# Cessna 172 -- Nonlinear Model

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

Last updated April 10, 2000

The linear aerodynamics model uses stability derivatives to approximate actual aircraft behavior. The Cessna 172 linear model is based on the following flight conditions:

Flight Conditions
Variable | Variable in Code | Description | Units | Value(s) | Source | Notes
--- | --- | --- | --- | --- | --- | ---
h | Altitude | altitude above sea level | ft | ? |  | not available
| Alpha | angle of attack | deg | ? |  | not available
V | V_true_kts | velocity (true air speed) | kts | ? |  | not available
q | Dynamic_pressure | dynamic pressure | lb/ft2 | ? |  | not available
C.G. | - | center of gravity location | % | ? |  | not available
CL | CL | lift coefficient | - | ? |  | not available
CD | CD | drag coefficient | - | ? |  | not available
Cm | Cm | pitching moment coefficient | - | ? |  | not available

The data input into the simulator is listed in the following tables:

Geometry
Variable | Variable in Code | Description | Units | Value(s) | Source | Notes
--- | --- | --- | --- | --- | --- | ---
b | bw | wingspan | ft | 35.8 | c172_aero.c |
| cbar | wing mean aerodynamic chord | ft | 4.9 | c172_aero.c |
S | Sw | wing surface area | ft2 | 174 | c172_aero.c |

Control Surface Geometry
Variable | Variable in Code | Description | Units | Value(s) | Source | Notes
--- | --- | --- | --- | --- | --- | ---
emax | demax | maximum elevator deflection | deg | +28 | c172_aero.c |
emin | demin | minimum elevator deflection | deg | -23 | c172_aero.c |
amax | damax | maximum aileron deflection | deg | +20 | c172_aero.c |
amin | damin | minimum aileron deflection | deg | -15 | c172_aero.c |
rmax | drmax | maximum rudder deflection | deg | +16 | c172_aero.c |
rmin | drmin | minimum rudder deflection | deg | -16 | c172_aero.c |

Mass Data
Variable | Variable in Code | Description | Units | Value(s) | Source | Notes
--- | --- | --- | --- | --- | --- | ---
GTOW | Weight | gross takeoff weight | lb | 2300 | c172_init.c | converted to Mass [slug/ft3] in code
Ixx | I_xx | roll inertia | slug ft2 | 948 | c172_init.c |
Iyy | I_yy | pitch inertia | slug ft2 | 1346 | c172_init.c |
Izz | I_zz | yaw inertia | slug ft2 | 1967 | c172_init.c |
Ixz | I_xz | lateral cross inertia | slug ft2 | 0 | c172_init.c |

Propulsion Data
Variable | Variable in Code | Description | Units | Value(s) | Source | Notes
--- | --- | --- | --- | --- | --- | ---
Tmax | simpleSingleMaxThrust | maximum thrust | lb | 350 | c172_engine.c | use c172 engine model in code

Aerodynamic Data
Variable | Variable in Code | Description | Units | Value(s) | Source | Notes
--- | --- | --- | --- | --- | --- | ---
CD0 | CDo | drag coefficient at =0 | - | 0.031 | c172_aero.c |
CD | CD_a | drag curve slope | 1/rad | 0.130 | c172_aero.c | not used in code
K | CDK | induced drag constant, i.e. 1/(pi*e*AR) | - | 0.054 | c172_aero.c |
CDe | CD_de | drag due to elevator | 1/rad | 0.060 | c172_aero.c | e positive down

CL

CL

lift coefficient vs. angle of attack

-

     alpha     CL
      -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

c172_aero.c

in deg

CL | CL_adot | lift due to angle of attack rate | 1/rad | 1.7 | c172_aero.c |
CLq | CL_q | lift due to pitch rate | 1/rad | 3.9 | c172_aero.c |
CLe | CL_de | lift due to elevator | 1/rad | 0.430 | c172_aero.c | e positive down
Cm0 | Cmo | pitch moment coefficient at =0 | - | -0.015 | c172_aero.c |
Cm | Cm_a | pitch moment due to angle of attack | 1/rad | -0.89 | c172_aero.c |
Cm | Cm_adot | pitch moment due to angle of attack rate | 1/rad | -5.2 | c172_aero.c |
Cmq | Cm_q | pitch moment due to pitch rate | 1/rad | -12.4 | c172_aero.c |
Cme | Cm_de | pitching moment due to elevator | 1/rad | -1.28 | c172_aero.c | e positive down
CY | CY_beta | side force fue to sideslip angle | 1/rad | -0.31 | c172_aero.c |
CYp | CY_p | side force due to roll rate | 1/rad | -0.037 | c172_aero.c |
CYr | CY_r | side force due to yaw rate | 1/rad | 0.21 | c172_aero.c |
CYa | CY_da | side force due to aileron | 1/rad | 0 | c172_aero.c | a positive right aileron up
CYr | CY_dr | side force due to rudder | 1/rad | 0.187 | c172_aero.c | r positive left
Cl | Cl_beta | dihedral effect | 1/rad | -0.089 | c172_aero.c |
Clp | Cl_p | roll damping | 1/rad | -0.47 | c172_aero.c |
Clr | Cl_r | roll moment due to yaw rate | 1/rad | 0.096 | c172_aero.c |
Cla | Cl_da | roll moment due to aileron | 1/rad | -0.178 | c172_aero.c | a positive right aileron up
Clr | Cl_dr | roll moment due to rudder | 1/rad | 0.0147 | c172_aero.c | r positive left
Cn | Cn_beta | weathercock stability | 1/rad | 0.065 | c172_aero.c |
Cnp | Cn_p | adverse yaw | 1/rad | -0.03 | c172_aero.c |
Cnr | Cn_r | yaw damping | 1/rad | -0.099 | c172_aero.c |
Cna | Cn_da | yaw moment due to aileron | 1/rad | 0.053 | c172_aero.c | a positive right aileron up
Cnr | Cn_dr | yaw moment due to rudder | 1/rad | -0.0657 | c172_aero.c | r positive left

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