poundal

The poundal is a non-SI unit of force. It is a part of the foot-pound-second system of units, a coherent subsystem of English units introduced in 1879, and one of several specialized subsystems of mechanical units used as aids in calculations. It is defined as 1 lb·ft·s⁻², or in words, as the force necessary to accelerate a pound of mass at 1 foot per second, per second. 1 pdl = 0.138 254 954 376 N exactly.

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 accelerates a pound of mass at about 32 ft/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 ft/s²); and that is the poundal, which is approximately ¹⁄₃₂ pounds of force.

For example, a force of 1200 poundals is required to accelerate a person of 150 pounds mass at 8 feet per second squared:

(150 lb_m) × (8 ft/s²) = (1200 pdl)

The poundal-as-force, pound-as-mass system is contrasted with an alternate system in which pounds are used as force (pounds-force), and instead, the mass unit is rescaled by a factor of 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, which is about 32 pounds mass. Using this system (slugs and pounds-force), the above expression could be expressed as:

(4.66 slug) × (8 ft/s²) = (37.3 lb_f)

Note that slugs and poundals are never used in the same system, since each exists to solve the same problem, so that both should not be used together.

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 lb_m) × (0.249 g) = (37.3 lb_f)

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^2 or lbf = slug ft/s^2 avoids the constant tied to acceleration of gravity on earth. One can avoid confusion between the pound (as a force) and the pound (as a mass) by switching to SI. Unfortunately, in return, one must accept occasional confusion over kg (mass) and kg (sometimes used as a force, where "kp" is meant).

See also

Slug (mass)