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Tire weights. Discussion on Unsprung Weight, Moment of Inertia... [LONG!]

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Old 04-08-2002, 12:46 PM
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Default Tire weights. Discussion on Unsprung Weight, Moment of Inertia... [LONG!]

A thread related to wheel aesthetics on another board ended up turning into a physics discussion on wheel and tire choices (a good turn of events I think). I thought it would be appropriate to pose the questions that I couldn't answer here for you guys to help out in the discussion. We've discussed the moment of inertia (rotational mass) and unsprung weight topics as far as wheels alone are considered, but were curious as to how these apply specifically to tires. If theoretically, you had a 15" tire and a 16" tire and the only way they differ is their aspect ratio and where the weight is placed on the tire- tire weight, width, contact patch, tire compound, tire construction are all the same - what effect would this have on the moment of inertia?

Here is what has been discussed so far and if I have made any errors in my side of the discussion, please feel free to correct me. I am by no means an expert, I just am always eager to learn.

Our starting discussion, discussing wheel weights:
Unsprung weight and rotating mass has a huge effect on how well your tire can stay in contact with the road, how easily you can rotate the tires from a standing stop, and how well you can stop your vehicle.

Everyone has their own priorities but changing from a 15.5 LB 14" wheel to a 20 LB 17" wheel is certainly not a performance enhancement. The car won't laterally accelerate as well, brake as well, or accelerate in a straight line as well as it did with 14" wheels, everything else held equal.
Also, theoretically, even if two wheels were identical in every single way except for diameter, the larger diameter wheel would ALWAYS be harder to turn than a smaller wheel. This means that even though they weigh the same, look the same, and have the same metalurgy, a bigger wheel will still ALWAYS be harder to turn.
I found the following quote to say a lot of things I wanted to convey, but was to lazy to fully type out. I also wanted to add that for performance alone, your primary concerns for wheel choice should be brake cooling, choosing the smallest wheels that will go over your brakes, and strength vs. lightness.

"By: James Rogerson

Noriel, et. al. Here's the skinny in semi-layman terms.
In rotational motion it is not mass alone that counts but mass times the square of the distance from the point (or line) about which the rotation is taking place. The body (wheel and tire) has an AVERAGE mass (m) to radius squared (r^2). This average mr^2 is a point called the 'moment of inertia'. The torque required to stop (or start) the rotating object in a given period of time depends not upon the mass of the object but its moment of inertia. The value of the moment of inertia depends on the distribution of the mass and can be changed without altering the total mass. Practical application: The figure skater spins slowly with arms extended, yet speeds up when their arms are brought close to the body. The rotational energy is the same, yet the moment of Inertia is increased and decreased. Simple, no? If more
is required, let me suggest reading on angular momentum and rotational motion. A good book for the non technical (guys like me) is 'Understanding Physics' by Isaac Asimov (yeah, the same). I've tried to paraphrase his discussion on this subject without the formulae and attendant squiggley lines."
This was post that started this thread, and as I haven't heard it discussed here I that it would be appropriate to post it here.

I'm not disagreeing, but nobody has ever factored in the TIRE into this whole equation. Anyone care to elaborate on the effects of the outer part of the rim, the tire, compensating for the smaller inner diameter? I mean sure it sounds perfect saying a lighter 15" rim is way better than a light 17" rim (let alone a heavy 17"), but once you put the tire on the end, wouldn't the 15" tire has more mass than a 17" tire? And isn't the most influencial weight on a rotational system is the weight furthest away from the axis of rotation thus almost cancelling out all factors when choosing a smaller wheel setup?
Here is my initial answer, but it still leaves some things to be answered.
Well, let's use an example. A 205-50-15 tire mounted on a 15"x7" wheel as opposed to a 205-40-17 tire mounted on a 17"x7" wheel. Let's assume the differences in wheel weight and construction are negligible.

For the 15" wheel you would have a 102.5mm sidewall height which converts to 4.04" sidewall height. Add that onto the 15" wheel diameter and you have a total outer diameter of 19.04".

For the 17" wheel you would have a 82mm sidewall height which converts to 3.23" sidewall height. Add that onto the 17" wheel diameter and you have a total outer diameter of 20.23".

For the sake of comparison I'll add the stock wheel and tire size of 195-60-14. For a stock 14" wheel you would have a 117mm sidewall height which converts to 4.61" sidewall height. Add that onto the 14" wheel diameter and you have a total outer diameter of 18.61".

