How to use the gpkit.tools.te_exp_minus1 function in gpkit
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convexengineering / SPaircraft / gpkitmodels / Commercial Sizing / Commerical_Flight_Profile_Simple_Performance.py View on Github 
self.fuseP = self.aircraftP.fuseP
self.engineP = self.aircraftP.engineP
#variable definitions
z_bre = Variable('z_{bre}', '-', 'Breguet Parameter')
Rng = Variable('Rng', 'nautical_miles', 'Cruise Segment Range')
constraints = []
constraints.extend([
#steady level flight constraint on D
self.aircraftP['D'] == aircraft['numeng'] * self.engineP['thrust'],
#taylor series expansion to get the weight term
TCS([self.aircraftP['W_{burn}']/self.aircraftP['W_{end}'] >=
te_exp_minus1(z_bre, nterm=3)]),
#breguet range eqn
# old version -- possibly unneeded numeng
# TCS([z_bre >= (self.aircraft['numeng'] * self.engineP['TSFC'] * self.aircraftP['thr']*
# self.aircraftP['D']) / self.aircraftP['W_{avg}']]),
# new version -- needs to be thought through carefully
# seems correct to me - I switched T to D below (steady level flight) but fogot
#about the Negn term
TCS([z_bre >= (self.engineP['TSFC'] * self.aircraftP['thr']*
self.aircraftP['D']) / self.aircraftP['W_{avg}']]),
#time
self.aircraftP['thr'] * state['V'] == Rng,
])self.fuseP = self.aircraftP.fuseP
self.engineP = self.aircraftP.engineP
#variable definitions
z_bre = Variable('z_{bre}', '-', 'Breguet Parameter')
Rng = Variable('Rng', 'nautical_miles', 'Cruise Segment Range')
constraints = []
constraints.extend([
#steady level flight constraint on D
self.aircraftP['D'] == aircraft['numeng'] * self.engineP['thrust'],
#taylor series expansion to get the weight term
TCS([self.aircraftP['W_{burn}']/self.aircraftP['W_{end}'] >=
te_exp_minus1(z_bre, nterm=3)]),
#breguet range eqn
# old version -- possibly unneeded numeng
# TCS([z_bre >= (self.aircraft['numeng'] * self.engineP['TSFC'] * self.aircraftP['thr']*
# self.aircraftP['D']) / self.aircraftP['W_{avg}']]),
# new version -- needs to be thought through carefully
# seems correct to me - I switched T to D below (steady level flight) but fogot
#about the Negn term
TCS([z_bre >= (self.engineP['TSFC'] * self.aircraftP['thr']*
self.aircraftP['D']) / self.aircraftP['W_{avg}']]),
#time
self.aircraftP['thr'] * state['V'] == Rng,
])self.fuseP = self.aircraftP.fuseP
self.engineP = self.aircraftP.engineP
#variable definitions
z_bre = Variable('z_{bre}', '-', 'Breguet Parameter')
Rng = Variable('Rng', 'nautical_miles', 'Cruise Segment Range')
constraints = []
constraints.extend([
# Steady level flight constraint on D
self.aircraftP['D'] == aircraft['numeng'] * self.engineP['thrust'],
# Taylor series expansion to get the weight term
TCS([self.aircraftP['W_{burn}']/self.aircraftP['W_{end}'] >=
te_exp_minus1(z_bre, nterm=3)]),
# Breguet range eqn
TCS([z_bre >= (self.engineP['TSFC'] * self.aircraftP['thr']*
self.aircraftP['D']) / self.aircraftP['W_{avg}']]),
# Time
self.aircraftP['thr'] * state['V'] == Rng,
])
return constraints, self.aircraftP#----------------------------------------------------
# Breguet Range
z_bre = VectorVariable(NSeg, 'z_{bre}', '-', 'breguet coefficient')
