Boeing 747 -- 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 April 11, 2000

The linear aerodynamics model uses stability derivatives to approximate actual aircraft behavior. The Boeing 747 linear model is based on the following flight conditions (low altitude cruise):

Variable	Variable in Code	Description	Units	Value(s)	Source	Notes
Flight Conditions
h	Altitude	altitude above sea level	ft	20000	Roskam pg 543
	Alpha	angle of attack	deg	2.5	Roskam pg 543
V	V_true_kts	velocity (true air speed)	kts	399	Roskam pg 543	Mach 0.65
q	Dynamic_pressure	dynamic pressure	lb/ft²	287.2	Roskam pg 543
C.G.	-	center of gravity location	%	25	Roskam pg 543
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	196	Roskam pg 543
	cbar	wing mean aerodynamic chord	ft	27.3	Roskam pg 543
S	Sw	wing surface area	ft²	5500	Roskam pg 543

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 636636 Roskam pg 543 converted to Mass
[slug/ft³] in code

I_xx I_xx roll inertia slug ft² 18200000 Roskam pg 543

I_yy I_yy pitch inertia slug ft² 33100000 Roskam pg 543

I_zz I_zz yaw inertia slug ft² 49700000 Roskam pg 543

I_xz I_xz lateral cross inertia slug ft² 970000 Roskam pg 543

Mass Data
Variable	Variable in Code	Description	Units	Value(s)	Source	Notes
W	Weight	weight at flight condition	lb	636636	Roskam pg 543	converted to Mass [slug/ft³] in code
I_xx	I_xx	roll inertia	slug ft²	18200000	Roskam pg 543
I_yy	I_yy	pitch inertia	slug ft²	33100000	Roskam pg 543
I_zz	I_zz	yaw inertia	slug ft²	49700000	Roskam pg 543
I_xz	I_xz	lateral cross inertia	slug ft²	970000	Roskam pg 543

Propulsion Data

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

T_max simpleSingleMaxThrust maximum thrust lb 39500 Roskam pg 544 estimated from C_{T_x}
at sea level

T_max simpleSingleMaxThrust maximum thrust lb 164000 MAM site engine rating (747-100)

T_max simpleSingleMaxThrust maximum thrust lb 254000 MAM site engine rating (747-400)

Propulsion Data
Variable	Variable in Code	Description	Units	Value(s)	Source	Notes
T_max	simpleSingleMaxThrust	maximum thrust	lb	39500	Roskam pg 544	estimated from C_{T_x} at sea level
T_max	simpleSingleMaxThrust	maximum thrust	lb	164000	MAM site	engine rating (747-100)
T_max	simpleSingleMaxThrust	maximum thrust	lb	254000	MAM site	engine rating (747-400)

Aerodynamic Data

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

C_D₀ CDo drag coefficient at =0 - 0.0164 Roskam pg 544

C_D CD_a drag curve slope 1/rad 0.20 Roskam pg 544

C_{D_e} CD_de drag due to elevator 1/rad 0 Roskam pg 544 e positive down

C_L₀ CLo lift coefficient at =0 - 0.21 Roskam pg 544

C_L CL_a lift curve slope 1/rad 4.4 Roskam pg 544

C_L CL_adot lift due to angle of attack rate 1/rad 7.0 Roskam pg 544

C_{L_q} CL_q lift due to pitch rate 1/rad 6.6 Roskam pg 544

C_{L_e} CL_de lift due to elevator 1/rad 0.32 Roskam pg 544 e positive down

C_m₀ Cmo pitch moment coefficient at =0 - 0 Roskam pg 544

C_m Cm_a pitch moment due to angle of attack 1/rad -1.0 Roskam pg 544

C_m Cm_adot pitch moment due to angle of attack rate 1/rad -4.0 Roskam pg 544

C_{m_q} Cm_q pitch moment due to pitch rate 1/rad -20.5 Roskam pg 544

C_{m_e} Cm_de pitching moment due to elevator 1/rad -1.3 Roskam pg 544 e positive down

C_Y CY_beta side force fue to sideslip angle 1/rad -0.90 Roskam pg 545

C_{Y_p} CY_p side force due to roll rate 1/rad 0 Roskam pg 545

C_{Y_r} CY_r side force due to yaw rate 1/rad 0 Roskam pg 545

C_{Y_a} CY_da side force due to aileron 1/rad 0 Roskam pg 545 a positive
right aileron up

