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73 changes: 73 additions & 0 deletions aircraft/climb.py
Original file line number Diff line number Diff line change
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from gpkit import Variable, VectorVariable, Model
import numpy as np

class Climb(Model):
"""
Model for climbing flight

References
---------
[1] Anderson, Introduction to flight
[2] https://en.wikipedia.org/wiki/Taylor_series
[3] https://en.wikipedia.org/wiki/Thrust_specific_fuel_consumption

Assumptions
-----------
- Assumes you want to minimize climb time
- Assumes constant thrust
- Assumes constant velocity
- Assumes constant air density
"""
def setup(self):

H = 30000 # final altitude
n = 3 # number of steps

h = np.linspace(0, H, n)
T0 = 288.15 # [K]
L = 0.0065 # [K/m]
p0 = 101325 # [Pa]
R = 8.31 # [J/(mol*K)]
g = 9.81 # [m/s^2]
M = 0.02896 # [kg/mol]

T = T0 - L*h # [K]
p = p0*(1 - L*h/T0)**(g*M/(R*L))# [Pa]
rho = p*M/(R*T) # [kg/m^3]

# Free variables
dt = VectorVariable(n, '\\Delta t', 's', 'Time to climb segment')
D = VectorVariable(n, 'D', 'N', 'Drag')
m_f = VectorVariable(n, 'm_f', 'kg', 'Mass of fuel burned')

# Fixed parameters
CD = Variable('C_D', 0.02, '-', 'Drag coefficient')
dh = Variable('\\Delta h', H/n, 'ft', 'Altitude step')
rho = VectorVariable(n, '\\rho', rho, 'kg/m^3', 'Air density')
S = Variable('S', 130, 'm^2', 'Reference area')
T = Variable('T', 1E6, 'N', 'Thrust')
TSFC = Variable('TSFC', 8.7E-4, 'g/(kN*s)', # [3]
'Thrust specific fuel consumption')
V = Variable('V', 100, 'm/s', 'Freestream velocity')
W = Variable('W', 600000, 'N', 'Aircraft weight')

objective = sum(m_f)

constraints = [# Climb time [1]
# uses Maclaurin series expansion of 1/(1-T/D) (ref [2])
dt >= (W/(V*T))*(1 + D/T + (D/T)**2 + (D/T)**3)*dh,

# Drag
D == 0.5*rho*V**2*S*CD,

# Fuel burn
m_f == TSFC*T*dt,
]

return objective, constraints

def test(self):
self.solve()

if __name__ == "__main__":
Climb().test()