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Ernie Rogers 04-09-2009 02:32 PM

Discussion on tire efficiency
 
Hello, folks,

Two discussions about tire efficiency have been going for a few days. This is an effort to consolidate into one clearly-labeled thread, and maybe give some useful information. The following "Lesson" on tire efficiency was created (by me) a few years back and became a presentation at a national TDI Club meeting.

I know I will offend a few folks with different views. And occasionally I may make errors so feel free to correct me. Here is the presentation, without substantial change--

Lessons on Fuel Economy
#1 Tires /Ernie Rogers

The purpose of this discussion is to help a car owner get the best possible fuel economy from his car, any car. At times I may talk about parts that are difficult to change, but mostly I will suggest ideas that are easy to do. Let’s talk about tires and some general principles about fuel economy. Later, I promise to write about some other topics, including air drag.

GENERAL PRINCIPLES

It takes fuel to make power. So your car consumes fuel in proportion to the power delivered to the wheels. The power needed by the wheels is the force to keep moving multiplied by how fast you are going. We can make an equation out of this—

We’ll measure the fuel flow in gallons per hour.
Define a proportionality constant for how much fuel is needed, C1
Call the force to move the car F(pounds) and the speed of the car v(miles per hour).

Putting the information together, we get:

Gallons per hour = C1 F(pounds) v(miles per hour).

If you divide the Gallons per hour by the v(miles per hour), you get something that is a measure of fuel economy:

Gallons per mile = C1 F(pounds)

Gallons per mile is the inverse of miles per gallon. This little formula teaches a powerful lesson about how parts of the problem are related to fuel economy. It says you should add up all of the forces opposing the motion of the car, and multiply that total force times C1, a number representing various other aspects of car efficiency such as the energy content of the fuel, the efficiency of the engine, and other losses from things like the gears and bearings, etc.

Looking at fuel economy in gallons per mile is helpful because we can see how the drag forces (and other forces) add together to cause consumption of fuel. (In Europe, the normal fuel economy units are liters per 100 km, a very nice choice.) Let’s use gallons per mile for awhile, and when we want we will switch to the inverse, miles per gallon.

With fuel prices getting way out of line, we would like to lower both C1 and F. Today’s discussion about tires involves one part of the total F. The total force the car must fight has four parts, representing air drag, energy to turn the wheels and tires, energy for acceleration, and energy to overcome gravity when going uphill. *

F = air drag + wheel rolling resistance + mass times acceleration + uphill grade.

To summarize, C1 is some constant related to the fuel and the efficiencies of various car parts (and of course they aren’t always exactly constant). C1 multiplied by the forces opposing the car’s motion gives a good measure of fuel economy. The forces can be looked at one at a time and then added together.


TIRES AND ROLLING RESISTANCE

The force due to energy losses by the tires is the “rolling resistance.” Even choosing a set of tires has a scientific basis and can be demonstrated mathematically, for those who remember some algebra. There is a simple formula for rolling resistance, Frr:

Frr = Crr Mg

This discussion will be about how to make the rolling resistance smaller. The first factor, Crr, is the “rolling resistance coefficient,” a commonly-used “constant” to indicate the efficiency of tires. Mg (mass times earth gravity) is the weight of the car. In truth, the rolling resistance coefficient can vary a little bit with speed so it’s not really constant, and other things besides the tires can be involved—but let’s ignore such details.

The first obvious way to lower rolling resistance is to throw away non-essential parts of your car, to lower the weight. Let’s skip that option for now. That leaves finding ways to change the tire characteristics to lower their essential efficiency property, the rolling resistance coefficient. One might ask, “how much does my car’s miles per gallon depend on Crr?”

Answer: For ordinary car tires, the rolling resistance coefficient varies from about—

Crr = 0.012 (cheap tires) to Crr = 0.0060 (very good tires).

So, rolling resistance can change by as much as a factor of two, depending on your tires. For a modern, efficient car, the effect on fuel economy is—

Cutting Crr in half causes—
at 60 mph: 14% better mileage
at 40 mph: 20% better mileage.