Using the 14" stock configuration as our base you have 2.31% increase in outer diameter for the 205-50-15 tire and a 8.70% increase in outer diameter for the 205-40-17 tire. This means that you have material further away from the axis which will increase your moment of inertia without considering any differences between tires of those particular sizes.

As for bringing tire weight into the equation, I have found no tire weights to make calculations for among similar tires. With tire weight though, more has to be taken into consideration because bigger tread blocks and stiffer sidewalls will make a tire heavier, but will increase your ultimate grip. It depends what you theorize will make your car faster, less unsprung weight or a higher CF (Bigger tread blocks typically mean more contact patch) with more predictible transient response (Less squirm with bigger tread blocks, and stiffer sidewalls). On a theoretical level, I would have to say I am not qualified to argue that point because there are too many factors involved. I would agree that they should be taken into consideration since most manufacturers use steel belts which equate to being heavy. I think Hoosier uses fiberglass in most of its race tires.


[Modified by mojoGSR92, 4:55 PM 4/8/2002]
Old 04-08-2002, 01:16 PM
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Default Re: Tire weights. Discussion on Unsprung Weight, Moment of Inertia... [LONG!] (mojoGSR92)

This was post that started this thread, and as I haven't heard it discussed here I that it would be appropriate to post it here.

I'm not disagreeing, but nobody has ever factored in the TIRE into this whole equation. Anyone care to elaborate on the effects of the outer part of the rim, the tire, compensating for the smaller inner diameter? I mean sure it sounds perfect saying a lighter 15" rim is way better than a light 17" rim (let alone a heavy 17"), but once you put the tire on the end, wouldn't the 15" tire has more mass than a 17" tire? And isn't the most influencial weight on a rotational system is the weight furthest away from the axis of rotation thus almost cancelling out all factors when choosing a smaller wheel setup?

Here is my initial answer, but it still leaves some things to be answered.

Well, let's use an example. A 205-50-15 tire mounted on a 15"x7" wheel as opposed to a 205-40-17 tire mounted on a 17"x7" wheel. Let's assume the differences in wheel weight and construction are negligible.

For the 15" wheel you would have a 102.5mm sidewall height which converts to 4.04" sidewall height. Add that onto the 15" wheel diameter and you have a total outer diameter of 19.04".

For the 17" wheel you would have a 82mm sidewall height which converts to 3.23" sidewall height. Add that onto the 17" wheel diameter and you have a total outer diameter of 20.23".

For the sake of comparison I'll add the stock wheel and tire size of 195-60-14. For a stock 14" wheel you would have a 117mm sidewall height which converts to 4.61" sidewall height. Add that onto the 14" wheel diameter and you have a total outer diameter of 18.61".

Using the 14" stock configuration as our base you have 2.31% increase in outer diameter for the 205-50-15 tire and a 8.70% increase in outer diameter for the 205-40-17 tire. This means that you have material further away from the axis which will increase your moment of inertia without considering any differences between tires of those particular sizes.

As for bringing tire weight into the equation, I have found no tire weights to make calculations for among similar tires. With tire weight though, more has to be taken into consideration because bigger tread blocks and stiffer sidewalls will make a tire heavier, but will increase your ultimate grip. It depends what you theorize will make your car faster, less unsprung weight or a higher CF (Bigger tread blocks typically mean more contact patch) with more predictible transient response (Less squirm with bigger tread blocks, and stiffer sidewalls). On a theoretical level, I would have to say I am not qualified to argue that point because there are too many factors involved. I would agree that they should be taken into consideration since most manufacturers use steel belts which equate to being heavy. I think Hoosier uses fiberglass in most of its race tires.
I've only take AP physics C mechanics only, but some of the basic concepts do apply.

While it's true that a smaller wheel would mean a heavier tire, I'd think that overall the smaller wheel/larger tire will still perform better.

All things kept equal, including tire construction and diameter, then the only diff between a 15" wheel/tire and a 14" wheel/tire would be the 1" of sidewall/tire on the 14" setup where metal would go on the 15" wheel setup. I'm guessing that the 1" of tire is lighter than 1" of metal in its place, so then that would make the 14" wheel/tire have a smaller moment of inertia.

