old Climb model

aircraft/climb.py

@@ -0,0 +1,73 @@
+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()