Hi,

I've been reading "Tires, Technology and Energy Consumption" by K.G. Duleep, who is leading part of the California effort to report tire rolling resistance. You can find a copy by Googling the title. There is a fine write up on the effect of tire rolling resistance on mileage in the first part of the report. But my interest is in the tire characteristics that have a significant impact on rolling resistance.

"Rotating tire drag can be 20 to 25% of total vehicle aerodynamic drag. Increasing the width of the tire, and changing the tread, or the rim and wheel can change tire drag by 3 to 6%. . . ." (pp. 13) There are two aspects, the profile drag and the air entrapment. Julian Edgar in March 19, 2005 (AutoSpeed.com) wrote an article, "Modifying Under-Car Airflow, Part2" about forming extended air shields to smooth the air around the front tires, an excellent approach. But you can also see the air entrapment on a rainy day observing the water-air mix spilling out of the wheel wells of other cars. The Honda Insight solves the rear wheel entrapment by a wheel well shield and air-tight wheel covers. I've also seen modified pizza pan, wheel spoke covers that would also reduce air entrapment.

"RR varies linearly with load and inversely with square root of inflation pressure." (pp. 14) The load effects are well known but this is the first relational formula showing the effects of tire inflation. So using English units:

PSI formula = relative drag effect
1/SQRT(35 psi) / ref. = 120.7% (Toyota psi)
1/SQRT(44 psi) / ref. = 107.7% (OEM)
1/SQRT(51 psi) / ref. = 100% (my current tires)

Because the drag reduction occurs by the square root of the pressure change, it is not as dramatic as a linear increase in pressure would suggest. It is important but not the only effect.

"For a given application and a constant tire technology, tire RR is inversely proportional to radius and aspect ratio but increases with increasing width (about 5% per 20mm). Effect of diameter is quite dominant." (pp. 14) Now here are two very important aspect of which we have some control. Let's start with inversely proportional to radius:

Rev/mile = relative drag effect
867 / ref = 94.3% (best case)
906 / ref = 98.6% (OEM)
919 / ref = 100% (my current tires)

Tire widths = relative drag effect
4.9 / ref = 90.7% (best case)
5.2 / ref = 96.3% (OEM)
5.4 / ref = 100% (my current tires)

"Toe-in creates additional side force, increasing RR by 1% per 0.15deg per wheel" (pp. 15) This is why I'm such a stickler for minimizing the real wheel drag by using a shim kit. But it also has an impact on front wheel drag. Unfortunately, the front wheels have a thrust force and this would tend to shift the wheel rolling toe. I have no easy answer for how to manage this beyond using whatever the current wheel alignment services use.

"Both ambient and tire temperature have a significant effect on RR. For example, from -20C to +20C, RR can be reduced by 50%." (pp. 15) Ok, so we must all move to warmer climates during the cold season. However, it also means it may make more sense to shift your morning commute to as late as possible to gain any possible warmth.

"RR increases with speed in a non-linear fashion. Current J2452 procedure fits a V+ V**2 curve, but dependence is small at speeds < 60mph." (pp. 17) Again, 65 miles per hour (104 km/hr) is probably the highest speed one might want to cruise at for fuel efficiency but 60 miles per hour is better. This matches my field data too.

What is important about this paper is using these relationships I can model expected tire performance as a function of diameter, tread width, and pressure. I can even do a 'what if" looking at finding an optimum solution. Shades of linear programming, this becomes a solvable problem:

drag-index = F1(tire pressure) + F2(tire diameter) + F3(tire width)

However, there is a simpler approach that uses the product of the relative efficiencies:

drag-merit = %F1(psi) * %F2(diameter) * %F3(width)

14" Prius Example

It turns out that even though the relative drag as a function of psi varies as the inverse square root, the higher pressure of the Sumitomo (IF YOU USE IT), predominates the other effects. Based upon this analysis, it looks like I might get lower rolling resistance performance with:The next question is how to test the relative fuel efficiency versus my current Sumitomo 175/65TR14. One approach is to buy two of the 175/70TR14s and swap them between the front and rear wheels. Most of the weight and rolling drag comes from the front wheels. I can use both mileage records as well as tire temperatures to determine how these two models of tires perform.