When you change the diameter of the wheel, not only do you change the moment of inertia, you change your final drive ratio slightly, smaller diameter = increased final drive, which increases the effects of gearing. It makes it hard to compare unless everything is kept equal... but in the real world, its hard to find tire sizes that have near equal diameters.
Old 04-08-2002, 01:30 PM
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Default Re: Tire weights. Discussion on Unsprung Weight, Moment of Inertia... [LONG!] (TypeSH)

All things kept equal, including tire construction and diameter, then the only diff between a 15" wheel/tire and a 14" wheel/tire would be the 1" of sidewall/tire on the 14" setup where metal would go on the 15" wheel setup. I'm guessing that the 1" of tire is lighter than 1" of metal in its place, so then that would make the 14" wheel/tire have a smaller moment of inertia.
This is what I'm getting at, but I've never actually seen it proved with numbers. It's easy to prove wheel weights with theoretical numbers, but proving tire weights and where that weight is and how it will effect the moment of inertia is a much harder thing to illustrate. Tires are much more complicated in this way.

When you change the diameter of the wheel, not only do you change the moment of inertia, you change your final drive ratio slightly, smaller diameter = increased final drive, which increases the effects of gearing. It makes it hard to compare unless everything is kept equal... but in the real world, its hard to find tire sizes that have near equal diameters.
For the sake of this discussion and its center on unsprung weight and moment of inertia, let us say that changing your final drive out so that your total gearing will always remain the same as stock will not be an issue. This way you will always have the same total gearing and the only physical concepts you are dealing with are unsprung weight and moment of inertia.
Old 04-08-2002, 01:36 PM
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Default Re: Tire weights. Discussion on Unsprung Weight, Moment of Inertia... [LONG!] (mojoGSR92)

Unless your interest in primarily academic the subject is pretty much a waste of time. The difference between a couple of pounds and an inch do not amount to anything practical on a road course.

Scott, who asks not to be flamed on the undeniable fundamental physics involved which he is not denying.....I said "practical"...
Old 04-08-2002, 01:52 PM
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Default Re: Tire weights. Discussion on Unsprung Weight, Moment of Inertia... [LONG!] (RR98ITR)

I think that depends on who is trying to extract performance from their vehicle. If it's a professional racer then saving weight in any area (because it all ads up) is going to be sought after. If it's a club racer then maybe you aren't so interested. But then again, I'm a club racer and I'm extremely interested in this topic. Anything I can do to make the car perform better. . .
Old 04-08-2002, 01:54 PM
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Default Re: Tire weights. Discussion on Unsprung Weight, Moment of Inertia... [LONG!] (RR98ITR)

Unless your interest in primarily academic the subject is pretty much a waste of time.
This is primarily an adademic topic, hence all of the discussion in theoretical terms. I'm just curious because I've only seen total conceptual arguments on unsprung weight and moment of inertia, but never one targeted only at tires.
Old 04-08-2002, 06:25 PM
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Default Re: Tire weights. Discussion on Unsprung Weight, Moment of Inertia... [LONG!] (mojoGSR92)

As all of you know the worst kind of rotational mass is the mass furthest from the axis point. A 17" wheel has a big portion of its weight in the form of the rim 8.5"s from the axis point. A 14" wheel has the portion of it's weight 7" from the axis point. Therefore a 17" wheel will have both the tire tread and the rim right near the outer diameter of the circle while the 14" rim w/ larger sidewall (heavier) tire will likely not have the rotational mass due to the fact that the rim will be nearer the axis. The rim being nearer the axis will compensate for the heavier tire.

I've never taken a physics class in my life, just stating what seems logical to me. Let me know if I'm smoking crack.

Leif


[Modified by leifintegra, 3:27 AM 4/9/2002]
Old 04-08-2002, 06:48 PM
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Default Re: Tire weights. Discussion on Unsprung Weight, Moment of Inertia... [LONG!] (leifintegra)

I haven't seen anything here that is outrageous but the one critical piece of data that is missing is an actual measurement of the moment of inertia of the options available. I think that Leif's logic is sound but am not able to convince myself that 14" or 17" wheels have a obviously greater moment of interia. Remember that the spokes have to be longer to get that "rim" out farther, and they have to be considered. A 1* "slice" of a tire with a short sidewall has less mass and a lower moment than one with taller sidewalls. What can we count on? Holding all other variables constant...

