Question

Which of the following is the correct formula for accelerating force?

(a) \(\frac{F}{W}=\Big\{\frac{F_N}{W}+\mu_R-sin\gamma_R\Big\}-\frac{L}{W}\Big(\frac{C_D}{C_L}-\mu_R\Big)\)

(b) \(\frac{F}{W}=\Big\{\frac{F_N}{W}-\mu_R+sin\gamma_R\Big\}-\frac{L}{W}\Big(\frac{C_D}{C_L}-\mu_R\Big)\)

(c) \(\frac{F}{W}=\Big\{\frac{F_N}{W}-\mu_R-sin\gamma_R\Big\}-\frac{L}{W}\Big(\frac{C_D}{C_L}-\mu_R\Big)\)

(d) \(\frac{F}{W}=\Big\{\frac{F_N}{W}-\mu_R-sin\gamma_R\Big\}-\frac{L}{W}\Big(\frac{C_D}{C_L}+\mu_R\Big)\)

I have been asked this question by my college director while I was bunking the class.

My question is taken from Estimation of Take-off Distances topic in division Take-off and Landing Performance of Aircraft Performance

Answer 1

Right option is (c) \(\frac{F}{W}=\Big\{\frac{F_N}{W}-\mu_R-sin\gamma_R\Big\}-\frac{L}{W}\Big(\frac{C_D}{C_L}-\mu_R\Big)\)

Easy explanation: The formula for accelerating force is given by: \(\frac{F}{W}=\Big\{\frac{F_N}{W}-\mu_R-sin\gamma_R\Big\}-\frac{L}{W}\Big(\frac{C_D}{C_L}-\mu_R\Big)\) where F is force, W is weight, μR is runway coefficient of the rolling friction, γR is runway slope, L is lift, CD and CL are the coefficients of drag and lift.