| poundal | |
|---|---|
| Unit system | Absolute English System |
| Unit of | Force |
| Symbol | pdl |
| Conversions | |
| 1 pdlin ... | ... 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 |
Thepoundal (symbol:pdl) is aunit offorce, introduced in 1877, that is part of theAbsolute English system of units,[citation needed] which itself is acoherent subsystem of thefoot–pound–second system.
The poundal is defined as the force necessary to accelerate 1pound-mass at 1 foot per second squared.[1]: 54 1 pdl =0.138254954376 N exactly.
English units require re-scaling of either force or mass to eliminate a numerical proportionality constant in the equationF = ma.[citation needed] The poundal represents one choice, which is to rescale units of force. Since a pound offorce (pound force) accelerates a pound ofmass (pound mass) at 32.174 049 ft/s2 (9.80665 m/s2; theacceleration 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 approximately1⁄32 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 | Gal | m/s2 | m/s2 |
| Mass (m) | slug | hyl | pound-mass | kilogram | pound | gram | tonne | kilogram |
| Force (F), weight (W) | pound | kilopond | pound-force | kilopond | poundal | dyne | sthène | newton |
| Pressure (p) | pound per square inch | technical atmosphere | pound-force per square inch | standard atmosphere | poundal per square foot | barye | pieze | 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 pounds are used asforce (pounds-force), and instead, themass 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 scaleup the unit ofmass 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 theslug, which is about 32 pounds mass. Using this system (slugs and pounds-force), the above expression could be expressed as:
Note: Slugs (32.174049 lb) and poundals (1/32.174049 lbF) 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 theacceleration due to Earth's gravity (calledg). 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):
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, computingF =ma on the moon or in deep space as poundals, lb⋅ft/s2 orlbf = slug⋅ft/s2, avoids the constant tied to acceleration of gravity on earth.
| newton | dyne | kilogram-force, kilopond | pound-force | poundal | |
|---|---|---|---|---|---|
| 1 N | ≡ 1 kg⋅m/s2 | = 105 dyn | ≈ 0.10197 kgf | ≈ 0.22481 lbF | ≈ 7.2330 pdl |
| 1 dyn | = 10−5 N | ≡ 1 g⋅cm/s2 | ≈ 1.0197×10−6 kgf | ≈ 2.2481×10−6 lbF | ≈ 7.2330×10−5 pdl |
| 1 kgf | = 9.80665 N | = 980665 dyn | ≡ gn × 1 kg | ≈ 2.2046 lbF | ≈ 70.932 pdl |
| 1 lbF | ≈ 4.448222 N | ≈ 444822 dyn | ≈ 0.45359 kgf | ≡ gn × 1 lb | ≈ 32.174 pdl |
| 1 pdl | ≈ 0.138255 N | ≈ 13825 dyn | ≈ 0.014098 kgf | ≈ 0.031081 lbF | ≡ 1 lb⋅ft/s2 |
| The value ofgn (9.80665 m/s2) as used in the official definition of the kilogram-force is used here for all gravitational units. | |||||