Editing Block and tackle (section)

== Mechanical advantage ==
[[Image:Polispasto2B.jpg|thumb|upright|A gun tackle has a single pulley in both the fixed and moving blocks with 2 rope parts (''n'') supporting the load (F<sub>B</sub>) of 100&nbsp;N. The mechanical advantage is 2, requiring a force of only 50&nbsp;N to lift the load.]]
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. Its [[mechanical advantage]] is the number of parts of the rope that act on the load. The mechanical advantage of a tackle dictates how much easier it is to haul or lift the load.

If [[friction]]al 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 blocks—in other words, the number of supporting rope sections.

===Rove to advantage===
An ideal block and tackle with a moving block supported by ''n'' rope sections has the mechanical advantage (MA),
<math display="block">MA = \frac{F_B}{F_A} = n,\!</math>
where F<sub>A</sub> is the hauling (or input) force and F<sub>B</sub> is the load.

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

[[Image:Polispasto4.jpg|thumb|upright|A double tackle has two pulleys in both the fixed and moving blocks with four rope parts (n) supporting the load (F<sub>B</sub>) of 100&nbsp;N. The mechanical advantage is 4, requiring a force of only 25&nbsp;N to lift the load.]]

<gallery>
Image:Pulley1a.svg|Separation of the pulleys in the gun tackle show the force balance that results in a rope tension of ''W/2.'' 
Image:Pulley3a.svg|Separation of the pulleys in the double tackle show the force balance that results in a rope tension of ''W/4.''
</gallery>

Ideal mechanical advantage correlates directly with [[velocity ratio]]. The velocity ratio of a tackle is the ratio between the velocity of the hauling line to that of 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.

===Rove to disadvantage===
The mechanical advantage of any 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."<ref>[http://www.sccheadquarters.com/UserData/root/Files/Training/Specialisations/Seamanship/Chapter%205%20-%20General%20Rigging.pdf sccheadquarters.com seamanship reference] {{webarchive |url=https://web.archive.org/web/20111111234251/http://www.sccheadquarters.com/UserData/root/Files/Training/Specialisations/Seamanship/Chapter%205%20-%20General%20Rigging.pdf |date=November 11, 2011 }}</ref>

* "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.<ref name="advantage">{{cite book |title=Handbook of Rigging: For Construction and Industrial Operations |publisher=McGraw-Hill Professional |isbn=978-0-07-149301-7 |last=MacDonald |first=Joseph A |date=14 January 2009 |pages=376 |quote=Tackle may be rigged to advantage - where the pull on the rope is in the same direction as that in which the load is to be moved; or it may be rigged to disadvantage - where the pull on the rope is in the opposite direction of that in which the load is to be moved}}</ref>
* "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.<ref name="advantage" />

Diagram 3 shows three rope parts supporting the load ''W'', which means the tension in the rope is ''W/3''. Thus, the mechanical advantage is three-to-one.

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.
<gallery>
Image:Pulley2.svg|Diagram 3:  The gun tackle "rove to advantage" has the rope attached to the moving pulley. The tension in the rope is ''W/3'' yielding an advantage of three.
Image:Pulley2a.svg|Diagram 3a: The Luff tackle adds a fixed pulley "rove to disadvantage."  The tension in the rope remains ''W/3'' yielding an advantage of three.
</gallery>

The decision of which to use depends on pragmatic considerations for the total [[ergonomics]] of working with a particular situation. Reeving to advantage is the most efficient use of equipment and resources. For example, if the load is to be hauled parallel to the ground, reeving to advantage enables the pulling force to be in the direction of the load movement, allowing obstacles to be managed more easily.

Reeving to disadvantage adds an extra sheave to change the direction of the pulling line to a potentially more ergonomic direction, which increases friction losses without improving the velocity ratio. Situations in which reeving to disadvantage may be more desirable include lifting from a fixed point overhead--the additional pulley allows pulling downwards instead of upwards so that the weight of the lifter can offset the weight of the load, or allows pulling sideways, enabling multiple lifters to combine effort.

=== Friction ===
[[File:PulleyShip.JPG|thumb|right|Wooden block on a sailing ship.]]
The formula used to find the effort required to raise a given weight using a block and fall:

<math display="block"> F_a  =\frac{L}{N} \frac{1}{\textit{eff}}</math>

where <math>F_a</math> is the [[force]] applied to the hauling part of the line (the input force), <math>L</math> is the weight of the load (the output force), <math>N</math> 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 <math>\textit{eff}</math> 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 <math>S</math> is the number of sheaves in the purchase, and there is a roughly <math>x</math>% loss of efficiency at each sheave due to friction, then:<ref>Notes on cargo work: Kemp and Young. 3rd Edition. {{ISBN|0-85309-040-8}}  Page 4</ref><ref name = "Stage_rigging">{{Cite book
  | last = Glerum | first = Jay O. | author-link =Jay O. Glerum
  | title = Stage rigging handbook | publisher = [[Southern Illinois University Press]]
  | date = 2007-04-03 | pages = 52–54 (320 pages total)
  | url = https://books.google.com/books?id=7yS4uno7P2UC | isbn = 978-0-8093-2741-6| edition = 3rd }}</ref>

<math display="block">\frac{1}{\textit{eff}} \approx 1 + S \frac{x}{100}.</math>

This approximation is more accurate for smaller values of <math>S</math> and <math>x</math>.<ref name = "Stage_rigging"/> A more precise estimate of efficiency is possible by use of the sheave friction factor, <math>K</math> (which may be obtainable from the manufacturer or published tables<ref name = "API_RP_9B"/>). The relevant equation is:<ref name = "API_RP_9B">{{Cite book
  | title = Recommended Practice on Application Care, and use of Wire Rope for Oil Field Service, Twelfth Edition
  | publisher = [[American Petroleum Institute]] | date = 2005-06-01 
  | pages = 33 | url = http://www.techstreet.com/standards/API/RP_9B?product_id=1221365
  }}</ref>

<math display="block"> \textit{eff} = \frac{K^N-1}{K^S N (K-1)}.</math>

Typical <math>K</math> values are 1.04 for roller bearing sheaves and 1.09 for plain bearing sheaves (with wire rope).<ref name = "API_RP_9B"/>

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,<ref group=notes>Friction may mean that the rope in a tackle "bunches" and jams when the force is released if the tackle has too much friction for the load to balance, or that the tackle does not "lower" the load</ref> or by the reduction in force needed to move the load being judged insufficient because undue friction has to be overcome as well.