The beast that gave meaning to power

By MUNGAI KIHANYA

The Sunday Nation

Nairobi,

12 March 2006

Patrick Githinji is troubled by the power ratings appearing in electric motors and generators. Some indicate it in kilowatts (kW), others use kilo-volt-ampere (kVA), and yet others quote it in horsepower (hp – not to be confused with the manufacturer of computers). But how are these quantities related?

Most people correctly assume that a horsepower is what a horse can do. But the next question would be “which horse?” – a racing breed that only carries a 50kg jockey very fast round the racetrack or a working beast that moves heavy loads very slowly?

Both the watt and the horsepower are historically connected to one individual – James Watt, the man who popularised the steam engine during the industrial revolution in Europe in the late 18th century (some history books say he invented the steam engine but that’s not true).

In order to sell his engine, James Watt had to convince potential customers that it was better than a horse (the main source of energy at that time). His target market were grain millers who used horses to turn the milling wheel. Watt found that a typical horse would be tied to a 12-foot bar and made to walk around in a circular path, thus turning the bar, which then turned the mill. The diameter of this circle was 24 feet (12 times 2), thus its circumference was about 75.4 feet (24 times 3.14).

Watt further found that the horse made 144 trips round this circle every hour, or 2.4 times per minute. Therefore, the average speed of the horse was 181 feet per minute (75.4 times 2.4). Watt estimated that the pulling force applied in doing the work was equal to 180 pounds of weight. Thus he worked out the rate of working of a horse as 181pounds times 180 feet per minute. This is equal to 32,580 foot-pounds per minute. The figure 32,580 is awkward so James Watt rounded it off to 33,000 foot-pounds per minute and that is value used to date.

Were all these calculations a wasted effort? No. Watt sold very many steam engines and died a very wealthy man.

Now what is a kilowatt? It is 1,000 watts. The watt (spelled with a small letter “w”) is the metric standard unit of power. It is named after (you guessed it!) the same James Watt who defined the horsepower scientifically. One watt is equivalent to working at a rate of one newton-metre per second (note, newton is spelled with a small n).

Now, one horsepower is 33,000 foot-pounds per minute, or 550 foot-pounds per second. One pound-force is approximately 4.45 newtons. Therefore one horsepower is 2,447.5 foot-newtons per second. But one foot is 12 inches and one inch is 2.54 centimetres, or 0.0245 metres. That is, one foot is 0.3048 of a metre. Thus, 2,447.5 foot-newtons per second are equal to 746 newton-metres per second (2,447.5 times 0.3048).

In other words, one horsepower is equal to 746 watts, or 0.746kW. But why did I have to go round so many calculations? Well, I’m following James Watt’s legacy and hoping to become rich! Next week – the kilo-volt-ampere conundrum.