Tires: Low Rolling Resistance

[TromboneAl]

Isn't the circumference 2 * pi * R? Or are we talking about different measurements? Pi R^2 is area.

If it's a circle.

Take the extreme case. You let almost all the air out of the tire so that you are almost riding on the rim. Much of the tire will be flopping around like Bob Dole on an island without a pharmacy.

Traction is broken when the hub gets closer to the ground.

 

[haha]

If it's a circle.

Take the extreme case. You let almost all the air out of the tire so that you are almost riding on the rim. Much of the tire will be flopping around like Bob Dole on an island without a pharmacy.

Traction is broken when the hub gets closer to the ground.

Now, that is an extreme case!

ha

 

[ERD50]

Isn't the circumference 2 * pi * R? Or are we talking about different measurements? Pi R^2 is area.

Thanks, I edited my original. Yes, we want circumference. Darn it, I *knew* the difference, went through both in my mind, but when it came to typing it I still did the wrong one. I'm getting old

If it's a circle.

Take the extreme case. You let almost all the air out of the tire so that you are almost riding on the rim. Much of the tire will be flopping around like Bob Dole on an island without a pharmacy.

Traction is broken when the hub gets closer to the ground.

Now, that is an extreme case!

ha

Yes, it's extreme, but it demonstrates the point. The effective radius is really the point from the hub to the ground, and that should be used to determine the effective rolling circumference. Or, to eliminate other variables in how that tire might move around - mark it and the pavement with a chalk line, push the car one revolution, and measure the distance.

I'll get right on it .

-ERD50

 

[samclem]

I think SteveL and HaHa are right--we care about circumference, not radius/diameter. To test this, you could put a chalk mark on the tire, inflate to 45 PSI and measure the ground distance covered by exactly one revolution (chalk mark at 6:00 to chalk mark at 6:00). Then deflate to 20 PSI and do it again. I'm fairly sure the length of the lines on the ground will be virtually the same regardless of tire pressure (those steel belts aren't getting any longer and shorter with tire pressure, I'll bet). If this is correct, the speedometer/odometer accuarcy won't vary due to tire pressure.

I think higher tire pressures increase gas mileage by reducing the amount of flex and distortion of the tire as it rolls. This flexing causes internal friction within the tire rubber (just as a paper clip heats up as you rapidly and repeatedly bend it at the same spot) and also increased "scuffing" of the tire rubber against the pavement as it squashes out to the sides.

 

[haha]

Or, to eliminate other variables in how that tire might move around - mark it and the pavement with a chalk line, push the car one revolution, and measure the distance.

This I buy.

Ha

 

[haha]

I think higher tire pressures increase gas mileage by reducing the amount of flex and distortion of the tire as it rolls. This flexing causes internal friction within the tire rubber (just as a paper clip heats up as you rapidly and repeatedly bend it at the same spot) and also increased "scuffing" of the tire rubber against the pavement as it squashes out to the sides.

Absolutely. Another effect is that due to the larger road footprint of a correctly inflated vs. an overinflated tire, there is more friction. Thus more rolling resitance (possibly bad) and more stopping and cornering adhesion (definitely good).

Ha

 

[jazz4cash]

This discussion is [-]getting[/-] way over the top, so I hesitate to add to the discussion, but the circumference will in fact grow with more pressure. Many cars have low tire pressure systems that compare revs per mile from the wheel speed sensors so they can "tell" when a tire is low on pressure without measuring the pressure directly. The wheel speed sensors were not put there for tire pressure monitoring, they are part of the anti-lock brake system. See the indirect TPMS discussion in the link below

Tire-pressure monitoring system - Wikipedia, the free encyclopedia

 

[haha]

... but the circumference will in fact grow with more pressure.

Quite possibly will, but no one denied that. We only said that the circumferance must mbe measured, not calculated from the "radius" - which in fact is not a true radius since a tire going down the road is a distorted cirlcle, not a perfect circle.

Ha

 

[jazz4cash]

Ha, here is the comment I referred to (and I think there are others)....I knew I shudda kept my big mouth shut.

