The gravitational metric system (original French term ) is a non-standard system of units, which does not comply with the

International System of Units The International System of Units, internationally known by the abbreviation SI (from French ), is the modern form of the metric system and the world's most widely used system of measurement. It is the only system of measurement with official s ...

(SI). It is built on the three base quantities

length Length is a measure of distance. In the International System of Quantities, length is a quantity with Dimension (physical quantity), dimension distance. In most systems of measurement a Base unit (measurement), base unit for length is chosen, ...

time Time is the continuous progression of existence that occurs in an apparently irreversible process, irreversible succession from the past, through the present, and into the future. It is a component quantity of various measurements used to sequ ...

and

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 ...

with

base units A base unit of measurement (also referred to as a base unit or fundamental unit) is a unit of measurement adopted for a '' base quantity''. A base quantity is one of a conventionally chosen subset of physical quantities, where no quantity in the ...

metre The metre (or meter in US spelling; symbol: m) is the base unit of length in the International System of Units (SI). Since 2019, the metre has been defined as the length of the path travelled by light in vacuum during a time interval of of ...

second The second (symbol: s) is a unit of time derived from the division of the day first into 24 hours, then to 60 minutes, and finally to 60 seconds each (24 × 60 × 60 = 86400). The current and formal definition in the International System of U ...

and kilopond respectively. Internationally used abbreviations of the system are MKpS, MKfS or MKS (from French or ). However, the abbreviation MKS is also used for the

MKS system of units The metre, kilogram, second system of units, also known more briefly as MKS units or the MKS system, is a physical system of measurement based on the metre, kilogram, and second (MKS) as base units. Distances are described in terms of metres, mass ...

, which, like the SI, uses

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 ...

kilogram The kilogram (also spelled kilogramme) is the base unit of mass in the International System of Units (SI), equal to one thousand grams. It has the unit symbol kg. The word "kilogram" is formed from the combination of the metric prefix kilo- (m ...

as a base unit.

Disadvantages

Nowadays, the mass as a property of an object and its weight, which depends on the gravity of the Earth at its position are strictly distinguished. However historically, the kilopond was also called kilogram, and only later the kilogram-mass (today's kilogram) was separated from the kilogram-force (today's kilopond). A kilopond originally referred to the weight of a mass of one kilogram. Since the gravitational acceleration on the surface of the Earth can differ, one gets different values for the unit kilopond and its derived units at different locations. To avoid this, the kilopond was first defined at sea level and a

latitude In geography, latitude is a geographic coordinate system, geographic coordinate that specifies the north-south position of a point on the surface of the Earth or another celestial body. Latitude is given as an angle that ranges from −90° at t ...

of 45 degrees, since 1902 via the

standard gravity The standard acceleration of gravity or standard acceleration of free fall, often called simply standard gravity and denoted by or , is the nominal gravitational acceleration of an object in a vacuum near the surface of the Earth. It is a constant ...

of . Further disadvantages are inconsistencies in the definition of derived units such as

horsepower Horsepower (hp) is a unit of measurement of power, or the rate at which work is done, usually in reference to the output of engines or motors. There are many different standards and types of horsepower. Two common definitions used today are t ...

(1 PS = 75 kp⋅m/s) and the missing link to electric, magnetic or thermodynamic units. In Germany, the kilopond lost its legal status as a unit of force on 1 January 1978, when for legal purposes the SI unit system was adopted. A kilopond can be converted to the SI unit newton by multiplication with the standard acceleration ''g''_n: :1 kp = ''g''_n ⋅ 1 kg = =

Units

Force

In English contexts the unit of force is usually formed by simply appending the suffix "force" to the name of the unit of mass, thus ''gram-force'' (gf) or ''

kilogram-force The kilogram-force (kgf or kgF), or kilopond (kp, from ), is a non-standard Gravitational metric system, gravitational metric unit of force. It is not accepted for use with the International System of Units (SI) and is deprecated for most uses. T ...

'' (kgf), which follows the tradition of

pound-force The pound of force or pound-force (symbol: lbf, sometimes lbf,) is a unit of force used in some systems of measurement, including English Engineering units and the foot–pound–second system. Pound-force should not be confused with poun ...

(lbf). In other, international, contexts the special name ''pond'' (p) or ''kilopond'' (kp) respectively is more frequent. ; 1 p = 1 gf := 1 g ⋅ ''g''_n = 9.80665 g⋅m/s² = 980.665 g⋅cm/s² = 980.665 dyn ; 1 kp = 1 kgf := 1 kg ⋅ ''g''_n = 9.80665 kg⋅m/s² = 980665 g⋅cm/s²

Mass

The hyl, metric

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 ...

(mug), or TME (), is the mass that accelerates at 1 m/s² under a force of 1 kgf. The unit, long obsolete, has also been used as the unit of mass in a metre–gram-force–second (mgfs) system. ; 1 TME := 1 kp / 1 m/s² = 1 kp⋅s²/m = ; 1 hyl := 1 kp⋅s²/m = ''or'' ; 1 hyl (alternate definition – mgfs) := 1 p⋅s²/m =

Pressure

The gravitational unit of pressure is the

technical atmosphere Technical may refer to: * Technical (vehicle), an improvised fighting vehicle * Technical area, an area which a manager, other coaching personnel, and substitutes are allowed to occupy during a football match * Technical advisor, a person who ad ...

(at). It is the gravitational force of one kilogram, i.e. 1 kgf, exerted on an area of one square centimetre. ; 1 at := 1 kp/cm² = 10 000 × ''g''_n kg/m² = 98 066.5 kg/(m⋅s²) = 98.066 5

kPa The pascal (symbol: Pa) is the unit of pressure in the International System of Units (SI). It is also used to quantify internal pressure, stress, Young's modulus, and ultimate tensile strength. The unit, named after Blaise Pascal, is an SI ...

Energy

There is no dedicated name for the unit of energy, "metre" is simply appended to " kilopond", but usually the symbol of the kilopond-metre is written without the middle dot. ; 1 kpm := 1 kp⋅m = ''g''_n kg⋅m = 9.806 65 kg⋅m²/s² = 9.806 65 J

Power

In 19th-century France there was as a unit of power, the

poncelet The poncelet (symbol p) is an obsolete unit of power, once used in France and replaced by (ch, metric horsepower). The unit was named after Jean-Victor Poncelet.François Cardarelli, ''Encyclopaedia of Scientific Units, Weights and Measures: T ...

, which was defined as the power required to raise a mass of 1

quintal The quintal or centner is a historical unit of mass in many countries that is usually defined as 100 base units, such as pounds or kilograms. It is a traditional unit of weight in France, Portugal, and Spain and their former colonies. It is com ...

(1 q = 100 kg) at a velocity of 1 m/s. The German or metric

(PS, ''Pferdestärke'') is arbitrarily selected to be three quarters thereof. ; 1 p_q := 1 q_f⋅m/s = 100 kp⋅m/s = 100 × ''g''_n kg⋅m/s = 980.665 kg⋅m²/s³ = 0.980 665 kW ; 1 PS := p_q = 75 kp⋅m/s = 75 × ''g''_n kg⋅m/s = 735.498 75 kg⋅m²/s³ = 0.735 498 75 kW

References

{{systems of measurement Systems of units Gravitational metric system