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 700 kg, and the total resistance (air drag plus friction with the runway) on each may be assumed constant and equal to 2700 N . The tension in the towrope between the transport plane and the first glider is not to exceed 12000 N.

If a speed of 40 m/s is required for takeoff, what minimum length of runway is needed?

What is the tension in the towrope between the two gliders while they are accelerating for the takeoff?

Explanation / Answer

  a)
First find the maximum acceleration.
(tension in rope) = (mass)×(force by acceleration) + (force by fraction)

12000 N = (2 × 700 kg)×a + (2 × 2700 N)
a = 4.71 m/s²

Now find the minimum length of the runway.
(Vf)² = (Vi)² + 2×a×d
where
Vf = final velocity = 40 m/s
Vi = initial velocity = 0 m/s
a = maximum acceleration = 4.71 m/s²
d = distance = ?
so
40² = 0² + 2×4.71×d
d = 169.85 m < - - - - - - - - answer

b)
(tension in rope) = (mass)×(force by acceleration) + (force by fraction)
T = (700 kg)×(5 m/s²) + 2700 N
T = 6200 N < - - - - - - - - answer

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