Don't see how tire pressure changes tire circumference. Yes, more of the tire is on the ground and the height is lower, but the circumference of the tire doesn't change. The tires do not "stretch" when inflated. Lower air pressure means more tire is in contact with the road surface, creating more resistance, taking more energy to be moved, generating more heat.

 

[haha]

Ha, here is the comment I referred to (and I think there are others)....I knew I shudda kept my big mouth shut.

I see. Do you have data about this stretch? It seems that a steel belted tire inflated to normal recommended pressures shouldn't stretch much, say within the range of approved pressures.

I admit I have zero experience measuring tire circumferance, and I have definitely seen light racing tires on a bicycle stretch, but I never considered if or how much an auto tire might stretch at normal pressures.

Ha

 

[samclem]

Emphasis added:

I think SteveL and HaHa are right--we care about circumference, not radius/diameter. To test this, you could put a chalk mark on the tire, inflate to 45 PSI and measure the ground distance covered by exactly one revolution (chalk mark at 6:00 to chalk mark at 6:00). Then deflate to 20 PSI and do it again. I'm fairly sure the length of the lines on the ground will be virtually the same regardless of tire pressure (those steel belts aren't getting any longer and shorter with tire pressure, I'll bet). If this is correct, the speedometer/odometer accuarcy won't vary due to tire pressure.

I guess it is possible that the tire circumference grows some tiny amount with increased pressure. But, this phenomenon would produce exactly the opposite impact on observed gas mileage: Higher tire pressures would produce lower observed gas mileage.
Why: Say we have two cars: one with larger circumference tires and one with smaller circumference tires. The car with the higher pressure (larger) tire would be traveling the same distance with fewer wheel revolutions as the other car. The speedometers/odometers in our cars measure wheel revs, so this car would (incorrectly) show less distance traveled than the car with the smaller tires. But the engines in both cars drove the cars the same distance, and did the same amount of work (discounting any other phenomenon caused by tire pressure). Even if we make the argument that the bigger tire gives the car a "taller" gearing and resulting better "true" mileage (as measured on the road surface), this will not have any impact provided we measure distance traveled by counting wheel revs.

So, even if tire circumference is effectively reduced by having reduced tire pressure (a point I'm not ready to cede as I think of those circumferential steel belts), the effect on observed mileage would be opposite to the one we see in real life, indicating other factors are far more important.

 

[NW-Bound]

Heh Heh Heh...

On this subject, my thought has always been along the line of thinking as T-Al, that an underinflated tire would have a lower effective radius, hence would require more revolutions for the same distance travelled.

Then I saw the "circumference" argument from SteveL and Haha.

To borrow from a Web link included below, let's call TAl+ERD50+myself+others the "radialist" camp, and SteveL+Haha+Samclem+others the "circumferencialist" camp.

I discovered that what I always take for granted has been challenged. And yet, it is not so easy to dismiss the "circumferencialist". To do so, their argument about "traction" must be addressed, but I got to admit I do not have an answer offhand. I can see the point that if the steel belt circumference is not very compressible, and if the tire does not slip, how do you satisfy the circumferencialist camp?

The best way to settle this is to go out and do some measurements yourself. However, I am afraid measuring the distance travelled with a few tire revolutions may not be decisive enough, due to the small errors required.

Heh Heh Heh...

The inquisitive mind just got to know who is right. Sooo, I searched the Web. This is fun. What an ER'ed guy do all day?

Heh Heh Heh...

Found several patents and engineering conference papers on applications of the "radialist" principle for mandated TPMS (Tire Pressure Monitoring System). Basically they compare the rpms from each wheel to determine if a tire has been underinflated, or use GPS for accurate determination of distance travelled.

http://ddl.stanford.edu/files/NLSlipAVEC2002.pdf

http://ieeexplore.ieee.org/Xplore/login.jspurl=/iel5/10947/34462/01644529.pdf?arnumber=1644529

http://www.embedded-control-europe.com/pdf/ecemay04p20.pdf

Method for monitoring tire pressure variation of automobile tire and system for realizing the same - Patent 7395177


Soo, the academia and industry are in the radialist camp.

Heh Heh Heh..



