anyone know the benifits of lightweight wheels?

[jmew0ng]

the real question is how much do the steelies weigh so we can have something to compare xD (without tires)

[fu_im_from_texas]

I've been thinking about this question for a few days. My gut reaction was: lighter wheels will make a significant improvement in accelleration and mpg. My calculations show the opposite. Maybe my logic is flawed? Here's what I've got so far.

Consider two cases:
1) Totally stock Yaris from 0-60mph
2) Yaris with lightweight rims from 0-60mph (NOTE: I'm assuming identical tires)

The easiest way to compare the two is from an energy standpoint.

Rotational Energy of a Wheel = .5*Mw*(Rw^2)*W^2

where:

Mw= Mass of the wheel
Rw= radius of the wheel
W= rotational speed (Radians/second)

For Case 1)
Mw= 15lbs. I base this on the wheel/tire combo weight of 33 lbs. tirerack.com says the tire weights 18lbs. 33-18=15
Rw = 7.5 inches. 15in diameter / 2
W = 92.15 (RAD/s). @ 60mph 1mile takes 60 sec. for stock tires tirerack.com says 880 rev/mile so 880/60 = 14.6Rev/second *2Pi= Rad/s

convert to metric

Mw= 6.8kg
Rw=.19m

Rotational Energy = .5*Mw*(Rw^2)*W^2 = .5*6.8*(.19^2)*92.15^2
=1042 watts = 1kWatt

For Case2)
Mw=10 lbs. = 4.5kg This seems like a reasonable lightweight 15 inch wheel
Rw=7.5 inches = .19m
W = 92.15 RAD/s

Rotational Energy = .5*Mw*(Rw^2)*W^2 = .5*4.5*(.19^2)*92.15^2
= 690 watts = .69 kWatt

1- (690/1042) = 33% less energy to accellerate the lighter wheel. This sounds like a lot untill you compare it with the total energy of the car @ 60mph.

Energy of Yaris = .5*M*(v^2)

Where:
M=mass of yaris=2200 lbs = 998kg
v=velocity=60 mph= 97 km/h

Energy of Yaris = .5*998*(97^2) = 4695 kWatts

so (Energy of Wheel) / (Energy of Yaris) @ 60mph is 1/4695 = .0002

.000002% of the total energy is insignificant.

Did I make a stupid error in my calc? i would have guessed lightweight wheels would make a big difference...but I proved the opposite. someone help? ...show me the error...

[fu_im_from_texas]

Originally Posted by fu_im_from_texas

...
so (Energy of Wheel) / (Energy of Yaris) @ 60mph is 1/4695 = .0002

.000002% of the total energy is insignificant.

...show me the error...

Woops, I moved the decimal point the wrong way...it should be .002%...which is still far less than 1%... anyone else see mathmatical errors?

[dallas]

Removing weight helps acceleration as it takes less energy to move the mass but beware of diameter too. If you go with a 17 wheel even if its lighter than the stock steel wheel (not many wheels like that) you have moved the mass 3inches further out from the hub (based on 14 wheels) so it will take more enery to turn the wheel. I have 205 50 15 tires on light weight 11lb wheels , the stock steel wheel and tire are still lighter.

[CaysE]

Originally Posted by dallas

Removing weight helps acceleration as it takes less energy to move the mass but beware of diameter too. If you go with a 17 wheel even if its lighter than the stock steel wheel (not many wheels like that) you have moved the mass 3inches further out from the hub (based on 14 wheels) so it will take more enery to turn the wheel. I have 205 50 15 tires on light weight 11lb wheels , the stock steel wheel and tire are still lighter.

This is not necessarily true, because you're not taking the tires into account. Tires can typically weigh between 15 and 20 lbs, and if you maintain the overall diameter of the wheel/tire combo, a lighter weight wheel with a larger diameter would require a tire with a shorter sidewall, thus a lighter tire. Depending on the actual weights and wheel design, the mass can even be moved inward.

[dallas]

I did consider the tires in my weight, and yes the shorter sidewall helps, but the mass of a wheels weight is not in the spokes so if you move it 3" further from the hub even thought the tire tread is the same diameter away as the 14wheel, you have added more mass further from the hub over a stock 14" wheel. I have yet to find a 17" wheel tire combo that I can afford that would weight less than the stock 14 wheel and tire combo.

