Lighter wheel/tire combos yield faster car acceleration, but how much? A quick search on this forum found someone saying 1 lb lighter wheels means 15 lbs is also saved from the rotational effect ..... not even close !!


------------------ Summary -----------------

A 1 lb weight reduction in the wheel/tire combo will net you a total of about 1.7 lbs saved (.7lb rotational). The absolute maximum total savings would be 2lbs, if all weight saved was ideally at the tire OD. A critical assumption is there is no change in the tire OD.

So the rule is 1.7 lbs net saving for each lb saved in the wheel/tire combo.

------------------ Analysis --------------------

The laws of physics rule here. Energy is needed to bring the wheel/tire mass up to speed (mph) and to spin it to the related rpm. Consider a lighter tire/wheel combo:

m = mass reduction
I = inertia reduction
w = rotational speed
v = car speed
r = tire radius
E = total energy saved by mass reduction "m"
^2 = squared

E = 1/2 m v^2 + 1/2 I w^2

E = E(speed) + E(rotation)

Rotary Inertia is the sum of each bit of mass times it's radius squared. If all the mass reduction is at the tire OD (the theoretical but not practical limit), the inertia reduction is the maximum possible value:

I = r^2 m

The relation between car speed and tire rpm:

v = r w

Combine 3 equations above:

E = 1/2 m v^2 + 1/2 (r^2 m) (v/r)^2

E = 1/2 m v^2 + 1/2 (m) (v)^2

E = 2 x E(speed) ... the 2X limit

So if you drop 10 lbs per corner, the net total weight savings is 4 x 17 = 68 lbs. For a 3700 lb car and driver, that's only a 1.8% change.

The main benefit of reducing wheel/tire or any unsprung weight is handling and comfort, by increasing the tires ability to keep good contact with the road. Total unsprung weight might be 80 lbs per corner, and 10 lbs would be a 13% change ... very significant.

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If just a 17" or 18" wheel is 10 lb lighter (reuse same tires), then the total net savings is about 13 lbs. The rotational part is 3 lbs.


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Where this analysis falls down is that it is not taking into account the rate of change of angular acceleration, only the rotational energy once the assembly is up to speed. Simply stated, the more acceleration available (horsepower and traction to support it) the more difference the reduction in rotating mass will improve performance. There is no constant that can be applied to all cars, so there is no "rule" that can be developed.

This is more than evident when doing chassis dyno tests. I've seen differences of 30HP (indicated) just by changing tire and wheels -- and this was only on a 450HP vehicle. This doesn't mean the engine gained 30HP, but the driveline losses were significantly reduced by going to a smaller/lighter assembly ONLY.

For low-powered street cars (14+ second 1/4 mile capability), the gain may be as little as you have described -- or even less. For high-powered cars or racing cars, the difference can be 5x or more greater. You must take in to account the energy require to spin up each of the four tire/wheel assemblies at the initial rate of angular acceleration and then at the new rate. It is a dynamic set of equations that requires integration as there are few constants. Since time is involved and can't be ignored.

Chris

 

The Energy method is valid for this problem. Regardless of how hard the acceleration is, it takes the same energy (rotation and translation) to bring the wheel/tire up to any fixed speed. Translation energy is integrated force x distance: high force values and low distance related to high acceleration, just the opposite for low acceleration.

Mr Martinez used the force-mass-acceleration method to evaluate the effect at audiworld:

http://www.audiworld.com/tech/wheel13.shtml

He came to the same conclusion. The acceleration variable dropped out in the analysis.

For your dyno run, I'm sure there was no big difference in the time to accelerate the different wheels. The hp difference you measured could be due to traction differences, and or different load loss due to hysterysis (heat loss).

 

OK, phrased differently, I will say the same amount of energy is consumed either way to get the car up to a certain speed. However, the car will get to the intended velocity sooner, which is what this is all about anyway! More energy is available to accelerate the car and less to the tire/wheel assembly. This results in greater acceleration no matter how you slice it.

Time cannot be factored out of the time equation (essentially an energy balance), just the torque equations. Take a quarter mile time, for example. You can't say that the kinetic energy of the car (plus the rotational energy of the on-board components) is the same if the car has a higher trap speed (higher velocity) after modification. In fact, you will find that the car usually burns more fuel after you have lightened it. Why? Not because there is less mass to haul down the track, but because higher speeds were reached. Time matters because velocity matters. It can only be factored out if you are not interested in distance, which is clearly not the case with motor vehicles.

Mr. Martinez's calculations ignore the energy balance, which is necessary to provide a real-world prediction. His equations, while factually correct, are written for a specific time slice and apply only instantaneously, not integrated over the whole acceleration event. That integration certainly takes time into account and, since angular acceleration is a squared term, the more change you make -- well, the more change you make!

I've been involved in this type of vehicle improvement for over 20 years as an engineer and tuner. I can say without hesitation that reducing rotating weight can make huge difference, even more if it is unsprung (although those benefits are different). I also know from both physics and from actual track testing that the more power on hand, the more difference the changes make. For a 6,000 lb. S-Class, don't expect much. But the quicker the car, the greater the positive effect of removing rotating weight. A small change on a top fuel dragster can make a significant difference in trap speed.

Chris

 

I said this in my 1st 10 words, 1st post.