Also found several forums whose members were also inquisitive on this very same question.

The most relevant info came from this guy, who has done what all of us would have done. He tapped into the wheel revolution sensors of his Prius ABS (Antilock Brake), and looked at the signals on an oscilloscope carried in his car (Obviously an EE like myself). He looked at the signals with both wheels at 43 psi, then with one deflated to 35psi.

His conclusion: Radialists win!

Quote: "But that difference between 43 and 35 psi, still quite tolerable from a safety standpoint, created a significantly measureable delta in wheel speed."

I don't profess to know how the tire gets deformed so as to deceive the circumferencialists, but the real world is what it is.

Heh Heh Heh...

Details are at

http://www.techno-fandom.org/~hobbit/cars/tpms/pts.txt

The next question is: How to explain the "circumference" enigma

 

[ERD50]

Heh Heh Heh...

Then I saw the "circumference" argument from SteveL and Haha.

To borrow from a Web link included below, let's call TAl+ERD50+myself+others the "radialist" camp, and SteveL+Haha+Samclem+others the "circumferencialist" camp.

Found several patents and engineering conference papers on applications of the "radialist" principle for mandated TPMS (Tire Pressure Monitoring System).

Soo, the academia and industry are in the radialist camp.

Heh Heh Heh..

His conclusion: Radialists win!

Good catch - I can't believe I didn't think about the TPMS - I know that is one way they do it, sense air pressure through deltas in rotation. What more 'real world' proof do we need?

The next question is: How to explain the "circumference" enigma

Ummm, I dunno. Although you correctly placed me in the "radialist" camp, I started making some sketches of tires and hubs (which ended up looking like bad cartoon drawings of bad boob jobs ), and I started having my doubts. Even though the 'apparent' radius is less - the tire still has to go around that whole circumference - you don't get rid of any tire. But I think it in fact does 'grow', and the steel belts must move around and/or displace space within/between the rubber (? got a better explanation?).

-ERD50

 

[NW-Bound]

An underinflated tire must undergo some bad deformation at the ground contact point, though I don't know if your bad boob jobs drawing would offer a plausible explanation . Whatever that deformation, it was severe enough to cause eventual catastrophic damages, a la Ford Explorer roll-overs.

Hopefully, some tire experts among us will offer an explanation.

 

[samclem]

NW-Bound, that was a truly monumental and worthy effort on your part--good sources and everything.

The most relevant info came from this guy, who has done what all of us would have done. He tapped into the wheel revolution sensors of his Prius ABS (Antilock Brake), and looked at the signals on an oscilloscope carried in his car (Obviously an EE like myself). He looked at the signals with both wheels at 43 psi, then with one deflated to 35psi.

His conclusion: Radialists win!

Quote: "But that difference between 43 and 35 psi, still quite tolerable from a safety standpoint, created a significantly measureable delta in wheel speed."

At this juncture I must make an observation about the (impressive) research provided by the Prius (nut!) at your link:

-- His measurements (indirectly) indicated that the difference in effective tire "radius" (his term, not mine) was tiny:

855 revs/mile --> effective radius = 11.794 in. @ 43 psi

856.875 revs/mile --> effective radius = 11.768 in. @ 35 psi

Because his device counted revolutions, he was effectively determining relative wheel circumferences (not radi), and they differed by only 0.2%. So, even if this circumferential "stretching" is occuring with higher tire pressure, the effect is miniscule.

But, back to my previous point and the association with MPG: If it is true that lower PSI tires truly do have a shorter circumference, then a car with such tires should produce a higher indicated MPG (if MPG is derived from tire roations, which is the case in virtually all cars). That's not what we see in the real world.

 

[NW-Bound]

I will admit to being excited at finding a report from this tinkerer that I missed the minuscule 0.026" difference in effective radii. However, he was going from an overinflated 43psi to a "Toyota recommended" 35psi. Had he gone from the recommended 35psi down to, say 25 or 20 psi, the effect might be quite a bit more. Still, the effective radius change would not be a large percentage.

