View source for Pound (force)

{{short description|Earth's gravitational pull on a one-pound mass}}
{{Wiktionary|pound-force|pound}}
{{redirect|lbf|the airport in Nebraska|LBF (airport)}}
{{other uses|Pound (disambiguation)}}
{{Infobox unit
| bgcolor      = 
| name         = Pound-force
| image        = 
| caption      = 
| standard     = [[English Engineering units]], [[British Gravitational System]]
| quantity     = 
| symbol       = lbf
| symbol2      = 
| extralabel   = 
| extradata    = 
| units1 = [[SI units]]
| inunits1     = {{convert|1|lbf|sigfig=7|disp=out|lk=on}}
| units2 = [[CGS units]]
| inunits2     = {{convert|1|lbf|dyn|sigfig=7|disp=out|lk=on}}
| units3 = [[Absolute English System]]
| inunits3     = {{convert|1|lbf|pdl|sigfig=7|disp=out|lk=on}}
}}
The '''pound of force''' or '''pound-force''' (symbol: '''lbf''',<ref>IEEE Standard Letter Symbols for Units of Measurement (SI Units, Customary Inch-Pound Units, and Certain Other Units), IEEE Std 260.1™-2004 (Revision of IEEE Std 260.1-1993)</ref> sometimes '''lb<sub>f</sub>''',<ref name="isbn_978-0135018583">{{Citation |last=Fletcher |first=Leroy S. |last2=Shoup |first2=Terry E. |year=1978 |title=Introduction to Engineering |publisher=Prentice-Hall |url=https://books.google.com/books?id=tyohAQAAIAAJ |isbn=978-0135018583 |lccn=77024142 |postscript=. |access-date=2017-08-03 |archive-date=2019-12-06 |archive-url=https://web.archive.org/web/20191206172653/https://books.google.com/books?id=tyohAQAAIAAJ |url-status=live }}{{rp|257}}</ref>) is a [[Units of measurement|unit]] of [[force]] used in some [[System of measurement|systems of measurement]], including [[English Engineering units]]{{efn|Despite its name, this system is based on [[United States customary units]] and is only used in the US.}} and the [[foot–pound–second system]].<ref>{{cite web|url=http://www.engineeringtoolbox.com/mass-weight-d_589.html|title=Mass and Weight|work=engineeringtoolbox.com|access-date=2010-08-03|archive-date=2010-08-18|archive-url=https://web.archive.org/web/20100818181516/http://www.engineeringtoolbox.com/mass-weight-d_589.html|url-status=live}}</ref> 

Pound-force should not be confused with ''[[pound (mass)|pound-mass]]'' (lb), often simply called "pound", which is a unit of [[mass]]; nor should these be confused with ''[[foot-pound]]'' (ft⋅lbf), a unit of [[energy (physics)|energy]], or ''[[pound-foot]]'' (lbf⋅ft), a unit of [[torque]].

== Definitions ==
The pound-force is equal to the gravitational force exerted on a [[mass]] of one [[Pound (mass)#Avoirdupois pound|avoirdupois pound]] on the surface of [[Earth]]. Since the 18th century, the unit has been used in low-precision measurements, for which small changes in [[Gravity of Earth|Earth's gravity]] (which varies from equator to pole by up to half a percent) can safely be neglected.<ref>Acceleration due to gravity varies over the surface of the Earth, generally increasing from about 9.78&nbsp;m/s<sup>2</sup> (32.1&nbsp;ft/s<sup>2</sup>) at the equator to about 9.83&nbsp;m/s<sup>2</sup> (32.3&nbsp;ft/s<sup>2</sup>) at the poles.</ref>

The 20th century, however, brought the need for a more precise definition, requiring a standardized value for acceleration due to gravity.  

=== Product of avoirdupois pound and standard gravity ===
The pound-force is the product of one [[Avoirdupois system|avoirdupois]] pound ([[International yard and pound|exactly]] {{cvt|1|lb|kg|sigfig=8|disp=out}}) and the [[standard gravity|standard acceleration due to gravity]], {{cvt|9.80665|m/s2|ft/s2|sigfig=8}}.<ref name="BS350">{{cite book|title=BS 350 : Part 1: 1974 Conversion factors and tables, Part 1. Basis of tables. Conversion factors|date=1974|publisher=British Standards Institution|page=43}}</ref><ref>In 1901 the [http://www1.bipm.org/en/CGPM/db/3/2/ third CGPM] {{Webarchive|url=https://web.archive.org/web/20120207064142/http://www1.bipm.org/en/CGPM/db/3/2/ |date=2012-02-07 }} declared (second resolution) that:
<blockquote>The value adopted in the International Service of Weights and Measures for the standard acceleration due to Earth's gravity is {{val|980.665|u=cm/s2}}, value already stated in the laws of some countries.</blockquote>
This value was the conventional reference for calculating the [[kilogram-force]], a unit of force whose use has been deprecated since the introduction of SI.</ref><ref>Barry N. Taylor, ''[http://arquivo.pt/wayback/20160515144655/http://physics.nist.gov/Pubs/SP811/sp811.html/appenB8.html#P Guide for the Use of the International System of Units (SI)]'', 1995, [[NIST]] Special Publication 811, Appendix B note 24</ref>

The standard values of acceleration of the standard gravitational field (''g''<sub>n</sub>) and the [[Pound (mass)#International pound|international avoirdupois pound]] (lb) result in a pound-force equal to 
{{cvt|1|lbf|N|sigfig=14|disp=out}}.{{efn|The [[International yard and pound|international avoirdupois pound is defined]] to be exactly {{val|0.45359237|u=kg}}.}}

