So, in this other thread, there was a discussion of how much faster you go with lighter wheels and tires. I did some math (always dangerous) and came up with some interesting numbers...

first off, the assumptions.

1) That the tire has most (all for my calculations) of it's mass at the radius of the tread. I made this 12".

2) That the wheel can be modeled as half the mass in the rim, and half in the spokes. And that the spokes are a disk. I think this isn't really true for really light wheels like the SSR Comps, but what do you expect for free! R rim and spoke = 9"

3) A Mini weighs 2800 lbs, less the weight saved in reducing the mass of the tires and wheels. Close enough!

4) I don't know the rest of the rotating mass of the other internals in the car, so I doubled the rotational contributions of the stock wheels and tires. I think this is an overestimate. But I kept the contribution the same, so I didn't double count the rotational benenfit!

So, what did I learn?

S-lites and Run-flats take about 4.44% of the work done by the motor (or brakes).........

If you go to 20 lb tires, and 17 lb wheels, you need to do .87% less work to get to any given speed (neglecting wind resistance, so no comments about how minis should be able to go the speed of light!)

To get the same benefit from stripping your interior, you have to take 1.61 times the weight out!

Seeing as the time in a 0-60 or 1/4 mile is relatively short and the delta small, you can say that you should be 0.87% faster to either of these speeds with the lighter tires and wheels. For a 7 second 0-60, that's a 0.061 second improvement. Interrestingly, going from 17 lb wheels to 13.5 lb wheels only give about .15% improvement, but this is due to the decreased radius contributing less to overall rotational moment. In English, lighter tires do more than lighter wheels. (duh!)

This is a bit less than I expected, but about a tenth of a second should be a good guide for the eye.

There will be other effects too, as a heavier tread will lift the car more as the rotational speed increases, but I don't even know if this matters for street tires. Sure does for dragsters though!

I've also ignored the fact that different amounts of energy go into the deformation of the rubber in the treads and the like. But I think that's probably small compared to rotational effects.

For what it's worth.....

Matt

 

THAT I agree with! I don't buy .3 or .4 seconds or 400 lbs. or other non-sense! 1/10 is about what I estimated, a car length. Not a big deal at ALL on the street by any means.

 

I didn't really care about the acceleration gain going to SSR Comps.

I was more concerned about the braking efficiency. From R90's to
Comps is night and day on braking... and that is worth the $2k or
watever i spent on the wheel/tire set.

 

And I haven't figured it out yet. Brakes just convert the kinetic energy to heat. So, to first order, any brake combo that has the thermal mass should do just fine. The issue will come with heat build up in the disc as you do repeated braking. So it's not an energy dissipation thing.

My best guess here is that the lessened unsprug weight allows for a more efficient contact patch, and it will sustain higher forces without sliding. But that would just be a guess.

Also, all the stuff above doesn't speak to handling improvements etc with less unsprung weight. I'm sure there's additional grip to be had that will imrpove track times more than the improvements in acceleration.....

Matt

 

Matt,

Did you calculate using moment of inertia equation?

I know modeling the wheel and tire is not a simple matter. The most trivial case for moment of inertia is either a uniform disc or a point mass at radius R and the wheel/tire combo is neither. I would say the mass concentration tends to be towards the outer circumference which is worst for angular acceleration (and deceleration). Excluding the rotational mass the weight of the car in linear acceleration the equation is F = MA where F is force, M is mass of the vehicle, and A is the linear acceleration. This is excluding the force needs to overcomes the rotational inertia of every part of the drive train that rotates. This includes the crank, frywheel, clutch, transmission gears, drive shafts, the brake rotors, and the wheel/tire combo.

For the wheel/tire combo the angular analog for mass is moment of inertia I = mr^2 where I is the moment of inertia, m is the point mass at radius r. For a uniform disc I = (mr^2)/2. The wheel/tire combo is somewhere between these two.

The significance of the wheel/tire combo for heavy vs light combo depends on their contributition to other total angular inertia in the entire drive train. This is a very complex calculation which I won't attempt.

On the other hand the difference observed on the non-braking dyno shows that heavy vs light wheels can be quite significant. Non-braking dyno is a dyno which relies on calculating the torque from the acceleration by the engine on the load which is the moment of inertia of the rollers.


Enough hand waving I hope this gets the idea across.

 

Besides the benefits in acceleration and braking lighter wheel/tire include the effect of reduced unsprung weight on handling in rough road surface. The reduced overall mass of the tire/wheel/suspension parts allows the tire to maintain contact patch as it tracks the hills and valleys of the rough surface. The most obvious comparision is a car with live axle (they should call it dead axle instead) vs one with independent rear suspension like the Mini. This is the same reason why lighter wheels improves ride quality also. Lighter wheel/tire also reduces energy loss but we are splitting hairs.

