gravitational system

technical system

Any system that uses weight, in its true sense, rather than mass, as its pertinent base unit is called a gravitational or technical system.
[Bullock M. L. Amer. J. Phys. Vol. 22, 293-9 (1954)] Weight is a force, being the product of mass and the effective acceleration of gravity (represented by the newton in the SI). The gram, kilogram, etc., are measures of mass, but the pound was properly a weight, so the British system is thus inherently a gravitational one. However, the pound has come to be regarded as a unit of mass, equalling close to 454 g, but it continues also to be interpreted, competingly, as that mass subjected to the acceleration of gravity. Physicists have long regarded the pound as a mass, which should be called the pound-mass if there is any ambiguity, but engineers have traditionally seen it as a weight (i.e. a force, distinguished where necessary as pound-force or lb-f). Similarly, engineers recognize a kilogram-force (kg-f) and have a gravitational version of the inherently non- gravitational SI.

The actual gravitational acceleration at Earth's surface, routinely represented by g, is about 9.81 m·s^-2 or 32.2 ft·s^-2, but varies with locale, by about ± 0.5%. In some cases the exact acceleration for a locale is pertinent, but any established system requires a fixed standard. For the gravitational SI system (the Potsdam or international gravimetric system) this is standard gravity, set in 1901 at = 9.806 65 m·s^-2 (32.174 0~ ft·s^-2). For the BI system, it has long been set at 32.174 ft·s^-2 (9.806 64~ m·s^-2). Adding a precautionary suffix to the units of mass gives

kilogram-force	= kilogram-mass × g
pound-force	= pound-mass × g

The inclusion of the numeric component of g in each makes these relationships not coherent, for a gravitational system or for a non-gravitational one. The relevant units that give coherence and the relationships are:

• non-gravitational systems:
newton	= kilogram-mass	× 1 m·s-2
poundal	= pound-mass	× 1 ft·s-2
• gravitational systems:
kilogram-force
(kg-force, kg-f)	= engineering mass unit	× 1 m·s-2
pound-force (lb-force, lb-f)	= slug	× 1 ft·s-2

These matching units, each related to the more familiar by the respective numeric component, are thus valued in the SI as follows:

• force units:
newton, the SI derived unit for force	= 1 N = 1 m·kg·s-2
poundal	= 0.031 080 997 1~ lb-f
	= 0.138 255 163~ N
kilogram-force (kg-force, kg-f)	= 9.806 65 N
pound-force (lb-force, lb-f) = 32.174 lb-
mass·ft·s-2	= 4.448 214 90~ N
• mass units:
kilogram-mass	= 1 kg
pound-mass	= 0.453 592 37 kg
engineering mass unit (hyl, metric slug, etc.)	= 9.806 65 kg
slug (g pound, gee pound)	= 32.174 lb-mass
	= 14.593 880 9~ kg

The kilogram-force is also called the kilopond, the term pond having been adopted in the gravitational version of the c.g.s. system for the gram-force. The pound-mass has no common distinctive name.

Corresponding weight versions of related units exist, e.g. milligram-force, tonne-force, etc., with the SI scene; ounce-force, ton-force, etc., with the British.