Question

Which of the following indicates the range formula in cruise method 2?

(a) R=\(\frac{1}{C}\big(\frac{2}{\rho SC_L}\big)^{\frac{1}{2}}\int_{W_{i}}^{W_{f}}\frac{dW}{W^{\frac{1}{2}}}\)

(b) R=\(\Big(\frac{2}{\rho SC_L}\Big)^{\frac{1}{2}}\frac{L}{D}\int_{W_{i}}^{W_{f}}\frac{dW}{W^{\frac{1}{2}}}\)

(c) R=\(\Big(\frac{2}{\rho SC_L}\Big)^{\frac{1}{2}}\frac{LC}{D}\int_{W_{i}}^{W_{f}}\frac{dW}{W^{\frac{1}{2}}}\)

(d) R=\(\frac{1}{C}\Big(\frac{2}{\rho SC_L}\Big)^{\frac{1}{2}}\frac{L}{D}\int_{W_{i}}^{W_{f}}\frac{dW}{W^{\frac{1}{2}}}\)

The question was posed to me during an internship interview.

The origin of the question is Cruise Method 2 in portion Cruising Performance of Aircraft Performance

Answer 1

Correct option is (d) R=\(\frac{1}{C}\Big(\frac{2}{\rho SC_L}\Big)^{\frac{1}{2}}\frac{L}{D}\int_{W_{i}}^{W_{f}}\frac{dW}{W^{\frac{1}{2}}}\)

The explanation: The correct range equation of cruise method 2 is given by R=\(\frac{1}{C}\Big(\frac{2}{\rho SC_L}\Big)^{\frac{1}{2}}\frac{L}{D}\int_{W_{i}}^{W_{f}}\frac{dW}{W^{\frac{1}{2}}}\) where R is range of the cruise, C is specific fuel consumption, S is span, ρ is density, CL is coefficient of lift, L/D is lift to drag ratio, Wf and Wi are final and initial weights.