X-15 -- 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 April 11, 2000
The linear aerodynamics model uses stability derivatives to approximate actual aircraft behavior. The X-15 linear model is based on the following flight conditions:
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| Variable |
Variable in Code |
Description | Units | Value(s) | Source | Notes |
|---|---|---|---|---|---|---|
| h | Altitude | altitude above sea level | ft | 60000 | Berndt communications |
|
Alpha | angle of attack | deg | ? | not available |
V
|
V_true_kts | velocity (true air speed) | kts | ? | not available | |
| q | Dynamic_pressure | dynamic pressure | lb/ft2 | ? | not available | |
| C.G. | - | center of gravity location |
% 
|
22 | Berndt site | |
| 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 | 22.36 | Berndt site | |
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cbar | wing mean aerodynamic chord | ft | 10.27 | Berndt site | |
| S | Sw | wing surface area | ft2 | 200 | Berndt site | |
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| Variable |
Variable in Code |
Description | Units | Value(s) | Source | Notes |
|---|---|---|---|---|---|---|
 emax
|
demax | maximum elevator deflection | deg | +35 | Berndt site | |
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emin
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demin | minimum elevator deflection | deg | -15 | Berndt site | |
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amax
|
damax | maximum aileron deflection | deg | +15 | Berndt site | |
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amin
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damin | minimum aileron deflection | deg | -15 | Berndt site | |
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rmax
|
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 |
|---|---|---|---|---|---|---|
| GTOW | Weight | gross takeoff weight | lb | 31240 | Berndt site |
converted to Mass [slug/ft3] in code |
| Ixx | I_xx | roll inertia | slug ft2 | 3650 | Berndt site | |
| Iyy | I_yy | pitch inertia | slug ft2 | 80000 | Berndt site | |
| Izz | I_zz | yaw inertia | slug ft2 | 82000 | Berndt site | |
| Ixz | I_xz | lateral cross inertia | slug ft2 | 590 | Berndt site | |
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| Variable |
Variable in Code |
Description | Units | Value(s) | Source | Notes |
|---|---|---|---|---|---|---|
| Tmax | simpleSingleMaxThrust | maximum thrust | lb | 51090 | Berndt site | sea level |
| Tmax | simpleSingleMaxThrust | maximum thrust | lb | 57000 | Berndt site | @ 45000 ft |
| Tmax | simpleSingleMaxThrust | maximum thrust | lb | 70000 | David pg 706 | @ peak altitude |
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| Variable |
Variable in Code |
Description | Units | Value(s) | Source | Notes |
|---|---|---|---|---|---|---|
| CD0 | CDo |
drag coefficient at =0
|
- | 0.095 | JSBsim | |
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CD
|
CD_a | drag curve slope | 1/rad | 0.6 | JSBsim | |
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CDe
|
CD_de | drag due to elevator | 1/rad | - |
not available
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| CL0 | CLo |
lift coefficient at =0
|
- | - | not available | |
|
CL
|
CL_a | lift curve slope | 1/rad | 3.5 | JSBsim | |
CL
|
CL_adot | lift due to angle of attack rate | 1/rad | - | not available | |
| CLq | CL_q | lift due to pitch rate | 1/rad | - | not available | |
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CLe
|
CL_de | lift due to elevator | 1/rad | 0.50 | JSBsim |
e positive down
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| Cm0 | Cmo |
pitch moment coefficient at =0
|
- | - | not available | |
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Cm
|
Cm_a | pitch moment due to angle of attack | 1/rad | -1.2 | JSBsim | |
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Cm
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Cm_adot | pitch moment due to angle of attack rate | 1/rad | 0 | JSBsim | |
| Cmq | Cm_q | pitch moment due to pitch rate | 1/rad | -6.2 | JSBsim | |
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Cme
|
Cm_de | pitching moment due to elevator | 1/rad | -0.9 | JSBsim |
e positive down
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CY
|
CY_beta | side force fue to sideslip angle | 1/rad | -1.4 | JSBsim | |
| CYp | CY_p | side force due to roll rate | 1/rad | - | not available | |
| CYr | CY_r | side force due to yaw rate | 1/rad | - | not available | |
|
CYa
|
CY_da | side force due to aileron | 1/rad | 0.05 | JSBsim |
a positive right aileron up |
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CYr
|
CY_dr | side force due to rudder | 1/rad | 0.45 | JSBsim |
r positive left
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Cl
|
Cl_beta | dihedral effect | 1/rad | -0.01 | JSBsim | |
| Clp | Cl_p | roll damping | 1/rad | -0.35 | JSBsim | |
| Clr | Cl_r | roll moment due to yaw rate | 1/rad | 0.04 | JSBsim | |
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Cla
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Cl_da | roll moment due to aileron | 1/rad | -0.06 | JSBsim |
a positive right aileron up |
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Clr
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Cl_dr | roll moment due to rudder | 1/rad | 0.012 | JSBsim |
r positive left
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Cn
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Cn_beta | weathercock stability | 1/rad | 0.5 | JSBsim | |
| Cnp | Cn_p | adverse yaw | 1/rad | 0 | JSBsim | |
| Cnr | Cn_r | yaw damping | 1/rad | -1.5 | JSBsim | |
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Cna
|
Cn_da | yaw moment due to aileron | 1/rad | -0.04 | JSBsim |
a positive right aileron up |
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Cnr
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Cn_dr | yaw moment due to rudder | 1/rad | -0.3 | JSBsim |
r positive left
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