<html> <head> <title>Pioneer -- Nonlinear Model</title> </head> <BODY bgcolor="FFFFFF" text="000000" link="0800FF" vlink="FF0000" alink="FF0FF8"> <font face="arial,helvetica"> <center><h1><b><i> Pioneer -- Nonlinear Model </i></b></h1></center> <b><i>Graduate Research done by <a href="http://fly.to/jeffscott/">Jeff Scott</a><br> Advisor: <a href="http://www.uiuc.edu/ph/www/m-selig">Prof. Michael Selig</a><br> Applied Aerodynamics Group<br> Department of Aeronautical and Astronautical Engineering<br> University of Illinois at Urbana-Champaign, Urbana, Illinois 61801<p> Last updated April 10, 2000</i></b> <p> 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: <p> <center> <table width="95%" border="1"> <tr> <td colspan="7" bgcolor="FFFFCC"> <font face="arial,helvetica" size="4"><b><center> Geometry </center></b></font> </td> </tr> <tr> <th> <font face="arial,helvetica"> Variable </font> </th> <th> <font face="arial,helvetica"> Variable<br>in Code </font> </th> <th> <font face="arial,helvetica"> Description </font> </th> <th> <font face="arial,helvetica"> Units </font> </th> <th> <font face="arial,helvetica"> Value(s) </font> </th> <th> <font face="arial,helvetica"> Source </font> </th> <th> <font face="arial,helvetica"> Notes </font> </th> </tr> <tr> <td valign="top"> <font face="arial,helvetica"> b </font> </td> <td valign="top"> <font face="arial,helvetica"> bw </font> </td> <td valign="top"> <font face="arial,helvetica"> wingspan </font> </td> <td valign="top"> <font face="arial,helvetica"> ft </font> </td> <td valign="top"> <font face="arial,helvetica"> 16.9 </font> </td> <td valign="top"> <font face="arial,helvetica"> Bray pg 33 </font> </td> <td valign="top"> <font face="arial,helvetica"> </font> </td> </tr> <tr> <td valign="top"> <font face="arial,helvetica"> <img src="../images/cbar.gif"> </font> </td> <td valign="top"> <font face="arial,helvetica"> cbar </font> </td> <td valign="top"> <font face="arial,helvetica"> wing mean aerodynamic chord </font> </td> <td valign="top"> <font face="arial,helvetica"> ft </font> </td> <td valign="top"> <font face="arial,helvetica"> 1.80 </font> </td> <td valign="top"> <font face="arial,helvetica"> Bray pg 33 </font> </td> <td valign="top"> <font face="arial,helvetica"> </font> </td> </tr> <tr> <td valign="top"> <font face="arial,helvetica"> S </font> </td> <td valign="top"> <font face="arial,helvetica"> Sw </font> </td> <td valign="top"> <font face="arial,helvetica"> wing surface area </font> </td> <td valign="top"> <font face="arial,helvetica"> ft<sup>2</sup> </font> </td> <td valign="top"> <font face="arial,helvetica"> 30.42 </font> </td> <td valign="top"> <font face="arial,helvetica"> Bray pg 33 </font> </td> <td valign="top"> <font face="arial,helvetica"> </font> </td> </tr> </table> <p> <table width="95%" border="1"> <tr> <td colspan="7" bgcolor="FFFFCC"> <font face="arial,helvetica" size="4"><b><center> Control Surface Geometry </center></b></font> </td> </tr> <tr> <th> <font face="arial,helvetica"> Variable </font> </th> <th> <font face="arial,helvetica"> Variable<br>in Code </font> </th> <th> <font face="arial,helvetica"> Description </font> </th> <th> <font face="arial,helvetica"> Units </font> </th> <th> <font face="arial,helvetica"> Value(s) </font> </th> <th> <font face="arial,helvetica"> Source </font> </th> <th> <font face="arial,helvetica"> Notes </font> </th> </tr> <tr> <td valign="top"> <font face="arial,helvetica"> <img src="../images/delta.gif">e<sub>max</sub> </font> </td> <td valign="top"> <font face="arial,helvetica"> demax </font> </td> <td valign="top"> <font