Another constraint that can lead to interesting engine power versus wing area trade-offs is the rate of climb requirement. If q denotes the dynamic pressure in the environmental conditions specified earlier, V is the calibrated airspeed in the climb, and V_{V} is the rate of ascent, the required thrust to weight ratio T/W as a function of the wing loading W/S can be calculated as:

The Python implementation once again sweeps a sensible range of wing loading values to build the appropriate constraint diagram:

In [56]: WSlistROC_Pa = np.linspace(Start_Pa,8500,Resolution)

TWlistROC = []

i = 0

for WS in WSlistROC_Pa:

TW = RateOfClimb_mps/ClimbSpeed_mpsCAS + CDmin *q_climb_Pa/WSlistROC_Pa[i] + k*WSlistROC_Pa[i]/q_climb_Pa TWlistROC.append(TW) i = i + 1

WSlistROC_kgm2 = [x*0.101971621 for x in WSlistROC_Pa] figROC = plt.figure()

We next compute the thrust to weight ratio required for a target ground run distance on take-off. If C™ and CD^{O} denote the take-off run lift and drag coefficients respectively, d_{GR} is the required ground run distance, V_{L} is the lift-off speed, ^_{TO} is the ground friction constant, the required thrust to weight ratio T/W as a function of the wing loading W/S can be calculated as:

Sweeping the range of wing loading values as before, in order to build the appropriate constraint diagram:

In [58]: WSlistGR_Pa = np.linspace(Start_Pa,8500,Resolution)