* Lighter is always going to be better than heavier
* Smaller outside diameter package is going to favorably affect drive ratio and braking leverage
* Shorter sidewalls are generally going going to result in decreased tire slip angles and quicker transitions
* None of these variables EVER acts alone, so my presumption sucks warm, tire-flavored compressed air - they are always interdependent so a gain in one may be offset by a loss somewhere else...

Kirk

Who used to live in Seattle and misses Pagliacci pizza...

Old 04-08-2002, 08:00 PM
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Default Re: Tire weights. Discussion on Unsprung Weight, Moment of Inertia... [LONG!] (mojoGSR92)

OK. I think I am going to present this whole argument to one of my mechanical engineering professors.

IMO, there is a lot that has to be calculated, and the only realistic way to calculate everything would be to input a detailed model of a wheel and tire into a program like Katia and see the outcome.

You could either assume the model in 2d or 3d. 3d would obviously be a lot more difficult, but more accurate none the less. Calculating the design of the actual wheel will give us an equation for the moment of inertia throught the section of spokes. Then, you'll have to know the density of the alloy, and then factor in the actual cylindrical shape of the outer rim in full diameter (7" for example). Now you have to find the density of rubber, and calculate weight from the beginning of the sidewill till the top of the sidewall just below the contact patch & belts. Then you'd need to calculate the density of the contact area (which is probably THE heaviest part of the whole wheel/tire combo and which is also at the furthest point from the axis of rotation). Once you have all this data, you can than literally calculate the actual value for the moment of inertia.

Now obviously, this will be quite tricky without having accurate information to work with. Therefore approximations must be made. I believe I still have some old 205/40-17 yoko A520's lying around I could weigh for fun and we can compare it with the weight of a wheel.

I did however also find this site http://www.miata.net/faq/tire_weights.html with references to the weights of several tires. I'm getting a little tired right now so I think I am gonna go for a walk. Let someone else critisize my post!
Old 04-09-2002, 06:32 AM
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Default Re: Tire weights. Discussion on Unsprung Weight, Moment of Inertia... [LONG!] (teg92)

On a sidenote, does anyone know of a good website for finding tire weights? There are all sorts of wheel weight sites, but I have yet to see an indexed tire weight site. It would be really nice to have around.
Old 04-09-2002, 08:17 AM
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Default Re: Tire weights. Discussion on Unsprung Weight, Moment of Inertia... [LONG!] (mojoGSR92)

Well I've pretty much pondered on it and come to the simple conclusions that, yes given a a comparable 14" or 15" setup with the exact same overall weight as a 17" combination with identical overall outer diameters, the 14" or 15" will have less moment of inertia. Why? "Its soooooo simpow...."

We can all agree the heaviest part of a tire is its tread, which no matter what size rim, will always be more or less located the same distance from the axis, hence no inertia savings there. But where is the heaviest part of a rim? Well, its the cylindrical outer circle, right? Well neglecting the actual weight of the wheel, no matter what, bringing that closer to the center will clearly reduce the moment of inertia, and the increased amounts of sidewall will pretty much have negligable effects. Yes the overall weight may still be comparable to a 17" setup, but the most important weight distrubution is completely different.

This should pretty much finish it off. Smaller = better and the influence that the increased tire size has on the overall moment of inertia is pretty much negligable since the size of sidewalls really have no impact.
Old 04-09-2002, 08:26 AM
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Default Re: Tire weights. Discussion on Unsprung Weight, Moment of Inertia... [LONG!] (mojoGSR92)


For the 15" wheel you would have a 102.5mm sidewall height which converts to 4.04" sidewall height. Add that onto the 15" wheel diameter and you have a total outer diameter of 19.04".

For the 17" wheel you would have a 82mm sidewall height which converts to 3.23" sidewall height. Add that onto the 17" wheel diameter and you have a total outer diameter of 20.23".

For the sake of comparison I'll add the stock wheel and tire size of 195-60-14. For a stock 14" wheel you would have a 117mm sidewall height which converts to 4.61" sidewall height. Add that onto the 14" wheel diameter and you have a total outer diameter of 18.61".

[Modified by mojoGSR92, 4:55 PM 4/8/2002]
you have to add two tire sidewalls to the wheel size to get total diameter. so:

14" = 23.22"
15" = 23.08" = 0.61% smaller
17" = 23.46" = 1.03% bigger


I have also been wishing tire companies would publish the tire weight so true wheel/tire package weights could be compared.

Phil

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