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Block and tackle: how much force do you need to lift a load?

Calculate the mechanical advantage of a pulley system, the pulling force with friction in each sheave, and the length of rope to pull.

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Results

Pulling force needed

53.9

Actual mechanical advantage

3.71

Ideal mechanical advantage = number of supporting segments

Rope to pull

40.0

Pulling force without friction
50.0
Efficiency of the system
93%

Trading distance for force

A pulley system, or block and tackle, lets you lift a heavy load with a smaller pull. It does not create energy: you pull a longer length of rope instead. Sailors, riggers, arborists, rescue teams and garage hoists all rely on the same principle, which Archimedes is said to have demonstrated by pulling a loaded ship single-handed.

Mechanical advantage

The ideal mechanical advantage equals the number of rope segments that support the moving block. With n supporting segments, each carries 1/n of the load, so:

  • Ideal pulling force = load ÷ n
  • Rope to pull = lift height × n

A single fixed pulley has an advantage of 1: it only changes the direction of the pull. A single movable pulley gives 2. A double block and a single block reeved together typically give 3 or 4.

Friction

Real sheaves lose a little force at each turn of the rope. If each sheave passes on a fraction e of the tension, the actual mechanical advantage becomes:

MA = (1 − eⁿ) ÷ (1 − e)

With good ball-bearing sheaves, e is about 0.95 to 0.97; with plain bushings or tight rope, 0.90 or less. This is why a 6:1 system rarely feels like 6:1, and why adding sheaves eventually adds more friction than advantage.

Example

Lifting 200 lb with 4 supporting segments, 5% friction per sheave, by 10 feet:

  • Ideal pull: 200 ÷ 4 = 50 lbf
  • Actual mechanical advantage: 3.71, an efficiency of 93%
  • Actual pull: about 54 lbf
  • Rope to pull: 40 ft

Choosing a system

  • Count the supporting segments at the moving block, not the number of pulleys.
  • Anchor the fixed block to a point rated well above the load plus the pulling force.
  • Use rope and hardware with a working load limit above the load, and remember that rope strength drops at knots and over small sheaves.
  • For frequent lifting, a chain hoist or an electric hoist is safer and faster than a rope tackle.

Safety

Never stand or work under a suspended load. Overhead lifting equipment in workplaces must be rated, inspected and used by trained people according to OSHA rules. A pulley system improvised for camping or a workshop should only lift loads that would not hurt anyone if they fell.

Frequently asked questions

What is the mechanical advantage of a pulley system?

Ideally, it equals the number of rope segments that support the moving block. With 4 supporting segments, you pull with a quarter of the load's weight but must pull 4 feet of rope for every foot the load rises.

How do I count the supporting segments?

Count the rope segments going up from the moving block, the one attached to the load. Include the end of the rope if it is tied to the moving block. Do not count the hauling line if it comes down from a fixed pulley.

Why is the real force higher than the ideal one?

Each sheave loses some force to friction in its bearing and to the stiffness of the rope bending around it. Losses of 3 to 5% per sheave are typical for ball-bearing pulleys and 8 to 10% for plain bushings, so adding more sheaves helps less and less.

Is a pulley system safe for lifting people?

Only with equipment rated and certified for it, such as rescue or fall protection systems, used by trained people. For loads overhead, use rated hoists and keep everyone out from under the load.

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Results are estimates provided for information purposes. They do not replace professional advice.

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