Quote:
Originally Posted by h0trod389
why is it, that on all engine dynos, the hp and the torque are are equal @ 5200 rpms?

There is some Rocket science behind the relationship of torque and horsepower which was developed by one James Watt in the 1700s to sell his new contraption the steam engine. At issue was how to measure the work an engine could do compared to the power standard of the day which was the "work" horse. Before I get into how and why torque and horsepower are the same at 5250 RPMs let me define what is "torque" and "horsepower"
Torque and horsepower are related to each other where torque is a force while horsepower is a measure of work accomplished with that force. A force is simply energy applied to a resistance, a person leaning against a wall applies a force to the wall which the wall resists, but nothing is happening, therefore, no work is accomplished thus no horsepower developed. Horsepower is a force causing a motion over a period of time, which can be used to produce work, such as applying enough force to knock the wall over. Mr. Watt developed this term to relate the amount of work his new fangled steam engine could do to the standard power source of the 18th century, the horse. For us today, being unfamiliar with mechanisms that harnessed the horse to accomplish work, his definitions seem arbitrary, however. they are not.
The terms of of one horsepower is the work required to raise 33,000 pounds one foot in one minute and that torque and horsepower are equal at 5250 RPM are well founded in the technology of the period to which he was trying to make comparisons of how many horses his engines could replace
Watt developed an equation based upon the typical application of a horse driven mill where the horse walks a circular path attached to a beam that rotates a shaft which in turn powers some application like a pump, or a saw, spinning, or flour mill. The standard of the time was a 12 foot long beam attached to a vertical shaft at one end that was rotated by a work horse such as the Clydesdale we see today in Budweiser beer ads.
The arithmetic looks like this; a 12 foot long beam forms the radius of a 75.4 foot circular path walked by the horse. Watt determined by expirement that the horse could pull continuously with a force of 180 pounds at a rate of 2.4 revolutions per minute. At this rate, the horse traveled at a speed close to 181 feet per minute which is about 2 miles per hour. That speed multiplied by the 180 pounds of force results a work factor done by the horse of 32,580 lbft./minute. As is typical of dynamometer salesmen today, Watt rounded this up to 33,000 lbft. min.
Now to get at a useful equation one needs to determine the amount of work accomplished per pound foot per revolution. Taking 33,000 pound feet and dividing it by the distance traveled by 1 pound on the end of a weightless foot long bar you get a circular diameter of 2 feet times Pi (3.1416) which means the pound on the end of the bar traveled 6.2832 feet, expressed as 6.2832 pound feet when divided into 33,000 lbft/min nets 5,250. The resulting familiar equation then; is that horsepower is equal to torque times RPM divided by 5250. Or in another form horsepower is equal to torque times RPM times 2 times Pi divided by 33,000.
Bogie