# T-37A Tweet -- Linear 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 June 7, 2000

The linear aerodynamics model uses stability derivatives to approximate actual aircraft behavior. The T-37A Tweet linear model is based on the following flight conditions (cruise):

Flight Conditions
Variable | Variable in Code | Description | Units | Value(s) | Source | Notes
--- | --- | --- | --- | --- | --- | ---
h | Altitude | altitude above sea level | ft | 30000 | Roskam pg 501 |
|  | Alpha | angle of attack | deg | 2 | Roskam pg 501 |
V | V_true_kts | velocity (true air speed) | kts | 270 | Roskam pg 501 | Mach 0.459
q | Dynamic_pressure | dynamic pressure | lb/ft2 | 92.7 | Roskam pg 501 |
C.G. | - | center of gravity location | % | 27 | Roskam pg 501 |
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 | 33.8 | Roskam pg 501 |
| cbar | wing mean aerodynamic chord | ft | 5.47 | Roskam pg 501 |
S | Sw | wing surface area | ft2 | 182 | Roskam pg 501 |

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

Mass Data
Variable | Variable in Code | Description | Units | Value(s) | Source | Notes
--- | --- | --- | --- | --- | --- | ---
W | Weight | weight at flight condition | lb | 6360 | Roskam pg 501 | converted to Mass [slug/ft3] in code
Ixx | I_xx | roll inertia | slug ft2 | 7985 | Roskam pg 501 |
Iyy | I_yy | pitch inertia | slug ft2 | 3326 | Roskam pg 501 |
Izz | I_zz | yaw inertia | slug ft2 | 11183 | Roskam pg 501 |
Ixz | I_xz | lateral cross inertia | slug ft2 | 0 | Roskam pg 501 |

Propulsion Data
Variable | Variable in Code | Description | Units | Value(s) | Source | Notes
--- | --- | --- | --- | --- | --- | ---
Tmax | simpleSingleMaxThrust | maximum thrust | lb | 850 | Roskam pg 502 | estimated from CTx at sea level
Tmax | simpleSingleMaxThrust | maximum thrust | lb | 5700 | David pg 251 | engine rating (A-37B Dragonfly)

Aerodynamic Data
Variable | Variable in Code | Description | Units | Value(s) | Source | Notes
--- | --- | --- | --- | --- | --- | ---
CD0 | CDo | drag coefficient at =0 | - | 0.020 | Roskam pg 502 |
CD | CD_a | drag curve slope | 1/rad | 0.25 | Roskam pg 502 |
CDe | CD_de | drag due to elevator | 1/rad | 0 | Roskam pg 502 | e positive down
CL0 | CLo | lift coefficient at =0 | - | 0.20 | Roskam pg 502 |
CL | CL_a | lift curve slope | 1/rad | 5.15 | Roskam pg 502 |
CL | CL_adot | lift due to angle of attack rate | 1/rad | 2.0 | Roskam pg 502 |
CLq | CL_q | lift due to pitch rate | 1/rad | 4.1 | Roskam pg 502 |
CLe | CL_de | lift due to elevator | 1/rad | 0.5 | Roskam pg 502 | e positive down
Cm0 | Cmo | pitch moment coefficient at =0 | - | 0.025 | Roskam pg 502 |
Cm | Cm_a | pitch moment due to angle of attack | 1/rad | -0.70 | Roskam pg 502 |
Cm | Cm_adot | pitch moment due to angle of attack rate | 1/rad | -6.95 | Roskam pg 502 |
Cmq | Cm_q | pitch moment due to pitch rate | 1/rad | -14.9 | Roskam pg 502 |
Cme | Cm_de | pitching moment due to elevator | 1/rad | -1.12 | Roskam pg 502 | e positive down
CY | CY_beta | side force fue to sideslip angle | 1/rad | -0.346 | Roskam pg 503 |
CYp | CY_p | side force due to roll rate | 1/rad | -0.0827 | Roskam pg 503 |
CYr | CY_r | side force due to yaw rate | 1/rad | 0.30 | Roskam pg 503 |
CYa | CY_da | side force due to aileron | 1/rad | 0 | Roskam pg 503 | a positive right aileron up
CYr | CY_dr | side force due to rudder | 1/rad | 0.2 | Roskam pg 503 | r positive left
Cl | Cl_beta | dihedral effect | 1/rad | -0.0944 | Roskam pg 503 |
Clp | Cl_p | roll damping | 1/rad | -0.442 | Roskam pg 503 |
Clr | Cl_r | roll moment due to yaw rate | 1/rad | 0.0926 | Roskam pg 503 |
Cla | Cl_da | roll moment due to aileron | 1/rad | -0.181 | Roskam pg 503 | a positive right aileron up
Clr | Cl_dr | roll moment due to rudder | 1/rad | 0.015 | Roskam pg 503 | r positive left
Cn | Cn_beta | weathercock stability | 1/rad | 0.1106 | Roskam pg 503 |
Cnp | Cn_p | adverse yaw | 1/rad | -0.0243 | Roskam pg 503 |
Cnr | Cn_r | yaw damping | 1/rad | -0.139 | Roskam pg 503 |
Cna | Cn_da | yaw moment due to aileron | 1/rad | 0.0254 | Roskam pg 503 | a positive right aileron up
Cnr | Cn_dr | yaw moment due to rudder | 1/rad | -0.0365 | Roskam pg 503 | r positive left

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