Poundal
| poundal | |
|---|---|
| Unit system | Absolute English System |
| Unit of | Force |
| Symbol | pdl |
| Conversions | |
| 1 pdl in ... | ... is equal to ... |
| AE base units | 1 lb⋅ft/s2 |
| SI units | 0.1382550 N |
| CGS units | 13,825.50 dyn |
| British Gravitational System | 0.03108095 lbf |
The poundal (symbol: pdl) is a unit of force, introduced in 1877, that is part of the Absolute English system of units,[1] 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.[2]: 54
1 pdl = 0.138254954376 N 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 F = ma.[citation needed] 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 1⁄32 pound-force.
|
Base |
Force | Weight | Mass | |||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 2nd law of motion | m = F/a | F = W ⋅ a/g | F = m ⋅ a | |||||||||||
| System | BG | GM | EE | M | AE | CGS | MTS | SI | ||||||
| Acceleration (a) | ft/s2 | m/s2 | ft/s2 | m/s2 | ft/s2 | [[Physics:Gal (unit) | Gal}}]] | m/s2 | m/s2 | |||||
| Mass (m) | slug | hyl | pound-mass | kilogram | [[Pound (mass) | pound}}]] | [[Gram | gram}}]] | [[Tonne | tonne}}]] | [[Kilogram | kilogram}}]] | ||
| Force (F), weight (W) |
[[Pound (force) | pound}}]] | kilopond | pound-force | kilopond | [[Poundal | poundal}}]] | [[Physics:Dyne | dyne}}]] | [[Sthène | sthène}}]] | [[Newton (unit) | newton}}]] | |
| Pressure (p) | [[Pounds per square inch | pounds per square inch}}]] | [[Technical atmosphere | technical atmosphere}}]] | [[Pounds per square inch | pounds-force per square inch}}]] | [[Physics:Atmosphere (unit) | atmosphere}}]] | poundals per square foot | [[Physics:Barye | barye}}]] | pieze | [[Pascal (unit) | pascal}}]] |
For example, a force of 1200 poundals is required to accelerate a person of 150 pounds mass at 8 feet per second squared:
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 lbf; this unit is called the slug, which is about 32 lb. Using slugs and lbf, the above equation could be expressed as:
Slugs (32.174049 lb) and poundals (1/32.174049 lbF) 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:
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 F = ma on the Moon or in deep space as pdl = lb⋅ft/s2 or lbf = slug⋅ft/s2, avoids the constant tied to acceleration of gravity on Earth.
Conversion
| 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. | |||||
References
- Obert, Edward F., “Thermodynamics”, McGraw-Hill Book Company Inc., New York 1948; Chapter I, Survey of Dimensions and Units, pages 1–24.
- ↑ Lindeburg, Michael R. (1990). Engineer-in-training Reference Manual. Professional Publications. p. 1-4. ISBN 9780912045085.
- ↑ Cardarelli, François (2003), "The Foot–Pound–Second (FPS) System", Encyclopaedia of Scientific Units, Weights and Measures: Their SI Equivalences and Origins, Springer, pp. 51–55, ISBN 978-1-85233-682-0, https://archive.org/details/encyclopaediaofs0000card/page/51.
- ↑ Comings, E. W. (1940). "English Engineering Units and Their Dimensions". Industrial & Engineering Chemistry 32 (7): 984–987. doi:10.1021/ie50367a028.
- ↑ Klinkenberg, Adrian (1969). "The American Engineering System of Units and Its Dimensional Constant gc". Industrial & Engineering Chemistry 61 (4): 53–59. doi:10.1021/ie50712a010.
Template:United States Customary Units
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