Unsprung, rotating mass: big wheels vs. small
 

Rdane and I were discussing this in an unrelated Rennlist thread, and it brought up enough questions for me that I thought I'd bring it here.

It's a commonly-held belief that there are meaningful differences between running 15-inch, 16-inch, 17-inch or 18-inch wheels, with regard to sidewall stiffness, slip angle characteristics and overall weight. As a rule, people seem to believe that a shorter sidewall is going to provide less flex, and will accordingly give more immediate turn-in response and more-responsive overall handling.

On the other hand, the bigger wheels are generally considered heavier. Unsprung weight and rotating inertial mass are big no-no's in making a car handle well.

And then there's tire sizing, which is its own crazy world. You can sometimes increase or decrease the overall diameter of your tire, although there's no direct correlation between this and wheel size. It begs the question: what the heck are tire manufacturers thinking? Why not standardize outside diameters, instead of the 35/40/45/50 percentage nonsense we currently have to deal with?

But back to the main issue. I did a quick comparison based on some data I found. The data comes from different sources, so it might not be reliable of consistent. It's not easy to find actual tire weights on the internet. But I found, for Dunlop SP-9000's that the following was (probably) true:

Size-------------Weight in pounds

245/40-17---------23.9
245/45-16---------25.1

Then, for wheels, the comparison might not be fair (or accurate, since it's not the same scale). But Sherwood Lee has accurately measured 16x9 Fuchs at 20.0 pounds. My 17x9 Lindsey 2-piece Fuchs weighed 17.5 pounds when I weighed them (although this was using the bathroom scale method, which isn't going to be tremendously accurate). Still, even with a 10% margin of error, the Lindsey's are going to be lighter.

Total weight for the 16-inch setup is 45.1 pounds.

Total weight for the 17-inch setup is 41.4 pounds.

That's a pretty significant difference. And the outside diameter of both tires is effectively identical. The Miatanet calculator puts them both at 24.7 inches, although there's a one revolution difference per mile, so it's not exact. The gearing would be identical between the two, but the 17-inch set-up would be almost 4 pounds lighter.

http://forums.pelicanparts.com/uploa...1085384365.jpg

Now, I also found another tire weight (Bridgestone RE-71's, I think) that listed a 1-pound heavier weight for the 245/40x17 than the 245/45x16. This doesn't seem to make sense, though, since they're both the same size tire (same outside diameter, same width), with the sidewall on the 17-inch one being 1/2 inch smaller to accommodate the larger rim.

By my reasoning, then, larger-diameter (lightweight) wheels would almost always produce a lighter overall wheel/tire package than smaller diameter (lightweight) wheels, since the tire (assuming the same overall diameter) is the heavier of the two objects.

But my reasoning might be nuts. :)

Ha, something useful from my recent excursion into Miatahood. Miata nuts are very, very into wheel/tire weights, consequently there's lots of data for the wheels and tires that fit. I can't offer you any of my own info, but this may give you more to go by.

tire weights
http://www.miata.net/faq/tire_weights.html

wheel weights
http://www.miata.net/faq/wheel_weights.html

more wheel weights including many Porsche wheels
http://www.wheelweights.net/

BTW, Jack, Bridgestone lists tire weights in their tire specs pages (or at least they do for the S03)

Doesn't the "where" the weight is come into play for acceleration and braking? - i.e., lighter overall may not help if the weight is all at the rim. Such inertial forces are a big deal on racing bicycles. Maybe the same with autos when you go larger???

Mechanical Engineers, please have at it......

must resist urge to dig out textbooks.....!!!!

I read on some Mini board that cars equiped with the 16" wheels accelerated better and where the fastest around an autocross. I don't know if that is true as I have not been following the Mini autocross scene lately.

a hollow cylinder is harder to turn than a solid cylinder of the same size if I remember correctly, and the farther out the weight is the worse it is, but if most of the weight is at the tire tread, and the tires are the same diameter, then I guess it wouldn't be much different. Is that right?

Interesting discussion. Though the wheel comparision is valid for your special case, I don't think it's fair to generalize your results.

All else being equal, the 17 inch wheel will weigh more than the 16. In the Lindsey case, they are using a non-fuch (BMW I think) rim that is obviously lighter than the fuch peice.

A better generic example would be a 16 inch Fuch vs a 15 inch Fuch, I think Sherwood lists those weights as well. The 16 is heavier for equal width.

Agreed. But if you're filling out the same overall diameter, it looks like tires generally weigh more than wheels. So shortening the sidewall on the tire should remove weight, while expanding the wheel size will add it back. The question is, which of the two is the bigger factor? To me, it looks like more tire is generally going to add more weight than more wheel.

It goes back to the gyro effect. Even though the 17" setup is lighter, some weight is further out from the center of the wheel which is what makes it harder to accelerate or turn. To highlight this further, if you have a metal gyro that's 3 feet in diameter, and another one, weighing the same amount but it's only 1 foot diameter, I'm pretty sure it would be more difficult to handle/move around the larger gyro. As well as slow it down or accelerate it.

