Wheel Inertia explained.

congrats, all the best!

 

We do? Erhh, I mean yes, of course.

 

we may have found our next bill wilson.

 

Wow! I always thought it was more complicated.

 

Can we assume that "r_wheel" would be the entire wheel+tyre assembly, which will be more or less the same for 15 or 17" rims?

Does a wider wheel cause a decrease in aerodynamic efficiency?

 

My Calculus has turned to rust (or aluminium corrosion) - over the last 40 yrs since I used it. Last time I picked up an alloy wheel (admittedly a long while ago), I thought it was lighter than the actual tyre - so wouldn't a mounted tyre increase the effective radius? Would it be a "simple" matter of cutting a sliver of a ½ wheel and tyre (across the radius) and determining the centre balance point, or would it change as rotational forces increase?

As far as aerodynamics is concerned, as a layman fascinated by physics, I can see that the bluff area of a wider tyre sticking out from under a car would probably have more effect on aerodynamics than a narrower one. But I do wonder (dream) if there could be some compensating effect by a rapidly rotating wheel similar to a golf ball?

Here in Australia, we don't get many choices - we get 2 models. If you want Sat Nav, you have to have it with 17", no spare, fake leather (&more) - & pay a crazy $8000 for the upgrade. One alternative only - no Sat Nav, spare tyre, 15", cloth (&more).

 

Ha! Reality is a LOT more complicated!

 

"Inertial effects" are significant during acceleration, but irrelevant during steady-state cruising. The effect of putting on wider (and we assume heavier) tires on fuel consumption during acceleration would be a greater than the effect of adding equal mass elsewhere, due mainly to their rotational inertia, but not as much greater as people often assume. The effect of putting on wider tires on fuel consumption during steady cruise would be entirely due to changes (probably but not necessarily increases) in aero drag and in rolling resistance.

Your initial post would be closer to a correct calculation of the car's kinetic energy if your definition of r_wheel substituted "radius of gyration" for "radius of the center of mass," which should be zero. Radius of gyration of the wheel is the radius of a hypothetical thin hoop of the same moment of inertia and the same mass concentrated at that radius, rotating about the same axis. As a guess, the radius of gyration of the wheel+tire assembly might be roughly 70% of the outside radius of the tire.

 

Which gets me thinking ... is there a gyroscopic effect on handling? I remember as a schoolboy we noticed it on bicycle wheels if we held them off the ground and then tilted the bike - the faster you spun the wheel, the bigger the effect and could even wobble the bike off the support? We didn't have options to put wider tyres on our bikes then.

 

Calculus hadn't been invented when I went to school.

 

Nobody will notice the insignificant changes in MPG between various wheel weights and the distribution of that weight. The energy lost by decelerating the extra momentum is a microscopic fraction of the energy lost due to rolling resistance and aerodynamic drag. Having a wider or taller tire will have a much more significant impact on fuel economy than any differences in weight.

Sure, you want to reduce the amount of kinetic energy being fed to the wheels in a drag race, but in day to day driving, nobody will notice the difference in MPG. On top of all that, the Prius will capture a portion of that energy back with regenerative braking.

To summarize; if your goal is to improve the acceleration and handling characteristics of the car, then buy lightweight wheels and tires. If your goal is to improve MPG, then keep the stock wheels and buy LRR tires because they are both optimized for lower rolling resistance and lower drag.

 

This is very simple! Larger wheels require wider tires which has more contact surface which has more rolling resistance.

 

Yes, but a larger rim also moves more weight away from the center of the wheel (hub). The weight of a tire is mostly in the bead and tread areas, not the relatively thin sidewalls. A larger rim moves the tire bead further outward compared to a rim with a smaller diameter.

 

I never claimed ignorance of how inertia works, nor did I disagree with your explanation of it.

Your myopic focus on inertia has allowed you to entirely miss my argument; that wheel weight and weight distribution is not going to make a significant difference in MPG compared to the larger factors of rolling resistance and aerodynamic drag.

People don't spend the majority of their time stopping their vehicle, which is the only time that inertia is wasted. Most of the time people are traveling, and any time the vehicle is in motion, rolling resistance and aerodynamic drag are constantly working against the power of the engine. In fact, at steady and level cruising speed, 100% of the engine power is consumed by rolling resistance and aerodynamic drag (minus drive-train losses, etc). If aerodynamic drag and rolling resistance went away, we could simply accelerate up to speed and then shut the engine off all the way to the next stop.

Regarding wider tires; they have higher aerodynamic drag due to a larger frontal area. While they might have lower rolling resistance, that will be more than offset by the increased aero-drag.

While I enjoy the engineering discussion, you can take your strawmen to another forum. This isn't the place for ego stroking.

 

A little knowledge is a dangerous thing, SpaceShip. Your partial knowledge of the physics of rotating objects doesn't mean you grasp where most of the energy needed to power a car goes. Redpoint5 is correct.

 

Low inertia provides a small overall benefit during acceleration and braking. However you have completely ignored the benefit of having higher inertia in a wheel - it wants to keep on rolling. For example, on a section of road where you might be coasting, you'll go slightly further with higher inertia wheels before losing enough speed before you'll get back onto the accelerator. Of coarse, like Redpoint5 says, that inertial effect is dwarfed by rolling resistance and aerodynamic drag effects.