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<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>
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<font face="arial,helvetica">
-
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<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>
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<font face="arial,helvetica">
Bray pg 61<br>
Table 4.9
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<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
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<tr>
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<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>
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<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
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</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>
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