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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):

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

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

Geometry
Variable Variable
in Code
Description Units Value(s) Source Notes
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
emax demax maximum elevator deflection deg +20 - guess
emin demin minimum elevator deflection deg -20 - guess
amax damax maximum aileron deflection deg +20 - guess
amin damin minimum aileron deflection deg -20 - guess
rmax drmax maximum rudder deflection deg +20 - guess
rmin 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
Ixx I_xx roll inertia slug ft2 18200000 Roskam pg 543
Iyy I_yy pitch inertia slug ft2 33100000 Roskam pg 543
Izz I_zz yaw inertia slug ft2 49700000 Roskam pg 543
Ixz I_xz lateral cross inertia slug ft2 970000 Roskam pg 543

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

Aerodynamic Data
Variable Variable
in Code
Description Units Value(s) Source Notes
CD0 CDo drag coefficient at =0 - 0.0164 Roskam pg 544
CD CD_a drag curve slope 1/rad 0.20 Roskam pg 544
CDe CD_de drag due to elevator 1/rad 0 Roskam pg 544 e positive down
CL0 CLo lift coefficient at =0 - 0.21 Roskam pg 544
CL CL_a lift curve slope 1/rad 4.4 Roskam pg 544
CL CL_adot lift due to angle of attack rate 1/rad 7.0 Roskam pg 544
CLq CL_q lift due to pitch rate 1/rad 6.6 Roskam pg 544
CLe CL_de lift due to elevator 1/rad 0.32 Roskam pg 544 e positive down
Cm0 Cmo pitch moment coefficient at =0 - 0 Roskam pg 544
Cm Cm_a pitch moment due to angle of attack 1/rad -1.0 Roskam pg 544
Cm Cm_adot pitch moment due to angle of attack rate 1/rad -4.0 Roskam pg 544
Cmq Cm_q pitch moment due to pitch rate 1/rad -20.5 Roskam pg 544
Cme Cm_de pitching moment due to elevator 1/rad -1.3 Roskam pg 544 e positive down
CY CY_beta side force fue to sideslip angle 1/rad -0.90 Roskam pg 545
CYp CY_p side force due to roll rate 1/rad 0 Roskam pg 545
CYr CY_r side force due to yaw rate 1/rad 0 Roskam pg 545
CYa CY_da side force due to aileron 1/rad 0 Roskam pg 545 a positive
right aileron up
CYr CY_dr side force due to rudder 1/rad 0.120 Roskam pg 545 r positive left
Cl Cl_beta dihedral effect 1/rad -0.160 Roskam pg 545
Clp Cl_p roll damping 1/rad -0.340 Roskam pg 545
Clr Cl_r roll moment due to yaw rate 1/rad 0.130 Roskam pg 545
Cla Cl_da roll moment due to aileron 1/rad -0.013 Roskam pg 545 a positive
right aileron up
Clr Cl_dr roll moment due to rudder 1/rad 0.008 Roskam pg 545 r positive left
Cn Cn_beta weathercock stability 1/rad 0.160 Roskam pg 545
Cnp Cn_p adverse yaw 1/rad -0.026 Roskam pg 545
Cnr Cn_r yaw damping 1/rad -0.280 Roskam pg 545
Cna Cn_da yaw moment due to aileron 1/rad -0.0018 Roskam pg 545 a positive
right aileron up
Cnr Cn_dr yaw moment due to rudder 1/rad -0.100 Roskam pg 545 r positive left


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