Block and tackle
Encyclopedia
.png)
Pulley
A pulley, also called a sheave or a drum, is a mechanism composed of a wheel on an axle or shaft that may have a groove between two flanges around its circumference. A rope, cable, belt, or chain usually runs over the wheel and inside the groove, if present...
s with a rope
Rope
A rope is a length of fibres, twisted or braided together to improve strength for pulling and connecting. It has tensile strength but is too flexible to provide compressive strength...
or cable
Cable
A cable is two or more wires running side by side and bonded, twisted or braided together to form a single assembly. In mechanics cables, otherwise known as wire ropes, are used for lifting, hauling and towing or conveying force through tension. In electrical engineering cables are used to carry...
threaded between them, usually used to lift or pull heavy loads.
The pulleys are assembled together to form blocks so that one is fixed and one moves with the load. The rope is threaded, or reeved, through the pulleys to provide mechanical advantage
Mechanical advantage
Mechanical advantage is a measure of the force amplification achieved by using a tool, mechanical device or machine system. Ideally, the device preserves the input power and simply trades off forces against movement to obtain a desired amplification in the output force...
that amplifies that force applied to the rope.
Hero of Alexandria
Hero of Alexandria
Hero of Alexandria was an ancient Greek mathematician and engineerEnc. Britannica 2007, "Heron of Alexandria" who was active in his native city of Alexandria, Roman Egypt...
described cranes formed from assemblies of pulleys. Illustrated versions of Hero's "book on raising heavy weights" show early block and tackle systems.
Overview
Although used in many situations, they are especially common on boatBoat
A boat is a watercraft of any size designed to float or plane, to provide passage across water. Usually this water will be inland or in protected coastal areas. However, boats such as the whaleboat were designed to be operated from a ship in an offshore environment. In naval terms, a boat is a...
s and sailing ship
Sailing ship
The term sailing ship is now used to refer to any large wind-powered vessel. In technical terms, a ship was a sailing vessel with a specific rig of at least three masts, square rigged on all of them, making the sailing adjective redundant. In popular usage "ship" became associated with all large...
s, where motorized aids are usually not available and the task must be performed manually.
A block is a set of pulleys or "sheaves
Pulley
A pulley, also called a sheave or a drum, is a mechanism composed of a wheel on an axle or shaft that may have a groove between two flanges around its circumference. A rope, cable, belt, or chain usually runs over the wheel and inside the groove, if present...
" all mounted on a single axle
Axle
An axle is a central shaft for a rotating wheel or gear. On wheeled vehicles, the axle may be fixed to the wheels, rotating with them, or fixed to its surroundings, with the wheels rotating around the axle. In the former case, bearings or bushings are provided at the mounting points where the axle...
. When rope or line is run through a block or a series of blocks the whole assembly is called a tackle.
Mechanical advantage
If frictionFriction
Friction is the force resisting the relative motion of solid surfaces, fluid layers, and/or material elements sliding against each other. There are several types of friction:...
al losses are neglected, the mechanical advantage
Mechanical advantage
Mechanical advantage is a measure of the force amplification achieved by using a tool, mechanical device or machine system. Ideally, the device preserves the input power and simply trades off forces against movement to obtain a desired amplification in the output force...
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, or the number of supporting ropes. The formula is derived using virtual work
Virtual work
Virtual work arises in the application of the principle of least action to the study of forces and movement of a mechanical system. Historically, virtual work and the associated calculus of variations were formulated to analyze systems of rigid bodies, but they have also been developed for the...
in detail in the article mechanical advantage
Mechanical advantage
Mechanical advantage is a measure of the force amplification achieved by using a tool, mechanical device or machine system. Ideally, the device preserves the input power and simply trades off forces against movement to obtain a desired amplification in the output force...
.
An ideal block and tackle with a moving block supported by n rope sections has the mechanical advantage,
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 tackle with a mechanical advantage of 4 (a double tackle) will be able to lift 100 lbs with only 25 lbs of tension on the hauling part of the line.
Ideal mechanical advantage correlates directly with velocity ratio
Velocity ratio
Velocity Ratio is defined by Classical mechanics as the distance that the point of Effort moved divided by the distance that the point of Load moved as given from here Thus VR = Distance / Distance =...
