In order to understand how a dynamometer measures torque and calculates power, it will help to know a few basic definitions and formulas.
Force and Work
If we hold a 10 lb. weight we are applying a 10 lb. force. If we move (displace) the weight a distance of 3 feet we have done work. We have done 30 lb-ft of work.
Work = Force x Displacement
Power is how much work can be done in a period of time.
Power = Work / Time or Force x Displacement / Time
The definition of 1 Horsepower is displacing 1 lb. 33,000 ft. in one minute or 33,000 lb-ft / minute.
1HP = 1 lb x 33,000 ft / 1 minute
Try It Yourself
Applying to Rotary Motion
We are dealing with engines where the force and power are delivered in rotary motion. This changes things a little.
Torque is the force applied through or derived through a lever or torque arm that will rotate about a fulcrum or pivot. For our purposes, the arm is a radius. If a 10 lb. force is applied at a 3 ft. radius we are applying 30 lb-ft of torque. We will use a brake and a torque arm when measuring the torque of an engine. Notice that although physically torque is a force, mathematically it already has the same units as work. (lb-ft.)
We know that Work is achieved when there is Force and Displacement. Power is Work factored by Speed. Since we are dealing with rotary motion it is called Angular Speed and it is expressed in Radians/sec or Revolutions/Minute. A radian is an angle where the radius is the same length as the length of the arc created by that angle. It is the same no matter the size of the circle. Hence, there are 2π radians in every revolution. Just like a revolution, radians have no unit of measure, which works out well because torque already has the displacement unit (feet) in it.
The formula for power now looks like this.
Power = Torque x 2π x Revolutions / Minute
We would like to get rid of the 2π and we need to consider that 1 H.P. = 33,0000 lb-ft. / min.
Here is what we have for an equation.
33,000 lb-ft / min = lb-ft. x 2π x revolutions/min
Divide each side by 2π (6.28315) and you get 5,252 lb-ft / min = lb-ft. x revolutions / min.
Next divide each side by 5252 and you end up with this equation:
1 Horsepower = Torque x R.P.M. / 5252
Because of this math, lb-ft of torque and horsepower will always be the same at 5,252 RPM.