Tire weights versus wheel weights

[Stretch]

I ran some calculations. I want to attempt to clear up something I often see, if I can:

QUOTE

I'm gonna reduce my unsprung weight by 50%. *That's the equivelant of taking 240lbs off the car.[/b]

Unsprung weight and moment of inertia are not the same thing. It's pretty easy to consider them the one and the same, or at least think of them as being directly proportional. They're not. I ran some numbers, and found the results somewhat surprising. It kind of deminished my excitement about lightweight rims as a means of making the car faster.

Lowering your unsprung weight helps the suspension react to bumps more quickly and easily.

Lowering your inertia helps braking and acceleration, and is what the "equivelant of dropping xxxlbs off the car" figures come from.

I tried calculating rotational inertia. While I don't think I did it correctly, I came up with about 2-3 times more inertia PER POUND being generated by the TIRE than the wheel, depending on the size. The reason for this is that inertia goes up exponetially, not linearly, as its diameter increases. Thus, a 3-lb reduction in tire weight is like an 9lb reduction in wheel weight. Since tires are generally 25-75% heavier than the wheels they are on, you can thus figure that sometimes over 80% of the total inertia is generated by the tire, not the wheel.

You know how people say reducing unsprung wheel weight by 1lb is like reducing your sprung weight by 4 or 8lbs? Absolute rubbish- it only depends where you lose it from, and that's not easily calculated. You could run Falken Azenis on your 13lb rims and still have more inertia than on the 10lbs heavier OEM wheels running just 3.5lb lighter Toyo's.

Though, the 13lb Azenis setup would be lighter overall and still handle better due to less unsprung weight.

Continental tires are also pretty lightweight. Another option is to run a slightly smaller diameter. Wider tires are heavier, too, but going skinnier can sacrifice grip.

This is also the reason why 16" wheels are faster than 18" wheels. Even at the SAME overall weight (and while 18lbs is a very heavy 16" wheel, that's about what most pricey forged 18" wheels are), the 18" wheel will have about 25% more inertia... and that's if they're the same weight.

Are my calculations right? Someone correct me if any of this is wrong... here's some equations:
http://www.physics.uoguelph.ca/tutorials/t...ue.inertia.html
http://www.speedworx.com/cgi-local/shop.pl...cs_26_wheel.htm

[ashutoshsm]

Well - my interpretation of how reduced unsprung weight helps a car's handling is more in terms of how much easier it is to steer the car and how easily it reacts to inputs.

Combine that with good rubber, and the handling improves substantially.

I don't know how much total unsprung weight there is in our cars - what qualifies as unsprung? Other than wheels and tires? But I'm pretty sure 5 lbs less on each corner would be a substantial percentage of the total and akin to 'a lighter car' because it would be more nimble.

Basically, the concept is - if you're reducing x lbs of weight from the car with the aim being to make it handle better and be more responsive, an identical effect can be achieved by reducing x/4 (or something similar) lbs from the unsprung weight alone.

Again, you can nitpick and say reduing weight from positions higher than the Center of Gravity of the car will be more effective, and a bunch more stuff - but the fact remains, its more effective (pound for pound) to reduce the unsprung weight.

[Stretch]

QUOTE

Originally posted by ashutoshsm


* * * * * * Well - my interpretation of how reduced unsprung weight helps a car's handling is more in terms of how much easier it is to steer the car and how easily it reacts to inputs.

Combine that with good rubber, and the handling improves substantially.

I don't know how much total unsprung weight there is in our cars - what qualifies as unsprung? Other than wheels and tires?[/b]

A-arms, brake rotors and calipers, shock shafts.

QUOTE

But I'm pretty sure 5 lbs less on each corner would be a substantial percentage of the total and akin to 'a lighter car' because it would be more nimble.[/b]

I don't see why reducing unsprung weight would make a car more nimble any more than reducing sprung weight would. Turn-in would be affected by sidewall stiffness...

[crossbow]

Steve,

I guess the best way for you to solve this argument, is to swap tires with significantly different unsprung weights.

Remember we have the G-tech pro...this can be analyzed and looked at with actual data.

If reducing the unsprung weight by 50% (about 50 lbs) drops .1 seconds off the 1/4 mile time, then its about equiv to 100 lbs of static weight.

We don't have to debate this. Lets just collect data and analyze it from a performance standpoint.

Acceleration and Braking.

Handling will be seen at Autox.

Nuff said.

