View source for Foot–pound–second system of units

{{short description|Physical system of measurement that uses the foot, pound, and second as base units}}
The '''foot–pound–second system''' ('''FPS system''') is a system of units built on three fundamental units: the [[foot (unit)|foot]] for [[length]], the [[pound (mass)|(avoirdupois) pound]] for either [[mass]] or [[force]] (see below), and the [[second]] for [[time]].<ref name=cardarelli>{{citation |title=Encyclopaedia of Scientific Units, Weights and Measures: Their SI Equivalences and Origins |last=Cardarelli |first=François |publisher=Springer |year=2003 |isbn=978-1-85233-682-0 |chapter=The Foot–Pound–Second (FPS) System |pages=[https://archive.org/details/encyclopaediaofs0000card/page/51 51–55] |chapter-url=https://archive.org/details/encyclopaediaofs0000card/page/51 }}.</ref>

== Variants ==
Collectively, the variants of the FPS system were the most common system in technical publications in English until the middle of the 20th century.<ref name=cardarelli/>

{{anchor|Stroud}}Errors can be avoided and translation between the systems facilitated by labelling all physical quantities consistently with their units. Especially in the context of the FPS system this is sometimes known as the '''Stroud system''' after [[William Stroud]], who popularized it.<ref>{{citation |title=The Stroud system of teaching dynamics |last1=Henderson |first1=James B. |last2=Godfrey |first2=C. |journal=The Mathematical Gazette |volume=12 |number=170 |year=1924 |pages=99–105 |doi=10.2307/3604647 |jstor=3604647|s2cid=125929042 }}.</ref>
{{GravEngAbs|system=English}}

=== Pound as mass unit ===
{{anchor|mass|Absolute English System}}
When the pound is used as a unit of mass, the core of the [[Coherence (units of measurement)|coherent system]] is similar and functionally equivalent to the corresponding subsets of the [[International System of Units]] (SI), using [[metre–kilogram–second system of units|metre, kilogram and second]] (MKS), and the earlier [[centimetre–gram–second system of units]] (CGS). This system is often called the '''Absolute English System'''.{{citation needed|date=January 2022}}

In this sub-system, the unit of [[force]] is a derived unit known as the [[poundal]].<ref name=cardarelli/>
:<math>\mathrm{1\,pdl} = \mathrm{1\,lb{\cdot}ft/s^2}.</math>

The international standard symbol for the pound as unit of mass rather than force 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>

{{Cleanup|section|date=October 2011}}
Everett (1861)<!--ref missing--> proposed the metric [[dyne]] and [[erg]] as the units of force and energy in the FPS system.

Latimer Clark's (1891) "Dictionary of Measures"<!--ref missing--> contains ''celo'' (acceleration), ''vel'' or ''velo'' (velocity) and ''pulse'' (momentum) as proposed names for FPS absolute units.<!--definitions or explanations missing-->

=== Pound as force unit ===
{{anchor|force|British gravitational system}}
The '''technical''' or '''gravitational FPS system'''<ref name="cr">{{Cite book |last=Coulson |first=J. M. |url=https://books.google.com/books?id=lEi8RU6Br6YC&lpg=PA5&pg=PA5 |title=Chemical Engineering Volume 1: Fluid Flow, Heat Transfer and Mass Transfer |last2=Richardson |first2=J. F. |last3=Backhurst |first3=J. R. |last4=Harker |first4=J. H. |date=1999-11-08 |publisher=Elsevier Science |isbn=978-0-7506-4444-0 |language=en}}</ref> or '''British gravitational system''' is a coherent variant of the FPS system that is most common among engineers in the United States. It takes the [[pound-force]] as a fundamental unit of force instead of the pound as a fundamental unit of mass.

In this sub-system, the unit of mass is a derived unit known as the [[slug (unit)|slug]].<ref name=cardarelli/>
:<math>\mathrm{1\,slug} = \mathrm{1\,lbf{\cdot}s^2/ft}.</math>

In the context of the gravitational FPS system, the pound-force (lbf) is sometimes referred to as the pound (lb).

=== Pound-force as force unit and pound-mass as mass unit ===
{{anchor|weight|British Engineering System}}
Another variant of the FPS system uses both the pound-mass and the pound-force, but neither the slug nor the poundal. The resulting system is sometimes also known as the '''[[English Engineering Units|English engineering system]]'''.  Despite its name, the system is based on United States customary units of measure; it is not used in England.<ref name=cr/>

== Other units ==

=== Molar units ===
The unit of substance in the FPS system is the pound-mole (lb-mol) = {{val|273.16|e=24}}.  Until the SI decided to adopt the gram-mole, the mole was directly derived from the mass unit as (mass unit)/(atomic mass unit).  The unit (lbf⋅s<sup>2</sup>/ft)-mol also appears in a former definition of the atmosphere.