face="arial,helvetica"> maximum elevator deflection </font> </td> <td valign="top"> <font face="arial,helvetica"> deg </font> </td> <td valign="top"> <font face="arial,helvetica"> +20 </font> </td> <td valign="top"> <font face="arial,helvetica"> Bray pg 31 </font> </td> <td valign="top"> <font face="arial,helvetica"> </font> </td> </tr> <tr> <td valign="top"> <font face="arial,helvetica"> <img src="../images/delta.gif">e<sub>min</sub> </font> </td> <td valign="top"> <font face="arial,helvetica"> demin </font> </td> <td valign="top"> <font face="arial,helvetica"> minimum elevator deflection </font> </td> <td valign="top"> <font face="arial,helvetica"> deg </font> </td> <td valign="top"> <font face="arial,helvetica"> -20 </font> </td> <td valign="top"> <font face="arial,helvetica"> Bray pg 31 </font> </td> <td valign="top"> <font face="arial,helvetica"> </font> </td> </tr> <tr> <td valign="top"> <font face="arial,helvetica"> <img src="../images/delta.gif">a<sub>max</sub> </font> </td> <td valign="top"> <font face="arial,helvetica"> damax </font> </td> <td valign="top"> <font face="arial,helvetica"> maximum aileron deflection </font> </td> <td valign="top"> <font face="arial,helvetica"> deg </font> </td> <td valign="top"> <font face="arial,helvetica"> +20 </font> </td> <td valign="top"> <font face="arial,helvetica"> Bray pg 31 </font> </td> <td valign="top"> <font face="arial,helvetica"> </font> </td> </tr> <tr> <td valign="top"> <font face="arial,helvetica"> <img src="../images/delta.gif">a<sub>min</sub> </font> </td> <td valign="top"> <font face="arial,helvetica"> damin </font> </td> <td valign="top"> <font face="arial,helvetica"> minimum aileron deflection </font> </td> <td valign="top"> <font face="arial,helvetica"> deg </font> </td> <td valign="top"> <font face="arial,helvetica"> -20 </font> </td> <td valign="top"> <font face="arial,helvetica"> Bray pg 31 </font> </td> <td valign="top"> <font face="arial,helvetica"> </font> </td> </tr> <tr> <td valign="top"> <font face="arial,helvetica"> <img src="../images/delta.gif">r<sub>max</sub> </font> </td> <td valign="top"> <font face="arial,helvetica"> drmax </font> </td> <td valign="top"> <font face="arial,helvetica"> maximum rudder deflection </font> </td> <td valign="top"> <font face="arial,helvetica"> deg </font> </td> <td valign="top"> <font face="arial,helvetica"> +20 </font> </td> <td valign="top"> <font face="arial,helvetica"> Bray pg 31 </font> </td> <td valign="top"> <font face="arial,helvetica"> </font> </td> </tr> <tr> <td valign="top"> <font face="arial,helvetica"> <img src="../images/delta.gif">r<sub>min</sub> </font> </td> <td valign="top"> <font face="arial,helvetica"> drmin </font> </td> <td valign="top"> <font face="arial,helvetica"> minimum rudder deflection </font> </td> <td valign="top"> <font face="arial,helvetica"> deg </font> </td> <td valign="top"> <font face="arial,helvetica"> -20 </font> </td> <td valign="top"> <font face="arial,helvetica"> Bray pg 31 </font> </td> <td valign="top"> <font face="arial,helvetica"> </font> </td> </tr> </table> <p> <table width="95%" border="1"> <tr> <td colspan="7" bgcolor="FFFFCC"> <font face="arial,helvetica" size="4"><b><center> Mass Data </center></b></font> </td> </tr> <tr> <th> <font face="arial,helvetica"> Variable </font> </th> <th> <font face="arial,helvetica"> Variable<br>in Code </font> </th> <th> <font face="arial,helvetica"> Description </font> </th> <th> <font face="arial,helvetica"> Units </font> </th> <th> <font face="arial,helvetica"> Value(s) </font> </th> <th> <font face="arial,helvetica"> Source </font> </th> <th> <font face="arial,helvetica"> Notes </font> </th> </tr> <tr> <td valign="top"> <font face="arial,helvetica"> GTOW </font> </td> <td valign="top"> <font face="arial,helvetica"> Weight </font> </td> <td valign="top"> <font face="arial,helvetica"> gross takeoff weight </font> </td> <td valign="top"> <font face="arial,helvetica"> lb </font> </td> <td valign="top"> <font face="arial,helvetica"> 420 </font> </td> <td valign="top"> <font face="arial,helvetica"> Bray pg 33 </font> </td> <td valign="top"> <font face="arial,helvetica"> converted to Mass <br>[slug/ft<sup>3</sup>] in code </font> </td> </tr> <tr> <td valign="top"> <font face="arial,helvetica"> I<sub>xx</sub> </font> </td> <td valign="top"> <font face="arial,helvetica"> I_xx </font> </td> <td valign="top"> <font face="arial,helvetica"> roll inertia </font> </td> <td valign="top"> <font face="arial,helvetica"> slug ft<sup>2</sup> </font> </td> <td valign="top"> <font face="arial,helvetica"> 34.832 </font> </td> <td valign="top"> <font face="arial,helvetica"> IAI (manufacturer)<br> MSS notes </font> </td> <td valign="top"> <font face="arial,helvetica"> </font> </td> </tr> <tr> <td valign="top"> <font face="arial,helvetica"> I<sub>yy</sub> </font> </td> <td valign="top"> <font face="arial,helvetica"> I_yy </font> </td> <td valign="top"> <font face="arial,helvetica"> pitch inertia </font> </td> <td valign="top"> <font face="arial,helvetica"> slug ft<sup>2</sup> </font> </td> <td valign="top"> <font face="arial,helvetica"> 67.08 </font> </td> <td valign="top"> <font face="arial,helvetica"> IAI (manufacturer)<br> MSS notes </font> </td> <td valign="top"> <font face="arial,helvetica"> </font> </td> </tr> <tr> <td valign="top"> <font face="arial,helvetica"> I<sub>zz</sub> </font> </td> <td valign="top"> <font face="arial,helvetica"> I_zz </font> </td> <td valign="top"> <font face="arial,helvetica"> yaw inertia </font> </td> <td valign="top"> <font face="arial,helvetica"> slug ft<sup>2</sup> </font> </td> <td valign="top"> <font face="arial,helvetica"> 82.22 </font> </td> <td valign="top"> <font face="arial,helvetica"> IAI (manufacturer)<br> MSS notes </font> </td> <td valign="top"> <font face="arial,helvetica"> </font> </td> </tr> <tr> <td valign="top"> <font face="arial,helvetica"> I<sub>xz</sub> </font> </td> <td valign="top"> <font face="arial,helvetica"> I_xz </font> </td> <td valign="top"> <font face="arial,helvetica"> lateral cross inertia </font> </td> <td valign="top"> <font face="arial,helvetica"> slug ft<sup>2</sup> </font> </td> <td valign="top"> <font face="arial,helvetica"> -4.902 </font> </td> <td valign="top"> <font face="arial,helvetica"> IAI (manufacturer)<br> MSS notes </font> </td> <td valign="top"> <font face="arial,helvetica"> </font> </td> </tr> </table> <p> <table width="95%" border="1"> <tr> <td colspan="7" bgcolor="FFFFCC"> <font face="arial,helvetica" size="4"><b><center> Propulsion Data </center></b></font> </td> </tr> <tr> <th> <font face="arial,helvetica"> Variable </font> </th> <th> <font face="arial,helvetica"> Variable<br>in Code </font> </th> <th> <font face="arial,helvetica"> Description </font> </th> <th> <font face="arial,helvetica"> Units </font> </th> <th> <font face="arial,helvetica"> Value(s) </font> </th> <th> <font face="arial,helvetica"> Source </font> </th> <th> <font face="arial,helvetica"> Notes </font> </th> </tr> <tr> <td valign="top"> <font face="arial,helvetica"> T<sub>max</sub> </font> </td> <td valign="top"> <font face="arial,helvetica"> simpleSingleMaxThrust </font> </td> <td valign="top"> <font