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SimPleAC_mission.py
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SimPleAC_mission.py
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import numpy as np
from gpkit import Model, Variable, SignomialsEnabled, SignomialEquality, VarKey, units,Vectorize
from gpkit.constraints.bounded import Bounded
from gpkit.constraints.tight import Tight
# Importing models
from gpkitmodels.SP.atmosphere.atmosphere import Atmosphere
# SimPleAC with mission design and flight segments, and lapse rate and BSFC model (3.4.2)
class SimPleAC(Model):
def setup(self):
self.engine = Engine()
self.wing = Wing()
self.fuse = Fuselage()
self.components = [self.engine, self.wing, self.fuse]
# Environmental constants
g = Variable("g", 9.81, "m/s^2", "gravitational acceleration")
rho_f = Variable("\\rho_f", 817, "kg/m^3", "density of fuel")
# Free Variables
W = Variable("W", "N", "maximum takeoff weight")
W_f = Variable("W_f", "N", "maximum fuel weight")
V_f = Variable("V_f", "m^3", "maximum fuel volume")
V_f_avail = Variable("V_{f_{avail}}", "m^3", "fuel volume available")
constraints = []
# Thrust and drag model
constraints += [self.fuse['C_{D_{fuse}}'] == self.fuse['(CDA0)'] / self.wing['S']]
# Fuel volume model
with SignomialsEnabled():
constraints += [V_f == W_f / g / rho_f,
V_f_avail <= self.wing['V_{f_{wing}}'] + self.fuse['V_{f_{fuse}}'], #[SP]
V_f_avail >= V_f]
return constraints, self.components
def dynamic(self,state):
return SimPleACP(self,state)
class SimPleACP(Model):
def setup(self,aircraft,state):
self.aircraft = aircraft
self.engineP = aircraft.engine.dynamic(state)
self.wingP = aircraft.wing.dynamic(state)
self.Pmodels = [self.engineP, self.wingP]
# Free variables
C_D = Variable("C_D", "-", "drag coefficient")
D = Variable("D", "N", "total drag force")
LoD = Variable('L/D','-','lift-to-drag ratio')
Re = Variable("Re", "-", "Reynolds number")
V = Variable("V", "m/s", "cruising speed")
constraints = []
constraints += [self.engineP['T'] * V <= self.aircraft.engine['\\eta_{prop}'] * self.engineP['P_{shaft}'],
C_D >= self.aircraft['C_{D_{fuse}}'] + self.wingP['C_{D_{wpar}}'] + self.wingP['C_{D_{ind}}'],
D >= 0.5 * state['\\rho'] * self.aircraft['S'] * C_D * V ** 2,
Re == (state['\\rho'] / state['\\mu']) * V * (self.aircraft['S'] / self.aircraft['A']) ** 0.5,
self.wingP['C_f'] >= 0.074 / Re ** 0.2,
LoD == self.wingP['C_L'] / C_D]
return constraints, self.Pmodels
class Fuselage(Model):
def setup(self):
# Free Variables
CDA0 = Variable("(CDA0)", "m^2", "fuselage drag area") #0.035 originally
C_D_fuse = Variable('C_{D_{fuse}}','-','fuselage drag coefficient')
# Free variables (fixed for performance eval.)
V_f_fuse = Variable('V_{f_{fuse}}','m^3','fuel volume in the fuselage', fix = True)
constraints = []
constraints += [V_f_fuse == 10*units('m')*CDA0,
V_f_fuse >= 1*10**-5*units('m^3')]
return constraints
class Wing(Model):
def setup(self):
# Non-dimensional constants
C_Lmax = Variable("C_{L,max}", 1.6, "-", "lift coefficient at stall", pr=5.)
e = Variable("e", 0.92, "-", "Oswald efficiency factor", pr=3.)
k = Variable("k", 1.17, "-", "form factor", pr=10.)
N_ult = Variable("N_{ult}", 3.3, "-", "ultimate load factor", pr=15.)
S_wetratio = Variable("(\\frac{S}{S_{wet}})", 2.075, "-", "wetted area ratio", pr=3.)
tau = Variable("\\tau", 0.12, "-", "airfoil thickness to chord ratio", pr=10.)
# Dimensional constants
W_w_coeff1 = Variable("W_{w_{coeff1}}", 2e-5, "1/m",
"wing weight coefficient 1", pr= 30.) #orig 12e-5
W_w_coeff2 = Variable("W_{w_{coeff2}}", 60., "Pa",
"wing weight coefficient 2", pr=10.)
