FE with Steel v. Alloy Wheels?

If you have a bathroom scale, you could pull a tire off of each car and weigh them on the scale. This will give a gross effect. The next part of the problem is more difficult.

You want to measure what is called the 'moment of inertia' (See Wiki for a complete description.) One of the better ways is to measure the oscillation of a rim in a rotary setup where a spring is used to let the rim oscillate back and forth. The frequency is proportional to the inertial mass.

So here is the deal. When the wheel is spun up, the force applied to turn the wheels becomes angular momentum, stored energy. When the wheel slows down, that energy is either captured by regenerative braking or released as heat by the brake pads and rim or disk. You want to minimize the heat loss.

There is also a linear energy storage and loss. Look for 'kinetic energy' in the usual places. This is usually easier to calculate than rotational energy but it is another part of the equation.

The math is not trivial but it is something college physics courses often cover. But it takes some measurements and math to get an accurate answer.

Now I'm fonder of 'back of the envelope' calculations. So look at the relative weights:

• ~3,000 lbs of car mass including rims, gas and passengers
• ~14.3 lbs each rim, ~53 lbs total rim mass
• 53/(3,000-53) = 1.8%
• assumption: worst case angular momentum is 2x linear momentum
• 3.6% of vehicle kinetic energy is tied up in rims

To me, this is a potentially measurable effect but rather slight. If you are already achieving near peak vehicle efficiency, this would be detectable. At the limits of performance, small changes add up.

Bob Wilson

 

I went from stock OEM Goodyears to BFG G-Force Sport 205-60-15 (not snow tires) on stock rims. The tire weight is 5lb more per tire. My mpgs dropped from 49-50 to 43-44, with more than 5000 miles on the new tires. They are wider and a stickier tread, but the 5 lbs certainly didn't help. The car feels sluggish at slow speeds, but has a much improved highway ride and corners much better. My driving is 99% freeway.

 

Wider tires = more rolling resistance since more rubber is in contact with the pavement. Tire pressure is also a component. If you could put bike tires on a Prius at a very high pressure you would probably get very good mileage. But,.... you would trade mileage for safety which is what many of us to a lesser degree are doing.

Bikes are a really good example of this. Ride a racing bike with very thin high pressure tires and then ride a mountain bike with thick knobbys. You get more speed with less work on the racing bike.

 

rolling resistance, tire width and tire pressure are probably affecting FE more than rim and tire weight.

I go from my spring-summer-fall alloy 195/55R16 to winter steelies 185/65R15, but this change occurs as temperatures are falling. I observed some FE reduction but it was much more likely tied to the temperatures falling than rim+tire weight.

Also in my case, the steelies are smaller and the tire is narrower, therefore even in constant temp I probably wouldn't be able to answer your question. You'd need someone with same size steel vs alloy wheels and same size tires. But then again, those people would probably swap tires as temps are getting colder.

 

With the winter season coming back, does anyone have more insight into this issue? I'm trying to make a business case to buy or not a second set of cheap alloy wheels for winter tires.

I still have to asks for prices to know what kind of price difference we're talking about.

So, the question is: which costs more:
1. Paying a premium for alloy wheels and rise FE; or
2. Paying less for steel wheels and lower FE?

 

Hi Philosophe, do you have any data on just how much extra weight we are talking about here (for just the rims - steel versus alloy).

As for the impact of adding rotational mass, be careful about what you read, the following quote for example is very misleading.

This is complete nonsense. To look at the real situation we first have to consider that the effect of extra rotational mass has three different components (not considering the unsprung versus sprung issue here as that is more related to handling and ride rather than FE). The three separate issues are.

1. Increased (rotational) mass increases rolling resistance (all other factors being equal). This is in direct proportion with 1 times the extra mass, there is no "multiplication factor" due to rotating mass here!

2. Increased (rotation) mass increases the fuel required to climb hills. This is again in direct proportion to 1 times the extra mass, once again there is no "multiplication factor" due to rotating mass here!

3. Increased rotation mass increases the fuel required to accelerate your vehicle. Now this is the only one of the three where rotation mass is worse than non-rotation mass. The "multiplication factor" of just how much worse this rotational mass is (compared to a static mass) depends on exactly how the rotation mass is distributed radially.

