def setup(self, aircraft, state, **kwargs):
#make submodels
self.aircraft = aircraft
self.wingP = aircraft.wing.dynamic(state)
self.fuseP = aircraft.fuse.dynamic(state)
self.engineP = aircraft.engine.dynamic(state)
self.Pmodels = [self.wingP, self.fuseP, self.engineP]
#variable definitions
Vstall = Variable('V_{stall}', 'knots', 'Aircraft Stall Speed')
D = Variable('D', 'N', 'Total Aircraft Drag')
W_avg = Variable('W_{avg}', 'N',
'Geometric Average of Segment Start and End Weight')
W_start = Variable('W_{start}', 'N', 'Segment Start Weight')
W_end = Variable('W_{end}', 'N', 'Segment End Weight')
W_burn = Variable('W_{burn}', 'N', 'Segment Fuel Burn Weight')
WLoadmax = Variable('W_{Load_{max}}', 'N/m^2', 'Max Wing Loading')
WLoad = Variable('W_{Load}', 'N/m^2', 'Wing Loading')
t = Variable('tmin', 'min', 'Segment Flight Time in Minutes')
thours = Variable('thr', 'hour', 'Segment Flight Time in Hours')
constraints = []
constraints.extend([
#speed must be greater than stall speed
state['V'] >= Vstall,
#Figure out how to delete
Vstall == 120 * units('kts'),
WLoadmax == 6664 * units('N/m^2'),
#compute the drag
TCS([D >= self.wingP['D_{wing}'] + self.fuseP['D_{fuse}']]),
#constraint CL and compute the wing loading
W_avg == .5 * self.wingP['C_{L}'] * self.aircraft['S'] *
state.atm['\\rho'] * state['V']**2,
WLoad == .5 * self.wingP['C_{L}'] * self.aircraft['S'] *
state.atm['\\rho'] * state['V']**2 / self.aircraft.wing['S'],
#set average weight equal to the geometric avg of start and end weight
W_avg == (W_start * W_end)**.5,
#constrain the max wing loading
WLoad <= WLoadmax,
#compute fuel burn from TSFC
W_burn == aircraft['numeng'] * self.engineP['TSFC'] * thours *
self.engineP['thrust'],
#time unit conversion
t == thours,
#make lift equal weight --> small angle approx in climb
self.wingP['L_{wing}'] == W_avg,
])
return constraints, self.wingP, self.engineP, self.fuseP
def setup(self):
fs = FlightState()
Propulsor.prop_flight_model = BladeElementProp
p = Propulsor()
pp = p.flight_model(p,fs)
pp.substitutions[pp.prop.T] = 100
self.cost = pp.motor.Pelec/(1000*units('W')) + p.W/(1000*units('lbf'))
return fs,p,pp
def test_constraint_creation_units(self):
v = VectorVariable(2, "v", "m/s")
c = (v >= 40*gpkit.units("ft/s"))
c2 = (v >= [20, 30]*gpkit.units("ft/s"))
if gpkit.units:
self.assertTrue(c.right.units)
self.assertTrue(c2.right.units)
else:
self.assertEqual(type(c.right), int)
self.assertEqual(type(c2.right), list)
def test_constraint_creation_units(self):
v = VectorVariable(2, "v", "m/s")
c = (v >= 40*gpkit.units("ft/s"))
c2 = (v >= np.array([20, 30])*gpkit.units("ft/s"))
if gpkit.units:
self.assertTrue(c.right.units)
self.assertTrue(NomialArray(c2.right).units)
else:
self.assertEqual(type(c.right), int)
self.assertEqual(type(c2.right), np.ndarray)
def test_constraint_creation_units(self):
v = VectorVariable(2, "v", "m/s")
c = (v >= 40*gpkit.units("ft/s"))
c2 = (v >= np.array([20, 30])*gpkit.units("ft/s"))
if gpkit.units:
self.assertTrue(c.right.units)
self.assertTrue(NomialArray(c2.right).units)
else:
self.assertEqual(type(c.right), int)
self.assertEqual(type(c2.right), np.ndarray)
def test_constraint_creation_units(self):
v = VectorVariable(2, "v", "m/s")
c = (v >= 40 * gpkit.units("ft/s"))
c2 = (v >= [20, 30] * gpkit.units("ft/s"))
if gpkit.units:
self.assertTrue(c.right.units)
self.assertTrue(c2.right.units)
else:
self.assertEqual(type(c.right), int)
self.assertEqual(type(c2.right), list)
def test_united_sub_sweep(self):
A = Variable("A", "USD")
h = Variable("h", "USD/count")
Q = Variable("Q", "count")
Y = Variable("Y", "USD")
m = Model(Y, [Y >= h*Q + A/Q])
m.substitutions.update({A: 500*gpkit.units("USD"),
h: 35*gpkit.units("USD"),
Q: ("sweep", [50, 100, 500])})
firstcost = m.solve(verbosity=0)["cost"][0]
self.assertAlmostEqual(1760*gpkit.ureg("USD")/firstcost, 1, 5)
def test_united_sub_sweep(self):
A = Variable("A", "USD")
h = Variable("h", "USD/count")
Q = Variable("Q", "count")
Y = Variable("Y", "USD")
m = Model(Y, [Y >= h*Q + A/Q])
m.substitutions.update({A: 500*gpkit.units("USD"),
h: 35*gpkit.units("USD"),
Q: ("sweep", [50, 100, 500])})
firstcost = m.solve(verbosity=0)["cost"][0]
self.assertAlmostEqual(firstcost, 1760, 3)
def test_Nozzle():
print "Testing Nozzle..."
