# X-15 -- 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 X-15 linear model is based on the following flight conditions:

Flight Conditions
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:

Geometry
Variable | Variable in Code | Description | Units | Value(s) | Source | Notes
--- | --- | --- | --- | --- | --- | ---
b | bw | wingspan | ft | 22.36 | Berndt site |
| cbar | wing mean aerodynamic chord | ft | 10.27 | Berndt site |
S | Sw | wing surface area | ft2 | 200 | Berndt site |

Control Surface Geometry
Variable | Variable in Code | Description | Units | Value(s) | Source | Notes
--- | --- | --- | --- | --- | --- | ---
emax | demax | maximum elevator deflection | deg | +35 | Berndt site |
emin | demin | minimum elevator deflection | deg | -15 | Berndt site |
amax | damax | maximum aileron deflection | deg | +15 | Berndt site |
amin | damin | minimum aileron deflection | deg | -15 | Berndt site |
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
--- | --- | --- | --- | --- | --- | ---
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 |

Propulsion Data
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

Aerodynamic Data
Variable | Variable in Code | Description | Units | Value(s) | Source | Notes
--- | --- | --- | --- | --- | --- | ---
CD0 | CDo | drag coefficient at =0 | - | 0.095 | JSBsim |
CD | CD_a | drag curve slope | 1/rad | 0.6 | JSBsim |
CDe | CD_de | drag due to elevator | 1/rad | - |  | not available e positive down
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
CLe | CL_de | lift due to elevator | 1/rad | 0.50 | JSBsim | e positive down
Cm0 | Cmo | pitch moment coefficient at =0 | - | - |  | not available
Cm | Cm_a | pitch moment due to angle of attack | 1/rad | -1.2 | JSBsim |
Cm | 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 |
Cme | Cm_de | pitching moment due to elevator | 1/rad | -0.9 | JSBsim | e positive down
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
CYr | CY_dr | side force due to rudder | 1/rad | 0.45 | JSBsim | r positive left
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 |
Cla | Cl_da | roll moment due to aileron | 1/rad | -0.06 | JSBsim | a positive right aileron up
Clr | Cl_dr | roll moment due to rudder | 1/rad | 0.012 | JSBsim | r positive left
Cn | 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 |
Cna | Cn_da | yaw moment due to aileron | 1/rad | -0.04 | JSBsim | a positive right aileron up
Cnr | Cn_dr | yaw moment due to rudder | 1/rad | -0.3 | JSBsim | r positive left

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