Well, this is very, very good. The tires on my own car were the best I could find (I think), and I measured their rolling resistance coefficient as Crr = 0.0065. You should be able to find several tire makes with Crr equal to 0.009 or better. It’s an unfortunate state of affairs that, at least so far, tire manufacturers seem intent on keeping their Crr values a secret. That could mean taking the time to evaluate tires for ourselves. We need to change that. Some tire properties that affect efficiency are things you can change without buying new tires. Let’s talk about them. Here is a list of tire properties that are expected to affect Crr:


Tire Properties

Profile (P, given as a percentage)
Tire pressure (p), which is connected to--
Contact patch area
Diameter (D) : related to P,
tire width (w) and
wheel rim diameter (d)
Rubber stiffness (depends on temperature)
Rubber internal friction (depends on temperature)

Here is some of the information you can find on the walls of my tires:

Michelin Energy MXV4 S8 205/60 R16 91V Max Press = 44 psi

The first part says something about the design and materials of construction. I know that the Energy MXV4 S8 tires have a rubber composition with very low internal friction, and that means very efficient. The tire size, 205/60 R16, can be used to calculate the approximate diameter of the tire. It tells me that the tire width is w = 205 mm. The “/60” is the tire profile, indicating the ratio of height to width, is P = 60%. The tire has radial cord placement, and the mating wheel rim diameter is d = 16 inches. Here’s how to calculate the tire diameter:

D = 2 ( w/25.4 ) P + d

So my tire diameter is: D = 2(205/25.4)(0.60) + 16 = 25.7 inches.

“91V” indicates the load and speed rating of the tire. Unless you are an unusually crazy driver, tires with the lower rating are just fine. In fact, tires with lower speed and load rating will usually be a little more efficient. (They have less rubber and cord to absorb energy.)

The maximum pressure (stated on the side of your tire) is the maximum safe gauge pressure when the tire is “cold,” before you have started to drive the car. “Cold” actually means the expected air temperature while you are driving—best viewed as the maximum air temperature until the next time you check your tires. Tire pressure changes with temperature, but not a lot. If the tire pressure is set to 35 psi at 70 degrees F, then the pressure will be 34.1 psi at 60 degrees and 35.9 psi at 80 degrees. So, a good rule of thumb would be to decrease tire pressure setting by 1 psi for every 10 degrees F that you think the air temperature will be higher while driving than it is while setting the pressure.

Of course, once you have driven your car for a few miles and the tires have begun to heat up (because they have internal friction, the thing we hate), you really don’t know the temperature of the air inside the tires. That’s why tire pressure should be measured “cold,” before you have driven more than about two miles.

Following are my impressions about how tire characteristics affect Crr, and then also their effect on mileage.

Profile

Engineers call this the “aspect ratio” of the tire. A large number like /65 tells you that the side wall is very tall, at 65% of the tire width. The experience of many drivers indicates that a tire’s efficiency declines with its profile number. I believe this is consistent with theory, since a long flexible side wall allows more give in the tire with less local flexing. Alternate flex and rebound of the walls and tread as a tire rolls is the main source of energy loss in a tire. I think the lowest profile a tire can have and be very efficient is P = 55%.

Tire Pressure and Contact Patch Area

A car is held up entirely by the air pressure in its tires, except for just a few pounds used to deflect the tire rubber a very small amount. Each tire forms a flat spot on the ground, called the “contact patch.” This portion of the tire transmits just enough force to exactly balance the load it supports. From this, you can calculate the area of the contact patch:

mg = (Contact Area) (Gauge Pressure)

mg is the weight supported by the tire, which equals the product of its contact area and its pressure. The amount of flexing of the tire is about proportional to the area of the contact patch. That means the tire rolling resistance increases as the tire patch area increases. Experience shows, however, that rolling resistance doesn’t increase in proportion to the contact area. The explanation is that a tire remains cooler at higher pressure, and the cooler rubber loses somewhat more energy than warmer rubber, all else being equal.

