F-4 Phantom -- 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 2, 2000

The linear aerodynamics model uses stability derivatives to approximate actual aircraft behavior. The F-4 linear model is based on the following flight conditions (subsonic cruise):

Variable	Variable in Code	Description	Units	Value(s)	Source	Notes
Flight Conditions
h	Altitude	altitude above sea level	ft	35000	Roskam pg 536
	Alpha	angle of attack	deg	2.6	Roskam pg 536
V	V_true_kts	velocity (true air speed)	kts	518.7	Roskam pg 536	Mach 0.9
q	Dynamic_pressure	dynamic pressure	lb/ft²	283.2	Roskam pg 536
C.G.	-	center of gravity location	%	29	Roskam pg 536
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	38.7	Roskam pg 536
	cbar	wing mean aerodynamic chord	ft	16	Roskam pg 536
S	Sw	wing surface area	ft²	530	Roskam pg 536

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

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 39000 Roskam pg 536 converted to Mass
[slug/ft³] in code

I_xx I_xx roll inertia slug ft² 25000 Roskam pg 536

I_yy I_yy pitch inertia slug ft² 122200 Roskam pg 536

I_zz I_zz yaw inertia slug ft² 139800 Roskam pg 536

I_xz I_xz lateral cross inertia slug ft² 2200 Roskam pg 536

Mass Data
Variable	Variable in Code	Description	Units	Value(s)	Source	Notes
W	Weight	weight at flight condition	lb	39000	Roskam pg 536	converted to Mass [slug/ft³] in code
I_xx	I_xx	roll inertia	slug ft²	25000	Roskam pg 536
I_yy	I_yy	pitch inertia	slug ft²	122200	Roskam pg 536
I_zz	I_zz	yaw inertia	slug ft²	139800	Roskam pg 536
I_xz	I_xz	lateral cross inertia	slug ft²	2200	Roskam pg 536

Propulsion Data

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

T_max simpleSingleMaxThrust maximum thrust lb 6670 Roskam pg 537 estimated from C_{T_x}
at sea level

T_max simpleSingleMaxThrust maximum thrust lb 32000 MAM site engine rating
(F-4A)

T_max simpleSingleMaxThrust maximum thrust lb 35800 MAM site engine rating
(F-4E)

Propulsion Data
Variable	Variable in Code	Description	Units	Value(s)	Source	Notes
T_max	simpleSingleMaxThrust	maximum thrust	lb	6670	Roskam pg 537	estimated from C_{T_x} at sea level
T_max	simpleSingleMaxThrust	maximum thrust	lb	32000	MAM site	engine rating (F-4A)
T_max	simpleSingleMaxThrust	maximum thrust	lb	35800	MAM site	engine rating (F-4E)

Aerodynamic Data

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

C_D₀ CDo drag coefficient at =0 - 0.0205 Roskam pg 537

C_D CD_a drag curve slope 1/rad 0.3 Roskam pg 537

C_{D_e} CD_de drag due to elevator 1/rad -0.1 Roskam pg 537 e positive down

C_L₀ CLo lift coefficient at =0 - 0.1 Roskam pg 537

C_L CL_a lift curve slope 1/rad 3.75 Roskam pg 537

C_L CL_adot lift due to angle of attack rate 1/rad 0.86 Roskam pg 537

C_{L_q} CL_q lift due to pitch rate 1/rad 1.8 Roskam pg 537

C_{L_e} CL_de lift due to elevator 1/rad 0.4 Roskam pg 537 e positive down

C_m₀ Cmo pitch moment coefficient at =0 - 0.025 Roskam pg 537

C_m Cm_a pitch moment due to angle of attack 1/rad -0.4 Roskam pg 537

C_m Cm_adot pitch moment due to angle of attack rate 1/rad -1.3 Roskam pg 537

C_{m_q} Cm_q pitch moment due to pitch rate 1/rad -2.7 Roskam pg 537

C_{m_e} Cm_de pitching moment due to elevator 1/rad -0.58 Roskam pg 537 e positive down

C_Y CY_beta side force fue to sideslip angle 1/rad -0.68 Roskam pg 538

C_{Y_p} CY_p side force due to roll rate 1/rad 0 Roskam pg 538

C_{Y_r} CY_r side force due to yaw rate 1/rad 0 Roskam pg 538

C_{Y_a} CY_da side force due to aileron 1/rad 0.016 Roskam pg 538 a positive
right aileron up

