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CATEGORIES (articles) > Engine, Gearbox > Technical > Pound force explained

Pound force explained


A pound-force (abbreviations: lbf or lbf) is a unit of force. A pound-force is a force equivalent to a mass of one avoirdupois pound multiplied by the standard acceleration due to gravity on the surface of the Earth.

Today, the standard acceleration due to gravity is usually taken to be 9.80665 m/s² (approximately 32.174 05 ft/s²). Other values for the standard acceleration have been used, including 32.16 ft/s² (approximately 9.80237 m/s²).

The actual acceleration due to gravity can vary from place to place. A pound-force is approximately the force due to gravity on a mass of one pound at the surface of the Earth.


Equivalence to other units of force

Based on a standard acceleration due to gravity of 9.80665 m/s², 1 pound-force is equal to:

  • approximately 4.448222 newtons (1 newton is approximately 0.22481 pounds-force)

Units of force
Newton
(SI unit)
Dyne Kilogram-force
(Kilopond)
Pound-force Poundal
1 N ≡ 1 kg·m·s−2 = 105 dyn ≈ 0.10197 kp ≈ 0.22481 lbf ≈ 7.2330 pdl
1 dyn = 10−5 N ≡ 1 g·cm·s−2 ≈ 1.0197×10−6 kp ≈ 2.2481×10−6 lbf ≈ 7.2330×10−5 pdl
1 kp = 9.80665 N = 980665 dyngn·(1 kg) ≈ 2.2046 lbf ≈ 70.932 pdl
1 lbf ≈ 4.448222 N ≈ 444822 dyn ≈ 0.45359 kpgn·(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.


Use of the pound as a unit of force

In most contexts, the term "pound" refers unambiguously to a unit of mass. However, in some contexts, by convention, the "pound" may be defined to refer to a unit of force. In circumstances where there may be ambiguity otherwise, the symbol "lbf" or the term "pounds-force" can be used for the unit of force and the term "pounds-mass" can be used for the unit of mass.

For example, in structural engineering applications the term "pound" is used almost exclusively to refer to a unit of force and not to refer to the unit of mass. In those applications, the preferred unit of mass is either:

  • the slug; or
  • the kip·s²/ft (where the kip is a unit of force equal to 1,000 pounds-force).
There are three practical ways of doing calculations with mass and force in the foot-pound-second (fps) systems (and other systems such as inch-pound-second systems not discussed here). Those three ways are summarised in the table below, which also sets out the corresponding position under the International System of Units (SI).
  SI fps
gravitational engineering absolute
unit of time s s s s
unit of distance m ft ft ft
unit of mass kg slug pound pound
unit of force and weight N pound-force pound-force poundal
Newton’s second law F = m·a F = m·a F = m·a/gc F = m·a
weight of an object W = m·g W = m·g W = m·g/gc W = m·g

The SI system and the absolute and gravitational fps systems are coherent systems of units. They have the advantage that force can be expressed as the product of mass and acceleration.

The engineering fps system requires the introduction of the factor gc into the relationship between force on the one hand and mass and acceleration on the other hand. The factor is a dimensionless constant equal to the value of the standard acceleration of gravity on Earth used to define a pound-force, when expressed in ft/s². This must be distinguished from the actual local value of the acceleration of gravity, g, which can vary from place to place. The factor is usually taken to be 32.17405 lb·ft/(lbf·s²).

No one of the three fps systems is more correct than the other two. Ordinary measurements are not made using these specialized subsets of mechanical units, which are used only in practical calculations.


Historical origins

Pounds-force had been used in low-precision measurements since the 18th century, but they were never well-defined units until the 20th century.

The second resolution of the third General Conference on Weights and Measures (CGPM) in 1901 declared that: The value adopted in the International Service of Weights and Measures for the standard acceleration due to gravity is 980.665 cm/s2, value already stated in the laws of some countries. This value was the conventional reference for calculating the kilogram-force, a unit of force that is now obsolete. ([1] 2/)






CATEGORIES (articles) > Engine, Gearbox > Technical > Pound force explained

 
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