One other option is to split the front tires on the front wheels. I can then look for asymmetrical drag and tire temperatures to determine relative performance. This has the advantage of needing only a single sample, a much more affordable approach. Unfortunately the different diameters will also change the camber and toe geometry.

Bob Wilson

 

Bob,
Am I reading this correctly?
1)A taller tire/wheel-holding the width the same-will have lower RR.(I'm guessing less deformation per mile since the tall tire makes fewer revs)
2)Aspect ratio-shorter sidewall but the same total height lowers the RR(I'm guessing because less sidewall to flex).I'm unclear that you are saying this-maybe you were just saying taller is better?
3)Wider tires are poison.
4)Pressure is good.
Thanks,
Charlie

 

#1, 3, and 4, yes.

#2 - Aspect ratio?? I don't remember anything in the paper about this.

Tire rubber has hysteresis which means bending it to one angle does not return the same amount of energy when it straightens. So every time the tire rotates, every part of the tread is bent upon reaching the pavement and then straightens at the end with a fixed loss of energy. A 'taller tire' or one that makes fewer revolutions per distance traveled avoids these extra, energy losing bends by reducing the tread deflection.

Wider tires hurt in two ways, profile drag and more tread material bent. Profile drag is just how much of a blunt object has to push aside the air or in wet conditions, water. But a wider tire also increases the mass of rubber that has to be bent with the resulting loss of energy.

Pressure is good, ask any interstate trucker what pressure his tires run at. The higher pressure ensures the minimum rubber deflection. The only problem is most suspensions are not good at handling high-frequency vibration loads. I suspect that addition of 'rubber donuts' to our suspensions could easily handle these vibrations and allow easier rides on harder tires.

The 'aspect ratio' has nothing to do with the measured tread width and it is the tread that holds the bulk rubber that undergoes the energy losing bending. Near as I can tell, the side wall size, the first number in a tire specification, has more to do with clearance in the wheel well and not rubbing against the body. The important number is the tread width.

Bob Wilson

 

Bob,
I got it.I was confused by,
" tire RR is inversely pro. to radius and aspect ratio" in what might be called paragraph 6 of your initial post.On rereading I understand aspect ratio going up is just a stand in for the radius going up.
The RR goes down as the radius goes up or as the aspect ratio goes up(holding the width constant).

Just how high do you go on tire pressure?On another site many folks go well over the sidewall.I'm generally chicken,and just go to the upper sidewall pressure.
I have an ancient Suburban that responds very well to hypermiling-PG,tire pressure etc.I will be hunting for tires soon.It takes 235/75 15 not a common size now.I suspect that the worn tread is improving my mpg.
Thanks,
Charlie

 

Yes, hysteretic energy losses in the tire rubber are indeed the principal causes of tire rolling resistance. However, I think that the primary place where this loss occurs is in the tread, not sidewall, rubber. Consider the behavior of the rolling tire. Suppose that its unloaded radius is r0, and that its radius (distance from center of axle to ground) when loaded is r1 (of course r1 < r0). Now, the circumference of the tire's tread is given by 2*pi*r0 while the distance the wheel (and hence vehicle) moves with each tire rotation is given by 2*pi*r1. This latter figure is substantially smaller than the former. There is a difference of 2*pi*(r0- r1) between these two figures, and this has to be "accommodated" by the tire in some way. What happens is that the tread rubber has to "squirm" this difference away as the tire rotates. This squirming leads to very significant hysteretic energy losses in the form of tire rolling resistance. I think that such losses are inevitable. Apart from designing less lossy rubber compounds, it seems to me that the smaller the difference in circumference, the lower the loss per revolution. The loss per distance travelled is probably a more meaningful measure, however. I would thus expect that the thing to do is to minimize the ratio (r0-r1)/r1 = (r0/r1)-1; i.e., low profile tires, large radius tires, and high inflation pressure.

