   0.102
  -3    -0.106   -0.091   -0.070   -0.043   0.028   0.062   0.096   0.103
  -2    -0.110   -0.094   -0.072   -0.044   0.029   0.063   0.097   0.104
  -1    -0.113   -0.097   -0.074   -0.045   0.030   0.064   0.098   0.106
   0    -0.116   -0.100   -0.076   -0.045   0.030   0.065   0.099   0.107
   1    -0.118   -0.102   -0.078   -0.045   0.031   0.066   0.099   0.108
   2    -0.119   -0.105   -0.079   -0.045   0.031   0.066   0.100   0.110
   3    -0.121   -0.107   -0.079   -0.045   0.032   0.067   0.100   0.111
   4    -0.122   -0.108   -0.080   -0.045   0.032   0.067   0.100   0.112
   5    -0.122   -0.110   -0.080   -0.044   0.032   0.068   0.100   0.113
   6    -0.123   -0.111   -0.080   -0.043   0.032   0.068   0.100   0.113
   7    -0.123   -0.111   -0.080   -0.042   0.032   0.068   0.099   0.114
   8    -0.122   -0.111   -0.079   -0.041   0.032   0.068   0.098   0.113
   9    -0.122   -0.111   -0.078   -0.040   0.032   0.067   0.096   0.113
  10    -0.121   -0.110   -0.077   -0.038   0.032   0.066   0.094   0.111
  11    -0.119   -0.109   -0.075   -0.037   0.031   0.065   0.092   0.110
  12    -0.118   -0.108   -0.073   -0.035   0.030   0.064   0.089   0.107
  13    -0.116   -0.106   -0.071   -0.033   0.029   0.062   0.086   0.104
  14    -0.114   -0.103   -0.068   -0.031   0.028   0.061   0.082   0.100
  15    -0.112   -0.100   -0.065   -0.029   0.027   0.058   0.078   0.096
  16    -0.109   -0.097   -0.062   -0.027   0.025   0.055   0.073   0.090
  17    -0.107   -0.093   -0.058   -0.025   0.024   0.052   0.068   0.084
 Bray pg 41
Table 4.4 		in deg
e in deg

e positive down

Cm Cmfa pitch moment coefficient vs. alpha - 
 alpha     Cm  
  -8     0.411
  -7     0.39
  -6     0.365
  -5     0.338
  -4     0.309
  -3     0.279
  -2     0.251
  -1     0.222
   0     0.194
   1     0.167
   2     0.139
   3     0.11
   4     0.08
   5     0.047
   6     0.012
   7    -0.027
   8    -0.07
   9    -0.116
  10    -0.168
  11    -0.223
  12    -0.281
  13    -0.342
  14    -0.404
  15    -0.465
  16    -0.522
  17    -0.573
 Bray pg 50
Table 4.7 		in deg
Cm Cm_adot pitch moment due to angle of attack rate 1/rad -11.0 Bray pg 33
Cmq Cm_q pitch moment due to pitch rate 1/rad -36.6 Bray pg 33
Cm Cmfade change in pitch moment due to elevator - 
 alpha e=-25  e=-20   e=-15  e=-10   e=-5    e=0    e=5   e=10   e=15   e=20   
  -6    0.9219   0.8532   0.7722   0.6464   0.5099   0.3524   0.2042   0.0376  -0.1100  -0.1353
  -4    0.8735   0.8031   0.7138   0.5998   0.4673   0.3050   0.1561  -0.0146  -0.1606  -0.1817
  -2    0.8270   0.7546   0.6717   0.5590   0.4248   0.2505   0.1051  -0.0750  -0.2137  -0.2356
   0    0.7798   0.7073   0.6258   0.5156   0.3705   0.1922   0.0403  -0.1391  -0.2678  -0.3001
   2    0.7413   0.6698   0.5939   0.4682   0.3111   0.1331  -0.0198  -0.1921  -0.3162  -0.3675
   4    0.6706   0.5983   0.5384   0.4039   0.2426   0.0681  -0.0833  -0.2594  -0.3780  -0.4532
   6    0.5870   0.5275   0.4621   0.3265   0.1675  -0.0041  -0.1556  -0.3327  -0.4518  -0.5296
   8    0.5293   0.4822   0.4109   0.2551   0.0901  -0.0826  -0.2472  -0.4179  -0.5384  -0.6121
  10    0.4276   0.3743   0.3178   0.1513  -0.0115  -0.1771  -0.3376  -0.5038  -0.6162  -0.6925
  12    0.3045   0.2520   0.2058   0.0404  -0.1199  -0.2850  -0.4361  -0.5937  -0.6994  -0.7772
  13    0.2379   0.1943   0.1426  -0.0216  -0.1775  -0.3435  -0.4882  -0.6446  -0.7465  -0.8266
  14    0.1698   0.1367   0.0705  -0.0911  -0.2419  -0.4058  -0.5455  -0.7024  -0.8015  -0.8897
  15    0.1088   0.0721   0.0028  -0.1512  -0.3048  -0.4655  -0.6097  -0.7536  -0.8507  -0.9399
  16    0.0503   0.0109  -0.0594  -0.2198  -0.3693  -0.5284  -0.6657  -0.8052  -0.9030  -0.9818
  17   -0.0060  -0.0452  -0.1230  -0.2834  -0.4290  -0.5830  -0.7117  -0.8406  -0.9229  -0.9877
  18   -0.0704  -0.1072  -0.1827  -0.3425  -0.4869  -0.6260  -0.7409  -0.8481  -0.9051  -0.9575
  19   -0.1576  -0.1668  -0.2384  -0.3938  -0.5246  -0.6414  -0.7367  -0.8320  -0.8863  -0.9439
  20   -0.2624  -0.2034  -0.2822  -0.4234  -0.5369  -0.6366  -0.7260  -0.8175  -0.8832  -0.9447
 Bray pg 34
Fig. 4.2 		in deg
e in deg

