# Inertia Flywheels

Calculate the required polar-moment-of-inertia to simulate a vehicle's weight with a flywheel.

### What flywheel inertia is needed to simulate a vehicle’s weight on an engine dyno?

First, determine the “Vehicle Speed Factor” to scale DYNO-MAX’s “Speedometer” formula readings to duplicate your vehicle’s real world engine tach to speedometer relationship. Then, use that same factor in the equations below to calculate the required simulation flywheel polar moment of inertia.

Required_Polar_Moment_of_Inertia = Simulated_Vehicle’s_Weight / Vehicle_Speed_Factor^2 * 6.1

Tip: Weight must be in pounds to return the polar moment of inertia as ft-lb-sec^2

Example:

Say we want to add a flywheel to our engine dynamometer’s driveline which will simulate a 2,000 pound car’s mass during acceleration testing. We’ll assume we already determined that a Vehicle Speed Factor of 28.01 does a good job of matching our car’s 4th gear highway tachometer/speedometer relationship to that on the engine dyno. We can use the above formula to come up with it’s required polar moment of inertia. Here’s how:

2000 / 28.01^2 * 6.1 = Required_Polar_Moment_of_Inertia

squaring our 28.01 Vehicle Speed Factor yields:

2000 / 784.5601 * 6.1 = Required_Polar_Moment_of_Inertia

finishing the math:

2000 / 784.5601 * 6.1 = 15.55 ft-lb-sec^2

With the above inertia value, it is easy to use DYNO-MAX’s Inertia Calculator to figure a good diameter, length, and material combination to deliver that inertia. For instance, a 16″ diameter steel flywheel that is 39-1/2″ long is a good match.

WARNING: BEFORE ACTUALLY CONSTRUCTING ANY FLYWHEEL, VERIFY THAT YOUR PLANNED OPERATING RPM, FLYWHEEL DIMENSIONS, AND CONSTRUCTION MATERIALS KEEP EVERYTHING SAFELY BELOW THE CALCULATED BURST SPEEDS, ETC.

The same DYNO-MAX Inertia Calculator also makes it easy to determine the equivalent inertia required should you choose to gear the flywheel up or down from the shaft where the Vehicle Speed Factor was referenced. remember that there is a exponential (square) relationship between shaft speed changes and the effective vehicle inertia simulation weight.