Stan

 

Stanley,
Are you sure that the distance the vehicle travels for one turn is Pie times the loaded radius?
I would have guesses that the distance traveled per turn would be the unloaded circumference;and I would have guessed that the loaded circumference was the same as the loaed circumference.
Why would the distance around the outside of the thread decrease because of the load?It really isn't a circle anymore,so the loaded radius-measure on the lower side-really can't tell you the exact circumference.
Forced to guess,I would almost bet that the loaded circumference might be tiny bit longer than the unloaded circumference.

Obviously,I'm a bit unclear on this,but what would you guess the difference would be in distance traveled per turn of the wheel -unloaded just sitting on a jack VS Loaded with the full weight of the vehicle?
You're sure the loaded wheel/tire travels a shorter distance. Ignore the tire slip.A loaded rear tire will slip one way(shorter distance traveled per one turn),while a front might slip the other way.
Thanks,
Charlie
PS-Ignore the above-I get it-you're not saying the wheel/tire loaded-doesn't travel the same distance that an unloaded tire would travel.You're saying that it sorta has to squirm to get that full distance - because it is deformed with an effectively shorter radius while loaded.

 

First, I want to thank you for an informed analysis although we may disagree about one aspect, the rolling drag as a function of radius:
We agree.

Again, perfect agreement.

Here we have a difference of opinion but it was due to an error in my earlier analysis. Given identical inflation pressure and tread width, the surface area that comes in contact with the ground will be nearly the same for two tires of different radius. But the tire with the smaller radius will have a greater deflection to achieve the same surface area and this additional defection is what increases the hysteresis loss.

To see what I mean, I've attached this sketch:

A little extreme but it shows the principle. Equal pressure tires with equal tread width have to support the weight of the vehicle by compressing the tread on the road enough that the weight is held up by the area times the pressure (and some very small amount of sidewall force.) But the tread on the larger radius tire does not have to deflect as much. Thus the hysteresis losses are less.

Again, thank you for an informed approach to analysis. However it also helps explain what higher pressures due. A higher tire pressure reduces the amount of area that has to be deflected by the road. Since pressure does not change the tread width, it has to change the front-to-back distance. This means an inverse, square-root, function (with appropriate constants) will explain the reduced tire deflection and reduced hysteresis losses.

I will go back and edit my original posting to be more precise.

Bob Wilson

 

Have you been able to model the benefits of a tire such as a 165/80-13? Intuitively, a slighty larger tire with smaller contact patch should improve RR.
It's similar to riding bicycles, when you want to go fast with the least effort, you get the skinniest tire and pump them up as much as you can.

 

Actually I have a spreadsheet that does a pretty good job of it. What I'd like to suggest is this:

1. Give me the OEM tire, brand and size
2. Give me your current tire, brand and size

What I'll do is make a modification of my spreadsheet called "FEH_tires.xls" and post it here. You'll see the input columns and can put in any tire you want to see the relative performance. Understand that relative performance rates all three effects, pressure, tread width, and diameter, the same although pressure is evaluated by an inverse of the square-root.

Once you have the spreadsheet, you can add any tires you want and look at the expected, relative performance, OK?

We can do the same for Hondas, Toyotas and even GM vehicles. In fact, the model doesn't care if it is a hybrid or not. It is a tire model. Just us hybrid owners really care. <grins>

Bob Wilson

 

Thanks for the offer to include the FEH group. In our case, there are dozens of potential options to choose from based on the P235/70-16 Continental OEM tire. There are several different tread designs (i.e. all-season, on/off road, mud/snow, highway, etc.) available. For example, I'm considering a narrower LT225/75-16 truck tire in load range D (65 psi vs. stock 44psi) for pontentially better RR. There are even load range E (80psi) tires available.

Basically I'm curious to see if someone models RR benefits of narrower tires and I think the Prius should be a good example. From what I've seen over the years, tires generally have been getting ever larger. Maybe now people will rethink this trend in light of fuel efficiency and environmental concerns.