Re: Thrust/HP

Date:         17 Aug 97 01:57:23 
From:         "P. Wezeman" <pwezeman@blue.weeg.uiowa.edu>
Organization: The University of Iowa
References:   1
Followups:    1
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On 8 Aug 1997, Wally wrote:

> At the expense of sounding stupid, could anyone explain the
> mathematical relationship of thrust(rocket or jet) and horsepower.
> More precisely, how does one convert from one to the other.  I can't
> begin to relate how long and often I've pondered this question. Any
> help would be greatly appreciated.

   Thrust is a unit of force. Force times distance is mechanical work,
which is a form of energy. For example, if you were to drag a table for
a distance of ten feet against a frictional force of fifty pounds you
would have to expend five hundred foot-pounds of energy (ten feet times
fifty pounds). Power is energy per unit time. If it took you five seconds
to move the table, you would be producing a power of five hundred
foot-pounds per five seconds, or one hundred foot-pounds per second.
(Force times distance) divided by time equals power. This is equivalent
to force times (distance divided by time), and since distance divided by
time equals speed, then power equals thrust times speed, which is a
handier formula. In the example, your speed is ten feet per five seconds,
which is two feet per second. Multiplying this by the force of fifty
pounds gives fifty pounds times two feet per second or fifty foot-pounds
per second, the same answer as before.
   A horsepower is a unit of power defined as 550 foot-pounds per second.
So if you take an airplanes thrust in pounds and multiply it by the
plane's speed in feet per second, you will get the power in foot-pounds
per second. Divide this figure by 550 foot pounds per second per
horsepower to get the power in horsepower.
   For example, suppose an aircraft is flying at six hundred miles per
hour with ten thousand pounds of engine thrust. Convert the speed to
feet per second by multiplying by 5,280 feet per mile and dividing
by 3,600 seconds per hour. This gives 880 feet per second. Multiplying
this by the thrust of ten thousand pounds gives a power of
8,800,000 foot pounds per second. Dividing this by 550 foot pounds per
second per horsepower gives 16,000 horsepower. This is thrust horsepower,
which is useful power actually delivered to the airplane.
   Typically, an airplane propeller is about 80 per cent efficient at
converting engine shaft horspower into thrust horsepower at design cruise
speed. Jet engines have propulsive efficiencies of 30 to 80 per cent
at converting the power of the jet blast into thrust horsepower at cruise
speed. At low speeds, such as at the start of the takeoff run, a jet or
propeller has a certain maxmum static thrust, and the thrust horsepower
will be quite low, in fact it will be zero at zero speed.

                        Peter Wezeman, anti-social Darwinist

                             "Carpe Cyprinidae"