Then you would have to factor in the concept of a spinning object. Even though the rotation is constant, the further out from the center you get, the faster that point will be travelling. I'm pretty sure that would be increased exponentially.

Jack, that's an excellent starting point for the discussion: lower weight is better.

But not the whole game: the polar moment of inertia of the wheel and tire combination must be taken into account. You could have a situation where you have higher overall weight but less mass distributed further from the hub and the heavier wheel would accelerate and decelerate faster. Consider, for example, a three-piece wheel that uses bolts to hold the hub to the rim, vs. a one-piece design.

The popular approach is to go with the largest possible diameter and smallest aspect ratio that will fit in the search for greater sidewall stiffness. But like everything else in racing, it's a multivariable thing-- I also would consider: spring rate of the sidewall, slip angle, tire temperature, price of the tires, using circumference to effect gearing changes in a "stock" class and rule-book limitations on width when making a decision.

It would make sense that the smaller sidewall would be the optimum choice. given that the tires weigh more.
And the faster you go the more expansion happens to the sidewall of the tire. (Is that correct?)

Chuck,

I think this discussion is focused on the specialized nature of Jack's wheels and other customized wheels, so the results are valid.
This is an interesting topic, maybe other considerations should be introduced, such as tire availabilty and tire cost for each size wheel.

I get that, but we're talking about two 24.7-inch gyros, here. It's the exact same overall diameter, just slightly different distribution of tire and wheel within that circle.

Where's the advantage for the heavier (16-inch) one?

It has been a while and rotational physics was not my forte but I think that rotational center of mass plays into this. Given two idential weights of 16" and 17" wheel/tire combos, the 17" will have its rotational center of mass farther away from the hub and therefore greater rotational intertia. As inertia is defined as the resistance of a body to change velocity or direction, it will take more effort to spin that combo up or slow it down. The slowing down is the hard part as the extra burden of slowing the wheel down falls almost entirely on the brakes. Throw in the probability that the larger wheel/tire set would be heavier and contribute greater unsprung weight, you really have to justify the benefits of shorter sidewalls.

Wait. Gary, we're talking about the rotational mass of the wheel and tire, not just the wheel. They're the same size -- 24.7 inches. No difference in the distance from center to the outside of the spinning mass.

If the two combos end up being the exact same size (as they are, in this example), but one (the 17-inch) is lighter, is there any possible advantage to the smaller wheel (with its bigger, heavier tire)?

Jack,
The way you just put it, it would seem that you have a valid point.

The only other thing that comes to mind is that mass has to do with density. Metal is more dense than rubber, so the concern would be with having an extra inch of (dense) metal that you have to accelerate vs. an extra inch of (not-so-dense) rubber.

This is my first hand experience.

I used a postal scale to first weight my 7 and 9 Fuchs with Bridgestone RE750s, 205/55/16s and 245/45/16s. RE750 tire diameters are 24.9" and 24.6". Then I weighted my 8 and 9 Fiske 10 spokes with SO3s, 235/45/17s and 255/40/17s. SO3 tire diameters are 25.3" and 25.1".

The front 17s Fiskes were a bigger weight gain on the 16" Fuchs than the only slightly heavier rears. Much of that was because of the 235 tire size and the 8" rim is a jump on the 205/7". Total overall gain from the lighter Fuchs set up and the heavier Fiske set up was 34# and change. Again IIRC something like 7# in the rear and 10# up front for each wheel and tire.

The tire patch gain (heavy rubber tread is the majority of tire weight not side wall) is over two inches in the front on this comparison and almost an inch in the rear. The SO3s weigh more. My impression, but I didn't get to weigh the wheels without tires, is the 9" Fuchs and the 9" Fiske's were very close # wise.

The 17" rear wheels gained 1/2 an inch in size over the 16s. Which would effectivly give you taller gearing. Upped my top end a bit, 7mph at 7K, again, IIRC by the gearing chart.

All that said much of differences can be dimished by careful selection of rim and more importantly tire size. (and yes the custom two piece welded Fuchs seem to be very light in comparison to either stock wheel because of the new technology and alloys in the rim halfs used)

Either side of the arguement can be supported by the right pick of tires I suspect. I gave my experience from my actual tires and rims. I also believe that a typical comparison will show 17s heavier than 16s given comparable set ups.

The difference in the larger tires on my car was noticable on the track. The gain in tire patch was impressive for braking but the loss of felt torque on a 180hp engine was not. That part sucked which peaked my interest in having the best of both worlds.

This has been posted before but to recap, a 10# difference in rotational mass is roughly worth 2-3hp. This can be calculated and seen on a sensitive enough dyno.

heavier wheels and tires and brake components are often worth the trade off in weight for grip or braking duration increase etc.

Lap times and # of laps the car is capable of are the measure of the viability of the trade offs.

Street users it makes no diff either way, go for the look you like.

The center of mass of a tire wheel combination is in .... the center.( it better be or you've got bigger problems).

The polar moment of rotation of a tire/wheel combination ( about the center or spindle) can be calculted if you know the weights of both and make some easy assumptions about how it is distributed)

30 years ago, when I was a Mechanical Engineer I could make that calcultion. At this point I can only speak conceptually.