Originally Posted by CaysE

This is not necessarily true, because you're not taking the tires into account. Tires can typically weigh between 15 and 20 lbs, and if you maintain the overall diameter of the wheel/tire combo, a lighter weight wheel with a larger diameter would require a tire with a shorter sidewall, thus a lighter tire. Depending on the actual weights and wheel design, the mass can even be moved inward.

[cleong]

I couldn't really understand the calculations you have done, and I am not a physics major, but would that be an instantaneous value (0.000002%) requiring multiplication by time factor?

[fu_im_from_texas]

Originally Posted by cleong

I couldn't really understand the calculations you have done, and I am not a physics major, but would that be an instantaneous value (0.000002%) requiring multiplication by time factor?

cleong,
The time factor would come into account if we were looking for the power required to accellerate to 60mph. Energy/time = power.

I simplified the problem by only concidering the energy required. I believe this is a valid way to model this situation...but there may be an error in my calc...

[CaysE]

fu, the weights of the wheels themselves could've told you the same thing without going through all that calculation. 10 lb wheels are 33% lighter than 15lb wheels, thus requiring 33% less energy to move them.

The second half of your equation is only comparing the total weight differences of the car with the two different wheels. The two front wheels are attached to the engine, so you'd also eventually conclude that you have more power to the ground due to less total weight of the moving drivetrain.

Cliffs notes: you're only looking at half the picture.

[Biggie™]

Originally Posted by fu_im_from_texas

Did I make a stupid error in my calc?

Yep!

You are comparing the amount of energy while driving at 60 mph, not the amount of energy it took to actually accelerate the extra 20 pounds of wheels.

Also you didn't factor the rotational weight effects. You just treated the wheels as a non independent part of a mass that is the car.

[fu_im_from_texas]

Originally Posted by CaysE

...fu, the weights of the wheels themselves could've told you the same thing without going through all that calculation. 10 lb wheels are 33% lighter than 15lb wheels, thus requiring 33% less energy to move them....

CaysE, You are right!...This is only true for the simplest case, which I examined here. If we concidered the case of 17inch 10lb rims, then the moment of inerti would be larger...the moment of inerta grows exponentialy with the radius of the rim.

Originally Posted by CaysE

Cliffs notes: you're only looking at half the picture.

Can you please provide a calculation for the other half of the picture?

Originally Posted by Biggie™

...You are comparing the amount of energy while driving at 60 mph, not the amount of energy it took to actually accelerate the extra 20 pounds of wheels...

Biggie, This is false. When the car is going 0mph the energy is 0. When the car is going 60mph the energy is about 4xxx kW. The difference, or amount of energy it takes to accellerate the mass is 4xxx-0 = 4xxx kW

Originally Posted by Biggie™

...
Also you didn't factor the rotational weight effects. You just treated the wheels as a non independent part of a mass that is the car....

The first portion of my calculation was the rotational effects...

One error I do see is I compaired the energy of 1 wheel, when there are 4 on a car....multipling the energy of 1 wheel x 4 still nets a neglegable ammount of energy...

Can anyone provide an alternate calculation?

[Biggie™]

Originally Posted by fu_im_from_texas

Biggie, This is false. When the car is going 0mph the energy is 0. When the car is going 60mph the energy is about 4xxx kW. The difference, or amount of energy it takes to accellerate the mass is 4xxx-0 = 4xxx kW

Wrong again buddy... In your equitation you are attempting to calculate the actual energy the Yaris possesses at 60 mph. Not the energy it took to get the car to 60mph. But thank you for letting us know what the ballistic energy of an object that is close to the mass of yaris being flung out at 60 mph.

What you need to do is calculate "force", mass multiplied by acceleration. And of course it will take less energy to accelerate a lighter object. The formula to calculate rotational acceleration is a bit more complex, but this is actually what you are looking for here. Try google...

[fu_im_from_texas]

Originally Posted by Biggie™

...What you need to do is calculate "force", mass multiplied...

Biggie,
I am approaching the problem from an energy stand point. I base this approach on the first law of thermodynamics - a law that states there is a conservation of energy.