<math display="block">\begin{align}
  1\,\text{lbf} &= 1\,\text{lb} \times g_\text{n} \\
                &= 1\,\text{lb} \times 9.80665\,\tfrac{\text{m}}{\text{s}^2} / 0.3048\,\tfrac{\text{m}}{\text{ft}}\\
                &\approx 1\,\text{lb} \times 32.174049\,\mathrm{\tfrac{ft}{s^2}}\\
                &\approx 32.174049\,\mathrm{\tfrac{ft {\cdot} lb}{s^2}} \\
  1\,\text{lbf} &= 1\,\text{lb} \times 0.45359237\,\tfrac{\text{kg}}{\text{lb}} \times g_\text{n} \\
                &= 0.45359237\,\text{kg} \times 9.80665\,\tfrac{\text{m}}{\text{s}^2}\\
                &= 4.4482216152605\,\text{N}
\end{align}</math>

This definition can be rephrased in terms of the [[Slug (unit)|slug]]. A slug has a mass of 32.174049&nbsp;lb.  A pound-force is the amount of force required to accelerate a slug at a rate of {{val|1|u=ft/s2}}, so:

<math display="block">\begin{align}
  1\,\text{lbf} &= 1\,\text{slug} \times 1\,\tfrac{\text{ft}}{\text{s}^2} \\
                &= 1\,\tfrac{\text{slug} \cdot \text{ft}}{\text{s}^2}
\end{align}</math>

== Conversion to other units ==
{{Units of force}}

== Foot–pound–second (FPS) systems of units ==
{{main|Foot–pound–second system}}
In some contexts, the term "pound" is used almost exclusively to refer to the unit of force and not the unit of mass. In those applications, the preferred unit of mass is the slug, i.e. lbf⋅s<sup>2</sup>/ft. In other contexts, the unit "pound" refers to a [[Pound (mass)|unit of mass]].  The international standard symbol for the pound as a unit of mass is lb.<ref>IEEE Std 260.1™-2004, IEEE Standard Letter Symbols for Units of Measurement (SI Units, Customary Inch-Pound Units, and Certain Other Units) </ref> 

{{GravEngAbs}}
In the "engineering" systems (middle column), the [[weight]] of the mass unit (pound-mass) on Earth's surface is approximately equal to the force unit (pound-force). This is convenient because one pound mass exerts one pound force due to gravity. Note, however, unlike the other systems the force unit is not equal to the mass unit multiplied by the acceleration unit<ref>The acceleration unit is the distance unit divided by the time unit squared.</ref>—the use of [[Newton's laws of motion|Newton's second law]], {{nowrap|1=''F'' = ''m'' ⋅ ''a''}}, requires another factor, [[gc (engineering)|''g<sub>c</sub>'']], usually taken to be 32.174049&nbsp;(lb⋅ft)/(lbf⋅s<sup>2</sup>).
"Absolute" systems are ''coherent'' systems of units: by using the slug as the unit of mass, the "gravitational" FPS system (left column) avoids the need for such a constant. The [[SI]] is an "absolute" metric system with kilogram and meter as base units.

==Pound of thrust==
{{further|thrust}}
The term '''pound of thrust''' is an alternative name for pound-force in specific contexts. It is frequently seen in US sources on jet engines and rocketry, some of which continue to use the FPS notation. For example, the thrust produced by each of the [[Space Shuttle]]'s two [[Space Shuttle Solid Rocket Booster|Solid Rocket Boosters]] was {{convert|14.7|MN|lbf|order=flip|lk=out}}, together {{convert|29.4|MN|lbf|order=flip|lk=off}}.<ref>{{cite web|url=http://www.braeunig.us/space/specs/shuttle.htm|title=Space Launchers - Space Shuttle|website=www.braeunig.us|access-date=16 February 2018|quote=Thrust: combined thrust 29.36 MN SL (maximum thrust at launch reducing by 1/3 after 50 s)|archive-date=6 April 2018|archive-url=https://web.archive.org/web/20180406061909/http://www.braeunig.us/space/specs/shuttle.htm|url-status=live}}</ref><ref>{{cite news | url = https://www.wired.com/2001/12/rd-180/ | title = From Russia, With 1 Million Pounds of Thrust | author = Richard Martin | newspaper = [[wired.com]] | date = 12 January 2001 | access-date = 25 November 2019 | archive-date = 25 September 2019 | archive-url = https://web.archive.org/web/20190925074918/https://www.wired.com/2001/12/rd-180/ | url-status = live }}</ref>

== See also ==
{{div col|colwidth=30em}}
* [[Foot-pound (energy)]]
* [[Ton-force]]
* [[Kip (unit)]]
* [[Mass in general relativity]] 
* [[Mass in special relativity]] 
* [[Mass versus weight]] for the difference between the two physical properties
* [[Newton (unit)|Newton]]
* [[Poundal]]
* [[Pounds per square inch]], a unit of [[pressure]]
{{div col end}}

==Notes and references==
{{notelist}}
{{reflist}}

== General sources ==
* Obert, Edward  F. (1948). ''Thermodynamics''. New York: D. J. Leggett Book Company. Chapter I "Survey of Dimensions and Units", pp. 1-24.

{{Imperial units}}
{{United States Customary Units}}

[[Category:Customary units of measurement in the United States]]
[[Category:Imperial units]]
[[Category:Units of force]]