=== Electromagnetic units ===
The electrostatic and electromagnetic systems are derived from units of length and force, mainly.  As such, these are ready extensions of any system of containing length, mass, time. Stephen Dresner<ref>{{cite book|last=Dresner|first=Stephen|title=Units of Measurement|year=1971|publisher=Hastings House|location=New York|pages=193–205}}</ref> gives the derived electrostatic and electromagnetic units in both the foot–pound–second and foot–slug–second systems.  In practice, these are most associated with the centimetre–gram–second system.  The 1929 "International Critical Tables" gives in the symbols and systems fpse = FPS electrostatic system and fpsm = FPS electromagnetic system.  Under the conversions for charge, the following are given.  The CRC Handbook of Chemistry and Physics 1979 (Edition 60), also lists fpse and fpsm as standard abbreviations.

; Electromagnetic FPS (EMU, stat-)
: 1 fpsm unit = 117.581866 [[cgsm]] unit (Biot-second) {{clarify|date=December 2016}}
; Electrostatic FPS (ESU, ab-)
: 1 fpse unit = 3583.8953 cgse unit (Franklin)
: 1 fpse unit = 1.1954588×10<sup>−7</sup> abs coulomb

=== Units of light ===
The ''[[candela|candle]]'' and the ''foot-candle'' were the first defined units of light, defined in the Metropolitan Gas Act (1860).<ref>{{cite book|last=Jerrard|first=H G|title=A Dictionary of Scientific Units|year=1985|publisher=Chapman and Hall|location=London|isbn=0412281007|pages=24}}</ref>  The foot-candle is the intensity of light at one foot from a ''standard candle''.  The units were internationally recognized in 1881, and adopted into the metric system.<ref>{{citation|first=Donald|last=Fenna|year=2003|title=Dictionary of weights and measures|isbn=978-0-19-860522-5}}</ref>

== Conversions ==
Together with the fact that the term "weight" is used for the gravitational force in some technical contexts (physics, engineering) and for mass in others (commerce, law),<ref>[http://ts.nist.gov/WeightsAndMeasures/Metric/upload/fs376-b.pdf NIST Federal Standard 376B], p. 13. {{webarchive |url=https://web.archive.org/web/20100816011202/http://ts.nist.gov/WeightsAndMeasures/Metric/upload/fs376-b.pdf |date=August 16, 2010 }}</ref> and that the distinction often does not matter in practice, the coexistence of variants of the FPS system causes confusion over the nature of the unit "pound". Its relation to international metric units is expressed in kilograms, not newtons, though, and in earlier times it was defined by means of a mass prototype to be compared with a [[weighing scale|two-pan balance]] which is agnostic of local gravitational differences.

In July 1959, the various national foot and avoirdupois pound standards were replaced by the international foot of precisely {{val|0.3048|u=m}} and the international pound of precisely {{val|0.45359237|u=kg}}, making conversion between the systems a matter of simple arithmetic. The conversion for the poundal is given by 1&nbsp;pdl =&nbsp;1&nbsp;lb·ft/s<sup>2</sup> = {{val|0.138254954376|ul=N}} (precisely).<ref name=cardarelli/>

To convert between the absolute and gravitational FPS systems one needs to fix the [[standard gravity|standard acceleration]] ''g'' which relates the pound to the pound-force.{{citation needed|date=April 2018}}
:<math>1\,\text{lbf} = 1\,\text{lb}\cdot g</math>
While ''g'' strictly depends on one's location on the Earth surface, since 1901 in most contexts it is fixed conventionally at precisely ''g''<sub>0</sub> =&nbsp;{{val|9.80665|u=m/s2}} ≈&nbsp;{{val|32.17405|u=ft/s2}}.<ref name=cardarelli/>

==See also==
*[[Metre–tonne–second system of units]] (MTS)
*[[FFF system]]
*[[Mars Climate Orbiter]]

==References==
{{reflist}}

{{systems of measurement}}
{{Imperial units}}
{{United States Customary Units}}

{{DEFAULTSORT:Foot-pound-second system}}
[[Category:Systems of units]]
[[Category:Imperial units]]
[[Category:Customary units of measurement in the United States]]