Poundal
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The poundal (symbol: pdl) is a unit of
force In physics, a force is an influence that can cause an Physical object, object to change its velocity unless counterbalanced by other forces. In mechanics, force makes ideas like 'pushing' or 'pulling' mathematically precise. Because the Magnitu ...
, introduced in 1877, that is part of the Absolute English system of units, which itself is a
coherent Coherence is, in general, a state or situation in which all the parts or ideas fit together well so that they form a united whole. More specifically, coherence, coherency, or coherent may refer to the following: Physics * Coherence (physics ...
subsystem of the foot–pound–second system. :1\,\text = 1\,\text\text/\text^2 The poundal is defined as the force necessary to accelerate 1 pound-mass at 1 foot per second squared.. 1 pdl = exactly.


Background

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 The pound or pound-mass is a unit of mass used in both the British imperial and United States customary systems of measurement. Various definitions have been used; the most common today is the international avoirdupois pound, which is leg ...
) at 32.174 049 ft/s2 (9.80665 m/s2; the 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/s2 rather than at 32.174 049 ft/s2; and that is the poundal, which is approximately pound force. For example, a force of 1200 poundals is required to accelerate a person of 150 pounds mass at 8 feet per second squared: \mathrm 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/s2 (rather than 32 ft/s2) given the application of one pound force; this gives us a unit of mass called the
slug Slug, or land slug, is a common name for any apparently shell-less Terrestrial mollusc, terrestrial gastropod mollusc. The word ''slug'' is also often used as part of the common name of any gastropod mollusc that has no shell, a very reduced ...
, which is about 32 pounds mass. Using this system (slugs and pounds-force), the above expression could be expressed as: \mathrm Note: Slugs () and poundals (1/) 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 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''): 150~\mathrm \cdot 0.249g = 37.3~\mathrm 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 on the moon or in deep space as poundals, lb⋅ft/s2 or avoids the constant tied to acceleration of gravity on earth.


Conversion


See also

*
Slug (unit) The slug is a derived unit of mass in a weight-based system of measures, most notably within the British Imperial measurement system and the United States customary measures system. Systems of measure either define mass and derive a force uni ...


References

* Obert, Edward F., “Thermodynamics”, McGraw-Hill Book Company Inc., New York 1948; Chapter I, Survey of Dimensions and Units, pages 1–24. {{United States Customary Units Units of force Imperial units Customary units of measurement in the United States