Many of us that are intent on obtaining the best fuel economy we can will operate our cars with somewhat higher tire pressure than is recommended by the car manufacturer. I set my tires at 40 psi cold, or about 10% below the maximum pressure stated on the tires by the tire maker. I have had no problem with uneven tire wear at the higher pressure (for good-quality tires), and the tires are found to last much longer than you would expect. The downside is that the high pressure makes the ride too bumpy for some people’s tastes.

Diameter

Tire diameter affects a lot of different aspects for a car. In most cases, increasing tire diameter makes things better.

Increasing D provides:

Lower rolling resistance
Higher engine efficiency
Longer tire life
Smoother ride and improved control.

Theory suggests that rolling resistance is proportional to one over the tire diameter. The reason large D is better is that there is less deflection of the rubber to get the needed contact area. In addition, most cars obtain best engine efficiency at lower engine RPM than you get with standard transmission gearing and normal-sized tires. That’s because car companies make cars the way people like them—with lots of acceleration—“perky,” as I might say. Engine RPM is lowered for a given speed when you increase tire diameter.

The standard factory tire size for my car was 205/55 R16, with a tire diameter of 24.9 inches. Changing the profile from 55% to 60%, to tire size 205/60R16, increased my tire diameter by 0.8 inches, a 3.2% increase in diameter. This small change has given about a 5% increase in fuel economy for my car. So far, I have driven 55,000 miles on these larger tires, and the tread wear has only been 3/32 of an inch. I still have at least another 3/32 of rubber before I need to think about replacing my tires. (The original tread depth was 9/32: the tires now have 5/32 to 6/32.) Michelin Energy tires are not known for giving long wear, unless you have larger-than-normal tires, as I do.

Pluses and minuses of increasing tire diameter: better mileage, tire life and handling, but less perky at the stop sign. Your speedometer and odometer may be less accurate, or sometimes better. Either way, don’t be fooled by the change with the gauges, this could cost you a ticket—lower your indicated speed proportionately and be mindful that the odometer is reading lower, and you should be pleasantly surprised with the higher mileage you obtain. By the way, experiments indicate that the width of the tires does not seem to affect fuel economy

Rubber Internal Friction and Stiffness

Some kinds of rubber are much more “efficient” than others. Remember super-balls? They were so surprising because they could bounce up almost as high as they fell. The ratio of <bounce up> to <fall> is the “coefficient of restitution” of the ball’s rubber. This is the efficiency with which the material returns strain energy as it rebounds. “Internal friction” is a common term for this kind of energy loss. The amount of energy lost by the tire rubber in each rotation is proportional to the amount of flexing, and that in turn is proportional to the weight of the car (for all four wheels combined). This is why rolling resistance is proportional to the car’s weight. These days, many tire companies put additives in the rubber to lower its internal friction.

Now, about stiffness. Remember, I said the weight of the car is held up entirely by the air pressure in the tire? Having stiffer rubber in the tire doesn’t have any practical effect in holding up the car. But, the deflection energy is proportional to stiffness. And a part of that energy is not returned when the rubber rebounds. The effect on mileage is plain to see—tires made of stiff rubber have high Crr, and result in lower miles per gallon.

Let’s look one logical step further while we are still here. Rubber gets softer in hot weather and becomes stiff in the cold. So, we might expect that car fuel economy could increase in hot weather, and this is usually observed to be true. (Engines usually run more efficiently when hot also.) The most efficient energy-saving tires are made of softer rubber, with comparatively flexible sidewalls and tread.

Summary

For best fuel economy from your wheels and tires---

1. Buy only top-quality tires that are known to have high efficiency. The rolling resistance coefficient should be Crr = 0.009 or less. Sporty low-profile tires have higher Crr.

2. Buy tires with a slightly larger diameter, but be sure that they don’t rub other car parts on turns or bouncy roads. Choosing higher-profile tires is a good way to increase diameter.