m = Rocket(1)
m.substitutions.update({
'k_A': 5,
'T_t': 1800 * units('K'),
'P_t': 5e8 * units('Pa'),
# 'mdot': 150*units('kg/s'),
})
m.cost = 1 / sum(m.nozzlePerformance.T)
sol = m.localsolve(verbosity=0)
print sol.table()
def setup(self, engine):
self.engine = engine
M2 = .6
M25 = .6
M0 = .8025
toclimb = [
engine['F'][0] == 94.971 * units('kN'),
engine['F'][1] == 30.109 * units('kN'),
engine['F'][2] == 22.182 * units('kN'),
engine.state['P_{atm}'][1] == 23.84 * units('kPa'), #36K feet
engine.state["T_{atm}"][1] == 218 * units('K'),
engine.state['M'][1] == M0,
engine.engineP['M_2'][1] == M2,
engine.engineP['M_{2.5}'][1] == M25,
engine.engineP['hold_{2}'][1] == 1 + .5 * (1.398 - 1) * M2**2,
engine.engineP['hold_{2.5}'][1] == 1 + .5 * (1.354 - 1) * M25**2,
engine.engineP['c1'][1] == 1 + .5 * (.401) * M0**2,
]
M2 = .6
M25 = .6
M0 = .8
cruise = [
engine.state['P_{atm}'][2] == 23.92 * units('kPa'), #36K feet
engine.state["T_{atm}"][2] == 219.4 * units('K'),
engine.state['M'][2] == M0,
engine.engineP['M_2'][2] == M2,
engine.engineP['M_{2.5}'][2] == M25,
engine.engineP['hold_{2}'][2] == 1 + .5 * (1.398 - 1) * M2**2,
engine.engineP['hold_{2.5}'][2] == 1 + .5 * (1.354 - 1) * M25**2,
engine.engineP['c1'][2] == 1 + .5 * (.401) * M0**2,
]
M2 = .6
M25 = .6
M0 = .2201
rotation = [
engine.state['P_{atm}'][0] == 101.325 * units('kPa'),
engine.state["T_{atm}"][0] == 288 * units('K'),
engine.state['M'][0] == M0,
engine.engineP['M_2'][0] == M2,
engine.engineP['M_{2.5}'][0] == M25,
engine.engineP['hold_{2}'][0] == 1 + .5 * (1.401 - 1) * M2**2,
engine.engineP['hold_{2.5}'][0] == 1 + .5 * (1.401 - 1) * M25**2,
engine.engineP['c1'][0] == 1 + .5 * (.401) * M0**2,
engine['W_{engine}'] <= 1.1 * 7870.7 * units('lbf'),
]
return rotation, toclimb, cruise
def run_M072_737(objective, fixedBPR, pRatOpt, mutategparg):
# User definitions
Nclimb = 3
Ncruise = 2
Nmission = 1
aircraft = 'M072_737'
m = Mission(Nclimb, Ncruise, objective, aircraft, Nmission)
substitutions = get_M072_737_subs()
if Nmission > 1:
substitutions.update({
'R_{req}': [3000. * units('nmi'), 2500. * units('nmi')],
'n_{pass}': [180., 180.],
})
else:
substitutions.update({
'R_{req}': 3000. * units('nmi'),
'n_{pass}': 180.,
})
if fixedBPR:
substitutions.update({
'\\alpha_{max}': 6.97,
})
if pRatOpt:
del substitutions['\pi_{f_D}']
## del substitutions['\pi_{lc_D}']
## del substitutions['\pi_{hc_D}']
m.substitutions.update(substitutions)
m = Model(m.cost, BCS(m))
m_relax = relaxed_constants(m, None, ['M_{takeoff}', '\\theta_{db}'])
sol = m_relax.localsolve(verbosity=4,
iteration_limit=200,
reltol=0.01,
mutategp=mutategparg)
post_process(sol)
percent_diff(sol, aircraft, Nclimb)
post_compute(sol, Nclimb)
return sol
def test_mul(self):
"Test monomial multiplication"
x = Monomial({'x': 1, 'y': -1}, 4)
# test integer division
self.assertEqual(x / 5, Monomial({'x': 1, 'y': -1}, 0.8))
# divide by scalar
self.assertEqual(x * 9, Monomial({'x': 1, 'y': -1}, 36))
# divide by Monomial
y = x * Variable('z')
self.assertEqual(y, Monomial({'x': 1, 'y': -1, 'z': 1}, 4))
# make sure x unchanged
self.assertEqual(x, Monomial({'x': 1, 'y': -1}, 4))
# mixed new and old vars
z = x * Monomial({'x': -1, 't': 2}, .5)
self.assertEqual(z, Monomial({'x': 0, 'y': -1, 't': 2}, 2))
x0 = Variable('x0')
self.assertEqual(0.0, 0.0 * x0)
x1 = Variable('x1')
n_hat = [1, 0]
p = n_hat[0] * x0 + n_hat[1] * x1
self.assertEqual(p, x0)
if gpkit.units:
self.assertNotEqual((x + 1), (x + 1) * gpkit.units("m"))
def test():
Nclimb = 3 # number of climb segments
Ncruise = 2 # number of cruise segments
Nmission = 1 # number of missions
config = 'optimalD8' # String describing configuration:
# currently one of: 'D8_eng_wing', 'optimal737', 'optimal777', 'optimalD8', 'D8_no_BLI', 'M072_737'
m = Mission(Nclimb, Ncruise, config, Nmission)
# Objective
m.cost = m['W_{f_{total}}'].sum()
# Inputs to the model
substitutions = get_optimalD8_subs()
substitutions.update({'R_{req}': 3000.*units('nmi'), #6000*units('nmi'),
'n_{pass}': 180.}) #450.,)
# Additional options
fixedBPR = False
pRatOpt = True
sol = optimize_aircraft(m, substitutions, fixedBPR, pRatOpt)
percent_diff(sol, config, Nclimb)
post_compute(sol, Nclimb)
sol.savetxt()
return sol
def setup(self, tailboom, htail, state):
N = self.N = tailboom.N
self.state = state
self.htail = htail
self.tailboom = tailboom
exec parse_variables(TailBoomBending.__doc__)
