def __init__(self):
CL = Variable('C_L', '-', 'Lift coefficient')
CLmax = Variable('C_{L_{max}}', '-', 'Max lift coefficient')
CD = Variable('C_D', '-', 'Drag coefficient')
D = Variable('D', 'N', 'Total aircraft drag (cruise)')
Dfuse = Variable('D_{fuse}', 'N', 'Fuselage drag')
Dht = Variable('D_{ht}', 'N', 'Horizontal tail drag')
Dvt = Variable('D_{vt}', 'N', 'Vertical tail drag')
Dwing = Variable('D_{wing}', 'N', 'Wing drag')
LD = Variable('\\frac{L}{D}', '-', 'Lift/drag ratio')
Lh = Variable('L_h', 'N', 'Horizontal tail downforce')
Lw = Variable('L_w', 'N', 'Wing lift')
M = Variable('M', '-', 'Cruise Mach number')
R = Variable('Range', 'nautical_miles', 'Range')
Sw = Variable('S_w', 'm**2', 'Wing reference area')
Te = Variable('T_e', 'N', 'Engine thrust at takeoff')
TSFC = Variable('c_T', 'lb/lbf/hr',
'Thrust specific fuel consumption')
V = Variable('V_{\\infty}', 'm/s', 'Cruise velocity')
VTO = Variable('V_{TO}', 'm/s', 'Takeoff speed')
W = Variable('W', 'N', 'Total aircraft weight')
Weng = Variable('W_{eng}', 'N', 'Engine weight')
Wfuel = Variable('W_{fuel}', 'N', 'Fuel weight')
Wfuse = Variable('W_{fuse}', 'N', 'Fuselage weight')
Wht = Variable('W_{ht}', 'N', 'Horizontal tail weight')
Wlg = Variable('W_{lg}', 'N', 'Landing gear weight')
Wpay = Variable('W_{pay}', 'N', 'Payload weight')
Wvt = Variable('W_{vt}', 'N', 'Vertical tail weight')
Wwing = Variable('W_{wing}', 'N', 'Wing weight')
Wzf = Variable('W_{zf}', 'N', 'Zero fuel weight')
a = Variable('a', 'm/s', 'Speed of sound (35,000 ft)')
g = Variable('g', 9.81, 'm/s^2', 'Gravitational acceleration')
lr = Variable('l_r', 5000, 'ft', 'Runway length')
rho = Variable('\\rho', 'kg/m^3', 'Air density (cruise)')
rho0 = Variable('\\rho_0', 'kg/m^3', 'Air density (sea level)')
xCG = Variable('x_{CG}', 'm', 'x-location of CG')
xCGeng = Variable('x_{CG_{eng}}', 'm', 'x-location of engine CG')
xCGfu = Variable('x_{CG_{fu}}', 'm', 'x-location of fuselage CG')
xCGht = Variable('x_{CG_{ht}}', 'm', 'x-location of htail CG')
xCGlg = Variable('x_{CG_{lg}}', 'm', 'x-location of landing gear CG')
xCGvt = Variable('x_{CG_{vt}}', 'm', 'x-location of vtail CG')
xCGwing = Variable('x_{CG_{wing}}', 'm', 'x-location of wing CG')
xTO = Variable('x_{TO}', 'm', 'Takeoff distance')
xi = Variable('\\xi', '-', 'Takeoff parameter')
xw = Variable('x_w', 'm', 'x-location of wing aerodynamic center')
y = Variable('y', '-', 'Takeoff parameter')
z_bre = Variable('z_{bre}', '-', 'Breguet parameter')
with SignomialsEnabled():
objective = Wfuel
# High level constraints
hlc = [
# Drag and weight buildup
D >= Dvt + Dfuse + Dwing + Dht,
Wzf >= Wvt + Wfuse + Wlg + Wwing + Wht + Weng + Wpay,
W >= Wzf + Wfuel,
# Range equation for a jet
V == M*a,
D == 0.5*rho*V**2*Sw*CD,
W == 0.5*rho*V**2*Sw*CL,
LD == CL/CD,
Lw >= W, # TODO: add Lh
R <= z_bre*LD*V/(TSFC*g),
Wfuel/Wzf >= te_exp_minus1(z_bre, nterm=3),
# CG relationships
TCS([xCG*W >= Wvt*xCGvt + Wfuse*xCGfu + Wlg*xCGlg
+ Wwing*xCGwing + Wht*xCGht + Weng*xCGeng
+ Wfuel*xCGwing + Wpay*xCGfu],
reltol=1E-2, raiseerror=False),
xw == xCGwing,
xCGeng == xCGwing,
#Takeoff relationships
xi >= 0.5*rho0*VTO**2*Sw*CD/Te,
4*g*xTO*Te/(W*VTO**2) >= 1 + y,
1 >= 0.0464*xi**2.73/y**2.88 + 1.044*xi**0.296/y**0.049,
VTO == 1.2*(2*W/(rho0*Sw*CLmax))**0.5,
xTO <= lr,
]
# Subsystem models
vt = VerticalTail.coupled737()
fu = Fuselage.coupled737()
lg = LandingGear.coupled737()
ht = HorizontalTail.coupled737()
wi = Wing.coupled737()
wb = WingBox()
substitutions = {
'C_{L_{max}}': 2.5,
'M': 0.78,
'Range': 3000,
'c_T': 0.3,
'W_{eng}': 10000,
'a': 297,
}
lc = LinkedConstraintSet([hlc, vt, fu, lg, ht, wi],
exclude=[vk.name for vk in wb.varkeys
if not vk.value])
Model.__init__(self, objective,
lc,
substitutions)
