Pound (force)

 ( Units Of Force ) 

The pound-force (symbol: lbfIEEE Standard Letter Symbols for Units of Measurement (SI Units, Customary Inch-Pound Units, and Certain Other Units), IEEE Std 260.1™-2004 (Revision of IEEE Std 260.1-1993), sometimes lb_f,) is a unit of force used in some systems of measurement including English Engineering units and the British Gravitational System. Pound force should not be confused with foot-pound, a unit of energy, or pound-foot, a unit of torque, and may be written as "lbf⋅ft". They should not be confused with pound-mass (symbol: lb), often simply called pound, which is a unit of mass.

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Definitions The pound-force is equal to the gravitational force exerted on a mass of one avoirdupois pound on the surface of Earth. Since the 18th century, the unit has been used in low-precision measurements, for which small changes in Earth's gravity (which varies from place to place by up to half a percent) can safely be neglected.Acceleration due to gravity varies over the surface of the Earth, generally increasing from about 9.78 m/s² (32.1 ft/s²) at the equator to about 9.83 m/s² (32.3 ft/s²) at the poles.

The 20th century, however, brought the need for a more precise definition. A standardized value for acceleration due to gravity was therefore needed.

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Product of avoirdupois pound and standard gravity The pound-force is the product of one avoirdupois pound (exactly ) and the standard gravity, (about ).In 1901 the third CGPM declared (second resolution) that:

The value adopted in the International Service of Weights and Measures for the standard acceleration due to Earth's gravity is , value already stated in the laws of some countries.

This value was the conventional reference for calculating the kilogram-force, a unit of force whose use has been deprecated since the introduction of SI.Barry N. Taylor, Guide for the Use of the International System of Units (SI), 1995, NIST Special Publication 811, Appendix B note 24

The standard values of acceleration of the Standard gravity ( g_n) and the international avoirdupois pound (lb) result in a pound-force equal to :The international avoirdupois pound is defined to be exactly .

$\backslash begin\{align\}$

 1\,\text{lbf} &= 1\,\text{lb} \times g_\text{n} \\
               &= 1\,\text{lb} \times 9.80665\,\tfrac{\text{m}}{\text{s}^2} / 0.3048\,\tfrac{\text{m}}{\text{ft}}\\
               &\approx 1\,\text{lb} \times 32.174049\,\mathrm{\tfrac{ft}{s^2}}\\
               &\approx 32.174049\,\mathrm{\tfrac{ft {\cdot} lb}{s^2}} \\
 1\,\text{lbf} &= 1\,\text{lb} \times 0.45359237\,\tfrac{\text{kg}}{\text{lb}} \times g_\text{n} \\
               &= 0.45359237\,\text{kg} \times 9.80665\,\tfrac{\text{m}}{\text{s}^2}\\
               &= 4.4482216152605\,\text{N}
     

\end{align}

This definition can be rephrased in terms of the slug. A slug has a mass of 32.174049 lb. A pound-force is the amount of force required to accelerate a slug at a rate of , so:

$\backslash begin\{align\}$

 1\,\text{lbf} &= 1\,\text{slug} \times 1\,\tfrac{\text{ft}}{\text{s}^2} \\
               &= 1\,\tfrac{\text{slug} \cdot \text{ft}}{\text{s}^2}
     

\end{align}

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Conversion to other units

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Foot–pound–second (FPS) systems of units In some contexts, the term "pound" is used almost exclusively to refer to the unit of force and not the unit of mass. In those applications, the preferred unit of mass is the slug, i.e. lbf⋅s²/ft. In other contexts, the unit "pound" refers to a unit of mass. The international standard symbol for the pound as a unit of mass is lb.IEEE Std 260.1™-2004, IEEE Standard Letter Symbols for Units of Measurement (SI Units, Customary Inch-Pound Units, and Certain Other Units)

In the "engineering" systems (middle column), the weight of the mass unit (pound-mass) on Earth's surface is approximately equal to the force unit (pound-force). This is convenient because one pound mass exerts one pound force due to gravity. Note, however, unlike the other systems the force unit is not equal to the mass unit multiplied by the acceleration unitThe acceleration unit is the distance unit divided by the time unit squared.—the use of Newton's Second Law, , requires another factor, g_c, usually taken to be 32.174049 (lb⋅ft)/(lbf⋅s²). "Absolute" systems are coherent systems of units: by using the slug as the unit of mass, the "gravitational" FPS system (left column) avoids the need for such a constant. The SI is an "absolute" metric system with kilogram and meter as base units.

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See also

• Foot-pound (energy)
• Ton-force
• Kip (unit)
• Mass in general relativity
• Mass in special relativity
• Mass versus weight for the difference between the two physical properties
• Newton
• Poundal
• Pounds per square inch, a unit of pressure

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Notes

• Obert, Edward F., “THERMODYNAMICS”, D.J. Leggett Book Company Inc., New York 1948; Chapter I, Survey of Dimensions and Units, pages 1-24.

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