e positive down

CY CY_beta side force fue to sideslip angle 1/rad -0.819 Bray pg 33
CYp CY_p side force due to roll rate 1/rad none not available
CYr CY_r side force due to yaw rate 1/rad none not available
CYa CY_da side force due to aileron 1/rad none not available
CY CYfbetadr change in side force due to rudder - 
 beta  r=-20  r=0   r=20    
 -20     0.19   -0.05   -0.25
   0     0.24    0.00   -0.22
  20     0.29    0.05   -0.18
 Bray pg 62
Fig. 4.19 		in deg
r in deg

r positive left

Cl Cl_beta dihedral effect 1/rad -0.023 Bray pg 33
Clp Cl_p roll damping 1/rad -0.450 Bray pg 33
Clr Cl_r roll moment due to yaw rate 1/rad 0.265 Bray pg 33
Cl Clfada change in roll moment due to aileron - 
  alpha  a=-5   a=-10  a=-15  a=-20  a=-25   
 -10.31  0.0140   0.0280   0.0366   0.0446   0.0533
  -8.22  0.0143   0.0281   0.0375   0.0463   0.0553
  -6.12  0.0148   0.0292   0.0386   0.0482   0.0568
  -4.01  0.0148   0.0299   0.0408   0.0484   0.0563
  -1.91  0.0153   0.0296   0.0400   0.0475   0.0568
   0.20  0.0158   0.0299   0.0405   0.0482   0.0573
   2.29  0.0160   0.0308   0.0424   0.0519   0.0604
   4.40  0.0160   0.0308   0.0424   0.0519   0.0604
   6.50  0.0152   0.0295   0.0422   0.0527   0.0614
   8.59  0.0144   0.0279   0.0407   0.0521   0.0616
  10.65  0.0128   0.0260   0.0382   0.0495   0.0597
  12.71  0.0118   0.0238   0.0364   0.0466   0.0558
  13.72  0.0109   0.0222   0.0332   0.0437   0.0524
  14.73  0.0105   0.0202   0.0307   0.0411   0.0487
  15.74  0.0093   0.0177   0.0280   0.0388   0.0461
  16.75  0.0093   0.0167   0.0267   0.0360   0.0423
  17.75  0.0087   0.0147   0.0238   0.0333   0.0376
  18.75  0.0073   0.0105   0.0179   0.0285   0.0342
  19.74  0.0061   0.0066   0.0130   0.0226   0.0280
  20.73  0.0016   0.0028   0.0077   0.0170   0.0229
 Bray pg 58
Table 4.8 		in deg
a in deg

a positive
right aileron up

Clr Cl_dr roll moment due to rudder 1/rad -0.00229 Bray pg 33 r positive left
Cn Cn_beta weathercock stability 1/rad 0.109 Bray pg 33
Cnp Cn_p adverse yaw 1/rad -0.110 Bray pg 33
Cnr Cn_r yaw damping 1/rad -0.200 Bray pg 33
Cn Cnfada change in yaw moment due to aileron - 
 alpha    a=-5  a=-10  a=-15  a=-20  a=-25   
  -8     0.0004   0.0013   0.0014   0.0022   0.0025
  -7     0.0002   0.0009   0.0008   0.0015   0.0018
  -6     0.0001   0.0004   0.0003   0.0008   0.0010
  -5    -0.0001   0.0000  -0.0002   0.0001   0.0003
  -4    -0.0002  -0.0004  -0.0007  -0.0005  -0.0004
  -3    -0.0004  -0.0007  -0.0011  -0.0012  -0.0012
  -2    -0.0005  -0.0011  -0.0016  -0.0019  -0.0019
  -1    -0.0007  -0.0015  -0.0021  -0.0025  -0.0026
   0    -0.0008  -0.0018  -0.0026  -0.0032  -0.0033
   1    -0.0010  -0.0022  -0.0030  -0.0038  -0.0040
   2    -0.0011  -0.0025  -0.0035  -0.0044  -0.0047
   3    -0.0013  -0.0029  -0.0040  -0.0050  -0.0054
   4    -0.0015  -0.0032  -0.0044  -0.0057  -0.0061
   5    -0.0016  -0.0035  -0.0049  -0.0063  -0.0068
   6    -0.0018  -0.0038  -0.0053  -0.0069  -0.0074
   7    -0.0019  -0.0041  -0.0057  -0.0075  -0.0081
   8    -0.0021  -0.0043  -0.0062  -0.0081  -0.0088
   9    -0.0022  -0.0046  -0.0066  -0.0087  -0.0094
  10    -0.0024  -0.0049  -0.0070  -0.0093  -0.0101
  11    -0.0026  -0.0051  -0.0074  -0.0098  -0.0107
  12    -0.0027  -0.0054  -0.0078  -0.0104  -0.0114
  13    -0.0029  -0.0056  -0.0082  -0.0110  -0.0120
  14    -0.0030  -0.0058  -0.0086  -0.0115  -0.0127
  15    -0.0032  -0.0060  -0.0090  -0.0121  -0.0133
  16    -0.0034  -0.0062  -0.0094  -0.0126  -0.0139
  17    -0.0035  -0.0064  -0.0098  -0.0132  -0.0145
 Bray pg 61
Table 4.9 		in deg
a in deg