face="arial,helvetica"> maximum thrust </font> </td> <td valign="top"> <font face="arial,helvetica"> lb </font> </td> <td valign="top"> <font face="arial,helvetica"> 150 </font> </td> <td valign="top"> <font face="arial,helvetica"> - </font> </td> <td valign="top"> <font face="arial,helvetica"> approximated from<br>max power of 27 hp </font> </td> </tr> </table> <p> <table width="95%" border="1"> <tr> <td colspan="7" bgcolor="FFFFCC"> <font face="arial,helvetica" size="4"><b><center> Aerodynamic Data </center></b></font> </td> </tr> <tr> <th> <font face="arial,helvetica"> Variable </font> </th> <th> <font face="arial,helvetica"> Variable<br>in Code </font> </th> <th> <font face="arial,helvetica"> Description </font> </th> <th> <font face="arial,helvetica"> Units </font> </th> <th> <font face="arial,helvetica"> Value(s) </font> </th> <th> <font face="arial,helvetica"> Source </font> </th> <th> <font face="arial,helvetica"> Notes </font> </th> </tr> <tr> <td valign="top"> <font face="arial,helvetica"> C<sub>D</sub> </font> </td> <td valign="top"> <font face="arial,helvetica"> CDfa </font> </td> <td valign="top"> <font face="arial,helvetica"> drag coefficient vs. angle of attack </font> </td> <td valign="top"> <font face="arial,helvetica"> - </font> </td> <td valign="top"> <pre> <u> alpha CD </u> -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</pre> </td> <td valign="top"> <font face="arial,helvetica"> Bray pg 50<br> Table 4.7 </font> </td> <td valign="top"> <font face="arial,helvetica"> <img src="../images/alpha.gif"> in deg </font> </td> </tr> <tr> <td valign="top"> <font face="arial,helvetica"> C<sub>D</sub> </font> </td> <td valign="top"> <font face="arial,helvetica"> CDfade </font> </td> <td valign="top"> <font face="arial,helvetica"> change in drag due to elevator </font> </td> <td valign="top"> <font face="arial,helvetica"> - </font> </td> <td valign="top"> <pre> alpha <img src="../images/delta.gif">e=-20 <img src="../images/delta.gif">e=-15 <img src="../images/delta.gif">e=-10 <img src="../images/delta.gif">e=-5 <img src="../images/delta.gif">e=5 <img src="../images/delta.gif">e=10 <img src="../images/delta.gif">e=15 <img src="../images/delta.gif">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</pre> </td> <td valign="top"> <font face="arial,helvetica"> Bray pg 45<br> Table 4.6 </font> </td> <td valign="top"> <font face="arial,helvetica"> <img src="../images/alpha.gif"> in deg<br> <img src="../images/delta.gif">e in deg <p> <img src="../images/delta.gif">e positive down </font> </td> </tr> <tr> <td valign="top"> <font face="arial,helvetica"> C<sub>L</sub> </font> </td> <td valign="top"> <font face="arial,helvetica"> CLfa </font> </td> <td valign="top"> <font face="arial,helvetica"> lift coefficient vs. angle of attack </font> </td> <td valign="top"> <font face="arial,helvetica"> - </font> </td> <td valign="top"> <pre> <u> alpha CL </u> -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</pre> </td> <td valign="top"> <font face="arial,helvetica"> Bray pg 50<br> Table 4.7 </font> </td> <td valign="top"> <font face="arial,helvetica"> <img src="../images/alpha.gif"> in deg </font> </td> </tr> <tr> <td valign="top"> <font face="arial,helvetica"> C<sub>L<sub><img src="../images/alphadot.gif"></sub></sub> </font> </td> <td valign="top"> <font face="arial,helvetica"> CL_adot </font> </td> <td valign="top"> <font face="arial,helvetica"> lift due to angle of attack rate </font> </td> <td valign="top"> <font face="arial,helvetica"> 1/rad </font> </td> <td valign="top"> <font face="arial,helvetica"> 2.42 </font> </td> <td valign="top"> <font face="arial,helvetica"> Bray pg 33 </font> </td> <td valign="top"> <font face="arial,helvetica"> </font> </td> </tr> <tr> <td valign="top"> <font face="arial,helvetica"> C<sub>L<sub>q</sub></sub> </font> </td> <td valign="top"> <font face="arial,helvetica"> CL_q </font> </td> <td valign="top"> <font face="arial,helvetica"> lift due to pitch rate </font> </td> <td valign="top"> <font face="arial,helvetica"> 1/rad </font> </td> <td valign="top"> <font face="arial,helvetica"> 8.05 </font> </td> <td valign="top"> <font face="arial,helvetica"> Bray pg 33 </font> </td> <td valign="top"> <font face="arial,helvetica"> </font> </td> </tr> <tr> <td valign="top"> <font face="arial,helvetica"> C<sub>L</sub> </font> </td> <td valign="top"> <font face="arial,helvetica"> CLfade </font> </td> <td valign="top"> <font face="arial,helvetica"> change in lift due to elevator </font> </td> <td valign="top"> <font face="arial,helvetica"> - </font> </td> <td valign="top"> <pre> alpha <img src="../images/delta.gif">e=-20 <img src="../images/delta.gif">e=-15 <img src="../images/delta.gif">e=-10 <img src="../images/delta.gif">e=-5 <img src="../images/delta.gif">e=5 <img src="../images/delta.gif">e=10 <img src="../images/delta.gif">e=15 <img src="../images/delta.gif">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</pre> </td> <td valign="top"> <font face="arial,helvetica"> Bray pg 41<br> Table 4.4 </font> </td> <td valign="top"> <font face="arial,helvetica"> <img src="../images/alpha.gif"> in deg<br> <img src="../images/delta.gif">e in deg <p> <img src="../images/delta.gif">e positive down </font> </td> </tr> <tr> <td valign="top"> <font face="arial,helvetica"> C<sub>m</sub> </font> </td> <td valign="top"> <font face="arial,helvetica"> Cmfa </font> </td> <td valign="top"> <font face="arial,helvetica"> pitch moment coefficient vs. alpha </font> </td> <td valign="top"> <font face="arial,helvetica"> - </font> </td> <td valign="top"> <pre> <u> alpha Cm </u> -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</pre> </td> <td valign="top"> <font face="arial,helvetica"> Bray pg 50<br> Table 4.7 </font> </td> <td valign="top"> <font face="arial,helvetica"> <img src="../images/alpha.gif"> in deg </font> </td> </tr> <tr> <td valign="top"> <font face="arial,helvetica"> C<sub>m<sub><img src="../images/alphadot.gif"></sub></sub> </font> </td> <td valign="top"> <font face="arial,helvetica"> Cm_adot </font> </td> <td valign="top"> <font face="arial,helvetica"> pitch moment due to angle of attack rate </font> </td> <td valign="top"> <font face="arial,helvetica"> 1/rad </font> </td> <td valign="top"> <font face="arial,helvetica"> -11.0 </font> </td> <td valign="top"> <font face="arial,helvetica"> Bray pg 33 </font> </td> <td valign="top"> <font face="arial,helvetica"> </font> </td> </tr> <tr> <td valign="top"> <font face="arial,helvetica"> C<sub>m<sub>q</sub></sub> </font> </td> <td valign="top"> <font face="arial,helvetica"> Cm_q </font> </td> <td valign="top"> <font face="arial,helvetica"> pitch moment due to pitch rate </font> </td> <td valign="top"> <font face="arial,helvetica"> 1/rad </font> </td> <td valign="top"> <font face="arial,helvetica"> -36.6 </font> </td> <td valign="top"> <font face="arial,helvetica"> Bray pg 33 </font> </td> <td valign="top"> <font face="arial,helvetica"> </font> </td> </tr> <tr> <td valign="top"> <font face="arial,helvetica"> C<sub>m</sub> </font> </td> <td valign="top"> <font face="arial,helvetica"> Cmfade </font> </td> <td valign="top"> <font face="arial,helvetica"> change in pitch moment due