# Block and tackle

A block and tackle[1][2] is a system of two or more pulleys with a rope or cable threaded between them, usually used to lift or pull heavy loads.

The pulleys are assembled together to form blocks and then blocks are paired so that one is fixed and one moves with the load. The rope is threaded, or reeved, through the pulleys to provide mechanical advantage that amplifies that force applied to the rope.[3]

Hero of Alexandria described cranes formed from assemblies of pulleys. Illustrated versions of Hero's "book on raising heavy weights" show early block and tackle systems.[4]

## Overview

 Seamen aboard the now-defunct USNS Southern Cross freighter rigged this block and tackle to make heavy lifts during cargo operations.

A block is a set of pulleys or "sheaves" mounted on a single axle. The assembly of two blocks with a rope threaded through the pulleys is called tackle. A block and tackle system amplifies the tension force in the rope to lift heavy loads. They are common on boats and sailing ships, where tasks are often performed manually.

If frictional losses are neglected, the mechanical advantage of a block and tackle is equal to the number of parts in the line that either attach to or run through the moving block -- in other words, the number of supporting ropes. The formula is derived using virtual work in detail in the article "mechanical advantage".

An ideal block and tackle with a moving block supported by n rope sections has the mechanical advantage,

$MA = \frac{F_B}{F_A} = n,\!$

where FA is the hauling, or input, force and FB is the load.

The mechanical advantage of a tackle dictates how much easier it is to haul or lift the load. A double tackle has a mechanical advantage of 4, so it will be able to lift a 100 N load with only 25 N of tension on the hauling part of the line.

Ideal mechanical advantage correlates directly with velocity ratio. The velocity ratio of a tackle refers to the relative velocities of the hauling line to the hauled load. A line with a mechanical advantage of 4 has a velocity ratio of 4:1. In other words, to raise a load at 1 metre per second, the hauling part of the rope must be pulled at 4 metres per second. Therefore the mechanical advantage of a double tackle is 4.

## Example Block and Tackle Configurations

Notice that there are two parts of the rope through each pulley in a block, and an additional part for the start of the rope that is attached to one of the blocks. If there are p pulleys in each of the blocks then there are 2p parts for one block and 2p+1 for the other block. This means if the block with the rope attachment is selected for the moving block, then the mechanical advantage is increased by one. This configuration requires the hauling rope to move in the same direction as the load.

The Gun tackle, Double tackle and Threefold purchase have the same number of pulleys in both blocks, one, two and three, respectively.

Various ways of rigging a tackle.[5]

For example, consider a block and tackle with two sheaves on both the moving block and the fixed block. One block has four lines running through its sheaves, and the other block also has four lines including the part of the line being pulled or hauled, with a fifth line attached to a secure point on the block. If the hauling part is coming out of the fixed block, the block and tackle will have a mechanical advantage of four. If the tackle is reversed, so that the hauling part is coming from the moving block, the mechanical advantage is now five.

In the diagram on the right the mechanical advantage of the tackles shown is as follows:

• Gun Tackle: 2
• Luff Tackle: 3
• Double Tackle: 4
• Gyn Tackle: 5
• Threefold purchase: 6

## Friction

The formula used to find the effort required to raise a given weight is:

$F_a =\frac{L}{N} \frac{1}{\textit{eff}}$

where $F_a$ is the force applied to the hauling part of the line (the input force), $L$ is the weight of the load (the output force), $N$ is the ideal mechanical advantage of the system (which is the same as the number of segments of line extending from the moving block), and $eff$ is the mechanical efficiency of the system (equal to one for an ideal frictionless system; a fraction less than one for real-world systems with energy losses due to friction and other causes). If $S$ is the number of sheaves in the purchase, and there is a roughly $x$% loss of efficiency at each sheave due to friction, then:[6][7]

$\frac{1}{\textit{eff}} \approx 1 + S \frac{x}{100}.$

This approximation is more accurate for smaller values of $S$ and $x$.[7] A more precise estimate of efficiency is possible by use of the sheave friction factor, $K$ (which may be obtainable from the manufacturer or published tables[8]). The relevant equation is:[8]

$\textit{eff} = \frac{K^N-1}{K^S N (K-1)}.$

Typical $K$ values are 1.04 for roller bearing sheaves and 1.09 for plain bearing sheaves (with wire rope).[8]

The increased force produced by a tackle is offset by both the increased length of rope needed and the friction in the system. In order to raise a block and tackle with a mechanical advantage of 6 a distance of 1 metre, it is necessary to pull 6 metres of rope through the blocks. Frictional losses also mean there is a practical point at which the benefit of adding a further sheave is offset by the incremental increase in friction which would require additional force to be applied in order to lift the load. Too much friction may result in the tackle not allowing the load to be released easily,[9] or by the reduction in force needed to move the load being judged insufficient because undue friction has to be overcome as well.

## Rigging methods

A tackle may be

• "Rove to advantage" – where the pull on the rope is in the same direction as that in which the load is to be moved. The hauling part is pulled from the moving block.[5]
• "Rove to disadvantage" – where the pull on the rope is in the opposite direction to that in which the load is to be moved. The hauling part is pulled from the fixed block.[5]

While roving to advantage is the most efficient use of equipment and resources--Roving to disadvantage simply adds an extra sheave to change the direction of the pulling line. This doesn't change the velocity ratio but increases friction losses--there are several situations in which roving to disadvantage may be more desirable, for example when lifting from a fixed point overhead. The decision of which to use depends on pragmatic considerations for the total ergonomics of working with a particular situation.

A block and tackle is characterized by the use of a single continuous rope to transmit a tension force around one or more pulleys to lift or move a load---the rope may be a light line or a strong cable. If the rope and pulley system does not dissipate or store energy, then its mechanical advantage is the number of parts of the rope that act on the load. This can be shown as follows.

Consider the set of pulleys that form the moving block and the parts of the rope that support this block. If there are p of these parts of the rope supporting the load W, then a force balance on the moving block shows that the tension in each of the parts of the rope must be W/p. This means the input force on the rope is T=W/p. Thus, the block and tackle reduces the input force by the factor p.

The mechanical advantage of the gun tackle can be increased by interchanging the fixed and moving blocks so the rope is attached to the moving block and the rope is pulled in the direction of the lifted load. In this case the block and tackle is said to be "rove to advantage."[10] Diagram 3 shows that now three rope parts support the load W which means the tension in the rope is W/3. Thus, the mechanical advantage is three.

By adding a pulley to the fixed block of a gun tackle the direction of the pulling force is reversed though the mechanical advantage remains the same, Diagram 3a. This is an example of the Luff tackle.