CP Runway Design.? 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 2500 N. The tension in the towrope between the transport plane and the first glider is not to exceed 12,000 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 tow-rope between the two gliders while they are accelerating for the takeoff?
Solution 18E Introduction We have to calculate the maximum force that can be applied to the rope. The maximum force will include the friction, air drag and the force due to acceleration. From this first we have to calculate the maximum possible acceleration and from the acceleration we have to calculate the distance required to achieve the required velocity. We can also calculate the tension on each rope from the acceleration and resistance. Step 1 Since the glider are tied one after another, the rope that is tied the first glider, will experience maximum tension. Total resistance on each glider is 2500 N Total air resistance on both glider is 5000 N Now maximum force that can be applied to the rope is 12000 N. So the force that can be applied to the rope due to acceleration is F = (12000 N 5000 N) = 7000 N a The total mass of the glider is M = 2 × (700 kg) = 1400 kg Hence the maximum possible acceleration is 7000 N 2 a = 1400 kg= 5 m/s Now the final speed required is 40 m/s. If the minimum distance required by the runway is s and since the flight is starting from rest, we can write that v = 2as v2 (40 m/s) a = 2a= 2(5 m/s )160 m So the minimum length of the runway to achieve the speed is 160 m.