to elevator </font> </td> <td valign="top"> <font face="arial,helvetica"> - </font> </td> <td valign="top"> <pre> alpha <img src="../images/delta.gif">e=-25 <img src="../images/delta.gif">e=-20 <img src="../images/delta.gif">e=-15 <img src="../images/delta.gif">e=-10 <img src="../images/delta.gif">e=-5 <img src="../images/delta.gif">e=0 <img src="../images/delta.gif">e=5 <img src="../images/delta.gif">e=10 <img src="../images/delta.gif">e=15 <img src="../images/delta.gif">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</pre> </td> <td valign="top"> <font face="arial,helvetica"> Bray pg 34<br> Fig. 4.2 </font> </td> <td valign="top"> <font face="arial,helvetica"> <img src="../images/alpha.gif"> in deg<br> <img src="../images/delta.gif">e in deg <p> <img src="../images/delta.gif">e positive down </font> </td> </tr> <tr> <td valign="top"> <font face="arial,helvetica"> C<sub>Y<sub><img src="../images/beta.gif"></sub></sub> </font> </td> <td valign="top"> <font face="arial,helvetica"> CY_beta </font> </td> <td valign="top"> <font face="arial,helvetica"> side force fue to sideslip angle </font> </td> <td valign="top"> <font face="arial,helvetica"> 1/rad </font> </td> <td valign="top"> <font face="arial,helvetica"> -0.819 </font> </td> <td valign="top"> <font face="arial,helvetica"> Bray pg 33 </font> </td> <td valign="top"> <font face="arial,helvetica"> </font> </td> </tr> <tr> <td valign="top"> <font face="arial,helvetica"> C<sub>Y<sub>p</sub></sub> </font> </td> <td valign="top"> <font face="arial,helvetica"> CY_p </font> </td> <td valign="top"> <font face="arial,helvetica"> side force due to roll rate </font> </td> <td valign="top"> <font face="arial,helvetica"> 1/rad </font> </td> <td valign="top"> <font face="arial,helvetica"> none </font> </td> <td valign="top"> <font face="arial,helvetica"> </font> </td> <td valign="top"> <font face="arial,helvetica"> not available </font> </td> </tr> <tr> <td valign="top"> <font face="arial,helvetica"> C<sub>Y<sub>r</sub></sub> </font> </td> <td valign="top"> <font face="arial,helvetica"> CY_r </font> </td> <td valign="top"> <font face="arial,helvetica"> side force due to yaw rate </font> </td> <td valign="top"> <font face="arial,helvetica"> 1/rad </font> </td> <td valign="top"> <font face="arial,helvetica"> none </font> </td> <td valign="top"> <font face="arial,helvetica"> </font> </td> <td valign="top"> <font face="arial,helvetica"> not available </font> </td> </tr> <tr> <td valign="top"> <font face="arial,helvetica"> C<sub>Y<sub><img src="../images/delta.gif">a</sub></sub> </font> </td> <td valign="top"> <font face="arial,helvetica"> CY_da </font> </td> <td valign="top"> <font face="arial,helvetica"> side force due to aileron </font> </td> <td valign="top"> <font face="arial,helvetica"> 1/rad </font> </td> <td valign="top"> <font face="arial,helvetica"> none </font> </td> <td valign="top"> <font face="arial,helvetica"> </font> </td> <td valign="top"> <font face="arial,helvetica"> not available </font> </td> </tr> <tr> <td valign="top"> <font face="arial,helvetica"> C<sub>Y</sub> </font> </td> <td valign="top"> <font face="arial,helvetica"> CYfbetadr </font> </td> <td valign="top"> <font face="arial,helvetica"> change in side force due to rudder </font> </td> <td valign="top"> <font face="arial,helvetica"> - </font> </td> <td valign="top"> <pre> beta <img src="../images/delta.gif">r=-20 <img src="../images/delta.gif">r=0 <img src="../images/delta.gif">r=20 -20 0.19 -0.05 -0.25 0 0.24 0.00 -0.22 20 0.29 0.05 -0.18</pre> </td> <td valign="top"> <font face="arial,helvetica"> Bray