[ashutoshsm]

Ummm - honestly, I could care less about how much the 1/4 mile times drop, because I'm not looking for an "acceleration-equivalency-of-unsprung-weight-with-sprung-weight" but a handling one :)

Also, I wouldn't trust Steve (or any of us) to be consistent enough to a 1/4 mile anyway for our purposes :)

Now, autocrossing with different wheels and tires and comparing results - that is a sweet idea. I think, with all of us (you guys - I'm out for the day) working together, and your jacks and stands, we can swap tires/wheels this Sunday between runs. You guys should see if you can find someone who'll provide you a swappable set of wheels and tires!

[crossbow]

Ashu,

Aye but the gtech also does 0-60 and 60-0.

So you'd be able to see accel differences and braking differences.

Very useful tool.

I care about 1/4 mile time, because that indicates a faster takeoff :).

[tireswap]

Stretch is totally correct though that there is no general.. 1lb = 10lb static... it varies. The ratio is about 1:1 towards the center of the wheel and it increases as you move out... but most of the time, the weight is on the outer portion of the wheel...

This is why autocrossers SWEAR by Hoosiers. They use fiberglass belts instead of steel for a 2-6lb savings PER tire... that coupled with a light wheel and youre talking huge numbers for reduced weight.

[tireswap]

Calculations: http://www.the-welters.com/racing/rotational.xls

"It's even better than double; about 2.5 times. The rule of thumb is
to multiply what you took off each wheel by 10."

[tireswap]

Another good read: http://www.sportcompactcarweb.com/editors/...hnobabble/inde
x.html

">Rotational Inertia
>The rotational inertia topic was so big, it took me two months (June and
>August '99) to get it sorted out. Here's the deal: There is this rule of
>thumb among racers that adding weight to something that rotates is far
>more detrimental to performance than if you add it to the body of the car.
>This is absolutely true, and by bumbling through some physics, and after
>slipping and falling on a radian, I managed to get a few formulas figured
>out that could tell you just how much worse.
>
>Any moving object has kinetic energy, as does an object sitting in place
>and rotating. An object that is both rotating and moving (like a rolling
>wheel, for example), has kinetic energy from both, meaning that
>accelerating or decelerating that rolling object will take more power than
>one that is just sliding along. How much more power is the question.
>
>The answer, it turns out, depends on how the weight is distributed on the
>wheel. An extra pound on the tread of a rolling tire has as much kinetic
>energy as 2 lbs on the floor of the car. As you move toward the center of
>the wheel, the rotational effect drops until, at the center, a pound is
>just a pound. The formula I derived to determine the exact relationship
>between weight on a wheel and weight in the car isn't worth repeating here
>for one simple reason. It requires that you know the moment of inertia of
>the wheel, and measuring that is virtually impossible. What you need to
>know is that changing to tires that are 1 lb heavier will effectively add
>8 lbs to the car (four tires, remember) and that adding a pound to the
>wheels will effectively add somewhere around 6 lbs to the car.
>
>That only considers acceleration and braking; handling is dramatically
>affected by unsprung weight as well, but no simple formula is going to
>tell you how big the effect is.
"

[tireswap]

Finally... from another forum:

------------------------
Geek answer (and hope the equations dont get garbled):

Dave's right, kinetic energy is the way to figure this out, the equation is
:

0.5 * (M * V^2 + I * W^2) : I=moment of inertia W=angular velocity, V =
speed of car
I is unknown, but is modeled as X * M * (Rw)^2 , with X varying from 0->1,
Rw = radius of wheel. With some simple math W = V / Rt , Rt = radius of
tire....

0.5 * (M * V^2 + X * M * (Rw)^2 * V^2/ (Rt)^2 ) is the equation for energy,
simplifying,

0.5 * M * V^2 * (1 + X (Rw/Rt)^2)

A weight bolted to the car has kinetic enegy 0.5 * M * V^2,
so you can see this (1 + X * (Rw/Rt)^2) is the above factor I mention in the
handwaving answer. Call this F = (1 + X * (Rw/Rt)^2)

An exmaple : 205/50/15 , Rw = 7.5 Rt ~=11.5(23inch tire guess), and the only
unknown is X. Guessing X is dangerous - if ALL the mass of the wheel were at
90% of radius X=0.8 (seems conservative). For the 205/50/15 (X=0.8) F=1.34
every pound saved on the wheel is like taking 1.34 lbs out of the chassis.
This is substantially different than the 2 that Dave calculated. For
handling, the benefits in unsprung weight are not so easy to calculate, as
energy isnt the correct analysis tool... how much faster a car is with X lbs
removed is also hard to calculate (which is what John wanted to know). A
full simulation is the only way to be accurate.

Saving weight on tires is far more effective, you dont pay the (Rw/Rt)^ 2
factor, and the tire is heavier to start with (at least for my car - not my
kart!)

Dan Cyr
F125 #72 (when i'm not doing physics)