In 1889 the W.Stroud proposed the foot-pound-second (FPS) unit system and is sometimes called the stroud system. The FPS unit system development was in parallel with the development of cgs system. This system became very widely employed in all branches of engineering, and most technical papers written in Britain, and USA before 1960 would have used these units despite the fact that scientific papers tended to use cgs units.
The main problem of this unit system was that the pound had been in common use as unit of both weight and mass. This makes no difference in general nad commercial usage, because of Earth's gravity, a mass of one pound weights exactly one pound. The difference may be illustrated by considering the same mass taken to another planet such as the Moon. Since the Moon's gravitational force is about one-sixth that of the Earth, the one-pound mass would weigh only one-sixth of a pound, although the mas itself would not have changed. Weight is the force with wich a mass is attracted by gravity, and, since it is an entirely different quantity, it requires a different unit. In the FPS system, whit the pound as the unit of mass, one force unit is required to impart one acceleration unit to a mass of one pound. The acceleration due to gravity is approximately \(32 \left[\frac{\mathrm{ft}}{\mathrm{s}^2}\right]\), so the weight of one pound mass is in fact equal to 32 force units, and the force unit must therefore be 1/32 pounds. This is termed the poundal.
In a variant of the FPS system, the pound-force (lbf) was taken as a base unit, and a unit of mass was derived from it by a reversal of previous considerations. This unit was named the slug, and was the mass which when acted upon by one pound-force experienced an acceleration of \(1 \left[\frac{\mathrm{ft}}{\mathrm{s}^2}\right]\), so was equal to 32.17 [lb]. This version of the FPS system was mostly used in the United States.
The FPS system was never fully coherent by the incorporation of electrical or molar units. It did however have derived units which were for the most part expressed clearly in terms of their base units and not given separate names as in the SI unit system. In the practise they were often abbreviated (psi for \(\frac{\mathrm{lbf}{\mathrm{in}^2}\) ), and they were often used in a non-standard way, or in a way that confused the two subsystems.
A selection of the FPS derived units is given in following table.
The main problem of this unit system was that the pound had been in common use as unit of both weight and mass. This makes no difference in general nad commercial usage, because of Earth's gravity, a mass of one pound weights exactly one pound. The difference may be illustrated by considering the same mass taken to another planet such as the Moon. Since the Moon's gravitational force is about one-sixth that of the Earth, the one-pound mass would weigh only one-sixth of a pound, although the mas itself would not have changed. Weight is the force with wich a mass is attracted by gravity, and, since it is an entirely different quantity, it requires a different unit. In the FPS system, whit the pound as the unit of mass, one force unit is required to impart one acceleration unit to a mass of one pound. The acceleration due to gravity is approximately \(32 \left[\frac{\mathrm{ft}}{\mathrm{s}^2}\right]\), so the weight of one pound mass is in fact equal to 32 force units, and the force unit must therefore be 1/32 pounds. This is termed the poundal.
In a variant of the FPS system, the pound-force (lbf) was taken as a base unit, and a unit of mass was derived from it by a reversal of previous considerations. This unit was named the slug, and was the mass which when acted upon by one pound-force experienced an acceleration of \(1 \left[\frac{\mathrm{ft}}{\mathrm{s}^2}\right]\), so was equal to 32.17 [lb]. This version of the FPS system was mostly used in the United States.
The FPS system was never fully coherent by the incorporation of electrical or molar units. It did however have derived units which were for the most part expressed clearly in terms of their base units and not given separate names as in the SI unit system. In the practise they were often abbreviated (psi for \(\frac{\mathrm{lbf}{\mathrm{in}^2}\) ), and they were often used in a non-standard way, or in a way that confused the two subsystems.
A selection of the FPS derived units is given in following table.
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