F-4 Phantom -- Linear Model
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):
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| Variable |
Variable in Code |
Description | Units | Value(s) | Source | Notes |
|---|---|---|---|---|---|---|
| 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 | |
| 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:
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| Variable |
Variable in Code |
Description | Units | Value(s) | Source | Notes |
|---|---|---|---|---|---|---|
| b | bw | wingspan | ft | 38.7 | Roskam pg 536 | |
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cbar | wing mean aerodynamic chord | ft | 16 | Roskam pg 536 | |
| S | Sw | wing surface area | ft2 | 530 | Roskam pg 536 | |
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| Variable |
Variable in Code |
Description | Units | Value(s) | Source | Notes |
|---|---|---|---|---|---|---|
 emax
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demax | maximum elevator deflection | deg | +20 | - | guess |
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emin
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demin | minimum elevator deflection | deg | -20 | - | guess |
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amax
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damax | maximum aileron deflection | deg | +20 | - | guess |
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amin
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damin | minimum aileron deflection | deg | -20 | - | guess |
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rmax
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drmax | maximum rudder deflection | deg | +20 | - | guess |
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rmin
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drmin | minimum rudder deflection | deg | -20 | - | guess |
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| 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 |
| Ixx | I_xx | roll inertia | slug ft2 | 25000 | Roskam pg 536 | |
| Iyy | I_yy | pitch inertia | slug ft2 | 122200 | Roskam pg 536 | |
| Izz | I_zz | yaw inertia | slug ft2 | 139800 | Roskam pg 536 | |
| Ixz | I_xz | lateral cross inertia | slug ft2 | 2200 | Roskam pg 536 | |
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| Variable |
Variable in Code |
Description | Units | Value(s) | Source | Notes |
|---|---|---|---|---|---|---|
| Tmax | simpleSingleMaxThrust | maximum thrust | lb | 6670 | Roskam pg 537 |
estimated from CTx at sea level |
| Tmax | simpleSingleMaxThrust | maximum thrust | lb | 32000 | MAM site |
engine rating (F-4A) |
| Tmax | simpleSingleMaxThrust | maximum thrust | lb | 35800 | MAM site |
engine rating (F-4E) |
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| Variable |
Variable in Code |
Description | Units | Value(s) | Source | Notes |
|---|---|---|---|---|---|---|
| CD0 | CDo |
drag coefficient at =0
|
- | 0.0205 | Roskam pg 537 | |
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CD
|
CD_a | drag curve slope | 1/rad | 0.3 | Roskam pg 537 | |
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CDe
|
CD_de | drag due to elevator | 1/rad | -0.1 | Roskam pg 537 |
e positive down
|
| CL0 | CLo |
lift coefficient at =0
|
- | 0.1 | Roskam pg 537 | |
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CL
|
CL_a | lift curve slope | 1/rad | 3.75 | Roskam pg 537 | |
CL
|
CL_adot | lift due to angle of attack rate | 1/rad | 0.86 | Roskam pg 537 | |
| CLq | CL_q | lift due to pitch rate | 1/rad | 1.8 | Roskam pg 537 | |
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CLe
|
CL_de | lift due to elevator | 1/rad | 0.4 | Roskam pg 537 |
e positive down
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| Cm0 | Cmo |
pitch moment coefficient at =0
|
- | 0.025 | Roskam pg 537 | |
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Cm
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Cm_a | pitch moment due to angle of attack | 1/rad | -0.4 | Roskam pg 537 | |
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Cm
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Cm_adot | pitch moment due to angle of attack rate | 1/rad | -1.3 | Roskam pg 537 | |
| Cmq | Cm_q | pitch moment due to pitch rate | 1/rad | -2.7 | Roskam pg 537 | |
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Cme
|
Cm_de | pitching moment due to elevator | 1/rad | -0.58 | Roskam pg 537 |
e positive down
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CY
|
CY_beta | side force fue to sideslip angle | 1/rad | -0.68 | Roskam pg 538 | |
| CYp | CY_p | side force due to roll rate | 1/rad | 0 | Roskam pg 538 | |
| CYr | CY_r | side force due to yaw rate | 1/rad | 0 | Roskam pg 538 | |
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CYa
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CY_da | side force due to aileron | 1/rad | 0.016 | Roskam pg 538 |
a positive right aileron up |
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CYr
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CY_dr | side force due to rudder | 1/rad | 0.095 | Roskam pg 538 |
r positive left
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Cl
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Cl_beta | dihedral effect | 1/rad | -0.08 | Roskam pg 538 | |
| Clp | Cl_p | roll damping | 1/rad | -0.24 | Roskam pg 538 | |
| Clr | Cl_r | roll moment due to yaw rate | 1/rad | 0.07 | Roskam pg 538 | |
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Cla
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Cl_da | roll moment due to aileron | 1/rad | -0.042 | Roskam pg 538 |
a positive right aileron up |
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Clr
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Cl_dr | roll moment due to rudder | 1/rad | 0.006 | Roskam pg 538 |
r positive left
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Cn
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Cn_beta | weathercock stability | 1/rad | 0.125 | Roskam pg 538 | |
| Cnp | Cn_p | adverse yaw | 1/rad | -0.036 | Roskam pg 538 | |
| Cnr | Cn_r | yaw damping | 1/rad | -0.27 | Roskam pg 538 | |
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Cna
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Cn_da | yaw moment due to aileron | 1/rad | 0.001 | Roskam pg 538 |
a positive right aileron up |
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Cnr
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Cn_dr | yaw moment due to rudder | 1/rad | -0.066 | Roskam pg 538 |
r positive left
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