horsepower (mechanical)
Powerexact by definition
The mechanical horsepower is defined as exactly 550 foot-pounds-force per second, which works out to 745.6998715822702 watts. The value is exact because the foot, the pound and standard gravity are all exactly defined. It is equivalently 33 000 ft·lbf per minute, which is the form Watt originally quoted.
Watch out: Several horsepowers exist. Mechanical or imperial horsepower is 745.6999 W. Metric horsepower, written PS or CV and used in European vehicle specifications, is 75 kgf·m/s or 735.49875 W, about 1.4 percent smaller. Electrical horsepower is defined as exactly 746 W for motor ratings, and boiler horsepower is a completely different quantity at about 9810 W.
| 1 hp | 745.69987 W |
James Watt introduced the unit in the 1780s to let customers compare his steam engines against the draft horses they would replace. He derived it from observations of horses turning a mill wheel and rounded the result upward, so a horsepower is somewhat more than a horse sustains over a working day.
About the horsepower (mechanical)
Horsepower is a marketing unit that became an engineering one. Watt needed a way to tell a mill owner how many horses his engine would displace, so he measured how much work a horse could do turning a wheel and defined a unit slightly above it. The figure of 33 000 foot-pounds per minute is round in the units of his day, and the modern definition of 550 ft·lbf/s is the same number divided by 60. Because the foot, the pound and standard gravity are now exactly defined, so is the horsepower, at 745.6998715822702 W.
The variants cause real confusion in automotive specifications. A European car quoted at 150 PS is 147 hp mechanical, since metric horsepower is defined as 75 kgf·m/s rather than 550 ft·lbf/s. Motor nameplates in North America use electrical horsepower, defined as exactly 746 W, a rounding that avoids carrying the awkward decimal. Boiler horsepower is not a variant at all but a separate unit describing the steam a boiler can raise, roughly 9.81 kW, and reading it as a mechanical horsepower is a thirteen-fold error.
The relation worth carrying is that power equals torque times angular speed. In customary units, \(\mathrm{hp} = \frac{\text{torque in lb·ft} \times \text{rpm}}{5252}\). The constant 5252 is \(33000/(2\pi)\), and it is the reason horsepower and torque curves always cross at 5252 rpm on a dynamometer chart.