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Learjet 24 -- 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 May 31, 2000

The linear aerodynamics model uses stability derivatives to approximate actual aircraft behavior. The Learjet 24 linear model is based on the following flight conditions (maximum weight cruise):

Variable	Variable in Code	Description	Units	Value(s)	Source	Notes
Flight Conditions
h	Altitude	altitude above sea level	ft	40000	Roskam pg 522
	Alpha	angle of attack	deg	2.7	Roskam pg 522
V	V_true_kts	velocity (true air speed)	kts	400.9	Roskam pg 522	Mach 0.7
q	Dynamic_pressure	dynamic pressure	lb/ft²	134.6	Roskam pg 522
C.G.	-	center of gravity location	%	32	Roskam pg 522
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	34	Roskam pg 522
	cbar	wing mean aerodynamic chord	ft	7	Roskam pg 522
S	Sw	wing surface area	ft²	230	Roskam pg 522

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 13000 Roskam pg 522 converted to Mass
[slug/ft³] in code

I_xx I_xx roll inertia slug ft² 28000 Roskam pg 522

I_yy I_yy pitch inertia slug ft² 18800 Roskam pg 522

I_zz I_zz yaw inertia slug ft² 47000 Roskam pg 522

I_xz I_xz lateral cross inertia slug ft² 1300 Roskam pg 522

Propulsion Data

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

T_max simpleSingleMaxThrust maximum thrust lb 2020 Roskam pg 523 estimated from C_{T_x}
at sea level

T_max simpleSingleMaxThrust maximum thrust lb 5900 David pg 559 engine rating
(Learjet 24F)

Aerodynamic Data

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

C_D₀ CDo drag coefficient at =0 - 0.0216 Roskam pg 523

C_D CD_a drag curve slope 1/rad 0.3 Roskam pg 523

C_{D_e} CD_de drag due to elevator 1/rad 0 Roskam pg 523 e positive down

C_L₀ CLo lift coefficient at =0 - 0.13 Roskam pg 523

C_L CL_a lift curve slope 1/rad 5.84 Roskam pg 523

C_L CL_adot lift due to angle of attack rate 1/rad 2.2 Roskam pg 523

C_{L_q} CL_q lift due to pitch rate 1/rad 4.7 Roskam pg 523

C_{L_e} CL_de lift due to elevator 1/rad 0.46 Roskam pg 523 e positive down

C_m₀ Cmo pitch moment coefficient at =0 - 0.05 Roskam pg 523

C_m Cm_a pitch moment due to angle of attack 1/rad -0.64 Roskam pg 523

C_m Cm_adot pitch moment due to angle of attack rate 1/rad -6.7 Roskam pg 523

C_{m_q} Cm_q pitch moment due to pitch rate 1/rad -15.5 Roskam pg 523

C_{m_e} Cm_de pitching moment due to elevator 1/rad -1.24 Roskam pg 523 e positive down

C_Y CY_beta side force fue to sideslip angle 1/rad -0.73 Roskam pg 524

C_{Y_p} CY_p side force due to roll rate 1/rad 0 Roskam pg 524

C_{Y_r} CY_r side force due to yaw rate 1/rad 0.4 Roskam pg 524

C_{Y_a} CY_da side force due to aileron 1/rad 0 Roskam pg 524 a positive
right aileron up

C_{Y_r} CY_dr side force due to rudder 1/rad 0.14 Roskam pg 524 r positive left

C_l Cl_beta dihedral effect 1/rad -0.11 Roskam pg 524

C_{l_p} Cl_p roll damping 1/rad -0.45 Roskam pg 524

C_{l_r} Cl_r roll moment due to yaw rate 1/rad 0.16 Roskam pg 524

C_{l_a} Cl_da roll moment due to aileron 1/rad -0.178 Roskam pg 524 a positive
right aileron up

C_{l_r} Cl_dr roll moment due to rudder 1/rad 0.019 Roskam pg 524 r positive left

C_n Cn_beta weathercock stability 1/rad 0.127 Roskam pg 524

C_{n_p} Cn_p adverse yaw 1/rad -0.008 Roskam pg 524

C_{n_r} Cn_r yaw damping 1/rad -0.2 Roskam pg 524

C_{n_a} Cn_da yaw moment due to aileron 1/rad 0.02 Roskam pg 524 a positive
right aileron up

C_{n_r} Cn_dr yaw moment due to rudder 1/rad -0.074 Roskam pg 524 r positive left

Learjet 24 -- Linear Model

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