# Free Variables (fixed for performance eval.)
A = Variable("A", "-", "aspect ratio",fix = True)
S = Variable("S", "m^2", "total wing area", fix = True)
W_w = Variable("W_w", "N", "wing weight")#, fix = True)
W_w_strc = Variable('W_{w_{strc}}','N','wing structural weight', fix = True)
W_w_surf = Variable('W_{w_{surf}}','N','wing skin weight', fix = True)
V_f_wing = Variable("V_{f_{wing}}",'m^3','fuel volume in the wing', fix = True)
constraints = []
# Structural model
constraints += [W_w_surf >= W_w_coeff2 * S,
W_w >= W_w_surf + W_w_strc]
# Wing fuel model
constraints += [V_f_wing**2 <= 0.0009*S**3/A*tau**2] # linear with b and tau, quadratic with chord
return constraints
def dynamic(self,state):
return WingP(self,state)
class WingP(Model):
def setup(self,wing,state):
self.wing = wing
# Free Variables
C_f = Variable("C_f", "-", "skin friction coefficient")
C_D_ind = Variable('C_{D_{ind}}', '-', "wing induced drag")
C_D_wpar = Variable('C_{D_{wpar}}', '-', 'wing profile drag')
C_L = Variable("C_L", "-", "wing lift coefficient")
constraints = []
# Drag model
constraints += [C_D_ind == C_L ** 2 / (np.pi * self.wing['A'] * self.wing['e']),
C_D_wpar == self.wing['k'] * C_f * self.wing["(\\frac{S}{S_{wet}})"]]
return constraints
class Engine(Model):
def setup(self):
# Dimensional constants
BSFC_ref = Variable("BSFC_{ref}", 0.32, "lbf/(hp*hr)", "reference brake specific fuel consumption")
eta_prop = Variable("\\eta_{prop}",0.8,'-',"propeller efficiency")
P_shaft_ref = Variable("P_{shaft,ref}",149,"kW","reference MSL maximum shaft power")
W_e_ref = Variable("W_{e,ref}",153, "lbf","reference engine weight")
h_ref = Variable("h_{ref}",15000,'ft','engine lapse reference altitude')
# Free variables
P_shaft_max = Variable("P_{shaft,max}","kW","MSL maximum shaft power")
W_e = Variable("W_e","N","engine weight")
constraints = []
constraints += [(W_e/W_e_ref)**1.92 >= 0.00441 * (P_shaft_max/P_shaft_ref)**0.759
+ 1.44 * (P_shaft_max/P_shaft_ref)**2.90]
return constraints
def dynamic(self,state):
return EngineP(self,state)
class EngineP(Model):
def setup(self,engine,state):
self.engine = engine
# Dimensional constants
# Free variables
BSFC = Variable("BSFC", "lbf/(hp*hr)", "brake specific fuel consumption")
P_shaft = Variable("P_{shaft}","kW","shaft power")
P_shaft_alt = Variable("P_{shaft,alt}","kW",'maximum shaft power at altitude')
Thrust = Variable("T","N","propeller thrust")
L = Variable("L","-","power lapse percentage")
constraints = []
with SignomialsEnabled():
constraints += [P_shaft <= P_shaft_alt,
L == (0.937 * (state['h']/self.engine['h_{ref}'])**0.0922)**10,
SignomialEquality(1, L + P_shaft_alt / self.engine['P_{shaft,max}']),
(BSFC/self.engine['BSFC_{ref}'])**(0.1) >= 0.984*(P_shaft/P_shaft_alt)**-0.0346,
BSFC/self.engine['BSFC_{ref}'] >= 1.,
]
return constraints
class Mission(Model):
def setup(self,aircraft,Nsegments):
self.aircraft = aircraft
W_f_m = Variable('W_{f_m}','N','total mission fuel')
t_m = Variable('t_m','hr','total mission time')
with Vectorize(Nsegments):
Wavg = Variable('W_{avg}','N','segment average weight')
Wstart = Variable('W_{start}', 'N', 'weight at the beginning of flight segment')
Wend = Variable('W_{end}', 'N', 'weight at the end of flight segment')
h = Variable('h','m','final segment flight altitude')
havg = Variable('h_{avg}','m','average segment flight altitude')
dhdt = Variable('\\frac{dh}{dt}','m/hr','climb rate')
W_f_s = Variable('W_{f_s}','N', 'segment fuel burn')
t_s = Variable('t_s','hr','time spent in flight segment')
R_s = Variable('R_s','km','range flown in segment')
state = Atmosphere()
self.aircraftP = self.aircraft.dynamic(state)
# Mission variables
hcruise = Variable('h_{cruise_m}', 'm', 'minimum cruise altitude')
Range = Variable("Range_m", "km", "aircraft range")
W_p = Variable("W_{p_m}", "N", "payload weight", pr=20.)