Beam.qbarFun = [1e-10] * N
Beam.SbarFun = [1.] * N
beam = self.beam = Beam(N)
I = tailboom.I
tailboom.I0 = I[0]
l = tailboom.l
S = htail.planform.S
E = tailboom.material.E
Sy = tailboom.Sy
qne = state.qne
CLmax = htail.planform.CLmax
deta = tailboom.deta
sigma = tailboom.material.sigma
constraints = [
beam.dx == deta, F >= qne * S,
beam["\\bar{EI}"] <= E * I / F / l**2 / 2,
Mr >= beam["\\bar{M}"][:-1] * F * l, sigma >= Mr / Sy,
th == beam["\\theta"][-1],
beam["\\bar{\\delta}"][-1] * CLmax * Nsafety <= kappa
]
self.tailboomJ = hasattr(tailboom, "J")
if self.tailboomJ:
constraints.append(tailboom.J >= 1e-10 * units("m^4"))
return constraints, beam
def map_relaxations(groupedDict, nt, nx, decimals = 3):
strkeys = groupedDict.keys()
relaxDict = {i:None for i in strkeys}
for i in strkeys:
dim = len(groupedDict[i])
nd = groupedDict[i]
# Mapping relaxations in time and space
dim1, dim2 = [0,0]
if dim == nx*nt:
[dim1,dim2] = [nt,nx]
elif dim == nt:
[dim1,dim2] = [nt, 1]
elif dim == nx:
[dim1,dim2] = [1, nx]
# Special cases where monomials (always tight) replace posys
# in the first section
elif dim == (nx-1)*nt and i == 'massCons':
[dim1,dim2] = [nt, nx]
a = np.array(nd)[:,0].reshape((nt, nx-1))
nd = np.concatenate((np.zeros((nt,1))*units(''), a), axis=1)
nd = nd.reshape((nx*nt,1))
else:
print 'Warning: tight constraint that does not' \
' obey the specified relaxations detected.'
nd = [mag(j) for j in np.array(nd)[:,0]]
nd = np.array(nd).reshape((dim2, dim1))
relaxDict[i] = np.round(nd, decimals=decimals)
return relaxDict
def setup(self, aircraft, state, **kwargs):
#submodels
self.aircraft = aircraft
self.aircraftP = AircraftP(aircraft, state)
self.wingP = self.aircraftP.wingP
self.fuseP = self.aircraftP.fuseP
#variable definitions
theta = Variable('\\theta', '-', 'Aircraft Climb Angle')
excessP = Variable('P_{excess}', 'W', 'Excess Power During Climb')
RC = Variable('RC', 'feet/min', 'Rate of Climb/Decent')
dhft = Variable('dhft', 'feet',
'Change in Altitude Per Climb Segment [feet]')
RngClimb = Variable('R_{climb}', 'nautical_miles',
'Down Range Covered in Each Climb Segment')
#constraints
constraints = []
constraints.extend([
RC == excessP / self.aircraftP['W_{avg}'],
RC >= 500 * units('ft/min'),
#make the small angle approximation and compute theta
theta * state['V'] == RC,
dhft == self.aircraftP['tmin'] * RC,
#makes a small angle assumption during climb
RngClimb == self.aircraftP['thr'] * state['V'],
self.aircraftP['W_{burn}'] == self.aircraft.engine['TSFC'][:2] *
self.aircraft.engine['F'][:2] * self.aircraftP['thr']
])
return constraints, self.aircraftP
def setup(self):
fs = FlightState()
p = Propulsor()
pp = p.flight_model(p,fs)
pp.substitutions[pp.prop.T] = 100
self.cost = 1./pp.motor.etam + p.W/(1000*units('lbf')) + 1./pp.prop.eta
return fs,p,pp
def test():
Nmissions = 2
Nsegments = 4
aircraft = SimPleAC()
m = Multimission(aircraft,Nmissions,Nsegments)
m.substitutions.update({
'h_{cruise_{mm}}':[5000*units('m'), 5000*units('m')],
'Range_{mm}' :[3000*units('km'), 2000*units('km')],
'W_{p_{mm}}' :[6250*units('N'), 8000*units('N')],
'C_{mm}' :[120*units('1/hr'), 360*units('1/hr')],
})
#m.cost = m['W_{f_{mm}}']*units('1/N') + sum(m.missions[i]['C_m']*m.missions[i]['t_m'] for i in range(0,Nmissions))
m.cost = (m.missions[0]['W_{f_m}']*units('1/N') + m.missions[1]['C_m']*m.missions[1]['t_m'])
sol = m.localsolve(verbosity = 2)
def setup(self, engine):
self.engine = engine
M2 = .6
M25 = .6
M0 = .5
engineclimb = [
engine['F'][1] == 13.798 * units('kN'),
engine['F'][0] == 11.949 * units('kN'),
engine.state['P_{atm}'][1] == 23.84 * units('kPa'), #36K feet
engine.state["T_{atm}"][1] == 218 * units('K'),
engine.state['M'][1] == M0,
engine.engineP['M_{2.5}'][1] == M25,
engine.engineP['hold_{2}'][1] == 1 + .5 * (1.398 - 1) * M2**2,
engine.engineP['hold_{2.5}'][1] == 1 + .5 * (1.354 - 1) * M25**2,
engine.engineP['c1'][1] == 1 + .5 * (.401) * M0**2,
]
M2 = .6
M25 = .6
M0 = .72
enginecruise = [
engine.state['P_{atm}'][0] == 23.84 * units('kPa'), #36K feet
engine.state["T_{atm}"][0] == 218 * units('K'),
engine.state['M'][0] == M0,
engine.engineP['M_2'][0] == M2,
engine.engineP['M_{2.5}'][0] == M25,
engine.engineP['hold_{2}'][0] == 1 + .5 * (1.398 - 1) * M2**2,
engine.engineP['hold_{2.5}'][0] == 1 + .5 * (1.354 - 1) * M25**2,
engine.engineP['c1'][0] == 1 + .5 * (.401) * M0**2,