C_{Y_r} CY_dr side force due to rudder 1/rad 0.095 Roskam pg 538 r positive left

C_l Cl_beta dihedral effect 1/rad -0.08 Roskam pg 538

C_{l_p} Cl_p roll damping 1/rad -0.24 Roskam pg 538

C_{l_r} Cl_r roll moment due to yaw rate 1/rad 0.07 Roskam pg 538

C_{l_a} Cl_da roll moment due to aileron 1/rad -0.042 Roskam pg 538 a positive
right aileron up

C_{l_r} Cl_dr roll moment due to rudder 1/rad 0.006 Roskam pg 538 r positive left

C_n Cn_beta weathercock stability 1/rad 0.125 Roskam pg 538

C_{n_p} Cn_p adverse yaw 1/rad -0.036 Roskam pg 538

C_{n_r} Cn_r yaw damping 1/rad -0.27 Roskam pg 538

C_{n_a} Cn_da yaw moment due to aileron 1/rad 0.001 Roskam pg 538 a positive
right aileron up

C_{n_r} Cn_dr yaw moment due to rudder 1/rad -0.066 Roskam pg 538 r positive left

Variable	Variable in Code	Description	Units	Value(s)	Source	Notes
Aerodynamic Data
C_D₀	CDo	drag coefficient at =0	-	0.0205	Roskam pg 537
C_D	CD_a	drag curve slope	1/rad	0.3	Roskam pg 537
C_{D_e}	CD_de	drag due to elevator	1/rad	-0.1	Roskam pg 537	e positive down
C_L₀	CLo	lift coefficient at =0	-	0.1	Roskam pg 537
C_L	CL_a	lift curve slope	1/rad	3.75	Roskam pg 537
C_L	CL_adot	lift due to angle of attack rate	1/rad	0.86	Roskam pg 537
C_{L_q}	CL_q	lift due to pitch rate	1/rad	1.8	Roskam pg 537
C_{L_e}	CL_de	lift due to elevator	1/rad	0.4	Roskam pg 537	e positive down
C_m₀	Cmo	pitch moment coefficient at =0	-	0.025	Roskam pg 537
C_m	Cm_a	pitch moment due to angle of attack	1/rad	-0.4	Roskam pg 537
C_m	Cm_adot	pitch moment due to angle of attack rate	1/rad	-1.3	Roskam pg 537
C_{m_q}	Cm_q	pitch moment due to pitch rate	1/rad	-2.7	Roskam pg 537
C_{m_e}	Cm_de	pitching moment due to elevator	1/rad	-0.58	Roskam pg 537	e positive down
C_Y	CY_beta	side force fue to sideslip angle	1/rad	-0.68	Roskam pg 538
C_{Y_p}	CY_p	side force due to roll rate	1/rad	0	Roskam pg 538
C_{Y_r}	CY_r	side force due to yaw rate	1/rad	0	Roskam pg 538
C_{Y_a}	CY_da	side force due to aileron	1/rad	0.016	Roskam pg 538	a positive right aileron up
C_{Y_r}	CY_dr	side force due to rudder	1/rad	0.095	Roskam pg 538	r positive left
C_l	Cl_beta	dihedral effect	1/rad	-0.08	Roskam pg 538
C_{l_p}	Cl_p	roll damping	1/rad	-0.24	Roskam pg 538
C_{l_r}	Cl_r	roll moment due to yaw rate	1/rad	0.07	Roskam pg 538
C_{l_a}	Cl_da	roll moment due to aileron	1/rad	-0.042	Roskam pg 538	a positive right aileron up
C_{l_r}	Cl_dr	roll moment due to rudder	1/rad	0.006	Roskam pg 538	r positive left
C_n	Cn_beta	weathercock stability	1/rad	0.125	Roskam pg 538
C_{n_p}	Cn_p	adverse yaw	1/rad	-0.036	Roskam pg 538
C_{n_r}	Cn_r	yaw damping	1/rad	-0.27	Roskam pg 538
C_{n_a}	Cn_da	yaw moment due to aileron	1/rad	0.001	Roskam pg 538	a positive right aileron up
C_{n_r}	Cn_dr	yaw moment due to rudder	1/rad	-0.066	Roskam pg 538	r positive left

F-4 Phantom -- Linear Model

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