View source for Poundal

{{Short description|Unit of force}}
{{Infobox unit
| bgcolor      = 
| name         = poundal
| image        = 
| caption      = 
| standard     = [[Absolute English System]]
| quantity     = Force
| symbol       = pdl
| symbol2      = 
| extralabel   = 
| extradata    = 
| units1 = AE base units
| inunits1     = 1 lb⋅ft/s<sup>2</sup>
| units2 = SI units
| inunits2     = {{convert|1|pdl|disp=out|sigfig=7}}
| units3 = CGS units
| inunits3     = {{convert|1|pdl|dyn|disp=out|sigfig=7}}
| units4 = [[British Gravitational System]]
| inunits4     = {{convert|1|pdl|lbf|disp=out|sigfig=7}}
}}

The '''poundal''' (symbol: '''pdl''') is a [[Units of measurement|unit]] of [[force]], introduced in 1877, that is part of the [[Absolute English]] system of units,{{fact|date=January 2025}} which itself is a [[Coherence (units of measurement)|coherent]] subsystem of the [[foot–pound–second system]].

:<math>1\,\text{pdl} = 1\,\text{lb}{\cdot}\text{ft}/\text{s}^2</math>
The poundal is defined as the force necessary to accelerate 1 [[pound-mass]] at 1 foot per second squared.<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>{{rp|54}}
1 pdl = {{val|0.138254954376|ul=N}} exactly.<!-- 1 pound-mass expressed in kilograms, times 1 foot expressed in meters, equals 1 poundal expressed in newtons -->

== Background ==
English units require re-scaling of either force or mass to eliminate a numerical proportionality constant in the equation ''F = ma''.{{cn|date=August 2023}} The poundal represents one choice, which is to rescale units of force. Since a pound of ''force'' ([[pound force]]) accelerates a pound of ''mass'' ([[Pound (mass)|pound mass]]) at 32.174&nbsp;049&nbsp;ft/s<sup>2</sup> (9.80665&nbsp;m/s<sup>2</sup>; the [[Standard gravity|acceleration of gravity]], ''g''), we can scale down the unit of force to compensate, giving us one that accelerates 1 pound mass at 1&nbsp;ft/s<sup>2</sup> rather than at 32.174&nbsp;049&nbsp;ft/s<sup>2</sup>; and that is the poundal, which is approximately {{Frac|1|32}} pound force.

{{GravEngAbs}}
For example, a force of 1200 poundals is required to accelerate a person of 150 pounds mass at 8 feet per second squared:
<math display=block>\mathrm{150~lb \times 8~\frac{ft}{s^2} = 1200~pdl}</math>

The poundal-as-force, pound-as-mass system is contrasted with an alternative system in which pounds are used as ''force'' (pounds-force), and instead, the ''mass'' unit is rescaled by a factor of roughly 32. That is, one pound-force will accelerate one pound-mass at 32 feet per second squared; we can scale ''up'' the unit of ''mass'' to compensate, which will be accelerated by 1&nbsp;ft/s<sup>2</sup> (rather than 32&nbsp;ft/s<sup>2</sup>) given the application of one pound force; this gives us a unit of mass called the [[slug (unit)|slug]], which is about 32 pounds mass. Using this system (slugs and pounds-force), the above expression could be expressed as:
<math display=block>\mathrm{4.66~slug \times 8~\frac{ft}{s^2} = 37.3~lbf}</math>

Note: Slugs ({{val|32.174049|u=lb}}) and poundals (1/{{val|32.174049|u=lbf}}) are never used in the same system, since they are opposite solutions of the same problem.

Rather than changing either force or mass units, one may choose to express acceleration in units of the [[standard gravity|acceleration due to Earth's gravity]] (called ''g''). In this case, we can keep both pounds-mass and pounds-force, such that applying one pound force to one pound mass accelerates it at one unit of acceleration (''g''):
<math display=block>150~\mathrm{lb} \cdot 0.249g = 37.3~\mathrm{lbf}</math>

Expressions derived using poundals for force and lb for mass (or lbf for force and slugs for mass) have the advantage of not being tied to conditions on the surface of the earth. Specifically, computing {{nowrap|1=''F'' = ''ma''}} on the moon or in deep space as poundals, lb⋅ft/s<sup>2</sup> or {{nowrap|1=lbf = slug⋅ft/s<sup>2</sup>,}} avoids the constant tied to acceleration of gravity on earth.

== Conversion ==
{{Units of force}}

== See also ==
*[[Slug (unit)]]

==References==
* Obert, Edward  F., “Thermodynamics”, McGraw-Hill Book Company Inc., New York 1948; Chapter I, Survey of Dimensions and Units, pages 1–24.
{{reflist}}

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

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