. 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.
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.
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:
where
is the forceForce
In physics, a force is any influence that causes an object to undergo a change in speed, a change in direction, or a change in shape. In other words, a force is that which can cause an object with mass to change its velocity , i.e., to accelerate, or which can cause a flexible object to deform...
applied to the hauling part of the line (the input force),
is the weight of the load (the output force), 
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 
is the mechanical efficiencyMechanical efficiency
Mechanical efficiency measures the effectiveness of a machine in transforming the energy and power that is input to the device into an output force and movement...
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
is the number of sheaves in the purchase, and there is a roughly 
% loss of efficiency at each sheave due to friction, then:
This approximation is more accurate for smaller values of
and 
. A more precise estimate of efficiency is possible by use of the sheave friction factor, 
(which may be obtainable from the manufacturer or published tables). The relevant equation is:
Typical
values are 1.04 for roller bearing sheaves and 1.09 for plain bearing sheaves (with wire rope).The increased force produced by a tackle is offset by both the increased length of rope needed and the friction
Friction
Friction is the force resisting the relative motion of solid surfaces, fluid layers, and/or material elements sliding against each other. There are several types of 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, 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.
- "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.
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
Ergonomics
Ergonomics is the study of designing equipment and devices that fit the human body, its movements, and its cognitive abilities.The International Ergonomics Association defines ergonomics as follows:...
of working with a particular situation.
The common wisdom prefers a block and tackle "rove to advantage." However, if the load is to be hauled against gravity, then there is a benefit to reeving the block and tackle to disadvantage, because in this case the weight of the individual can offset the weight of the load. On the other hand, if the load is to be hauled parallel to the ground, there is a benefit to reeving the block and tackle to advantage, because the pulling force is in the direction of the load movement allowing the individual to manage obstacles. It is important to notice that the mechanical advantage
Mechanical advantage
Mechanical advantage is a measure of the force amplification achieved by using a tool, mechanical device or machine system. Ideally, the device preserves the input power and simply trades off forces against movement to obtain a desired amplification in the output force...
is different if the block and tackle is "rove to advantage" or "rove to disadvantage." The mechanical advantage will always be one greater when "rove to advantage" than when "rove to disadvantage."
See also
- BlockBlock (sailing)In sailing, a block is a single or multiple pulley. One or a number of sheaves are enclosed in an assembly between cheeks or chocks. In use a block is fixed to the end of a line, to a spar or to a surface...
- CraneCrane (machine)A crane is a type of machine, generally equipped with a hoist, wire ropes or chains, and sheaves, that can be used both to lift and lower materials and to move them horizontally. It uses one or more simple machines to create mechanical advantage and thus move loads beyond the normal capability of...
- DeadeyeDeadeyeA deadeye is an item used in the standing and running rigging of traditional sailing ships. It is a smallish round thick wooden disc with one or more holes through it, perpendicular to the plane of the disc. Single and triple-hole deadeyes are most commonly seen...
- TripodTripodA tripod is a portable three-legged frame, used as a platform for supporting the weight and maintaining the stability of some other object. The word comes from the Greek tripous, meaning "three feet". A tripod provides stability against downward forces, horizontal forces and moments about the...
- Two six heaveTwo six heave"Two, six, heave" is a phrase used to coordinate seamen's pulling. It derives from the orders used in firing shipboard cannons in the British Royal Navy. The team of six men had numbered roles...
- Trucker's hitchTrucker's hitchThe trucker's hitch is a compound knot commonly used for securing loads on trucks or trailers. This general arrangement, using loops and turns in the rope itself to form a crude block and tackle, has long been used to tension lines and is known by multiple names...
- WinchWinchA winch is a mechanical device that is used to pull in or let out or otherwise adjust the "tension" of a rope or wire rope . In its simplest form it consists of a spool and attached hand crank. In larger forms, winches stand at the heart of machines as diverse as tow trucks, steam shovels and...
- Z-dragZ-dragA Z-Drag is an arrangement of lines and pulleys commonly used in rescue situations. The basic arrangement provides a theoretical mechanical advantage of three. The name comes from the fact that the arrangement of lines is roughly Z shaped...