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| The '''poundal''' (symbol: '''pdl''') is a [[Units of measurement|unit]] of [[force]] that is part of the [[foot–pound–second system]] of units, in [[Imperial units]] introduced in 1877, and is from the specialized subsystem of English absolute (a coherent system).
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| :<math>1\,\text{pdl} = 1\,\tfrac{\text{lb}_m \cdot \text{ft}}{\text{s}^2} </math>
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| The poundal is defined as the force necessary to accelerate 1 [[pound-mass]] to 1 foot per second per second.
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| 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 -->
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| == Background ==
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| English units require re-scaling of either force or mass to eliminate a numerical proportionality constant in the equation ''F = ma''. 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 32.174 049 ft/s<sup>2</sup> (9.80665 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 ft/s<sup>2</sup> rather than at 32.174 049 ft/s<sup>2</sup>; and that is the poundal, which is approximately {{Frac|1|32}} of a pound force.
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| For example, a force of 1200 poundals is required to accelerate a person of 150 pounds mass at 8 feet per second squared: | |
| :<math>150\,\text{lb}_m \cdot 8\,\tfrac{\text{ft}}{\text{s}^2} = 1200\,\text{pdl}</math>
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| {{GravEngAbs}}
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| 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 ft/s<sup>2</sup> (rather than 32 ft/s<sup>2</sup>) given the application of one pound force; this gives us a unit of mass called the [[Slug (mass)|slug]], which is about 32 pounds mass. Using this system (slugs and pounds-force), the above expression could be expressed as:
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| :<math>4.66\,\text{slug} \cdot 8\,\tfrac{\text{ft}}{\text{s}^2} = 37.3\,\text{lb}_F</math>
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| Note: Slugs (32.174 049 {{lbm}}) and poundals (1/32.174 049 {{lbf}}) are never used in the same system, since they are opposite solutions of the same problem.
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| 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''):
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| :<math>150\,\text{lb}_m \cdot 0.249\,\text{g} = 37.3\,\text{lb}_F</math> | |
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| Expressions derived using poundals for force and {{lbm}} 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 ''F'' = ''ma'' on the moon or in deep space as poundals, {{lbm}}·ft/s<sup>2</sup> or {{lbf}} = slug·ft/s<sup>2</sup>, avoids the constant tied to acceleration of gravity on earth.
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| == Conversion ==
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| {{Units of force}}
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| == See also ==
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| [[Slug (mass)]]
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| ==References==
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| * Obert, Edward F., “Thermodynamics”, McGraw-Hill Book Company Inc., New York 1948; Chapter I, Survey of Dimensions and Units, pages 1–24.
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| {{reflist}}
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| <!--Categories-->
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| [[Category:Units of force]] | |
| [[Category:Imperial units]]
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| [[Category:Customary units of measurement in the United States]]
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