engine['W_{engine}'] <= 10502.8 * units('lbf'),
]
return engineclimb, enginecruise
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
def setup(self):
fs = FlightState()
m = Motor()
mp = MotorPerf(m,fs)
self.mp = mp
mp.substitutions[m.Qmax] = 100
mp.substitutions[mp.Q] = 10
self.cost = 1./mp.etam + m.W/(100.*units('lbf'))
return self.mp, fs, m
def setup(self):
exec parse_variables(Section.__doc__)
constraints = [
# Taking averages,
A_in * A_out == A_avg**2,
# Volume of chamber
V_chamb == A_avg * l,
# Area ratio
A_in / A_out == k_A,
# Mass flow rate
rho_in * u_in * A_in == mdot_in,
rho_out * u_out * A_out == mdot_out,
# Chamber pressure
P_chamb**2 == P_in * P_out,
# Product generation rate
q == rho_p * A_b * r,
A_b == l_b * l,
A_p_out + r * l_b * dt <= A_p_in,
# Stagnation quantities
P_t_in >= P_in + 0.5 * rho_in * u_in**2,
T_t_in >= T_in + u_in**2 / (2 * c_p),
# Ideal gas law
P_out == rho_out * R * T_out,
# Pressure increase
P_out + dP <= P_in,
# Making sure burn surface length is feasible
l_b >= 2 * np.pi**0.5 * (A_avg)**0.5,
l_b <= l_b_max * 2 * np.pi**0.5 * (A_avg)**0.5,
# Constraining areas
Tight([A_avg + A_p_in <= np.pi * radius**2]),
]
with SignomialsEnabled():
constraints += [
# Flow acceleration (conservation of momentum)
# Note: assumes constant rate of burn through the chamber
dP + rho_in * u_in**2 >= q * u_out / V_chamb *
(2. / 3. * l) + rho_in * u_in * u_out,
# Burn rate (Saint-Robert's Law, coefficients taken for Space Shuttle SRM)
Tight([
r >= r_c * (P_chamb / 1e6 * units('1/Pa'))**0.35 *
(1 + 0.5 * r_k * (u_in + u_out))
]),
# Mass flows
Tight([mdot_in + q >= mdot_out]),
mdot_out >= mdot_in,
# Temperatures
Tight([
T_t_out * mdot_out <=
mdot_in * T_t_in + q * T_amb + q * k_comb_p / c_p
]),
# Stagnation quantities
Tight([P_t_out <= P_out + 0.5 * rho_out * u_out**2]),
Tight([T_t_out <= T_out + u_out**2 / (2 * c_p)]),
]
return constraints
def setup(self, engine):
self.engine = engine
M2 = .6
M25 = .6
M0 = .8
climb = [
engine['F'][0] == 5496.4 * 4.4 * units('N'),
engine['F'][1] == 5961.9 * 4.4 * units('N'),
engine.state["T_{atm}"] == 218 * units('K'),
engine.state['P_{atm}'][0] == 23.84 * units('kPa'), #36K feet
engine.state['M'][0] == M0,
engine.engineP['M_2'][0] == M2,
engine.engineP['M_{2.5}'][0] == M25,
engine.engineP['hold_{2}'] == 1 + .5 * (1.398 - 1) * M2**2,
engine.engineP['hold_{2.5}'] == 1 + .5 * (1.354 - 1) * M25**2,
engine.engineP['c1'] == 1 + .5 * (.401) * M0**2,
]
M2 = .6
M25 = .6
M0 = .8
cruise = [
engine.state['P_{atm}'][1] == 23.84 * units('kPa'), #36K feet
engine.state['M'][1] == M0,
engine.engineP['M_2'][1] == M2,
engine.engineP['M_{2.5}'][1] == M25,
engine['W_{engine}'] <= 5216 * units('lbf'),
]
return climb, cruise
def test_quantity_sub(self):
if gpkit.units:
x = Variable("x", 1, "cm")
y = Variable("y", 1)
self.assertEqual(x.sub({x: 1*gpkit.units.m}).c.magnitude, 100)
# NOTE: uncomment the below if requiring Quantity substitutions
# self.assertRaises(ValueError, x.sub, x, 1)
self.assertRaises(ValueError, x.sub, {x: 1*gpkit.ureg.N})
self.assertRaises(ValueError, y.sub, {y: 1*gpkit.ureg.N})
v = gpkit.VectorVariable(3, "v", "cm")
subbed = v.sub({v: [1, 2, 3]*gpkit.ureg.m})
self.assertEqual([z.c.magnitude for z in subbed], [100, 200, 300])
v = VectorVariable(1, "v", "km")
v_min = VectorVariable(1, "v_min", "km")
m = Model(v.prod(), [v >= v_min],
{v_min: [2*gpkit.units("nmi")]})
cost = m.solve(verbosity=0)["cost"]
self.assertAlmostEqual(cost/(3.704*gpkit.ureg("km")), 1.0)
m = Model(v.prod(), [v >= v_min],
{v_min: np.array([2])*gpkit.units("nmi")})
cost = m.solve(verbosity=0)["cost"]
self.assertAlmostEqual(cost/(3.704*gpkit.ureg("km")), 1.0)
def test_quantity_sub(self):
if gpkit.units:
x = Variable("x", 1, "cm")
y = Variable("y", 1)
self.assertEqual(x.sub({x: 1 * gpkit.units.m}).c.magnitude, 100)
# NOTE: uncomment the below if requiring Quantity substitutions
# self.assertRaises(ValueError, x.sub, x, 1)
self.assertRaises(ValueError, x.sub, {x: 1 * gpkit.ureg.N})
self.assertRaises(ValueError, y.sub, {y: 1 * gpkit.ureg.N})
v = gpkit.VectorVariable(3, "v", "cm")
subbed = v.sub({v: [1, 2, 3] * gpkit.ureg.m})
self.assertEqual([z.c.magnitude for z in subbed], [100, 200, 300])
v = VectorVariable(1, "v", "km")
v_min = VectorVariable(1, "v_min", "km")
m = Model(v.prod(), [v >= v_min],
{v_min: [2 * gpkit.units("nmi")]})
cost = m.solve(verbosity=0)["cost"]