C_{Y_r} CY_dr side force due to rudder 1/rad 0.120 Roskam pg 545 r positive left

C_l Cl_beta dihedral effect 1/rad -0.160 Roskam pg 545

C_{l_p} Cl_p roll damping 1/rad -0.340 Roskam pg 545

C_{l_r} Cl_r roll moment due to yaw rate 1/rad 0.130 Roskam pg 545

C_{l_a} Cl_da roll moment due to aileron 1/rad -0.013 Roskam pg 545 a positive
right aileron up

C_{l_r} Cl_dr roll moment due to rudder 1/rad 0.008 Roskam pg 545 r positive left

C_n Cn_beta weathercock stability 1/rad 0.160 Roskam pg 545

C_{n_p} Cn_p adverse yaw 1/rad -0.026 Roskam pg 545

C_{n_r} Cn_r yaw damping 1/rad -0.280 Roskam pg 545

C_{n_a} Cn_da yaw moment due to aileron 1/rad -0.0018 Roskam pg 545 a positive
right aileron up

C_{n_r} Cn_dr yaw moment due to rudder 1/rad -0.100 Roskam pg 545 r positive left

Variable	Variable in Code	Description	Units	Value(s)	Source	Notes
Aerodynamic Data
C_D₀	CDo	drag coefficient at =0	-	0.0164	Roskam pg 544
C_D	CD_a	drag curve slope	1/rad	0.20	Roskam pg 544
C_{D_e}	CD_de	drag due to elevator	1/rad	0	Roskam pg 544	e positive down
C_L₀	CLo	lift coefficient at =0	-	0.21	Roskam pg 544
C_L	CL_a	lift curve slope	1/rad	4.4	Roskam pg 544
C_L	CL_adot	lift due to angle of attack rate	1/rad	7.0	Roskam pg 544
C_{L_q}	CL_q	lift due to pitch rate	1/rad	6.6	Roskam pg 544
C_{L_e}	CL_de	lift due to elevator	1/rad	0.32	Roskam pg 544	e positive down
C_m₀	Cmo	pitch moment coefficient at =0	-	0	Roskam pg 544
C_m	Cm_a	pitch moment due to angle of attack	1/rad	-1.0	Roskam pg 544
C_m	Cm_adot	pitch moment due to angle of attack rate	1/rad	-4.0	Roskam pg 544
C_{m_q}	Cm_q	pitch moment due to pitch rate	1/rad	-20.5	Roskam pg 544
C_{m_e}	Cm_de	pitching moment due to elevator	1/rad	-1.3	Roskam pg 544	e positive down
C_Y	CY_beta	side force fue to sideslip angle	1/rad	-0.90	Roskam pg 545
C_{Y_p}	CY_p	side force due to roll rate	1/rad	0	Roskam pg 545
C_{Y_r}	CY_r	side force due to yaw rate	1/rad	0	Roskam pg 545
C_{Y_a}	CY_da	side force due to aileron	1/rad	0	Roskam pg 545	a positive right aileron up
C_{Y_r}	CY_dr	side force due to rudder	1/rad	0.120	Roskam pg 545	r positive left
C_l	Cl_beta	dihedral effect	1/rad	-0.160	Roskam pg 545
C_{l_p}	Cl_p	roll damping	1/rad	-0.340	Roskam pg 545
C_{l_r}	Cl_r	roll moment due to yaw rate	1/rad	0.130	Roskam pg 545
C_{l_a}	Cl_da	roll moment due to aileron	1/rad	-0.013	Roskam pg 545	a positive right aileron up
C_{l_r}	Cl_dr	roll moment due to rudder	1/rad	0.008	Roskam pg 545	r positive left
C_n	Cn_beta	weathercock stability	1/rad	0.160	Roskam pg 545
C_{n_p}	Cn_p	adverse yaw	1/rad	-0.026	Roskam pg 545
C_{n_r}	Cn_r	yaw damping	1/rad	-0.280	Roskam pg 545
C_{n_a}	Cn_da	yaw moment due to aileron	1/rad	-0.0018	Roskam pg 545	a positive right aileron up
C_{n_r}	Cn_dr	yaw moment due to rudder	1/rad	-0.100	Roskam pg 545	r positive left

Boeing 747 -- Linear Model

Flight Sim Home * Aircraft Models * Boeing 747 Model * Boeing 747 References

**Flight Sim Home * Aircraft Models * Boeing 747 Model * Boeing 747 References**