For example the absolute worst case scenario is where the extra mass is entirely concentrated at the rolling radius in which case the multiplication factor is 2x (each extra kg of rotational mass is equivalent to 2kg of static mass). For a set of car rims however this worst case is completely impossible, because the tire occupies approx the outer 33% of the complete wheel radius. So for a rim a crude "ball park" approximation would be to take the extra mass as if it where concentrated at say 50% to 60% of the overall wheel radius. This give an increase in energy due to rotation of only about 25% to 36% (multiplication factor of approx 1.25 to 1.36).

So in summary. If you used rims that were each 3kg heavier, giving a total increase in mass for all four wheels of 12kg, then the adverse effect would be equivalent to :

1. Adding 12kg of static weight (eg luggage) for impact on rolling resistance.

2. Adding 12kg of static weight for impact on hill climbing.

3. Adding about 16kg of static weight for impact of acceleration.

Considering the three above factors I would say that for the Prius factor one (rolling resistance) is probably the biggest concern because it's happening all the time and is never recovered. Factors two and three above both involve larger forces than that of rolling resistance, but they don't happen all the time and are both mitigated in a Prius by the regenerative energy recovery system. If you where to take an "overall average" of those three factors to determine the net equivalent mass then it would depend on your driving style and terrain covered, but honestly I doubt that it would amount to more than an extra 14kg (for that example of 12kg added rotational mass).

 

Wheel Tech - Road Wheel Weights Can Affect Your Vehicle's Show...and Go

So in this example they saved almost 1/2 MPG with lighter wheels and the same tires.

 

Realizing things are more complex than that, if I oversimplify things just to get the order of magnitude we're talking about:

17lbs wheels @ 10,9L/100km
27lbs wheels @ 11,1L/100km
an increase of 2%. I then (wrongly) assume the same percentage of difference apply to my Prius.

If I keep my car 250 000km, having 4 months /12 with the winter wheels, this is 85 000km with them on. At a theoretical 6L/100km (don't know yet with Montreal's winters), this is 5000L of gas, at a conservative 1,50$/L (average of next 8-10 years), this is CAN$7500 of gas.

2% of that is CAN$150.

Therefore, I can spend a max of CAN$37,50 more on an alloy wheel that would be 10 lbs lighter than a plain steel wheel. I can get steel wheels at about CAN$55-65.

Simplistic conclusion on this simplistic calculations: I probably won't find light alloy wheels that would be cheap enough to justify their premium over the TCO of the car... or will I...

And then I do not consider the fact that a steel wheel is probably better suited to go through the winter here...

I'm heading to a tire reseller... We'll see...

 

One unknown factor in that test (linked by jimbo) is that we don't know how (or if) the aerodynamics of the two wheels differs. This could definitely have an impact on the results which is quite seperate to the weight issue.

If all other factors are equal then I'm pretty confident that the overall impact on a Prius will be no more than that of adding about 20% more (than the extra mass of rims) in static weight. So Philosophe how about you try a simple test and drive a tank with 48Lbs of added dead weight to your Prius (40 Lbs + 20%) and see how this effects your fuel economy.

Taking the weight of car plus driver/passenger at approx 3200Lb then 48Lb is exactly a 1.5% increase. My best guess is that an (x)% increase in weight would probably only give about an (x/2)% increase in fuel consumption (because not all aspects of fuel consumption are related to weight, aerodynamimc losses for example are independant of weight).

I'd be interested to see the results of that test, as I said though I wouldn't expect you to see more than about 1% difference on the Prius FE.

 

Yes I think that's a fairly sound assessment of the situation. Personally I think it will be more like a 1% difference than a 2% difference so more like $19 extra per wheel by my estimation.

 

The choice is even easier than I expected: the tire reseller gave me prices: steel wheels are CAN$55 and alloy wheels start at around CAN$150.

So, for me this is a case closed: steel it will be.

 

you might want to hop off to Canadian Tire for some ugly, cheap, plastic wheel discs to help the aerodynamics and hide the steel rims.