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Marchetti S-211 -- 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 Marchetti S-211 linear model is based on the following flight conditions (cruise 1):

Variable	Variable in Code	Description	Units	Value(s)	Source	Notes
Flight Conditions
h	Altitude	altitude above sea level	ft	25000	Roskam pg 494
	Alpha	angle of attack	deg	0	Roskam pg 494
V	V_true_kts	velocity (true air speed)	kts	361.2	Roskam pg 494	Mach 0.6
q	Dynamic_pressure	dynamic pressure	lb/ft²	198.0	Roskam pg 494
C.G.	-	center of gravity location	%	25	Roskam pg 494
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	26.3	Roskam pg 494
	cbar	wing mean aerodynamic chord	ft	5.4	Roskam pg 494
S	Sw	wing surface area	ft²	136	Roskam pg 494

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 4000 Roskam pg 494 converted to Mass
[slug/ft³] in code

I_xx I_xx roll inertia slug ft² 800 Roskam pg 494

I_yy I_yy pitch inertia slug ft² 4800 Roskam pg 494

I_zz I_zz yaw inertia slug ft² 5200 Roskam pg 494

I_xz I_xz lateral cross inertia slug ft² 200 Roskam pg 494

Propulsion Data

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

T_max simpleSingleMaxThrust maximum thrust lb 600 Roskam pg 495 estimated from C_{T_x}
at cruise 1

T_max simpleSingleMaxThrust maximum thrust lb 2500 David pg 801 engine rating

Aerodynamic Data

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

C_D₀ CDo drag coefficient at =0 - 0.0205 Roskam pg 495

C_D CD_a drag curve slope 1/rad 0.12 Roskam pg 495

C_{D_e} CD_de drag due to elevator 1/rad 0 Roskam pg 495 e positive down

C_L₀ CLo lift coefficient at =0 - 0.149 Roskam pg 495

C_L CL_a lift curve slope 1/rad 5.5 Roskam pg 495

C_L CL_adot lift due to angle of attack rate 1/rad 4.2 Roskam pg 495

C_{L_q} CL_q lift due to pitch rate 1/rad 10.0 Roskam pg 495

C_{L_e} CL_de lift due to elevator 1/rad 0.38 Roskam pg 495 e positive down

C_m₀ Cmo pitch moment coefficient at =0 - -0.08 Roskam pg 495

C_m Cm_a pitch moment due to angle of attack 1/rad -0.24 Roskam pg 495

C_m Cm_adot pitch moment due to angle of attack rate 1/rad -9.6 Roskam pg 495

C_{m_q} Cm_q pitch moment due to pitch rate 1/rad -17.7 Roskam pg 495

C_{m_e} Cm_de pitching moment due to elevator 1/rad -0.88 Roskam pg 495 e positive down

C_Y CY_beta side force fue to sideslip angle 1/rad -1.0 Roskam pg 496

C_{Y_p} CY_p side force due to roll rate 1/rad -0.14 Roskam pg 496

C_{Y_r} CY_r side force due to yaw rate 1/rad 0.61 Roskam pg 496

C_{Y_a} CY_da side force due to aileron 1/rad 0 Roskam pg 496 a positive
right aileron up

C_{Y_r} CY_dr side force due to rudder 1/rad 0.028 Roskam pg 496 r positive left

C_l Cl_beta dihedral effect 1/rad -0.11 Roskam pg 496

C_{l_p} Cl_p roll damping 1/rad -0.39 Roskam pg 496

C_{l_r} Cl_r roll moment due to yaw rate 1/rad 0.28 Roskam pg 496

C_{l_a} Cl_da roll moment due to aileron 1/rad -0.10 Roskam pg 496 a positive
right aileron up

C_{l_r} Cl_dr roll moment due to rudder 1/rad 0.05 Roskam pg 496 r positive left

C_n Cn_beta weathercock stability 1/rad 0.17 Roskam pg 496

C_{n_p} Cn_p adverse yaw 1/rad 0.09 Roskam pg 496

C_{n_r} Cn_r yaw damping 1/rad -0.26 Roskam pg 496

C_{n_a} Cn_da yaw moment due to aileron 1/rad 0.003 Roskam pg 496 a positive
right aileron up

C_{n_r} Cn_dr yaw moment due to rudder 1/rad -0.12 Roskam pg 496 r positive left

Marchetti S-211 -- Linear Model

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