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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):

Variable	Variable in Code	Description	Units	Value(s)	Source	Notes
Flight Conditions
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
C_L	CL	lift coefficient	-	?		not available
C_D	CD	drag coefficient	-	?		not available
C_m	Cm	pitching moment coefficient	-	?		not available

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

Variable	Variable in Code	Description	Units	Value(s)	Source
Geometry
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

e_max demax maximum elevator deflection deg +20 - guess

e_min demin minimum elevator deflection deg -20 - guess

a_max damax maximum aileron deflection deg +20 - guess

a_min damin minimum aileron deflection deg -20 - guess

r_max drmax maximum rudder deflection deg +20 - guess

r_min 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

I_xx I_xx roll inertia slug ft² 7985 Roskam pg 501

I_yy I_yy pitch inertia slug ft² 3326 Roskam pg 501

I_zz I_zz yaw inertia slug ft² 11183 Roskam pg 501

I_xz I_xz lateral cross inertia slug ft² 0 Roskam pg 501

Propulsion Data

Variable Variable
in Code Description Units Value(s) Source Notes

T_max simpleSingleMaxThrust maximum thrust lb 850 Roskam pg 502 estimated from C_{T_x}
at sea level

T_max 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

C_D₀ CDo drag coefficient at =0 - 0.020 Roskam pg 502

C_D CD_a drag curve slope 1/rad 0.25 Roskam pg 502

C_{D_e} CD_de drag due to elevator 1/rad 0 Roskam pg 502 e positive down

C_L₀ CLo lift coefficient at =0 - 0.20 Roskam pg 502

C_L CL_a lift curve slope 1/rad 5.15 Roskam pg 502

C_L CL_adot lift due to angle of attack rate 1/rad 2.0 Roskam pg 502

C_{L_q} CL_q lift due to pitch rate 1/rad 4.1 Roskam pg 502

C_{L_e} CL_de lift due to elevator 1/rad 0.5 Roskam pg 502 e positive down

C_m₀ Cmo pitch moment coefficient at =0 - 0.025 Roskam pg 502

C_m Cm_a pitch moment due to angle of attack 1/rad -0.70 Roskam pg 502

C_m Cm_adot pitch moment due to angle of attack rate 1/rad -6.95 Roskam pg 502

C_{m_q} Cm_q pitch moment due to pitch rate 1/rad -14.9 Roskam pg 502

C_{m_e} Cm_de pitching moment due to elevator 1/rad -1.12 Roskam pg 502 e positive down

C_Y CY_beta side force fue to sideslip angle 1/rad -0.346 Roskam pg 503

C_{Y_p} CY_p side force due to roll rate 1/rad -0.0827 Roskam pg 503

C_{Y_r} CY_r side force due to yaw rate 1/rad 0.30 Roskam pg 503

C_{Y_a} CY_da side force due to aileron 1/rad 0 Roskam pg 503 a positive
right aileron up

C_{Y_r} CY_dr side force due to rudder 1/rad 0.2 Roskam pg 503 r positive left

C_l Cl_beta dihedral effect 1/rad -0.0944 Roskam pg 503

C_{l_p} Cl_p roll damping 1/rad -0.442 Roskam pg 503

C_{l_r} Cl_r roll moment due to yaw rate 1/rad 0.0926 Roskam pg 503

C_{l_a} Cl_da roll moment due to aileron 1/rad -0.181 Roskam pg 503 a positive
right aileron up

C_{l_r} Cl_dr roll moment due to rudder 1/rad 0.015 Roskam pg 503 r positive left

C_n Cn_beta weathercock stability 1/rad 0.1106 Roskam pg 503

C_{n_p} Cn_p adverse yaw 1/rad -0.0243 Roskam pg 503

C_{n_r} Cn_r yaw damping 1/rad -0.139 Roskam pg 503

C_{n_a} Cn_da yaw moment due to aileron 1/rad 0.0254 Roskam pg 503 a positive
right aileron up

C_{n_r} Cn_dr yaw moment due to rudder 1/rad -0.0365 Roskam pg 503 r positive left

T-37A Tweet -- Linear Model

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