3. Keep tire pressure higher than normal, up to 10% below sidewall stated pressure, and check tires regularly to be sure the pressure is correct. It’s best to check tire pressure cold. If you think the air temperature will be hotter when driving, subtract one psi of pressure for each 10 degrees hotter.

Suppose you are ready to buy a new set of tires. How do you choose? It’s best if you can know the Crr for the tires. Here is an idea. First, ask if the tires you are buying have a satisfaction guarantee, and how that works. This is partial compensation for not knowing what their “official rolling resistance coefficient” is. Most dealers or tire companies will offer a 30-day satisfaction guarantee. Now, you can drive on them and see how your mileage changes. If you don’t get satisfactory results, you can take them back. You can also measure the rolling resistance coefficient of the tires yourself. That would be a good topic for another lesson.


Ernie Rogers

____________________________

* In the introductory section, the four components of force are spelled out in words. Here is the algebraic equation including all four parts:

F = Cd A 1/2 rho V2 + Crr Mg + M a + Mg • (grade%/100)
The first term, the aerodynamic drag, could be the topic of another lesson.

Drive Stick 04-09-2009 05:22 PM

That's simply too much information for one post

snowfish 04-09-2009 11:19 PM

I agree with Drive Stick, but let’s see it I’m on the right page……..

In order to have a lower Crr, that would mean the tire would provide less traction, right. The more it sticks (higher Crr) the harder to get it to turn.

I must have a really low Crr on the Metro now. If we have the slightest snow or ice, I can get stuck on level ground. Yet, on level glare ice, I can push it easier than letting the car do the work!

But on dry payment, we got 53mph a couple weeks ago in March. Now this is Minnesota, so March is not that warm. It was like 45-50 degrees that day. These tires will remain our “summer issue”

I’ve since acquired my “winter issue” tires for next snow season. I’m sure the M&S small truck tires have a much higher Crr, but I should be able to drift bust like nobody’s business!

Kind of a trade off between better FE and spinning your wheels.

I may have missed it, in the above post, but are tires labeled, or coded, for Crr?

bwilson4web 04-09-2009 11:54 PM

Quote:

Originally Posted by Ernie Rogers (Post 96756)
. . .

Rubber Internal Friction and Stiffness

Some kinds of rubber are much more “efficient” than others. Remember super-balls? They were so surprising because they could bounce up almost as high as they fell. The ratio of <bounce up> to <fall> is the “coefficient of restitution” of the ball’s rubber. This is the efficiency with which the material returns strain energy as it rebounds. “Internal friction” is a common term for this kind of energy loss. The amount of energy lost by the tire rubber in each rotation is proportional to the amount of flexing, and that in turn is proportional to the weight of the car (for all four wheels combined). This is why rolling resistance is proportional to the car’s weight. These days, many tire companies put additives in the rubber to lower its internal friction.
. . .

Can this be used for non-destruct measurement of relative tire rolling resistance?

Bob Wilson

Frank Lee 04-09-2009 11:58 PM

No kidding, my ADD kicked in early on. Everything ahead of "Tires and Rolling Resistance" can be deleted.

Quote:

Cutting Crr in half causes—
at 60 mph: 14% better mileage
at 40 mph: 20% better mileage.
Is that true? :confused:

almightybmw 04-10-2009 01:53 AM

Quote:

Originally Posted by Drive Stick (Post 96790)
That's simply too much information for one post

I suggest reading slower and thinking about what the words say versus just "reading" them. No offense intended; I read it slowly taking about 7 minutes to apply the thoughts to my own experiences. It helps concrete the information in your mind and reference it.

Quote:

Originally Posted by snowfish
I may have missed it, in the above post, but are tires labeled, or coded, for Crr?

Manufacturers currently do not post that data due to auto makers pushing for them to not. Every tire for every size will have a different Crr, thus making this an extremely time consuming process to measure each, but no more so than load and speed testing. It may also be for safety reasons. If people know the Crr of their tire and get in an accident, lawyers could use that against the manufacturer. Covering their proverbial arses.



