Back in the "BC era" - before computers - engine lab dynos were usually electric - essentially a big DC generator with a large resistance grid that you used to control the load. Water brake dynos were also in use, but the old DC generator type was easier to control for lab work, especially if you wanted to control speed at various constant values over a wide range of loads.

The dynamometer frames were mounted on bearings that allowed them to rotate freely, but they were constrained by a lever arm that rested on a scale.

To do a WOT power run, you set the load high then opened the throttle fully and adjusted the load to achieve a steady speed. Then the operator read the scale and RPM. He then reduced load to allow the engine to accelerate and then added more load to stabilize at the next test speed, read the scale and RPM, and so on and so forth at more test speeds up to the maximum speed planned for the test.

So what you ended up with was a data set of RPM and scale load reading in pounds, and knowing the lever arm length allowed you to compute the torque at each RPM point. Then, using torque and the famous HP = T X N/5252 formula you computed horsepower and could then plot both the torque and power curves versus RPM.

So where did this formula come from?

Answer: Basic physics.

"Work" (which is the same as energy) is a force acting through a distance or a torque acting through an angle. If I use one "unit" of force, say pounds, to push a brick across a table one unit of length, say feet, I have expended one unit of work or one foot-pound, which was dissipated as one foot-pound of friction energy.

Similarly, if I use a one foot lever and one pound of force to rotate a shaft that has some friction resistance through one unit of arc length (which is that same distance as the radius) I have expended one foot-pound of energy that was also dissipated as one foot-pound of friction energy. Recall that pi is the ratio of the circumference of a circle to its diameter, which can also be expressed as circumference is equal to 2Pi times radius. One radian is defined as the length of arc along the circle equal to the radius, so there are 2pi radians in a complete circle.

I other words, if I apply a force on a one foot lever arm through a complete revolution, the distance is two pi feet so the work is 2pi time the force. If I apply the force on the lever arm for ten revolutions the total work is ten times the work for one revolution.

Since torque and work/energy have the same fundamental units the current convention is to use "force-length" or pound-feet for torque, and "length-force" or foot-pounts for work/energy to avoid confusion in what we are dealing with.

Recall that power is work or energy over a period of time, so a torque, T, in pound-feet, from a shaft that rotates a complete revolution, which is 2pi radians, over a time period, t, produces power as follows

Power = torque(2pi)/t

If our old fashioned dyno shows 50 lbs at a scale with a two foot lever arm, which is 100 lb-ft at 6000 RPM ( time period of .01 second for one revolution) the power produced is

100(6.28)/.01 = 62,800 ft-lb/sec

Or we can convert to ft-lb/minute by multiplying by 60 and the result is 3,768,000 lb-ft/minute.

Back in the early eighteeth century, James Watt, inventor of the steam engine, spent a considerable amount of time studying horse drawn pumps that pumped water out of coal mines. The horses were harnessed to a capstan and walked around in a circle.

Watt determined that a typical draught horse could deliver 33,000 ft-lb/minute of power continuously over a long period of time and DEFINED this amount of power as ONE HORSEPOWER.

So the above relationship can be rearranged as follows where N is engine speed in revolutions per minute.

HP = T(2pi)N/33000 = TxN/5252

There are many units for power. We are still stuck with Watt's definition from the archane English system of units. Nations that have adopted the SI (Metric) standard use kilowatts and 1KW = 1.34 HP, or 1HP = 0.746 KW.

In the above example our 100 lb-ft of torque at 6000 RPM is delivering 3,768,000/33,000 = 114 horsepower, which is the same as 100 x 6000/5252. In other words 100 pounds of force is being applied with a one foot lever arm over 6000 revolutions in one minute - force over a distance, in this case using a one foot lever arm a total of 6000 times in a circle in one minute.

The power would be the same if it was 400 lb-ft at 1500 from a truck engine.

The common inertia chassis dyno of today continuously records instantaneous angular acceleration and rotational speed of the drum, and this data combined with the known drum rotational inertia is input into a simple software formula that computes instantaneous power. The famous formula, rearranged to HP(5252)/RPM is then used to compute torque from the power data. The basic output data is HP and Torque versus MPH, but most shops have an inductive pickup that they can attach to a plug wire so HP and torque versus engine RPM can be displayed and printed.

So the old fashioned electric dyno "output" is load on the scale that we use to compute torque and then with the RPM data compute power. An inertia dyno continuously records instantaeous roller acceleration and RPM, and uses this data to compute instantaneous power and then torque and plots out a continuous curve of both. Same end, different means.

Modern water brake lab dynos can be programmed to allow the engine to accelerate and measure power in the same way. The usual acceleration value is 300 RPM/sec. It's a lot easier to get a torque/power chart using the inertia technique than the way I did BC - a lot easier on both the operator and the engine!

Duke