The pound of force or pound-force (symbol: lbf, sometimes lb
f,
) is a
unit of
force
In physics, a force is an influence that can cause an Physical object, object to change its velocity unless counterbalanced by other forces. In mechanics, force makes ideas like 'pushing' or 'pulling' mathematically precise. Because the Magnitu ...
used in some
systems of measurement
A system of units of measurement, also known as a system of units or system of measurement, is a collection of units of measurement and rules relating them to each other. Systems of measurement have historically been important, regulated and defi ...
, including
English Engineering units
Some fields of engineering in the United States use a system of measurement of physical quantities known as the English Engineering Units. Despite its name, the system is based on United States customary units of measure.
Definition
The English E ...
and the
foot–pound–second system.
Pound-force should not be confused with
pound-mass (lb), often simply called "pound", which is a unit of
mass
Mass is an Intrinsic and extrinsic properties, intrinsic property of a physical body, body. It was traditionally believed to be related to the physical quantity, quantity of matter in a body, until the discovery of the atom and particle physi ...
; nor should these be confused with
foot-pound
The foot-pound force (symbol: ft⋅lbf, ft⋅lbf, or ft⋅lb ) is a unit of work or energy in the engineering and gravitational systems in United States customary and imperial units of measure. It is the energy transferred upon applying a ...
(ft⋅lbf), a unit of
energy
Energy () is the physical quantity, quantitative physical property, property that is transferred to a physical body, body or to a physical system, recognizable in the performance of Work (thermodynamics), work and in the form of heat and l ...
, or
pound-foot (lbf⋅ft), a unit of
torque
In physics and mechanics, torque is the rotational analogue of linear force. It is also referred to as the moment of force (also abbreviated to moment). The symbol for torque is typically \boldsymbol\tau, the lowercase Greek letter ''tau''. Wh ...
.
Definitions
The pound-force is equal to the gravitational force exerted on a
mass
Mass is an Intrinsic and extrinsic properties, intrinsic property of a physical body, body. It was traditionally believed to be related to the physical quantity, quantity of matter in a body, until the discovery of the atom and particle physi ...
of one
avoirdupois pound on the surface of
Earth
Earth is the third planet from the Sun and the only astronomical object known to Planetary habitability, harbor life. This is enabled by Earth being an ocean world, the only one in the Solar System sustaining liquid surface water. Almost all ...
. Since the 18th century, the unit has been used in low-precision measurements, for which small changes in
Earth's gravity
The gravity of Earth, denoted by , is the net acceleration that is imparted to objects due to the combined effect of gravitation (from mass distribution within Earth) and the centrifugal force (from the Earth's rotation).
It is a vector qu ...
(which varies from equator to pole by up to half a percent) can safely be neglected.
The 20th century, however, brought the need for a more precise definition, requiring a standardized value for acceleration due to gravity.
Product of avoirdupois pound and standard gravity
The pound-force is the product of one
avoirdupois pound (
exactly ) and the
standard acceleration due to gravity, approximately .
The standard values of acceleration of the standard gravitational field (''g''
n) and the
international avoirdupois pound (lb) result in a pound-force equal to
().
This definition can be rephrased in terms of the
slug
Slug, or land slug, is a common name for any apparently shell-less Terrestrial mollusc, terrestrial gastropod mollusc. The word ''slug'' is also often used as part of the common name of any gastropod mollusc that has no shell, a very reduced ...
. 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:
Conversion to other units
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⋅s
2/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.
In the "engineering" systems (middle column), the
weight
In science and engineering, the weight of an object is a quantity associated with the gravitational force exerted on the object by other objects in its environment, although there is some variation and debate as to the exact definition.
Some sta ...
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 unit—the use of
Newton's second law
Newton's laws of motion are three physical laws that describe the relationship between the motion of an object and the forces acting on it. These laws, which provide the basis for Newtonian mechanics, can be paraphrased as follows:
# A body re ...
, , requires another factor,
''gc'', usually taken to be 32.174049 (lb⋅ft)/(lbf⋅s
2).
"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.
Pound of thrust
The term pound of thrust is an alternative name for pound-force in specific contexts. It is frequently seen in US sources on jet engines and rocketry, some of which continue to use the FPS notation. For example, the thrust produced by each of the
Space Shuttle
The Space Shuttle is a retired, partially reusable launch system, reusable low Earth orbital spacecraft system operated from 1981 to 2011 by the U.S. National Aeronautics and Space Administration (NASA) as part of the Space Shuttle program. ...
's two
Solid Rocket Boosters was , together .
See also
*
Foot-pound (energy)
The foot-pound force (symbol: ft⋅lbf, ft⋅lbf, or ft⋅lb ) is a unit of work or energy in the engineering and gravitational systems in United States customary and imperial units of measure. It is the energy transferred upon applying a ...
*
Ton-force
*
Kip (unit)
*
Mass in general relativity
*
Mass in special relativity
The word "mass" has two meanings in special relativity: ''invariant mass'' (also called rest mass) is an invariant quantity which is the same for all Observer (special relativity), observers in all reference frames, while the relativistic mass i ...
*
Mass versus weight
In common usage, the mass of an object is often referred to as its weight, though these are in fact different concepts and quantities. Nevertheless, one object will always weigh more than another with less mass if both are subject to the same g ...
for the difference between the two physical properties
*
Newton
*
Poundal
*
Pounds per square inch
The pound per square inch (abbreviation: psi) or, more accurately, pound-force per square inch (symbol: lbf/in2), is a unit of measurement of pressure or of stress based on avoirdupois units and used primarily in the United States. It is the pre ...
, a unit of
pressure
Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country and eve ...
Notes and references
General sources
* Obert, Edward F. (1948). ''Thermodynamics''. New York: D. J. Leggett Book Company. Chapter I "Survey of Dimensions and Units", pp. 1-24.
{{United States Customary Units
Customary units of measurement in the United States
Imperial units
Units of force