self.assertAlmostEqual(cost / (3.704 * gpkit.ureg("km")), 1.0)
m = Model(v.prod(), [v >= v_min],
{v_min: np.array([2]) * gpkit.units("nmi")})
cost = m.solve(verbosity=0)["cost"]
self.assertAlmostEqual(cost / (3.704 * gpkit.ureg("km")), 1.0)
def test():
m = Mission(SimPleAC(),4)
m.substitutions.update({
'h_{cruise_m}' :5000*units('m'),
'Range_m' :3000*units('km'),
'W_{p_m}' :3000*units('N'),
'\\rho_{p_m}' :1500*units('kg/m^3'),
'C_m' :120*units('1/hr'),
'V_{min_m}' :35*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)
def test_vector(self):
v = VectorVariable(3, "v")
kd = KeyDict()
kd[v] = np.array([2, 3, 4])
self.assertTrue(all(kd[v] == kd[v.key]))
self.assertTrue(all(kd["v"] == np.array([2, 3, 4])))
self.assertEqual(v[0].key.idx, (0,))
self.assertEqual(kd[v][0], kd[v[0]])
self.assertEqual(kd[v][0], 2)
kd[v[0]] = 6
self.assertEqual(kd[v][0], kd[v[0]])
self.assertEqual(kd[v][0], 6)
self.assertTrue(all(kd[v] == np.array([6, 3, 4])))
v = VectorVariable(3, "v", "m")
kd[v] = np.array([2, 3, 4])
if gpkit.units:
kd[v[0]] = gpkit.units("inch")
def test_vector(self):
v = VectorVariable(3, "v")
kd = KeyDict()
kd[v] = np.array([2, 3, 4])
self.assertTrue(all(kd[v] == kd[v.key]))
self.assertTrue(all(kd["v"] == np.array([2, 3, 4])))
self.assertEqual(v[0].key.idx, (0, ))
self.assertEqual(kd[v][0], kd[v[0]])
self.assertEqual(kd[v][0], 2)
kd[v[0]] = 6
self.assertEqual(kd[v][0], kd[v[0]])
self.assertEqual(kd[v][0], 6)
self.assertTrue(all(kd[v] == np.array([6, 3, 4])))
v = VectorVariable(3, "v", "m")
kd[v] = np.array([2, 3, 4])
if gpkit.units:
kd[v[0]] = gpkit.units("inch")
def setup(self, alt, **kwargs):
p_sl = Variable("p_{sl}", 101325, "Pa", "Pressure at sea level")
T_sl = Variable("T_{sl}", 288.15, "K", "Temperature at sea level")
L_atm = Variable("L_{atm}", .0065, "K/m", "Temperature lapse rate")
M_atm = Variable("M_{atm}", .0289644, "kg/mol",
"Molar mass of dry air")
p_atm = Variable("P_{atm}", "Pa", "air pressure")
R_atm = Variable("R_{atm}", 8.31447, "J/mol/K",
"air specific heating value")
TH = 5.257386998354459 #(g*M_atm/R_atm/L_atm).value
rho = self.rho = Variable('\\rho', 'kg/m^3', 'Density of air')
T_atm = self.T_atm = Variable("T_{atm}", "K", "air temperature")
h = self.h = alt['h']
"""
Dynamic viscosity (mu) as a function of temperature
References:
http://www-mdp.eng.cam.ac.uk/web/library/enginfo/aerothermal_dvd_only/aero/
atmos/atmos.html
http://www.cfd-online.com/Wiki/Sutherland's_law
"""
mu = Variable('\\mu', 'kg/(m*s)', 'Dynamic viscosity')
T_s = Variable('T_s', 110.4, "K", "Sutherland Temperature")
C_1 = Variable('C_1', 1.458E-6, "kg/(m*s*K^0.5)",
'Sutherland coefficient')
with SignomialsEnabled():
constraints = [
# Pressure-altitude relation
(p_atm / p_sl)**(1 / 5.257) == T_atm / T_sl,
# Ideal gas law
rho == p_atm / (R_atm / M_atm * T_atm),
#temperature equation
SignomialEquality(T_sl, T_atm + L_atm * h),
#constraint on mu
mu == C_1 * T_atm**1.5 / (6.64 * units('K^.28') * T_s**0.72),
]
#like to use a local subs here in the future
subs = None
return constraints
def setup(self, aircraft, state, **kwargs):
#submodels
self.aircraft = aircraft
self.aircraftP = AircraftP(aircraft, state)
self.wingP = self.aircraftP.wingP
self.fuseP = self.aircraftP.fuseP
self.engineP = self.aircraftP.engineP
#variable definitions
theta = Variable('\\theta', '-', 'Aircraft Climb Angle')
excessP = Variable('P_{excess}', 'W', 'Excess Power During Climb')
RC = Variable('RC', 'feet/min', 'Rate of Climb/Decent')
dhft = Variable('dhft', 'feet', 'Change in Altitude Per Climb Segment [feet]')
RngClimb = Variable('R_{climb}', 'nautical_miles', 'Down Range Distance Covered in Each Climb Segment')
TotRngClimb = Variable('TotRngClimb', 'nautical_miles', 'Down Range Distance Covered in Climb')
#constraints
constraints = []
constraints.extend([
#constraint on drag and thrust
self.aircraft['numeng']*self.engineP['thrust'] >= self.aircraftP['D'] + self.aircraftP['W_{avg}'] * theta,
#climb rate constraints
TCS([excessP + state['V'] * self.aircraftP['D'] <= state['V'] * aircraft['numeng'] * self.engineP['thrust']]),
RC == excessP/self.aircraftP['W_{avg}'],
RC >= 500*units('ft/min'),
#make the small angle approximation and compute theta
theta * state['V'] == RC,
dhft == self.aircraftP['tmin'] * RC,
#makes a small angle assumption during climb
## RngClimb == self.aircraftP['thr']*state['V'],
])
