# Flywheel Inertia

Glenn Salpaka, the owner of Falicon Crankshaft Components (now part of Race Winning Brands), used to say that half his shop was devoted to removing mass and the other half was devoted to adding more. The inertia of the flywheel has a significant impact on the performance of the power plant (and vehicle). Different motorsports have different requirements. Trials bikes typically use very heavy (high inertia) flywheels.

Moment of Inertia (MoI) is defined as the resistance of an object to rotational acceleration by a torque.

The flywheel's mass, in and of itself, is not as important as where that mass is located. Mass at the perimeter has a much greater effect than mass at the center - in fact, it follows a distance-squared relationship.

A reasonable way to model a flywheel is by using the MoI formula for a cylinder. The MoI of a cylinder that has an outside radius RO and an inside radius RI with a mass M is:

I = 0.5 * M * (RO2 + RI2)

The units for MoI are frequently lb*in² and kg*mm².

I have it on good authority that top trials riders pin the throttle (storing energy in a massive flywheel), then simultaneously diminish the throttle and dump the clutch for the launch. This backing-off of the throttle is what allows them to stop at the top. Look at the photo at the top of this section's parent page. Notice the position of the rider's throttle hand - it certainly appears the throttle is closed.

Note that the following MoI estimates are for the flywheel only. The effect of the crank wheels is neglected, not because it is unimportant, but because it requires engine disassembly to make any measurements. Similarly, the rotor in an electric motor is not considered. Even the MoI of the clutch can have an effect. This has been demonstrated in road racing where a high MoI is undesirable.

The bottom line, this is far from a comprehensive look at MoI.

The following MoI estimates are based on geometry and the assumption of uniform steel construction. Magnets have a lower density than steel. Also, the estimates do not account for the disk that holds the perimeter to the center. These omissions tend to offset one another. Below are some calculated values from my spreadsheet:

Sherco 125 (Leonelli) = 7,391 kg*mm²

Sherco 200 (Ducati Energia) = 11,387 kg*mm²

OSSA TR280i (Kokusan Denki) = 10,386 kg*mm²

GasGas TXT 321 (Kokusan Denki) = 11,441 kg*mm² (In fact, this bike even had an additional flywheel on the clutch side of the crank!)

EM ePure Race (Electric Motion) = 2,259 kg*mm²

Polaris XC700 (Ducati Energia) = 2,748 kg*mm² (As used on 800cc twin Tul-aris 2T road racer)

3 very different flywheels, representing extremes in my collection: Yamaha TZ250 GP road racer, Polaris XC700 snowmobile, GasGas TXT 321 trials bike

Outboard side of four trials flywheels

Inboard side of the same four trials flywheels

## A Physical Feeling for Inertia Values

It's difficult for me to get a physical feeling for whether the MoI numbers that come out of an equation are realistic or not. The spreadsheet makes the simplifying assumption that the flywheel is a uniform cylinder.

However, those values agreed well with my experimentally determined values. For example, the Sherco 125 flywheel is a Leonelli part number 026.D30. The cylindrical calculation yielded 7391 kg*mm2, whereas the rolling experiment yielded 7586 kg*mm2.

To get some feeling for the MoI numbers, I decided to consider the inertia of a point mass at a 1-foot radius. My calculation of 7400 kg*mm2 is equivalent to 0.175 pound*foot2 That would look like a point mass of 0.175 pounds (2.8 ounces) whirling around at the end of a 1-foot rod.

Finally, I also calculated the kinetic energy (in joules) stored in a spinning flywheel. It's worth mentioning that the energy stored is a function of rotational speed squared. Joules have a lot of meaning to me in electronics but much less so in mechanics. So I converted joules into something I did have a feeling for - vertical leap. The energy stored in a typical trials flywheel at 6000 rpm would lift 300 pounds straight up several feet. Interesting. For a more detailed accounting, see the spreadsheet.

## Determining MoI by Experiment

The spreadsheet also includes MoI valves that were derived experimentally by timing how long it took a given flywheel to roll down an inclined plane on an axle. The 2-part stub axles for this experiment are shown in the adjacent photo. They go through the flywheel's internal taper so that it can be supported on both sides.

The biggest challenge is determining the rolling time (roughly 10 seconds) accurately. I used a stopwatch. I considered building an electronic timer to improve the accuracy but did not feel it was worth the effort.

Stub axles that allow a flywheel to roll down an inclined plane.

## Effect of Gearing on Inertia

One non-obvious fact about gearing is that it affects inertia by the square of the gear ratio. Thus, a 5:1 gear reduction changes inertia by a factor of 25.

Whether the gearing increases the reflected inertia or reduces it depends on your point of view. If the driven thing runs faster than the driver, its inertia appears to increase by a factor of N-squared. Conversely, if the driven thing runs slower than the driver, its inertia appears to decrease by a factor of N-squared. This effect is called reflected inertia.

As a concrete example, think about rotating the rear wheel to turn the engine over on a stand with the spark plug removed. It's easier to turn the motor over in a higher gear. This is because you are accelerating the rear wheel's inertia plus that of the crankshaft, flywheel, clutch, and gearbox (all of which are turning at a higher speed than the rear wheel).

For a trials bike, the overall reduction ratio for 1st might be on the order of 30:1 whereas top gear might be 10:1. Squaring these ratios highlights the difference (900 versus 100). This makes the engine's reflected inertia an order of magnitude greater in 1st gear versus top gear (as seen by the rear wheel).

The situation is exactly the opposite from the engine's point of view when looking at the reflected inertia of the rear wheel (its inertia is an order of magnitude less in 1st gear than in top gear).

This also explains why it is nearly impossible to bump-start a trials bike in a low gear (especially on a low-traction surface). Whereas it is possible on a high-traction surface in a tall gear (assuming the clutch is not too draggy).