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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