Pulleys

A container weighing as much as twenty cars dangles from a harbour crane, held by a motor that could never hoist it directly. The secret hangs between jib and hook: a block and tackle, a bundle of pulleys and rope. For more than two thousand years people have used it to lift loads that are really too heavy for them, from ancient building sites to today's sailing boats.

Fixed and movable pulley

A pulley mounted in place only changes the rope's direction: you pull comfortably downwards, the load goes up, but the force stays the same. Only the movable pulley saves force. It hangs on the load and is carried by two strands of rope, each strand taking half the weight. So you pull with half the force, but you have to haul in twice as much rope.

Counting strands

Combining fixed and movable pulleys gives the true block and tackle. The rule for the force is strikingly simple: count the strands of rope that carry the load. With $n$ supporting strands the load's weight $G$ is split into $n$ parts and your pulling force is only $F = G/n$, as long as friction and the pulleys' own weight stay small. The golden rule of mechanics collects its price: for the load to rise one metre, every supporting strand must shorten by one metre, so you haul in $n$ metres of rope.

From crane to sailing boat

A crane's hook block often runs eight or more strands, letting a modest motor winch lift loads weighing tonnes, just slowly, because it must wind up enormous lengths of rope. On sailing boats block and tackle systems sheet in the mainsail: no arm could win against the wind's push on the sail, but with four or six strands one hand is enough. The same principle sits in mountain rescue hauling systems, lifts and towing winches.

Where the advantage meets its limits

So why not simply fit a hundred pulleys? Every extra pulley adds bearing friction, and the rope has to bend more often, part of your pull is lost as heat. With many pulleys friction eventually eats up the gain. Lifting also becomes painfully slow: with ten strands you haul in ten metres of rope for every metre of lift. Good engineers therefore pick the smallest advantage that does the job.