You are approching the problem from the standpoint of Force. You are useing Newtons second law of motion. F=ma...

Both are valid. There is 300+ years of emperical evidence that shows that conservation of energy, and F=ma will ultimately get you to the same answer. I am using conservation of energy because, in this case, it is the simpler approach...

Originally Posted by Biggie™

... Try google...

I have a degree in mechanical engineering from the university of texas @ austin. I have taken several classes in physics, dynamics, and dynamic system controlls. My approach to the problem is correct. Google will give you a ton of information. Information is dangerous when it is applied incorrectly...

I am not trying to give you a hard time here, because we are all trying to figure out the same answer to the same tough problem ...

[CaysE]

I can't calculate the other half of the picture, because it's more complicated.... dependant on what gear your in, gear ratios, the power output of the motor, and the weight of the moving parts of the drivetrain.

You can roughly determine the increase in HP to the ground by guessing the percentage of weight that is taken away from the total weight of the moving drivetrain with two lighter weight wheels, and comparing this to given HP numbers from the flywheel and the ground.

Like I said, you only have half the picture, which is that there's a .08% decrease in the required energy to move the car. The other half is that you have more power available to output 4695 kWatts faster. The percentage decrease in the required energy to move the drivetrain is much larger than .08%.

[fu_im_from_texas]

Originally Posted by CaysE

I can't calculate the other half of the picture, because it's more complicated.... dependant on what gear your in, gear ratios, the power output of the motor, and the weight of the moving parts of the drivetrain.

...

We are assuming that gear ratios, power output, and drivetrain weight are all constants...the only change is the wheel weight...

please provide a calculation for the other half...

[CaysE]

I CAN'T provide a calculation. I have no idea what the weight of the drivetrain is, the given flywheel HP and BHP numbers are, or the gear ratios. You need to take into account what gear you're in and the ratio, because the number will be different for every gear. I can go 60mph in 2nd gear or 6th gear in my car... the difference in power output is significant.

If you get those numbers, feel free to calculate it yourself. I find it hard to see a reason for these calculations aside from getting empirical evidence to back up the fact that lightweight wheels do improve braking performance, suspension response, and acceleration. You don't need these numbers to understand what's going on.

[eTiMaGo]

Man, I need to find my old physics textbooks

Back on the original topic, I find it easier to explain these phenomena with basic everyday examples...

Effect of total car weight

Imagine you're at the supermarket. How much easier is it to push the trolley around when it is empty compared to when it is full? It's a lot easier to speed up, stop, and turn when you have less weight.

Effect of wheel weight (or pulley, or any rotating mass)

Imagine you have two tops (spinning tops, what kids used to play with long ago...), a heavy one and a lighter one. Think of how much extra twisting force you have to give the heavy one to get it to spin at the same speed as the lighter one. It will also keep spinning longer, and if you try to stop it by hand, you will need more stength to do so.

Also, imagine you are riding a bicycle, and you want to go up a low curb or something similar. You'd usually slow down, because when you go fast, the inertia of the wheel (the same force that lets your bike stay upright instead of falling over, when you are moving), will want to drive the bike straight through the curb, instead of up and over it. In car terms, the lighter the wheel, the less inertia it has, and the easier the suspension can react to bumps at higher speeds.

In reality there is always a compromise somewhere... smaller lighter wheels will help with response, but that means running a taller sidewall which can flex and make the handling less precise.

Also, something I've been pondering, the Yaris is quite tall and kinda top-heavy, so heavier wheels may be an advantage in stabilizing the car, shifting the center of gravity down a bit, keeping the car a bit more planted at speed? This would only be really useful on a highway, but just something that might be worth to consider.

Anyway, I hope that helped, for the less technically-minded out there

[kurokoma-kun]

Originally Posted by eTiMaGo

I find it easier to explain these phenomena with basic everyday examples...Anyway, I hope that helped, for the less technically-minded out there

eTiMaGo, you are my hero Your point about the weight balance is, I think, what I was asking about originally. Lowering the center of gravity is next step for me.

I don't mind admitting that once you start getting into differential equations and so forth I am completely lost. This is why I was not able to pursue a career in science, because at some point, interactions get so complex they can only be explained mathematically, and I have no intuitive understanding of it.