t_cruise = Variable('t_{cruise}', 1, 'days', 'time to station')
t_station = Variable('t_{station}',6, 'days', 'time on station')
R = Variable('R', 200, 'nautical_miles', 'range to station')
R_cruise = Variable('R_{cruise}', 180, 'nautical_miles',
'range to station during climb')
constraints.extend([
z_bre >= P_shafttot*t*BSFC*g/W_end,
R_cruise/NCruise1 <= V[iCruise1]*t[iCruise1],
R/NCruise2 <= V[iCruise2]*t[iCruise2],
t[iLoiter] >= t_station/NLoiter,
sum(t[iCruise+iClimb]) <= t_cruise,
FuelOilFrac*W_fuel/W_end >= te_exp_minus1(z_bre, 3)
])
#----------------------------------------------------
# Aerodynamics model
CLmax = Variable('C_{L-max}', 1.5, '-', 'Maximum lift coefficient')
e = Variable('e', 0.95, '-', 'Spanwise efficiency')
AR = Variable('AR', '-', 'Aspect ratio')
b = Variable('b', 'ft', 'Span')
Re = VectorVariable(NSeg, 'Re', '-', 'Reynolds number')
# fuselage drag
Kfuse = Variable('K_{fuse}', 1.1, '-', 'Fuselage form factor')
S_fuse = Variable('S_{fuse}', 'ft^2', 'Fuselage surface area')
Cffuse = VectorVariable(NSeg, 'C_{f-fuse}', '-',
'Fuselage skin friction coefficient')self.fuseP = self.aircraftP.fuseP
self.engineP = self.aircraftP.engineP
#variable definitions
z_bre = Variable('z_{bre}', '-', 'Breguet Parameter')
Rng = Variable('Rng', 'nautical_miles', 'Cruise Segment Range')
constraints = []
constraints.extend([
#steady level flight constraint on D
self.aircraftP['D'] == aircraft['numeng'] * self.engineP['thrust'],
#taylor series expansion to get the weight term
TCS([self.aircraftP['W_{burn}']/self.aircraftP['W_{end}'] >=
te_exp_minus1(z_bre, nterm=3)]),
#breguet range eqn
TCS([z_bre >= (self.engineP['TSFC'] * self.aircraftP['thr']*
self.aircraftP['D']) / self.aircraftP['W_{avg}']]),
#time
self.aircraftP['thr'] * state['V'] == Rng,
])
Model.__init__(self, None, constraints + self.aircraftP)self.fuseP = self.aircraftP.fuseP
self.engineP = self.aircraftP.engineP
#variable definitions
z_bre = Variable('z_{bre}', '-', 'Breguet Parameter')
Rng = Variable('Rng', 'nautical_miles', 'Cruise Segment Range')
constraints = []
constraints.extend([
#steady level flight constraint on D
self.aircraftP['D'] == aircraft['numeng'] * self.engineP['thrust'],
#taylor series expansion to get the weight term
TCS([self.aircraftP['W_{burn}']/self.aircraftP['W_{end}'] >=
te_exp_minus1(z_bre, nterm=3)]),
# new version -- needs to be thought through carefully
# seems correct to me - I switched T to D below (steady level flight) but fogot
#about the Negn term
TCS([z_bre >= (self.engineP['TSFC'] * self.aircraftP['thr']*
self.aircraftP['D']) / self.aircraftP['W_{avg}']]),
#time
self.aircraftP['thr'] * state['V'] == Rng,
])
Model.__init__(self, None, constraints + self.aircraftP)self.perf = aircraft.dynamic(self.state)
Wstart = Variable('W_{start}', 'N', 'Segment Start Weight')
Wend = Variable('W_{end}', 'N', 'Segment End Weight')
Wburn = Variable("W_{burn}", "N", "fuel burned weight")
d = Variable("d", "nautical_miles", "flight distance")
t = Variable("t", "hrs", "flight time")
zbre = Variable('z_{bre}', '-', 'Breguet Parameter')
Wfuel = Variable("W_{fuel}", "N", "flight segment fuel weight")