pg 62<br> Fig. 4.19 </font> </td> <td valign="top"> <font face="arial,helvetica"> <img src="../images/beta.gif"> in deg<br> <img src="../images/delta.gif">r in deg <p> <img src="../images/delta.gif">r positive left </font> </td> </tr> <tr> <td valign="top"> <font face="arial,helvetica"> C<sub>l<sub><img src="../images/beta.gif"></sub></sub> </font> </td> <td valign="top"> <font face="arial,helvetica"> Cl_beta </font> </td> <td valign="top"> <font face="arial,helvetica"> dihedral effect </font> </td> <td valign="top"> <font face="arial,helvetica"> 1/rad </font> </td> <td valign="top"> <font face="arial,helvetica"> -0.023 </font> </td> <td valign="top"> <font face="arial,helvetica"> Bray pg 33 </font> </td> <td valign="top"> <font face="arial,helvetica"> </font> </td> </tr> <tr> <td valign="top"> <font face="arial,helvetica"> C<sub>l<sub>p</sub></sub> </font> </td> <td valign="top"> <font face="arial,helvetica"> Cl_p </font> </td> <td valign="top"> <font face="arial,helvetica"> roll damping </font> </td> <td valign="top"> <font face="arial,helvetica"> 1/rad </font> </td> <td valign="top"> <font face="arial,helvetica"> -0.450 </font> </td> <td valign="top"> <font face="arial,helvetica"> Bray pg 33 </font> </td> <td valign="top"> <font face="arial,helvetica"> </font> </td> </tr> <tr> <td valign="top"> <font face="arial,helvetica"> C<sub>l<sub>r</sub></sub> </font> </td> <td valign="top"> <font face="arial,helvetica"> Cl_r </font> </td> <td valign="top"> <font face="arial,helvetica"> roll moment due to yaw rate </font> </td> <td valign="top"> <font face="arial,helvetica"> 1/rad </font> </td> <td valign="top"> <font face="arial,helvetica"> 0.265 </font> </td> <td valign="top"> <font face="arial,helvetica"> Bray pg 33 </font> </td> <td valign="top"> <font face="arial,helvetica"> </font> </td> </tr> <tr> <td valign="top"> <font face="arial,helvetica"> C<sub>l</sub> </font> </td> <td valign="top"> <font face="arial,helvetica"> Clfada </font> </td> <td valign="top"> <font face="arial,helvetica"> change in roll moment due to aileron </font> </td> <td valign="top"> <font face="arial,helvetica"> - </font> </td> <td valign="top"> <pre> alpha <img src="../images/delta.gif">a=-5 <img src="../images/delta.gif">a=-10 <img src="../images/delta.gif">a=-15 <img src="../images/delta.gif">a=-20 <img src="../images/delta.gif">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</pre> </td> <td valign="top"> <font face="arial,helvetica"> Bray pg 58<br> Table 4.8 </font> </td> <td valign="top"> <font face="arial,helvetica"> <img src="../images/alpha.gif"> in deg<br> <img src="../images/delta.gif">a in deg <p> <img src="../images/delta.gif">a positive<br>right aileron up </font> </td> </tr> <tr> <td valign="top"> <font face="arial,helvetica"> C<sub>l<sub><img src="../images/delta.gif">r</sub></sub> </font> </td> <td valign="top"> <font face="arial,helvetica"> Cl_dr </font> </td> <td valign="top"> <font face="arial,helvetica"> roll moment due to rudder </font> </td> <td valign="top"> <font face="arial,helvetica"> 1/rad </font> </td> <td valign="top"> <font face="arial,helvetica"> -0.00229 </font> </td> <td valign="top"> <font face="arial,helvetica"> Bray pg 33 </font> </td> <td valign="top"> <font face="arial,helvetica"> <img src="../images/delta.gif">r positive left </font> </td> </tr> <tr> <td valign="top"> <font face="arial,helvetica"> C<sub>n<sub><img src="../images/beta.gif"></sub></sub> </font> </td> <td valign="top"> <font face="arial,helvetica"> Cn_beta </font> </td> <td valign="top"> <font face="arial,helvetica"> weathercock stability </font> </td> <td valign="top"> <font face="arial,helvetica"> 1/rad </font> </td> <td valign="top"> <font face="arial,helvetica"> 0.109 </font> </td> <td valign="top"> <font face="arial,helvetica"> Bray pg 33 </font> </td> <td valign="top"> <font face="arial,helvetica"> </font> </td> </tr> <tr> <td valign="top"> <font face="arial,helvetica"> C<sub>n<sub>p</sub></sub> </font> </td> <td valign="top"> <font face="arial,helvetica"> Cn_p </font> </td> <td valign="top"> <font face="arial,helvetica"> adverse yaw </font> </td> <td valign="top"> <font face="arial,helvetica"> 1/rad </font> </td> <td valign="top"> <font face="arial,helvetica"> -0.110 </font> </td> <td valign="top"> <font face="arial,helvetica"> Bray pg 33 </font> </td> <td valign="top"> <font face="arial,helvetica"> </font> </td> </tr> <tr> <td valign="top"> <font face="arial,helvetica"> C<sub>n<sub>r</sub></sub> </font> </td> <td valign="top"> <font face="arial,helvetica"> Cn_r </font> </td> <td valign="top"> <font face="arial,helvetica"> yaw damping </font> </td> <td valign="top"> <font face="arial,helvetica"> 1/rad </font> </td> <td valign="top"> <font face="arial,helvetica"> -0.200 </font> </td> <td valign="top"> <font face="arial,helvetica"> Bray pg 33 </font> </td> <td valign="top"> <font face="arial,helvetica"> </font> </td> </tr> <tr> <td valign="top"> <font face="arial,helvetica"> C<sub>n</sub> </font> </td> <td valign="top"> <font face="arial,helvetica"> Cnfada </font> </td> <td valign="top"> <font face="arial,helvetica"> change in yaw moment due to aileron </font> </td> <td valign="top"> <font face="arial,helvetica"> - </font> </td> <td valign="top"> <pre> alpha <img src="../images/delta.gif">a=-5 <img src="../images/delta.gif">a=-10 <img src="../images/delta.gif">a=-15 <img src="../images/delta.gif">a=-20 <img src="../images/delta.gif">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</pre> </td> <td valign="top"> <font face="arial,helvetica"> Bray pg 61<br> Table 4.9 </font> </td> <td valign="top"> <font face="arial,helvetica"> <img src="../images/alpha.gif"> in deg<br> <img src="../images/delta.gif">a in deg <p> <img src="../images/delta.gif">a positive<br>right aileron up </font> </td> </tr> <tr> <td valign="top"> <font face="arial,helvetica"> C<sub>n</sub> </font> </td> <td valign="top"> <font face="arial,helvetica"> Cnfbetadr </font> </td> <td valign="top"> <font face="arial,helvetica"> change in yaw moment due to rudder </font> </td> <td valign="top"> <font face="arial,helvetica"> - </font> </td> <td valign="top"> <pre> beta <img src="../images/delta.gif">r=-25 <img src="../images/delta.gif">r=-20 <img src="../images/delta.gif">r=-15 <img src="../images/delta.gif">r=-10 <img src="../images/delta.gif">r=-5 <img src="../images/delta.gif">r=0 <img src="../images/delta.gif">r=5 <img src="../images/delta.gif">r=10 <img src="../images/delta.gif">r=15 <img src="../images/delta.gif">r=20 <img src="../images/delta.gif">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</pre> </td> <td valign="top"> <font face="arial,helvetica"> Bray pg 63<br> Fig. 4.20 </font> </td> <td valign="top"> <font face="arial,helvetica"> <img src="../images/beta.gif"> in deg<br> <img src="../images/delta.gif">r in deg <p> <img src="../images/delta.gif">r positive left </font> </td> </tr> </table> </center> <p> <hr> <p> <h5><b><center> <a href="http://amber.aae.uiuc.edu/~jscott/sis/">Flight Sim Home</a> * <a href="../index.html">Aircraft Models</a> * <a href="index.html">Pioneer Model</a> * <a href="refs.html">Pioneer References<br> </h5></b></center> </font> </body> </html>