 

I'm running SSR Comps (12.8 # each) but I like the SSR GT7 (16.3# each) for a difference of 3.5# each or a total of 14#. Alex at Tire Rack said the weight difference is like carrying 60# in your MINI at all times.

Needless to say I'm still running SSR Comps.

Earl

 

the ratio is between 1.5 and 2.0; typcially 1.6 to 1.8.

on a mcs, you can improve .2 0-60; forget that equivalent 400 lb equivalent lunacy


http://www.mini2.com/forum/showthread.php?t=21269

 

Hey everyone,

I just read something interesting in the current Autoweek magazine on page 12 of the SuperTuners section -- it's an advertisement for Center Line wheels. They are touting their new manufacturing process that produces a light forged wheel, with the related performance gains. Here's a quote:

"Wheels are rotating mass, and every one-pound reduction in rotating mass is equivalent to roughly an eight-pound reduction in static weight. With lighter wheels, there is a benefit from increased fuel savings, better braking performance, and better acceleration."

I've heard some say the benefit is 2 lbs and some say it's 4 lbs, but here they are saying it's 8 lbs. This may be too good to be true, so I'm going to stick with the 4 lbs I've heard from some. I think it all boils down to what size your engine is. I think that for a smaller engine (like the MINI), weight is important, but for a large V-8 engine, weight is not near as crucial -- for acceleration anyway. :smile: :smile:

 

Thats my "percieved" feel- guaged by the seat of my pants. (these are my tire testing pants...

What you lack in skill and finness is easly overbearn with enough horsepower, agreed. Ever seen a fox body Mustang auto cross with Miatas? great example.

Alex

 

As my post above, Im more concerned about increasing braking
capacity when it comes to making the wheels lighter weight. :smile:


It is a night/day difference vs 17" R90's with DSST's vs 16" Comps
with GS-D3's.

 

Alex -- I'm with you man. I've not seen the Mustang vs Miata at an autocross ............ I need to get down to one and even if I don't participate, at least watch and enjoy the sights! :smile:

kenchan -- I too believe braking is extremely crucial (for safety), and I'm glad the MINI is already a top braker in stock form. :smile:

 

First off, sorry for not answering earlier, I haven't checked this thread in a while....

So here goes...

I haven't seen Mustang vs Miata AutoX, but I do see them a couple times a year at track events. For biginners, the Miata is easier to get around the track. For experts, the Mustangs kick some serious butt! But if you want the best of both worlds, drive the Monster Miatas: The Miata with the 5.0 EFI in it. A poor mans modern Cobra!

As far as the breaking thing, lighter wheels should only contribute to breaking distance in three ways....
1) Improved contact patch (this is what I think is happening) due to lowered unsprug weight.
2) Decreased energy dissapation, but we're only talking on the order of a % here, so it shouldn't be that. And this would only be true if the break system were operating at it's limits, where it can't dissapate enough heat on it's own, and they were exhibiting the onset of fade with the heavier wheels.

For the effictive mass ratio of rotational mass to just extra weight in the car, it's just calculated via moment of intertias of the differing mass distributions. It's pretty easy stuff, and for the model of the wheel and tire, I did it with a piece of junkmail and a pencil. For a good reference, see
http://hyperphysics.phy-astr.gsu.edu/hbase/mi.html
So yes, Zociac, I did model a complex shape for the tire. All it's weight was at the tread (not true, but close), and for the wheel, I broke it into a disk and a cylinder (not true but close as well). the moments of the relavent shapes are burried in the link above, if you want to know more (and the Dr is from a PhD in Applied Physics )

So that 8 to one is cr*p. (but it was from an "Add", so what should we expect?) So is the 4:1 (sorry Alex). Flyboy has it right.

The dyno thing is something that is confused in many posts as well. A rolling cylinder dynomometer turns the entire drive system, down to the tread (but only of all four wheels on very few dynos.....) So to get all this stuff moving, work has to be done on the system. But at constant speed, you only have the parasitic losses (friction), and the drag of the dyno. So, the speed that the dyno ramps RPM determines how much this effect will change a particular dyno run. If a "step and scan" technique is used, the RPM is stepped to new level, and held constant while HP is read, and on and on,, then you would get the highest (and true) wheel HP numbers.... This could also be corrected for if you do the dyno runs at two different rates, and fit for the rotating mass of the car subsystems. But dynoing cars isn't easy, so it would be hard to get the repeatability.....

But the increased efficiency contact patch also works for acceration, I just don't know how to model it. It would be cool if someone had two sets of wheels with the same tires and did some 0-60s with the two sets. Then at least one could get an empirical relationship...... I also wonder if the effect is symmetrical, does it have as much benefit in breaking as acceleration..... Hmmmmmmmm

Matt

 

eeee...? stock wheels are too heavy imho. the braking effort and
distance is much shorter with the Comps.

