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<title>Pioneer -- Nonlinear Model</title>
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<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>
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