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Mmmm.. very interesting thread.. my question is..Light weight, good width, 17" rim, and tire = how many lbs? if you can shave 15lbs off of each tire.. then we might be talking.. from 52 to 37 I think would be worth doing.. i haven't even looked into rim weight yet to see how low I can go. But i always found that logic that the weight of the tire affected performance that much to be a little fishy.. although the big diameter-20s I can definetly see.
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I'd have to see the science behind that. There is absolutely no doubt in my mind that I dropped time in the 1/4 based on a wheel swap. Just sitching from the 18s to the 17s shaved almost 2 tenths off of my ET. True, you won't notice that kind of difference in the seat of your pants, but bigger wheels definitely hurt my car's performance.
I've got all the equations, but not enough time to write them out as a derivation tonight. But basically everything boils down to two basic equations of motion.
[linear acceleration] = [net force] / [mass]
[rotational acceleration] = [torque] / [rotational moment of inertia]
car linear and wheel/tire rotational accelerations are related through [effective tire rolling circumference]
a good enough approximation of tire and wheel MOI for these comparative purposes can be constructed from a couple of basic mass MOI equations
I don't doubt that you shaved that much time, but in order to determine how much of that was due to wheel/tire weight and how much to slight diameter differences I'd need more information. Never mind if the 17's were a softer compound and gave you a noticeably quicker short time.
I've got all the equations, but not enough time to write them out as a derivation tonight. But basically everything boils down to two basic equations of motion.
[linear acceleration] = [net force] / [mass]
[rotational acceleration] = [torque] / [rotational moment of inertia]
car linear and wheel/tire rotational accelerations are related through [effective tire rolling circumference]
a good enough approximation of tire and wheel MOI for these comparative purposes can be constructed from a couple of basic mass MOI equations
I don't doubt that you shaved that much time, but in order to determine how much of that was due to wheel/tire weight and how much to slight diameter differences I'd need more information. Never mind if the 17's were a softer compound and gave you a noticeably quicker short time.
Norm
Actually, if you carry out those equations you'll notice a NOTICEABLE difference in vehicle acceleration.
Let's first take the mass moment of inertia of a perfect disk: m*r^2. Now if you can cut the mass by 30%, and radius by 10%, you'll end up with only 57% of the origional inertia.
If you want to go more precise: the inertia is integration of (r^2 dm). Which means the mass furthest away from center - the tire, makes a huge difference. If you can cut a tire's mass by 30%, the wheel by 30%, and radius by 10%,the actual inertia would be even less than 57% of origional. On top of all this you loose a little linear mass as well.
Now if you want the actual numbers, you'll have to jam all the equations together by relatingtorque and linear forcethrough wheel raius like you mentioned. But I'll bet with a super light track wheel / tire setup, you can cut up to 4 - 5 tenth on 0-60 and 2 - 3 in the 1/4 mile.
There's a reason LeMans prototypes don't roll on 24" Dubz, and it's not just because of regulations...
My simulation divides the wheel into a disc (wheel center) plus a ring (barrel). Same for the tire (sidewalls and tread). Obviously I have made a couple of assumptions regarding mass distribution, but I feel that it is moreconsistent to distribute mass based on radial and width dimensions than to try to guess what a good overall mean radius is in either case. You are absolutely correct about the tires being the relatively bigger effect - the rotational inertia of a 25 lb 235/50-18 is about 2.5 times that of a 25 lb 18 x 8.5 wheel. So, roughly, one lb of tire = 2.5 lbs of wheel, at least in this case. I guess the guys shaving a couple of lbs of tread off ofeach tire for auto-X have more in mind than reducing tread squirm and marginally improving the effective gearing.
What happens is you have some of the engine torque being "bled off" in rotationally accelerating the things that rotate. What is left goes into forward traction force. Say you have 260 ft-lbs available at the flywheel after deducting whatever torque is required to spin up the flywheel/crank/balancer. If 10 ft-lbs of engine torque is required to rotationally accelerate all four wheels at a rate consistent with the vehicle acceleration (close enough to the numbers I get in the spreadsheet), that leaves 250 for linear acceleration. Assuming that you can get down to 57% wheel/tire inertia, that means that the distribution of torque gets close to 5.7 (rotational) and 254.3 (linear). That is not much of a change, though the clocks will certainly pick it up, and there is no question in my mind that this is the kind of thing that can turn a "photo finish" loss into a win.
I will point out that a 10% diameter reduction will be worth more in terms of effective overall gearing than for its contribution to lower rotational inertia.
If anyone is interested,PM me with an e-mail address (or e-mail me directly) andI will send out a copy of the spreadsheet. The version thatI have been using here is 125k or so (see the embedded thumbnail - if you see a red "X", click on it anyway and the pic should show up) Two other uploaded imagesthat do not display are not very legible but something is refusing to let me delete them, and I am editing out all those annoying apostrophes. Good thing I am an early riser on the East Coast I guess.
One thing about all this is the additional weight is not ALL at the furthest most outter edge of tire. It is'distributed' throughout the wheel. How much is actually in the hub nearest the center of wheel?This will reduce the effect of the rotating mass argument. So I think some of the calculations of how much effect the weight has is specious (I always wanted to use that word in a sentence ).
Just my $.02 and may have missed something so please don't chop a Jazzer's head off if so
It is kind of buried in the text where OICW mentions "the inertia is integration of (r^2 dm)". There are simplified formulas for a number of common shapes that are much easier to use, but they are all based on an integration.
This integration combines both the mass and radius effects into a single quantity, and is computed for every point over the radial distance from the axle center (radius = zero) out to the outermost edge and added up into a total amount. So an ounce of material out at the edge (such as wheel flanges or tire treads) really does compute to have a much greater rotational inertia effect than an ounce of material locatedin near the wheel bolt circle does.
Don"t feel bad - integration is a calculus topic. IOW,not clear to a lot of folks to begin with and not something that most of the people who do (did?) understand it use on a daily basis.
I went all the way through statistics and quantitative methods II in college, which was the most difficult math at Loyola University when I attended, with straight As, and I have no idea how to keep up with what you guys are talking about, lol. Then again, I know longer have the drive to try and understand it either, lol.
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RE: Tire/Wheel Combo Weight
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