 

Dr Obnxs,

I don't think your understanding the entire concept correctly. First off the MCS is 2640lbs not 2800lbs, not sure where you got that number.

Its as simple as a little test, get a bicycle and prop it up so you can turn the rear wheel using the crank with your hands. Now just start turning the crank with your hand and see how quickly you can get to the point in which your no longer accelerating. Now do the same thing but with a 5lb weight attached to the wheel, your not going to accelerate as quickly. It takes more power to turn the heavier wheel inturn making you slower. Than on top of that it will take you longer to slow that same wheel down from the same top speed.

Going to lightweight wheels makes a huge difference and its very worth it in more ways than one.

 

I'm shopping for new wheels, and I've been focused on getting through the twisties as easily as possible. I've been thinking the less angular momentum the better. Has anybody quantified what happens to agility when wheel weight or diameter is decreased?

 

so how much does the standard rims and tire weigh on a 2005 mcs? what is the optimal weight for a replacement that'll improve speed/braking/etc.... ?
by this I mean, what would make it worthwhile? 5lbs? 10lbs?

 

Using the kinetic energy equations for linear motion and circular motion I did some rough calculation to see for a 10-lb difference in wheel weight impact to acceleration and braking I found the delta due to 10-lb per wheel amounts to 3% of the linear motion of the 2600-lb vehicle mass.

The equations are:
1) kinetic energy due to linear motion = 1/2 MV^2 where M is the 2600 lb of the vehicle and V is the speed of the vehicle.
2) kinetic energy due to circular motion = 1/2 Iw^2 where I is the moment of inertia of the wheel/tire combo and w is the angular velocity in radian per second.
3) moment of inertia of a uniform disc I = 1/2 mr^2 where m is the mass of the wheel/tire combo and r is the radius of the tire.

3% of 2600 lb amounts to 78 lb so the 10 lb per wheel saving equats to about 2x reduction of non-rotating mass. If you replace wheel/tire combo that save you 20 lb per wheel the reduction will be 6%. This gets fairly significant.

 

There's a sticky thread at the top of this forum that tells you the weights of all the MINI wheels. I think the 16in Xlites are 16-17lbs and 17in Slites are 22lbs.

I run a 13.5lb 16x7 Rota Slipstream for track and autocross. I also have a set of 14.5 lb Rota Grids for street use.

On top of all that you also have to note tire weight.

 

Whoa looks like we have a few too many math professors here on NAM.....

 

kenchan -- thanks for this observation. It's good to know saving weight (i.e., lighter wheels) plays that important of a role in all this, and the SSR Comps are my favorite wheel. When I can I'll upgrade to light wheels, and better brakes too. I just wanted to note that the MINI stops very well, and I think the numbers are around 122 ft or so from 60 mph to 0, but don't know which tires they used. I've also seen some numbers in the low to mid 130's. Like you, I value stopping quick with minimal effort.

 

Well double checking my math I found a mistake. I mistakenly use 12 inch instead of 1 foot for the radius of the wheels to keep all units of length uniform. This accounted for 144 times exaggeration of rotational mass contribution to the kinetic energy. The correct contribution of the wheel/tire combo for 10-lb lighter wheel is a very insignificant 0.02%. Simply put, the 2600 lb mass of the overall vehicle (yes that includes the wheels and tires too) overwhelms the rotational mass).

It seems the most important benefit of lighter wheel/tire is in the unsprung weight saving in the tractional characteristic. This benefit only plays out in less than smooth road surface in a turn, and improvement in ride quality and traction when acceleratiing/decelerating.

 

I need you all to show your work or your not going to get credit.



just kidding, don't bother.

 

I came back to this thread based on discussions in others...

You are exactly right, BUT a good bicycle wheel is a pound or two, and the full mass of a good race bike is a bit south of 20 lbs. So the % contributions are wayyyyyyyyyyyyy off in the analogy you use. Fact is, the energy is dominated by the mass of the car. So the relative effect of adding mass to the wheels is much smaller....

Matt

 

Here's a real world measurement by some guys who were having way too much fun:
http://forums.vwvortex.com/zerothread?id=776885

They progressively shed weight off a Sentra and measured its acceleration.
Their first step was to replace 19" wheels with 15", taking 13 lbs off at each corner.

Step 1: Baseline
Curb Weight: 2,762 lbs
1/4 Mile:16.3 @ 84.0 mph
60-foot:2.9 sec.
0-60 mph:8.6 sec.

Step 2: 15-inch Wheels
Curb Weight:2,707 lbs
1/4 Mile:16.0 @ 85.5 mph
60-foot:2.8 sec.
0-60 mph: 8.1 sec.