Dynojet - Technical
I have not found a good tech explanation of how the Dynojet works, but I remember when Dynojet provided "white papers" on the subject.
Dynojet 48" drums
The method starts with the acceleration of the 1600 lb ??, 48" dia drum. Each drum's inertia is measured at the factory, and that value is stamped on the ID or side, and is part of the ID for each drum. The software for a specific dyno is factory calibrated based on the drums used. For example, if replacement drums have less inertia than the original value when calibrated, the accelleration would be a bit too quick and the power overestimated. The calibration factor is always used to properly increase or reduce the predicted power. These corrections are only a few percent at most. If a drum needs to be replaced in the field, the new drum will have a different correction factor that gets programed into the software by a Dynojet tech.
The key concept is that the HP required to create the measured drum acceleration is the same as the HP delivered to the drum by the engine, at any time or rpm during the test run. That is not true
for the Torque to accelerate the drum vs the torque at the axle.
I could not find equations for the inertial dyno that went beyond the F=ma linear analogy. Sooo
Id = Drum Inertia (constant, measured at factory)
T = Torque, ft-lbs, applied to Drum by tires
R = Radius of Roller (aka Drum)
w = rotational speed of Drum, rd/sec
N = RPM of Drum
n = rpm of engine
a = angular acc'n of Drum, dw/dt
t = time per rev (related to a tachometer)
The Hp that drives the Drum equals the hp that the engine puts out, less transmission, inertia, and tire flex losses. You can't say that about torque, without getting into gearing, tire and Roller radii, etc.
Hp = TN/5252
T = I x a , a = angular acceleration of the drum
w = 2 (pi) / dt , = angular velocity in radians / sec
a= (w2-w1) / (dt) measured, based on per-rev time increment, measured with tach.
Once the Hp is measured at a specific Drum speed (rpm), the related engine speed is used for the x axis in the dyno plot.
As long as the engine is fully loaded, the results should be accurate as far as hp delivered to the pavement. If too low a gear is used, the engine may not get fully loaded. If too long a pull, any knock may reduce timing advance, if the engine has a knock sensor.
In the old days, Dynojets were drum only and Mustangs were eddy current or torque arm load only. Now both can have inertia plus eddy current resistance too. Mustangs have taken it a step further now, being able to add aero drag loads for simulating a 1/4 mile ET:
Patent US5531107 - Method and apparatus for establishing virtual inertia in a chassis dynamometer - Google Patents
The SAE correction factor (J1349) adjusts for conditions other than the standard temp, humidity, pressure, etc that are noted in that standard. Note the max value should be about 1.03 . If you wanted to see how much power you were making on a nice cold day, mutiply your peak hp by the inverse of the fractional correction factor. Always ask that the SAE CF be used and the Value printed on the dyno graph
A good read on simple vs complex dynos