I know I learned a few things from this post. Post length has no affect on information digestion. If it helps copy and paste into seperate pages to section the information so the "ADD" doesn't kick in like turbo boost.


EDIT: I copy and pasted into word. just a hair over 6 pages. Damn awesome. You go man.

CapriRacer 04-10-2009 07:38 AM

Hey, wait!! You guys started the discussion without me!!

And if you haven't freaked out by the volume of information Ernie posted, allow me to add:

Barry's Tire Tech

If you read everything on the web site - and not just that page, - you'll find the Ernie and I disagree about calculating the size of the contact patch, and the role air plays in holding up the vehicle, and a few other things that aren't important to the discusssion at hand, so I won't debate those issues here.

But for those who don't want to wade through all that information:

1) Rolling Resistance in tires is mostly caused by Hysteresis - the internal energy consumption of the tire. You could look at this is as internal friction generating heat.

2) Most of the rolling resistance is caused by 3 things: The material properties the tire is made out of, the amount of movement that those materials experience, and the amount of material there is.

3) Most of the energy loss occurs in the tread area, and because most of the tread area is tread rubber, it becomes the most important item in a tire's rolling resistance.

4) The amount of movement that causes this energy loss is mostly controlled by inflation pressure - very little is controlled by the stiffness of the sidewall by itself.

5) Tread rubber chemistry results in a 3 way technology triangle: Treadwear / Traction / Rolling Resistance. Put another wasy: To improve one, you have to sacrifice on of the others (or both).


**********************

OK, that's enough for now. Carry on.

hummingbird 04-10-2009 08:19 AM

While we are at it, a small query -

The contact patch varies with tyre pressure, as at higher pressures, the vehicle weight is countered by a smaller deformation of the tyres and thus a smaller contact patch.

As the tyres are pumped up to say 50 or 60 PSI (which the auto company did not intend nor prescribe), would its overall dia change to affect the effective turns of tyre per mile and hence the odometer accuracy? What would the delta be from say 30 PSI to 50 (or for that matter 60 PSI) for a vehicle ~2400 lbs?

IMO tread wear should also affect the odometer the same way.

Blue Bomber Man 04-10-2009 08:27 AM

Great post Ernie and everything seems spot on except I think I disagree with the stiffness argument.

Quote:

Now, about stiffness. Remember, I said the weight of the car is held up entirely by the air pressure in the tire? Having stiffer rubber in the tire doesn’t have any practical effect in holding up the car. But, the deflection energy is proportional to stiffness. And a part of that energy is not returned when the rubber rebounds. The effect on mileage is plain to see—tires made of stiff rubber have high Crr, and result in lower miles per gallon.

Train wheels are made of steel and thus are exceptionally stiff. They use these tires specifically for this reason, since the majority of a train's losses are due to rolling resistance. This stiffness decreases that internal resistance that you speak of.

Quote:

No kidding, my ADD kicked in early on. Everything ahead of "Tires and Rolling Resistance" can be deleted.

Quote:
Cutting Crr in half causes—
at 60 mph: 14% better mileage
at 40 mph: 20% better mileage.
Is that true?
Those numbers seem appropriate. According to a governmental study every 10% decrease in rolling resistance will result in in a 1-2% increase in fuel economy. Those numbers seem basically inline with that study. The difference between velocities is due to the proportion of rolling resistance and wind resistance when compared to the total energy. Energy lost to rolling resistance is linear and is related to mass, Crr and miles traveled. Wind resistance is not linear and goes up much faster.

Blue Bomber Man 04-10-2009 08:36 AM

Quote:

5) Tread rubber chemistry results in a 3 way technology triangle: Treadwear / Traction / Rolling Resistance. Put another wasy: To improve one, you have to sacrifice on of the others (or both).
Not according to a joint Federal and Californian study on tire rolling resistance. It states they are related, and altering one will generally effect the others, but that it is possible to improve all 3 with out sacrifice. Some tires are better than other tires in all three categories that you mention.


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