Question

A helicopter hovers 100ft over a rescue litter holding a person, attaches a cable with LSS to the litter, then starts flying forward while a hoist inside the helicopter pulls in the cable, raising the litter. Motion is in 2D. The hoist cable pulls in at a rate that is initially accelerating, then reaches a constant velocity of 225 fpm. The helicopter is initially stationary directly above the litter, then a constant forward thrust force of 5000N is applied from the rotors. This is the resulting force after accounting for drag.

Assume the system can be modeled as a rigid pendulum changing length, and the cable is 3/16” steel.

It is desired that the angle between the litter and vertical stays less than 10 degrees. The litter is allowed to reach an angle of 10 degrees after 5 seconds.

Find an expression for the acceleration of the litter as a function of angular position, angular velocity, and angular acceleration of the cable, as well linear acceleration of the helicopter and linear acceleration of the cable being pulled in by hoist.

Answer 1