I read further down this time, and saw that the next post in the thread said

"Sorry, but the Department of Transportation has already considered
(and rejected) indirect tire pressure monitoring based upon ABS
sensors. They found that while it could detect severe loss of
pressure, it wasn't able to detect slight losses as effectively as
they wanted.

So the mandated TPMS systems are direct pressure measurement types."


Anyway, I was not thinking about the relationship of the tire radius to the MPG at all. We all know MPG is rather severely degraded with tire underinflation, as we all can extend from our experience of physical exertion with an underinflated bicycle tire. With an underinflated tire, the higher rolling resistance swamps out the small effective radius change, and the car computer still properly displays a lower MPG. I have no problem with that at all.

 

[FUEGO]

This would make a good final exam question for an Engineering Dynamics/Mechanics class. Maybe throw in some Mechanics of Materials and different deformation characteristics of steel vs rubber, drop a couple of moduli of elasticities, a question on elastic vs plastic deformation, and you might even stump the smart students.

If the professor were sadistic.

 

[NW-Bound]

If the professor were sadistic.

Aren't most of them?

Nah... Mundane appearing as this problem is, a definitive answer must come from an expert in this field, someone who works at Michelin, GoodYear, or at least in Detroit.

 

[SteveL]

While we are close to counting the angels on the head of this pin, I once more enter the discussion....

If you take the two Prius tire radii and calculate the difference, it means that the circumfrence has changed by .224 inches. These tire/wheel combos make about 854 revolutions per mile, meaning in each mile, the better inflated tire goes about 4 feet further. I submit that this difference is not material in whatever difference is mileage produced by differences in inflation.

Lower inflation means more tire on the ground, more friction, more heat, and more energy spent just moving the weight of the car on the tire.

 

[Gardnr]

UPDATE: These tires give me significantly worse gas mileage than the Toyo Ultras did! The average of the last five tankfuls with the old tires: 40.84 MPG. The average of the first five tankfuls with the new tires: 36.98 MPG.

We drive 15,000 miles per year, and use 38 more gallons per year, or, at $3/gallon, $114.

I guess it's not worth taking the tires back.

I'm no mechanical engineer (or engineer of any stripe) but I do know that cold weather has a detrimental effect on mileage; higher density air, and other factors in a cold engine. Made even worse if you're making shorter trips and thus more miles on a cold engine. I know that my mileage is significantly and consistently lower in the winter.

I didn't see it in the discussion so I'll ask. Have you made any attempt at factoring in (correcting for) cold weather operation to the decrease in mileage? I'm not sure how to do that other than to take historical data for your car and correcting for the difference you normally see in cold weather.

Just a thought to keep you guys busy.

 

[ls99]

Had missed most of this thread due to a trip of 3 days (560 miles round trip) for a family friend's funeral.

Having had a suitable nap, got a chance to read the thread. Most impressed with the amount of energy and analysis expand by both the radial and circumference camps. Most of all of the Prius owner's multi decimal results.

My interest was in the mileage question of tires. The one item not mentioned in the discussions is thread squirm. All new tires will give lower mileage due to thread squirm. SO even if replacing old worn out tires with exact same brand, the new ones will give poorer mileage than the nearly worn ones.

My other interest is in inflation pressures. Some years ago reading about pursuit driving, the instructor's opinion was to run tires at maximum sidewall pressure. It will give (very) firm ride and handling. From an old graph I copied It shows rolling resistance decreasing by about 8% if pressure is incrased from 32 psi to 40 psi. Allows for faster tuns on corners (tire will have less tendency to roll off of rim) and higher hydroplaning speeds. Hydroplaning speeds change from about 45 mph at 32 psi to about 68 mph at 45 psi.

So in that spirit on highway trips my tires are at max allowed sidewall pressure. Have no compulsion at measuring precise mileage, but do enjoy the very positive handling of the car. This 560 mile run was in DW's 2006 Buick LeSabre, average outdoor temperature of 32 F for the run, Rain by the buckets both directions, indicated mileage by the car's cpu of 27 mpg, at majority of the time speeds well north of 65.
Having recently put new tires on this car was comforting. They a very high speed rated, directional tread, max pressure on sidewall 51 psi. So, traveling at high speed in the rain at full rated pressure i had no hydroplaning issues. Dry pavement handling is phenomenal. Though for around town, to please wife's ride comfort I drop pressures to 35 psi. The high performance tires are in part to compensate for DW's (and my) lead foot. ( I nick named her Mario Andretti).

