More information about rotating mass. Listed below is the part that pertains to wheel size.
Rotating Mass, Available Horsepower, and Acceleration
What does a rotating mass actually do?
A rotating mass does not really consume or dissipate energy. A rotating mass stores energy. The rotating mass eventually either returns energy to the system in a useful way, or something converts the stored energy to some other form of unwanted energy. The conversion might be with a friction, converting to heat. The energy stored might be helpful, like the smoothing of cylinder pulses in an engine flywheel. The energy stored also might not do anything at all, or the stored energy can even be harmful, reducing acceleration or braking.
Accelerating an unnecessary rotating mass requires energy, and the acceleration process saps some of the horsepower we have available to accelerate our vehicles. Reducing available horsepower affects acceleration in a very predictable manner, and the horsepower amount needed to spin something up gives us some feel for how important a part change might be.
Four things determine the effect of rotating mass. Every one of these things is important:
- How quickly and often a rotating mass speeds up or slows down. Every time it is forced to speed up or slow down, it takes or releases energy
- How heavy the rotating mass is. More weight (with no other changes) stores or releases more energy
- The rotating weight's distance outwards from the centerline. The further out, the more energy pushed in and out of a given weight
- How fast the weight spins, or the speed the weight travels in a given circle diameter. The higher the RPM, the more energy stored
Here are how these things work:
- If we push energy into the rotating mass and pull energy out several times, we move more power around than if we make a slow, smooth, change in speed. It takes much more effort to repeatedly speed and slow something in a short period of time than to gradually speed it or slow it
- The amount of weight is the least important thing! If we double the weight (with no other changes) we only double the stored energy
- Weight distance from the center line is very important, because it determines the weight's circular velocity (speed)! Stored energy goes up by the SQUARE of the radius change. If we replace a 4-inch diameter hollow driveshaft with an 8-inch diameter tube of exactly the same weight, it is not just double. It is twice the size squared, or four times the stored energy when it weighs the same!
- The faster we spin the weight, the more energy it stores. If we double RPM, we multiply stored energy four times. Again it is a square of the change, just like weight distance from centerline is a square.
The above is very important. If we double the effective "circle size" the weight is rotating at, we get four times the stored energy. If we simply double the weight without changing the spinning radius, we just double stored energy:
- If we reduce mass from twenty pounds to ten pounds, keeping the same distance out and same peak RPM, we reduce stored energy to half the original amount. Reducing weight is a one-for-one change.
- If we cut diameter in half while keeping the same weight and RPM, stored energy will be 1/4 the original stored energy. This change is a square. Twice is a "four times" effect. 2*2=4. Four times is a sixteen time effect on stored energy. 4*4=16
- If we cut RPM in half, we would reduce stored energy to 1/4 the original amount. Once again this is a squared change. Change RPM three times, and the stored energy changes nine times. 3*3=9
We should carefully think about what this means when we change things. Some changes are worthwhile, some are not. We also cannot use carte blanche rules, like the silly rumor that reducing a rotating weight is like dropping the vehicle weight four times that amount. As a matter of fact, it is probably never four times. It is more likely closer to one, and might even be less than one!
Wheel Changes
Let's assume, just as an example, all of a wheel's weight is at the outer edge and remains at the outer edge. If we reduce a wheel's diameter but keep the overall weight the same, the wheel is a spinning ring with smaller diameter. The smaller diameter increases the wheel's RPM at the same vehicle speed. The smaller diameter also moves the spinning weight closer to the center.
Let's say we cut diameter in half. Now think about how fast the wheel spins. RPM will be twice what it was at the same speed. The half size diameter reduction spins the wheel twice as fast, and that would increase stored energy to four times the original amount if the weight was the same distance out. But the weight isn't the same distance out. The spinning weight is now half size. This 1/2 size reduction decreases stored energy by four times!
If we did not change the weight or weight distribution, and we reduced a wheel and tire diameter by half but drove the same speed, nothing would change. It would be a major change that just broke even. Moving the weight closer to the rotation center reduced stored energy, but the increased RPM to maintain the same speed increased stored energy the same amount. One cancelled the other, and stored energy did not change!
If we change tire and wheel diameter without changing weight distribution and weight in the tire and wheel, we don't change a thing. In this example, we gained nothing from a significant physical change. We also lost nothing.
Lightening the tire or wheel some distance out from the hub reduces stored energy. This is especially true if the weight reduction is far out from the center. If we change the weight one-pound fourteen inches out, it is like changing weight four-pounds seven inches out. Which brings up an important point we almost never hear mentioned, a lower weight part might not be lighter at the outside edge. It might be lighter in the center, where the weight reduction doesn't mean much.
It is more important to make something as light as possible on the OUTER edge, rather than near the (wheel) center. Spending money on smaller or lighter rotors to save rotating weight should be down the list, because the rotating weight is closer to the wheel hub. Unless the rotors are huge and we take weight out of the rotor's outer areas, things will not change much. (A light rotor and wheel is good for reducing un-sprung weight, and that helps keep our tires in contact with the road. It also reduces vehicle weight. But this is a different problem. Here we are talking about rotation, not the bounce inertia or "dead weight".)
If we spent money on the same weight reduction in the wheel, reducing weight out a little further away from the center, we would do much better. We would be removing weight further out from the center, where it does the most good.
If we spent our money on a lighter tire we would be getting the very most return for the weight change. The tire's weight change is mostly outside between the rim edge and the tread area. We get maximum effect from the weight change!
Think about this carefully. If we buy a lighter tire, we know for sure the weight comes off the most critical area. If we buy a lighter rotor, it is close to the center and, for the same weight change, the return is much less.
The wheels also speed up and slow down gradually. With an 11-second car, we have 11-seconds to speed the wheel up. Most of the horsepower pushed into the wheel and stored is pushed in near the end, when acceleration is least. Since we have more time to push the bigger amount of energy into the wheel, it takes less horsepower than we might expect.