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# Gravitational metric system

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### Gravitational metric system

In the gravitational metric system the base unit of force is not normalised to one mass unit (gram or kilogram) times one length unit (metre or centimetre) per time unit squared (second) but it depends on a selected or locally measured gravitational constant gn. It is a non-standard unit and does not comply with SI, the International System of Units. This constant is usually set to an acceleration of 9.80665 m/s2, based on the gravitational acceleration on the surface of the Earth. Other derived units inherit this factor. Sometimes alternatively the base unit of mass is the one carrying the constant.

Where the difference between weight and mass is not important or not understood, gravitational units are still common despite adoption of the SI, an absolute metric system.

## Contents

• Units 1
• Force 1.1
• Mass 1.2
• Pressure 1.3
• Energy 1.4
• Power 1.5
• References 2

## Units

### Force

In English contexts the unit of force is usually formed by simply appending "force" to the unit of mass, thus gram-force (gf) or kilogram-force (kgf), which follows the tradition of pound-force (lbf). In other, international contexts the special name pond (p) or kilopond (kp) respectively is more frequent.

1 p = 1 gf
= 1 g · gn = 9.80665 g·m/s2 = 980.665 g·cm/s2 = 980.665 dyn
1 kp = 1 kgf
= 1 kg · gn = 9.80665 kg·m/s2 = 980 665 g·cm/s2
Three approaches to mass and force units[1][2]
Base force, length, time weight, length, time mass, length, time
Force (F) F = ma = wa/g F = ma/gc = wa/g F = ma = wa/g
Weight (w) w = mg w = mg/gcm w = mg
System BG GM EE M AE CGS MTS SI
Acceleration (a) ft/s2 m/s2 ft/s2 m/s2 ft/s2 Gal m/s2 m/s2
Mass (m) slug hyl lbm kg lb g t kg
Force (F) lb kp lbF kp pdl dyn sn N
Pressure (p) lb/in2 at PSI atm pdl/ft2 Ba pz Pa

### Mass

The hyl, metric slug (mug), or TME (German: technische Masseneinheit, technical mass unit), is the mass that accelerates at 1 m/s² under a force of 1 kgf.[3] The hyl has also been used as the unit of mass in a metre-gram force-second (mgfs) system.[4]

1 TME
= 1 kp / 1 m/s² = 1 kp·s²/m = 9.806 65 kg
1 hyl
= 1 kp·s²/m = 9.806 65 kg or
1 hyl (alternate definition - mgfs)
= 1 p·s²/m = 9.806 65 g

### Pressure

The (only) gravitational unit of pressure is the technical atmosphere (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 × gn kg/m² = 98 066.5 kg/(m·s²) = 98.066 5 kPa

### 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 = gn 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, which was defined as the power required to raise a mass of 1 quintal (1 q = 100 kg) at a velocity of 1 m/s. The German or metric horsepower (PS, Pferdestärke) is arbitrarily selected to be three quarters thereof.

1 pq
= 1 qf·m/s = 100 kp·m/s = 100 × gn kg·m/s = 980.665 kg·m²/s³ = 0.980 665 kW
1 PS
= 34 pq = 75 kp·m/s = 75 × gn kg·m/s = 735.498 75 kg·m²/s³ = 0.735 498 75 kW

## References

1. ^ Michael R. Lindeburg (2011). Civil Engineering Reference Manual for the Pe Exam. Professional Publications.
2. ^ Wurbs, Ralph A, Fort Hood Review Sessions for Professional Engineering Exam (PDF), retrieved October 26, 2011
3. ^ Measurements, Units of Measurement, Weights and Measures - Numericana
4. ^ metre-kilogram-force-second systems of units
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