So hope i did not open another can of worms on the hydroplaning issue.

Cheers!

By the way stunt drivers driving pickup trucks, tipped on two wheels, don't roll standard LT rated tires off the rim because the inflate them to 100+ psi.

 

[jazz4cash]

You guys are hopeless and dangerous and should stick to ER discussions....or just keep havin fun, but stay away from my tires.

FWIW, the tire with the larger circumference does not tell the speedometer it's dimensions have changed. The speedo uses transmission output rpms for it's calculation. The larger circumference tire would have travelled more miles than the odo would register.

I lost the logic behind why anyone believes larger circumference hurts fuel economy...it does not. Increasing tire pressure will improve fuel economy by lowering N/V ratio (more circumfernce means more miles travelled per engine revolution) AND reducing Rolling Resistance (less tread deflection & squirm). The instrumentation discussed here is likely not precise enough to measure these differences.

Best, easiest way to measure rolling resistance is making timed coastdown runs from say 60 mph to 50 mph with a stopwatch. Repeat test in opposite direction of travel and average the results. Adjust tire pressure and repeat test in each direction. Running the test in neutral would improve accuracy, but it's generally illegal on public roads.

 

[samclem]

FWIW, the tire with the larger circumference does not tell the speedometer it's dimensions have changed. The speedo uses transmission output rpms for it's calculation. The larger circumference tire would have travelled more miles than the odo would register.

I lost the logic behind why anyone believes larger circumference hurts fuel economy...it does not. Increasing tire pressure will improve fuel economy by lowering N/V ratio (more circumfernce means more miles travelled per engine revolution) AND reducing Rolling Resistance (less tread deflection & squirm). The instrumentation discussed here is likely not precise enough to measure these differences.

Everyone agrees that higher pressure = better mileage.

A car with a larger circumference tire will produce lower indicated MPG, if all other factors are equal. That's because (for the reasons you describe) the odometer will (incorrectly) show that the car with the bigger tires didn't travel as far.

And here's another hair-splitting point: We shouldn't be using the term "circumference" for the distance around the (two-dimensional representation of a) tire. As ERD50's "bad boob job" drawings would clearly show (if only they were published!), the actual shape of a rolling tire is not a true circle, and the term we should be using is "perimeter."

 

[SteveL]

The angels keep flapping.......
Imagine a front-wheel drive car with a solid rear axle, with one of the two rear tires under inflated enough to show a bigger footprint on the ground. As the car goes forward, the rear axle will revolve and the tires will make the same number of revolutions, since the wheels are bolted to the axle. If the lower pressure tire was making less distance, it would be dragging, and get very hot, perhaps catching fire.

Under-inflation, unless to the point where the tire comes off the rim, doesn't materially change the circumference (perimeter) of a tire.

 

[ERD50]

Under-inflation, unless to the point where the tire comes off the rim, doesn't materially change the circumference (perimeter) of a tire.

How do you come to that conclusion? If by 'materially', we mean enough for an indirect TPMS to measure it, then yes, it changes 'materially'.

Tire-pressure monitoring system - Wikipedia, the free encyclopedia


edit/add - come to think of it - this description is probably flawed as well (and I'm not sure what it attempts to prove anyway):

The angels keep flapping.......
Imagine a front-wheel drive car with a solid rear axle, with one of the two rear tires under inflated enough to show a bigger footprint on the ground. As the car goes forward, the rear axle will revolve and the tires will make the same number of revolutions, since the wheels are bolted to the axle. If the lower pressure tire was making less distance, it would be dragging, and get very hot, perhaps catching fire.

You are correct that given a solid axle and two tires of different effective perimeters, that something has to give (or go in a circle). But, the most likely scenario would be that the under-inflated tire would have a larger footprint and therefore *more* traction, causing the other tire to drag (or skip-ahead I guess). No idea how much hotter it would get though.

-ERD50