Poundal

The poundal (symbol: pdl) is a unit of force, introduced in 1877, that is part of the Absolute English system of units,Template:Fact which itself is a coherent subsystem of the foot–pound–second system. The poundal is defined as the force necessary to accelerate 1 pound-mass at 1 foot per second squared.Template:Rp

$1\text{pdl}=1\text{lb}\cdot \text{ft}/{\text{s}}^2$

1 pdl = Template:Val exactly, using the definitions for the international foot and pound.

Background

English units require re-scaling of either force or mass to eliminate a numerical proportionality constant in the equation Template:Nowrap.Template:Cn The poundal represents one choice, which is to rescale units of force. Since 1 pound-force accelerates 1 pound-mass at 32.174 049 ft/s² (9.80665 m/s²; the acceleration of gravity, g), the unit of force can be scaled down such that it accelerates 1 pound-mass at 1 ft/s²; this unit is called the poundal, which is approximately Template:Frac pound-force.

Template:GravEngAbs For example, a force of 1200 poundals is required to accelerate a person of 150 pounds mass at 8 feet per second squared: $$\mathrm{150.}\mathrm{l}\mathrm{b}\mathrm{\times }\mathrm{8.00}\frac{ft}{s^2}\mathrm{=}\mathrm{1200}\mathrm{p}\mathrm{d}\mathrm{l}.$$

The poundal-as-force, pound-as-mass system is contrasted with an alternative system in which the pound-force remains, instead of the pound-mass. A unit of mass is scaled such that it is accelerated by only 1 ft/s² with 1 lb_f; this unit is called the slug, which is about 32 lb_m. Using slugs and lbf, the above equation could be expressed as: $$\mathrm{4.66}\mathrm{s}\mathrm{l}\mathrm{u}\mathrm{g}\mathrm{\times }\mathrm{8.00}\frac{ft}{s^2}\mathrm{=}\mathrm{37.3}\mathrm{l}\mathrm{b}\mathrm{f}.$$

Slugs (Template:Val) and poundals (1/Template:Val) tend not to be used together in the same context, as 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 (g). In this case, we can keep both pounds-mass and pounds-force, such that applying 1 pound-force to 1 pound-mass accelerates it at 1 g: $$150\mathrm{l}\mathrm{b}\cdot 0.249g=37.3\mathrm{l}{\mathrm{b}}_{\mathrm{f}}.$$

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 Template:Nowrap on the Moon or in deep space as Template:Nowrap or Template:Nowrap avoids the constant tied to acceleration of gravity on Earth.

References

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