A transport plane takes off from a level landing field with two gliders in tow,

Question

A transport plane takes off from a level landing field with two gliders in tow, one behind the other. The mass of each glider is 720 kg, and the total resistance (air drag plus friction with the runway) on each may be assumed constant and equal to 2480 N. The tension in the towrope between the transport plane and the first glider is not to exceed 12,500 N. A) if a speed of 40 m/s is required for takeoff, what minimum length of runway is needed? B) What is the tension in the towrope between the two gliders while they are accelerating for the takeoff?

Explanation / Answer

Assuming no tall trees, telephone lines, or buildings at the end of the runway, then S = Ux^2/2A is the minimum run of the gliders at Ux = 40 mps. P = 12500 N the max allowed tension, which is the pull force and d = 2480 N is the drag/friction force for each of the two gliders with mass m = 720 kg.

A, the average rate of acceleration, is found from the net takeoff force, f = (2m)A = P - D = 12500 - 2*d = 12500 - 4960 = 7540 N so A = 7540/2m = 7540/1440 = 5.236m/s^2. Then

S = 40^2/(2*5.236) = 152,788m T/O run. ANS.

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