I've seen energy-balance analysis of power plants, but not ET runs. Doesn't make sense to me, with a variable output engine with several shifts. Please favor me with a related link. Most of the details above are irrelevent, generally related to ET runs, which times are generally related in seconds to the (hp/weight)^.33

http://www.stealth316.com/2-calc-hp-et-mph.htm

Both he and I used the principles of dynamics & physics to determine the wheel/tire "polar mass moment of inertia" as a function of the wheel/tire mass. Just as the mass of the wheel/tire doesn't change due to speed or acceleration, neither does the polar mass moment of inertia. This is true however you choose to predict ET times.

Squared? Nope. related examples:

Torque = I x (ang acc'n), Force = Mass x Acc'n

What were you talking about? Wheels & tires are unsprung weight. And for 99+% of the people on this forum with manual trans's, a light flywheel (sprung mass) will help 0-60 or 1/4 mile times more than lighter wheels/tires.

If the wheels and tires are a significant % of the car weight, then changes in tire/wheel mass (dm), and the related change in polar moment of inertia (typically .7dm, 1.0 dm theoretical limit), would affect trap speed sigfnificantly.

I trust your experience a lot more than your knowledge of physics. Among other things, I did fully build an SCCA DP race engine, busting the rules by adding and tunning triple DCOE's to the I6. I can use a wrench, as well as an FEA program.

 

Theory/math is nice and all, but how does it effect real-world results?

Modified magazine did a test and found.........probably none at all:
http://www.modified.com/tech/modp-09...est/index.html

A 17.4# Volk RE30 and 18.4# SSR Type-F both had slower times than a 20.3# AME TM02 and a 20.8# 5Zigen FN01R-C (same tire, driver, track, and day).

I am curious if anyone has done any real-world tests of their own.

 

when considering rotational mass it also depends on where the mass is

if a large percentage of the mass is further from the center of rotation it will have a more significant effect.

light weight wheels are great for performance but, heavier wheels tend to offer more comfort and small sharp impacts are easier for the suspension manage as the heavier wheel will react slower. This dynamic is one reason AMG wheels are typically not very light

 

Squared? Yes.

The equation for angular kinetic energy: E(rot) = 1/2 * I(rot) x w^2

Where:
E = angular rotational energy
I = rotational mass moment of intertia
w = angular velocity

Of course they are, but I've done a lot of work with flywheels and clutches as well. Lightening them correctly can unleash quite a bit potential energy, but they are not sprung. Hence, the clarification to satisfy reasonable scrutiny.

An insult? Hmmm......

Not that I go to Wikipedia for my physics, but this one is just too easy:

http://en.wikipedia.org/wiki/Rotational_energy

Congratulations on your accomplishments!

 

With all due respect to Jay (he is a great guy and does an honest job, in my opinion), the magazines are notoriously under-budgeted for any realistic data gathering exercise. That test, while interesting, doesn't pass the laugh test as far as actual results are concerned. There are much better ways to arrive at rotational moment of inertia, but those weren't available for that test.

I have been involved in real-world testing. Some of those results were believable and some weren't, depending on conditions, repeatability, method of data collection, etc. The ones I've been involved with were for companies doing product development, so they are not public. The results almost always indicated lighter is better and less rotational inertia is better. Whether or not a change can be justified for a particular budget, well, that is a bit more subjective!

Chris

 

yes for ang velocity, as I said. The problem is you didn't initially say that. You said:

"That integration certainly takes time into account and, since angular acceleration is a squared term, the more change you make -- well, the more change you make!"

I'm still waiting to see your eq'n with (ang acc'n)-squared .

News flash: Flywheels ARE sprung weight .... rotating sprung weight. My lightened flywheel ( RX7 ) made significant improvements in acc'n in first 3 gears.

flywheel data
WT, Inertia -meas'd-
20.0 1.068 (OEM)
17.5 .733 (NEW)

No need to. All those equations were in my 1st post. Did you read it?

Thanks, but this is my favorite wheel design/analysis/test project:

Hed 3 Bike Wheel and Reviews

I designed it about 15 years ago and it's still Lance Armsrong's choise in TDF time-trials.

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And that was the point of my analysis. By looking at the limit ... all added weight on a wheel tire combo was applied at the largest radius ... the tire radius. In that (impossible) worst case, a 10 lb heavier combo got you an extra 10 lbs of mass based on just the inertia. I like to put a number to it, vs just "a more significant effect".

hmmmm .... for comfort would you want solid wheels of concrete, or wheels with no weight?

 

In the world of bicycle racing, wheels are replaced to save even 1-2 grams and even if the cost is over $2000 per wheel!

No one there argues about the benefits of lighter wheels whether in climbing the Alp d'Huez or a sprint finish.

 

Nothing like a mountain top finish, cat 1 or HC, in the TDF

 

From post #1, the rotational effective weight due to a 3 lb wheel weight difference is .3 x 3 = 1 lb .... ie negligible. My guess was that the slight 1/2 sec minimum variation in ET was due to production differences in the tires. It would have been interesting if they switched tires on the fastest and slowest wheels.

Great article on wheel fabrication. But the most significant test result for me was this:

"As the tires heated up after just one cold run, the change in rolling resistance was more than the difference between all the wheels."

Tires with innefficient structural designs will generate more heat, and may have more rolling resistance under load.

 

Great post guys. Didnt understand all of it but a good read while board off my *** in china.
thank you