V_min = Variable("V_{min_m}", "m/s", "takeoff speed", pr=20.)
TOfac = Variable('T/O factor_m', '-','takeoff thrust factor')
cost_index = Variable("C_m", '1/hr','hourly cost index')
constraints = []
# Setting up the mission
with SignomialsEnabled():
constraints += [havg == state['h'], # Linking states
h[1:Nsegments-1] >= hcruise, # Adding minimum cruise altitude
# Weights at beginning and end of mission
Wstart[0] >= W_p + self.aircraft.wing['W_w'] + self.aircraft.engine['W_e'] + W_f_m,
Wend[Nsegments-1] >= W_p + self.aircraft.wing['W_w'] + self.aircraft.engine['W_e'],
# Lift, and linking segment start and end weights
Wavg <= 0.5 * state['\\rho'] * self.aircraft['S'] * self.aircraftP.wingP['C_L'] * self.aircraftP['V'] ** 2,
Wstart >= Wend + W_f_s, # Making sure fuel gets burnt!
Wstart[1:Nsegments] == Wend[:Nsegments-1],
Wavg == Wstart ** 0.5 * Wend ** 0.5,
# Altitude changes
h[0] == t_s[0]*dhdt[0], # Starting altitude
dhdt >= 1.*units('m/hr'),
havg[0] == 0.5*h[0],
havg[1:Nsegments] == (h[1:Nsegments]*h[0:Nsegments-1])**(0.5),
SignomialEquality(h[1:Nsegments],h[:Nsegments-1] + t_s[1:Nsegments]*dhdt[1:Nsegments]),
# Thrust and fuel burn
W_f_s >= self.aircraftP.engineP['BSFC'] * self.aircraftP.engineP['P_{shaft}'] * t_s,
self.aircraftP.engineP['T'] * self.aircraftP['V'] >= self.aircraftP['D'] * self.aircraftP['V'] + Wavg * dhdt,
# Max MSL thrust at least 2*climb thrust
self.aircraft.engine['P_{shaft,max}'] >= TOfac*self.aircraftP.engineP['P_{shaft}'][0],
# Flight time
t_s == R_s/self.aircraftP['V'],
# Aggregating segment variables
self.aircraft['W_f'] >= W_f_m,
R_s == Range/Nsegments, # Dividing into equal range segments
W_f_m >= sum(W_f_s),
t_m >= sum(t_s)
]
# Maximum takeoff weight
constraints += [self.aircraft['W'] >= W_p + self.aircraft.wing['W_w'] + self.aircraft['W_f'] + self.aircraft.engine['W_e']]
# Stall constraint
constraints += [self.aircraft['W'] <= 0.5 * state['\\rho'] *
self.aircraft['S'] * self.aircraft['C_{L,max}'] * V_min ** 2]
# Wing weight model
constraints += [self.aircraft.wing['W_{w_{strc}}']**2. >=
self.aircraft.wing['W_{w_{coeff1}}']**2. / self.aircraft.wing['\\tau']**2. *
(self.aircraft.wing['N_{ult}']**2. * self.aircraft.wing['A'] ** 3. *
((W_p+self.aircraft.fuse['V_{f_{fuse}}']*self.aircraft['g']*self.aircraft['\\rho_f']) *
self.aircraft['W'] * self.aircraft.wing['S']))]
# Upper bounding variables
constraints += [t_m <= 100000*units('hr'),
W_f_m <= 1e10*units('N')]
return constraints, state, self.aircraft, self.aircraftP
def test():
m = Mission(SimPleAC(),4)
m.substitutions.update({
'h_{cruise_m}' :5000*units('m'),
'Range_m' :3000*units('km'),
'W_{p_m}' :6250*units('N'),
'C_m' :120*units('1/hr'),
'V_{min_m}' :25*units('m/s'),
'T/O factor_m' :2,
})
m.cost = m['W_{f_m}']*units('1/N') + m['C_m']*m['t_m']
sol = m.localsolve(verbosity = 2)
if __name__ == "__main__":
# Most basic way to execute the model
m = Mission(SimPleAC(),4)
m.substitutions.update({
'h_{cruise_m}' :5000*units('m'),
'Range_m' :3000*units('km'),
'W_{p_m}' :6250*units('N'),
'C_m' :120*units('1/hr'),
'V_{min_m}' :25*units('m/s'),
'T/O factor_m' :2,
})
m.cost = m['W_{f_m}']*units('1/N') + m['C_m']*m['t_m']
sol = m.localsolve(verbosity = 4)
#print sol.table()