Rescue Hoist: Effort, Turns and the Limits of Leverage
A manually operated rescue hoist has a crank handle whose grip travels on a circle of radius 320 mm. The crank turns a winding drum of diameter 160 mm; crank and drum are fixed to the same shaft. A 96 kg load hangs from a single line wound on the drum. Trials show the hoist runs at 75 per cent efficiency because of bearing friction and the line guide. The mass of the rope and drum is negligible. The operator can sustain a steady 30 turns per minute and about 35 kgf at the grip before grip and balance deteriorate. The job is to raise the load 4.0 m from a stretcher on the floor.
1. Calculate the ideal effort at the crank grip, the actual effort needed at 75 per cent efficiency, and state whether this operator can manage it.
Read the worked answer
Mechanical advantage of the crank and drum (both on one shaft, so torque is shared):
MA = crank radius / drum radius = 320 mm / 80 mm = 4
Ideal effort: 96 kg / 4 = 24 kgf
Actual effort at 75 per cent efficiency: the operator must supply the ideal effort divided by the efficiency, because friction adds to the input required rather than reducing the load:
24 / 0.75 = 32 kgf
Can the operator manage it? Yes - 32 kgf is below the 35 kgf limit stated, but only by 3 kgf. That is a thin margin for a task done at night, possibly at arm's length, and any extra friction (a badly wound line, a dry bearing) would push the requirement past the limit. The task is feasible but should be treated as near the operator's ceiling.
2. How many turns of the crank are needed to raise the load 4.0 m, and how long will that take at the stated rate?
Read the worked answer
Line taken up per turn = drum circumference = pi x diameter = 3.1416 x 0.160 m = 0.5027 m
Turns required: 4.0 / 0.5027 = 7.96, so 8 full turns in practice (a part turn is still a turn of the handle).
Time at 30 turns per minute:
- 7.96 / 30 = 0.265 minutes
- 0.265 x 60 = 15.9 seconds, so about 16 seconds of steady winding.
Two practical points follow. First, 16 seconds is short enough that the load should be raised in one controlled lift rather than rested part-way, which avoids a swing on restart. Second, the answer is a steady-rate figure: starting torque from rest is higher than running torque, so the true peak effort is above the 32 kgf calculated earlier.
3. A suggestion is made to double the crank radius to 640 mm so the load is 'twice as easy'. Evaluate the suggestion quantitatively and explain the real cost.
Read the worked answer
Quantitatively it works.
- New MA = 640 / 80 = 8
- Ideal effort = 96 / 8 = 12 kgf
- Actual effort at 75 per cent efficiency = 12 / 0.75 = 16 kgf
Effort halves, and the margin against the 35 kgf limit becomes very comfortable.
The real cost: nothing is free, only traded. The load still has to be raised 4.0 m, so the work done on the load is unchanged. The handle now travels on a circle of twice the radius:
- Grip travel per turn = 2 x pi x 0.640 = 4.02 m, against 2.01 m before
- Turns still needed: 4.0 / 0.5027 = about 8
- So the operator walks the grip through roughly 32 m of arc instead of 16 m for the same lift
Force is halved and distance doubled - the same work, less friction loss per unit of effort only if the mechanism stays efficient. Practical penalties: a longer crank is more easily bent, needs more clear floor space to swing, is harder to control when lowering, and can let an operator apply a force the drum and line were never designed for. The honest answer is that a longer crank is a good fix for effort, not a fix for work, and it must be matched to the strength of the shaft, drum and line.