with SignomialsEnabled():
constraints.extend([
#time
TCS([self.aircraftP['thr'] * state['V'] >= RngClimb + (.5*theta**2)*self.aircraftP['thr'] * state['V']]),
])
return constraints, self.aircraftP
def SimPleAC_setup():
a = SimPleAC()
m = Mission(a, 4)
subs = {
'h_{cruise_m}': 5000 * units('m'),
'Range_m': 3000 * units('km'),
'W_{p_m}': 3000 * units('N'),
'\\rho_{p_m}': 1500 * units('kg/m^3'),
'C_m': 120 * units('1/hr'),
'V_{min_m}': 35 * units('m/s'),
'T/O factor_m': 2,
}
m.substitutions.update(subs)
m.cost = m['W_{f_m}'] #+m['C_m']*m['t_m']*units('N')
return m, subs
def setup(self):
# Free Variables
S = Variable('S_{fuse}', 'm^2', 'fuselage surface area')
l = Variable('l_{fuse}', 'm', 'fuselage length')
r = Variable('r_{fuse}', 'm', 'fuselage minor radius')
f = Variable('f_{fuse}', '-', 'fuselage fineness ratio', fix = True)
k = Variable('k_{fuse}', '-', 'fuselage form factor')
# Free variables (fixed for performance eval.)
V = Variable('V_{fuse}', 'm^3', 'total volume in the fuselage', fix = True)
V_f_fuse = Variable('V_{f_{fuse}}','m^3','fuel volume in the fuselage')
W_fuse = Variable('W_{fuse}', 'N', 'fuselage weight')
p = 1.6075
constraints = [f == l/r/2,
f <= 6,
k >= 1 + 60/f**3 + f/400,
3*(S/np.pi)**p >= 2*(l*2*r)**p + (2*r)**(2*p),
V == 4./6.*np.pi*r**2*l,
V_f_fuse >= 1*10**-10*units('m^3'),
]
return constraints
def setup(self,aircraft,Nmissions,Nsegments):
self.aircraft = aircraft
self.missions = []
for i in range(0,Nmissions):
self.missions.append(Mission(self.aircraft,Nsegments))
# Multimission objective variables
W_f_mm = Variable('W_{f_{mm}}','N','multimission fuel weight')
with Vectorize(Nmissions):
# Mission variables
hcruise = Variable('h_{cruise_{mm}}', 'm', 'minimum cruise altitude')
Range = Variable("Range_{mm}", "km", "aircraft range")
W_p = Variable("W_{p_{mm}}", "N", "payload weight", pr=20.)
V_min = Variable("V_{min_{mm}}", 25, "m/s", "takeoff speed", pr=20.)
cost_index = Variable("C_{mm}", '1/hr','hourly cost index')
TOfac = Variable('T/O factor_{mm}', 2.,'-','takeoff thrust factor')
constraints = []
# Setting up the missions
for i in range(0,Nmissions):
constraints += [
self.missions[i]['h_{cruise_m}'] == hcruise[i],
self.missions[i]['Range_m'] == Range[i],
self.missions[i]['W_{p_m}'] == W_p[i],
self.missions[i]['V_{min_m}'] == V_min[i],
self.missions[i]['C_m'] == cost_index[i],
self.missions[i]['T/O factor_m'] == TOfac[i],
# Upper bounding relevant variables
W_f_mm <= 1e11*units('N'),
]
# Multimission constraints
constraints += [W_f_mm >= sum(self.missions[i]['W_{f_m}'] for i in range(0,Nmissions))]
return constraints, self.aircraft, self.missions
def setup(self, DF70=False):
self.DF70 = DF70
W = Variable("W", "lbf", "Installed/Total engine weight")
mfac = Variable("m_{fac}", 1.0, "-", "Engine weight margin factor")
bsfc_min = Variable("BSFC_{min}", 0.3162, "kg/kW/hr", "minimum BSFC")
Pref = Variable("P_{ref}", 10.0, "hp", "Reference shaft power")
Wengref = Variable("W_{eng-ref}", 10.0, "lbf",
"Reference engine weight")
Weng = Variable("W_{eng}", "lbf", "engine weight")
Pslmax = Variable("P_{sl-max}", "hp",
"Max shaft power at sea level")
path = os.path.dirname(__file__)
df = pd.read_csv(path + os.sep + "power_lawfit.csv").to_dict(
orient="records")[0]
constraints = [
FitCS(df, Weng/Wengref, [Pslmax/Pref]),
W/mfac >= 2.572*Weng**0.922*units("lbf")**0.078]
return constraints
def test_mul(self):
"Test monomial multiplication"
x = Monomial({"x": 1, "y": -1}, 4)
# test integer division
self.assertEqual(x / 5, Monomial({"x": 1, "y": -1}, 0.8))
# divide by scalar
self.assertEqual(x * 9, Monomial({"x": 1, "y": -1}, 36))
# divide by Monomial
y = x * Variable("z")
self.assertEqual(y, Monomial({"x": 1, "y": -1, "z": 1}, 4))
# make sure x unchanged
self.assertEqual(x, Monomial({"x": 1, "y": -1}, 4))
# mixed new and old vars
z = x * Monomial({"x": -1, "t": 2}, .5)
self.assertEqual(z, Monomial({"x": 0, "y": -1, "t": 2}, 2))
x0 = Variable("x0")
self.assertEqual(0.0, 0.0 * x0)
x1 = Variable("x1")
n_hat = [1, 0]
p = n_hat[0] * x0 + n_hat[1] * x1
self.assertEqual(p, x0)
self.assertNotEqual((x + 1), (x + 1) * gpkit.units("m"))
def setup(self):
constraints = []
# Steady level flight relations
CD = Variable('C_D', '-', 'Drag coefficient')
CL = Variable('C_L', '-', 'Lift coefficient')
P_shaft = Variable('P_{shaft}', 'W', 'Shaft power')
S = Variable('S', 'm^2', 'Wing reference area')