a positive
right aileron up

Cn Cnfbetadr change in yaw moment due to rudder - 
  beta  r=-25   r=-20  r=-15  r=-10   r=-5   r=0    r=5    r=10    r=15   r=20   r=25  
 -20     0.0067   0.0027  -0.0027  -0.0094  -0.0154  -0.0214  -0.0274  -0.0334  -0.0401  -0.0455  -0.0495
 -17.5   0.0000   0.0013  -0.0054  -0.0127  -0.0214  -0.0277  -0.0340  -0.0427  -0.0500  -0.0567  -0.0554
 -15     0.0040   0.0020  -0.0040  -0.0114  -0.0200  -0.0283  -0.0366  -0.0452  -0.0526  -0.5860  -0.0606
 -12.5   0.0087   0.0074   0.0027  -0.0047  -0.0134  -0.0222  -0.0310  -0.0397  -0.0471  -0.0052  -0.0531
 -10     0.0121   0.0101   0.0054  -0.0014  -0.0101  -0.0188  -0.0275  -0.0362  -0.0430  -0.0477  -0.0497
  -7.5   0.0161   0.0127   0.0087   0.0013  -0.0064  -0.0161  -0.0258  -0.0335  -0.0409  -0.0449  -0.0483
  -5     0.0200   0.0174   0.0134   0.0067  -0.0020  -0.0131  -0.0242  -0.0329  -0.0396  -0.0436  -0.0462
  -2.5   0.0275   0.0235   0.0188   0.0127   0.0047  -0.0067  -0.0181  -0.0261  -0.0322  -0.0369  -0.0409
   0     0.0335   0.0295   0.0255   0.0188   0.0114   0.0000  -0.0074  -0.0148  -0.0215  -0.0255  -0.0295
   2.5   0.0382   0.0348   0.0288   0.0228   0.0154   0.0060  -0.0034  -0.0108  -0.0168  -0.0228  -0.0262
   5     0.0429   0.0389   0.0328   0.0261   0.0121   0.0101   0.0081  -0.0059  -0.0126  -0.0187  -0.0227
   7.5   0.0476   0.0429   0.0375   0.0288   0.0248   0.0154   0.0060   0.0020  -0.0067  -0.0121  -0.0168
  10     0.0516   0.0462   0.0422   0.0348   0.0295   0.0188   0.0081   0.0028  -0.0046  -0.0086  -0.0140
  11.25  0.0549   0.0489   0.0442   0.0375   0.0315   0.0201   0.0087   0.0027  -0.0040  -0.0088  -0.0147
  12.5   0.0563   0.0509   0.0462   0.0395   0.0335   0.0235   0.0135   0.0075   0.0008  -0.0039  -0.0093
  13.75  0.0570   0.0509   0.0469   0.0402   0.0342   0.0268   0.0194   0.0134   0.0067   0.0027  -0.0034
  15     0.0523   0.0482   0.0429   0.0369   0.0322   0.0255   0.0188   0.0141   0.0081   0.0001  -0.0013
  16.25  0.0503   0.0442   0.0415   0.0355   0.0308   0.0255   0.0202   0.0155   0.0095   0.0068   0.0007
  17.5   0.0509   0.0428   0.0422   0.0355   0.0308   0.0235   0.0162   0.0115   0.0048   0.0042  -0.0039
  18.75  0.0509   0.0436   0.0429   0.0362   0.0308   0.0235   0.0162   0.0108   0.0041   0.0034  -0.0039
  20     0.0509   0.0442   0.0429   0.0369   0.0322   0.0248   0.0174   0.0127   0.0067   0.0054  -0.0013
 Bray pg 63
Fig. 4.20 		in deg
r in deg

r positive left

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