# 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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