V = Variable('V', 'm/s', 'Cruise velocity')
W = Variable('W', 'lbf', 'Aircraft weight')
eta_prop = Variable(r'\eta_{prop}', 0.7, '-', 'Propulsive efficiency')
rho = Variable(r'\rho', 'kg/m^3')
constraints.extend([P_shaft == V*W*CD/CL/eta_prop, # eta*P = D*V
W == 0.5*rho*V**2*CL*S])
# Aerodynamics model
Cd0 = Variable('C_{d0}', 0.01, '-', "non-wing drag coefficient")
CLmax = Variable('C_{L-max}', 1.5, '-', 'maximum lift coefficient')
e = Variable('e', 0.9, '-', "spanwise efficiency")
A = Variable('A', 20, '-', "aspect ratio")
b = Variable('b', 'ft', 'span')
mu = Variable(r'\mu', 1.5e-5, 'N*s/m^2', "dynamic viscosity")
Re = Variable("Re", '-', "Reynolds number")
Cf = Variable("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*A) + cl_16*CL**16,
b**2 == S*A,
CL <= CLmax,
Re == rho*V/mu*(S/A)**0.5,
Cf >= 0.074/Re**0.2])
# Engine Weight Model
W_eng = Variable('W_{eng}', 'lbf', 'Engine weight')
W_engmin = Variable('W_{min}', 1.3, 'lbf', 'min engine weight')
W_engmax = Variable('W_{max}', 275, 'lbf', 'max engine weight')
eta_t = Variable('\\eta_t', 0.75, '-', 'percent throttle')
eng_cnst = Variable('eng_{cnst}', 0.0011, '-',
'engine constant based off of power weight model')
constraints.extend([W_eng >= W_engmin,
W_eng <= W_engmax,
W_eng >= P_shaft*eng_cnst/eta_t * units('lbf/watt')])
# Weight model
W_airframe = Variable('W_{airframe}', 'lbf', 'Airframe weight')
W_pay = Variable(r'W_{pay}', 4, 'lbf', 'Payload weight')
W_fuel = Variable('W_{fuel}', 'lbf', 'Fuel Weight')
W_zfw = Variable('W_{zfw}', 'lbf', 'Zero fuel weight')
wl = Variable('wl', 'lbf/ft^2', 'wing loading')
f_airframe = Variable('f_{airframe}', 0.3, '-',
'Airframe weight fraction')
g = Variable('g', 9.81, 'm/s^2', 'Gravitational acceleration')
constraints.extend([W_airframe >= W*f_airframe,
W_zfw >= W_airframe + W_eng + W_pay,
wl == W/S,
W >= W_pay + W_eng + W_airframe + W_fuel])
# Breguet Range
z_bre = Variable("z_bre", "-", "breguet coefficient")
h_fuel = Variable("h_{fuel}", 42e6, "J/kg", "heat of combustion")
eta_0 = Variable("\\eta_0", 0.2, "-", "overall efficiency")
t = Variable('t', 7, 'days', 'time on station')
constraints.extend([z_bre >= g*t*V*CD/(h_fuel*eta_0*CL),
W_fuel/W_zfw >= te_exp_minus1(z_bre, 3)])
# Atmosphere model
h = Variable("h", "ft", "Altitude")
p_sl = Variable("p_{sl}", 101325, "Pa", "Pressure at sea level")
T_sl = Variable("T_{sl}", 288.15, "K", "Temperature at sea level")
L_atm = Variable("L_{atm}", 0.0065, "K/m", "Temperature lapse rate")
T_atm = Variable("T_{atm}", "K", "air temperature")
M_atm = Variable("M_{atm}", 0.0289644, "kg/mol",
"Molar mass of dry air")
R_atm = Variable("R_{atm}", 8.31447, "J/mol/K")
TH = (g*M_atm/R_atm/L_atm).value.magnitude # dimensionless
constraints.extend([h <= 20000*units.m, # Model valid to top of troposphere
T_sl >= T_atm + L_atm*h, # Temp decreases w/ altitude
rho <= p_sl*T_atm**(TH-1)*M_atm/R_atm/(T_sl**TH)])
# http://en.wikipedia.org/wiki/Density_of_air#Altitude
# station keeping requirement
footprint = Variable("d_{footprint}", 100, 'km',
"station keeping footprint diameter")
lu = Variable(r"\theta_{look-up}", 5, '-', "look up angle")
R_earth = Variable("R_{earth}", 6371, "km", "Radius of earth")
tan_lu = lu*pi/180. + (lu*pi/180.)**3/3. # Taylor series expansion
# approximate earth curvature penalty as distance^2/(2*Re)
constraints.extend([
h >= tan_lu*0.5*footprint + footprint**2/8./R_earth])
# wind speed model
V_wind = Variable('V_{wind}', 'm/s', 'wind speed')
wd_cnst = Variable('wd_{cnst}', [0.002, 0.0015], 'm/s/ft',
'wind speed constant predited by model')
wd_ln = Variable('wd_{ln}', [13.009, 8.845], 'm/s',
'linear wind speed variable')
h_min = Variable('h_{min}', 11800, 'ft', 'minimum height')
h_max = Variable('h_{max}', 20800, 'ft', 'maximum height')
constraints.extend([V_wind >= wd_cnst*h + wd_ln, # model predicting worse case scenario at 45 deg latitude
V >= V_wind,
h >= h_min,
h <= h_max])
objective = W
return objective, constraints
"Debug examples"
from gpkit import Variable, Model, units
x = Variable("x", "ft")
x_min = Variable("x_min", 2, "ft")
x_max = Variable("x_max", 1, "ft")
y = Variable("y", "volts")
m = Model(x/y, [x <= x_max, x >= x_min])
m.debug()
print "# Now let's try a model unsolvable with relaxed constants\n"
Model(x, [x <= units("inch"), x >= units("yard")]).debug()
print "# And one that's only unbounded\n"
