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2000-10-22 21:05:31 +00:00
<html>
<head>
<title>Cessna 172 -- Nonlinear Model</title>
</head>
<BODY
bgcolor="FFFFFF" text="000000" link="0800FF"
vlink="FF0000" alink="FF0FF8">
<font face="arial,helvetica">
<center><h1><b><i>
Cessna 172 -- 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 linear aerodynamics model uses stability derivatives to approximate
actual aircraft behavior. The Cessna 172 linear model is based on the
following flight conditions:
<p>
<center>
<table width="95%" border="1">
<tr>
<td colspan="7" bgcolor="FFFFCC">
<font face="arial,helvetica" size="4"><b><center>
Flight Conditions
</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>
<tr>
<td valign="top">
<font face="arial,helvetica">
h
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
Altitude
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
altitude above sea level
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
ft
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
?
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
not available
</font>
</td>
</tr>
<td valign="top">
<font face="arial,helvetica">
<img src="../images/alpha.gif">
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
Alpha
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
angle of attack
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
deg
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
?
</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">
V<sub><img src="../images/inf.gif"></sub>
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
V_true_kts
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
velocity (true air speed)
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
kts
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
?
</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">
q
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
Dynamic_pressure
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
dynamic pressure
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
lb/ft<sup>2</sup>
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
?
</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.G.
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
-
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
center of gravity location
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
% <img src="../images/cbar.gif">
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
?
</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>L</sub>
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
CL
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
lift coefficient
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
-
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
?
</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>D</sub>
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
CD
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
drag coefficient
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
-
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
?
</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>m</sub>
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
Cm
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
pitching moment coefficient
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
-
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
?
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
not available
</font>
</td>
</tr>
</table>
</center>
<p>
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">
35.8
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
c172_aero.c
</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">
4.9
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
c172_aero.c
</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">
174
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
c172_aero.c
</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">
+28
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
c172_aero.c
</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">
-23
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
c172_aero.c
</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">
c172_aero.c
</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">
-15
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
c172_aero.c
</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">
+16
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
c172_aero.c
</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">
-16
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
c172_aero.c
</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">
2300
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
c172_init.c
</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">
948
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
c172_init.c
</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">
1346
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
c172_init.c
</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">
1967
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
c172_init.c
</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">
0
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
c172_init.c
</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">
350
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
c172_engine.c
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
use c172 engine model in code
</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>0</sub></sub>
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
CDo
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
drag coefficient at <img src="../images/alpha.gif">=0
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
-
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
0.031
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
c172_aero.c
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
</font>
</td>
</tr>
<tr>
<td valign="top">
<font face="arial,helvetica">
C<sub>D<sub><img src="../images/alpha.gif"></sub></sub>
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
CD_a
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
drag curve slope
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
1/rad
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
0.130
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
c172_aero.c
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
not used in code
</font>
</td>
</tr>
<tr>
<td valign="top">
<font face="arial,helvetica">
K
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
CDK
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
induced drag constant, i.e. 1/(pi*e*AR)
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
-
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
0.054
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
c172_aero.c
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
</font>
</td>
</tr>
<tr>
<td valign="top">
<font face="arial,helvetica">
C<sub>D<sub><img src="../images/delta.gif">e</sub></sub>
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
CD_de
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
drag due to elevator
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
1/rad
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
0.060
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
c172_aero.c
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
<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">
CL
</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>
-5 -0.14
0 0.31
10 1.21
12 1.276
13.75 1.51249
15 1.591
16 1.63
17.35 1.60878
18 1.53712
19 1.376
20 1.142</pre>
</td>
<td valign="top">
<font face="arial,helvetica">
c172_aero.c
</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">
1.7
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
c172_aero.c
</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">
3.9
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
c172_aero.c
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
</font>
</td>
</tr>
<tr>
<td valign="top">
<font face="arial,helvetica">
C<sub>L<sub><img src="../images/delta.gif">e</sub></sub>
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
CL_de
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
lift due to elevator
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
1/rad
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
0.430
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
c172_aero.c
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
<img src="../images/delta.gif">e positive down
</font>
</td>
</tr>
<tr>
<td valign="top">
<font face="arial,helvetica">
C<sub>m<sub>0</sub></sub>
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
Cmo
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
pitch moment coefficient at <img src="../images/alpha.gif">=0
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
-
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
-0.015
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
c172_aero.c
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
</font>
</td>
</tr>
<tr>
<td valign="top">
<font face="arial,helvetica">
C<sub>m<sub><img src="../images/alpha.gif"></sub></sub>
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
Cm_a
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
pitch moment due to angle of attack
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
1/rad
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
-0.89
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
c172_aero.c
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
</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">
-5.2
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
c172_aero.c
</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">
-12.4
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
c172_aero.c
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
</font>
</td>
</tr>
<tr>
<td valign="top">
<font face="arial,helvetica">
C<sub>m<sub><img src="../images/delta.gif">e</sub></sub>
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
Cm_de
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
pitching moment due to elevator
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
1/rad
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
-1.28
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
c172_aero.c
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
<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">
-0.31
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
c172_aero.c
</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">
-0.037
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
c172_aero.c
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
</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">
0.21
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
c172_aero.c
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
</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">
0
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
c172_aero.c
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
<img src="../images/delta.gif">a positive<br>right aileron up
</font>
</td>
</tr>
<tr>
<td valign="top">
<font face="arial,helvetica">
C<sub>Y<sub><img src="../images/delta.gif">r</sub></sub>
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
CY_dr
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
side force due to rudder
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
1/rad
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
0.187
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
c172_aero.c
</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>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">
-0.089
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
c172_aero.c
</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">
-0.47
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
c172_aero.c
</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">
0.096
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
c172_aero.c
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
</font>
</td>
</tr>
<tr>
<td valign="top">
<font face="arial,helvetica">
C<sub>l<sub><img src="../images/delta.gif">a</sub></sub>
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
Cl_da
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
roll moment due to aileron
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
1/rad
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
-0.178
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
c172_aero.c
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
<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">
0.0147
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
c172_aero.c
</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">
0.065
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
c172_aero.c
</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">
-0.03
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
c172_aero.c
</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">
-0.099
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
c172_aero.c
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
</font>
</td>
</tr>
<tr>
<td valign="top">
<font face="arial,helvetica">
C<sub>n<sub><img src="../images/delta.gif">a</sub></sub>
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
Cn_da
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
yaw moment due to aileron
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
1/rad
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
0.053
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
c172_aero.c
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
<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><img src="../images/delta.gif">r</sub></sub>
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
Cn_dr
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
yaw moment due to rudder
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
1/rad
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
-0.0657
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
c172_aero.c
</font>
</td>
<td valign="top">
<font face="arial,helvetica">
<img src="../images/delta.gif">r positive left
</font>
</td>
</tr>
</table>
</center>
<p>
<hr>
<p>
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