R = Variable("R", "nautical_miles", "flight segment range")
constraints = [
self.perf["W_{avg}"] == (Wstart*Wend)**0.5,
Wfuel >= sum(Wburn),
zbre >= self.perf["TSFC"]*t*self.perf["D"]/self.perf["W_{avg}"],
Wburn/Wend >= te_exp_minus1(zbre, nterm=3),
Wstart >= Wend + Wburn,
d == t*self.state["V"],
R == d*N]
if N > 1:
constraints.extend([Wend[:-1] >= Wstart[1:]])
return constraints, self.state, self.perf# Weight breakdown
constraints.extend([W_airframe >= f_airframe*MTOW,
W_zfw >= W_pay + W_avionics + W_airframe + W_engtot])
#----------------------------------------------------
# Breguet Range
z_bre = VectorVariable(NSeg, 'z_{bre}', '-', 'breguet coefficient')
BSFC = VectorVariable(NSeg,'BSFC', [0.5,.55,0.6], 'lbf/hr/hp', 'brake specific fuel consumption')
t = VectorVariable(NSeg, 't', 'days', 'time on station')
R = Variable('R', 200, 'nautical_miles', 'range to station')
g = Variable('g', 9.81, 'm/s^2', 'Gravitational acceleration')
constraints.extend([z_bre >= V*t*BSFC*CD/CL/eta_prop,
R == V[NCruise]*t[NCruise],
t[NLoiter] == 5*units('days'),
W_fuel/W_end >= te_exp_minus1(z_bre, 3)])
#----------------------------------------------------
# Aerodynamics model
Cd0 = Variable('C_{d0}', 0.02, '-', 'Non-wing drag coefficient')
CLmax = Variable('C_{L-max}', 1.5, '-', 'Maximum lift coefficient')
e = Variable('e', 0.9, '-', 'Spanwise efficiency')
AR = Variable('AR', '-', 'Aspect ratio')
b = Variable('b', 'ft', 'Span')
mu = Variable(r'\mu', 1.5e-5, 'N*s/m^2', 'Dynamic viscosity')
Re = VectorVariable(NSeg, 'Re', '-', 'Reynolds number')
Cf = VectorVariable(NSeg, 'C_f', '-', 'wing skin friction coefficient')
Kwing = Variable('K_{wing}', 1.3, '-', 'wing form factor')
cl_16 = Variable('cl_{16}', 0.0001, '-', 'profile stall coefficient')
constraints.extend([CD >= Cd0 + 2*Cf*Kwing + CL**2/(pi*e*AR) + cl_16*CL**16,def setup(self, perf):
z_bre = Variable("z_{bre}", "-", "Breguet coefficient")
t = Variable("t", "days", "Time per flight segment")
f_fueloil = Variable("f_{(fuel/oil)}", 0.98, "-", "Fuel-oil fraction")
Wfuel = Variable("W_{fuel}", "lbf", "Segment-fuel weight")
g = Variable("g", 9.81, "m/s^2", "gravitational acceleration")
constraints = [
TCS([z_bre >= (perf["P_{total}"]*t*perf["BSFC"]*g
/ (perf["W_{end}"]*perf["W_{start}"])**0.5)]),
f_fueloil*Wfuel/perf["W_{end}"] >= te_exp_minus1(z_bre, 3),
perf["W_{start}"] >= perf["W_{end}"] + Wfuel
]
return constraintsdef __init__(self, **kwargs):
T_tp = 216.65
k = GRAVITATIONAL_ACCEL/(GAS_CONSTANT*T_tp)
p11 = Variable('p_{11}', 22630, 'Pa', 'Pressure at 11 km')
objective = 1/rho # maximize density
constraints = [h >= 11*units.km,
h <= 20*units.km,
# Temperature is constant in the tropopause
T == T_tp,
# Pressure-altitude relation, using taylor series exp
TCS([np.exp(k*11000)*p11/p >=
1 + te_exp_minus1(g/(R*T)*h, 15)], reltol=1E-4),
# Ideal gas law
rho == p/(R*T),
]
su = Sutherland()
lc = su.link(constraints)
Model.__init__(self, objective, lc, **kwargs)gpkit
Package for defining and manipulating geometric programming models.
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- gpkit.units
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