Poundal
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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 lbm) × (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 lbf)
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 lbm) × (0.249 g) = (37.3 lbf)
The advantage of using poundals (rather than using slugs or g) is that it is not tied to the conditions on the surface of the Earth, since it is not based on Earth's gravity. One pound-mass exerts a downward force of about one pound-force, but only on Earth's surface; in space or on the moon, for example, one pound-mass does not exert a pound-force under natural gravity conditions, and thus the pound-force becomes an arbitrary unit with no meaningful properties anymore. The pound-mass, however, is the same whether on Earth, in space, or anywhere else, and the poundal— which accelerates it at one foot per second squared— remains relevant.
| newton (SI unit) |
dyne | kilogram-force, kilopond |
pound-force | poundal | |
|---|---|---|---|---|---|
| 1 N | ≡ 1 kg·m/s² | = 105 dyn | ≈ 0.10197 kp | ≈ 0.22481 lbf | ≈ 7.2330 pdl |
| 1 dyn | = 10−5 N | ≡ 1 g·cm/s² | ≈ 1.0197×10−6 kp | ≈ 2.2481×10−6 lbf | ≈ 7.2330×10−5 pdl |
| 1 kp | = 9.80665 N | = 980665 dyn | ≡ gn·(1 kg) | ≈ 2.2046 lbf | ≈ 70.932 pdl |
| 1 lbf | ≈ 4.448222 N | ≈ 444822 dyn | ≈ 0.45359 kp | ≡ gn·(1 lb) | ≈ 32.174 pdl |
| 1 pdl | ≈ 0.138255 N | ≈ 13825 dyn | ≈ 0.014098 kp | ≈ 0.031081 lbf | ≡ 1 lb·ft/s² |
| The value of gn as used in the official definition of the kilogram-force is used here for all gravitational units. | |||||
| System | Gravitational | Engineering | Absolute | |||
|---|---|---|---|---|---|---|
| Force (F) | F = m·a | F = m·a/gc = w·a/g | F = m·a | |||
| Weight (w) | w = m·g | w = m·g/gc ≈ m | w = m·g | |||
| Units | English | Metric | English | Metric | English | Metric |
| Acceleration (a) | ft/s2 | m/s2 | ft/s2 | m/s2 | ft/s2 | m/s2 |
| Mass (m) | slug | hyl | pound-mass | kilogram | pound | kilogram |
| Force (F) | pound | kilopond | pound-force | kilopond | poundal | newton |