# the value of x_min was used up in the previous model!
x_min = Variable("x_min", 2, "ft")
Model(x/y, [x >= x_min]).debug()
def SimPleAC():
"Creates SimpleAC model"
# Env. constants
g = Variable("g", 9.81, "m/s^2", "gravitational acceleration")
mu = Variable("\\mu", 1.775e-5, "kg/m/s", "viscosity of air")
rho = Variable("\\rho", 1.23, "kg/m^3", "density of air")
rho_f = Variable("\\rho_f", 817, "kg/m^3", "density of fuel")
# Non-dimensional constants
C_Lmax = Variable("C_{L,max}", 1.6, "-", "max CL with flaps down")
e = Variable("e", 0.92, "-", "Oswald efficiency factor")
k = Variable("k", 1.17, "-", "form factor")
N_ult = Variable("N_{ult}", 3.3, "-", "ultimate load factor")
S_wetratio = Variable("(\\frac{S}{S_{wet}})", 2.075, "-",
"wetted area ratio")
tau = Variable("\\tau", 0.12, "-", "airfoil thickness to chord ratio")
W_W_coeff1 = Variable("W_{W_{coeff1}}", 2e-5, "1/m",
"wing weight coefficent 1") # 12e-5 originally
W_W_coeff2 = Variable("W_{W_{coeff2}}", 60., "Pa",
"wing weight coefficent 2")
# Dimensional constants
Range = Variable("Range", 3000, "km", "aircraft range")
TSFC = Variable("TSFC", 0.6, "1/hr", "thrust specific fuel consumption")
V_min = Variable("V_{min}", 25, "m/s", "takeoff speed")
W_0 = Variable("W_0", 6250, "N", "aircraft weight excluding wing")
# Free Variables
LoD = Variable("L/D", "-", "lift-to-drag ratio")
D = Variable("D", "N", "total drag force")
V = Variable("V", "m/s", "cruising speed")
W = Variable("W", "N", "total aircraft weight")
Re = Variable("Re", "-", "Reynold's number")
CDA0 = Variable("(CDA0)", "m^2", "fuselage drag area") # 0.035 originally
C_D = Variable("C_D", "-", "drag coefficient")
C_L = Variable("C_L", "-", "lift coefficient of wing")
C_f = Variable("C_f", "-", "skin friction coefficient")
W_f = Variable("W_f", "N", "fuel weight")
V_f = Variable("V_f", "m^3", "fuel volume")
V_f_avail = Variable("V_{f_{avail}}", "m^3", "fuel volume available")
T_flight = Variable("T_{flight}", "hr", "flight time")
# Free variables (fixed for performance eval.)
A = Variable("A", "-", "aspect ratio")
S = Variable("S", "m^2", "total wing area")
W_w = Variable("W_w", "N", "wing weight")
W_w_strc = Variable("W_w_strc", "N", "wing structural weight")
W_w_surf = Variable("W_w_surf", "N", "wing skin weight")
V_f_wing = Variable("V_f_wing", "m^3", "fuel volume in the wing")
V_f_fuse = Variable("V_f_fuse", "m^3", "fuel volume in the fuselage")
objective = W_f
constraints = []
# Weight and lift model
constraints += [
W >= W_0 + W_w + W_f,
W_0 + W_w + 0.5 * W_f <= 0.5 * rho * S * C_L * V ** 2,
W <= 0.5 * rho * S * C_Lmax * V_min ** 2,
T_flight >= Range / V,
LoD == C_L/C_D]
# Thrust and drag model
C_D_fuse = CDA0 / S
C_D_wpar = k * C_f * S_wetratio
C_D_ind = C_L ** 2 / (np.pi * A * e)
constraints += [
W_f >= TSFC * T_flight * D,
D >= 0.5 * rho * S * C_D * V ** 2,
C_D >= C_D_fuse + C_D_wpar + C_D_ind,
V_f_fuse <= 10*units("m")*CDA0,
Re <= (rho / mu) * V * (S / A) ** 0.5,
C_f >= 0.074 / Re ** 0.2]
# Fuel volume model
with SignomialsEnabled():
constraints += [
V_f == W_f / g / rho_f,
# linear with b and tau, quadratic with chord
V_f_wing**2 <= 0.0009*S**3/A*tau**2,
V_f_avail <= V_f_wing + V_f_fuse, # [SP]
Tight([V_f_avail >= V_f])]
# Wing weight model
constraints += [
W_w_surf >= W_W_coeff2 * S,
W_w_strc**2. >= W_W_coeff1**2/tau**2 * N_ult**2*A**3*(V_f_fuse*g*rho_f
+ W_0)*W*S,
W_w >= W_w_surf + W_w_strc]
m = Model(objective, constraints)
return m
def test_pint_366(self):
# test for https://github.com/hgrecco/pint/issues/366
if gpkit.units:
self.assertIn(unitstr(gpkit.units("nautical_mile")),
("nmi", "nautical_mile"))
self.assertEqual(gpkit.units("nautical_mile"), gpkit.units("nmi"))
