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Changes in tire circumference under a load

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DRankin
Join Date: Jan 2000
Posts: 5116 Northern Nevada
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2002-06-21          39740


Some recent threads about tire pressure, tire loading, changes in tire height with loads and “axle wind-up” got me thinking. So I did a little experiment.
The front end of my Deere 4100 is currently equipped with 145-12 all season radial tires. For this experiment I loaded the FEL with 12 cinderblocks (about 330 lbs.) and I parked the tractor on a concrete slab. I measured the height by laying a level on top of the tire and with the bubble centered, measured from the slab to the underside of the level. With the FEL resting on the ground and all hydraulic pressure relieved, the tire measured 20+½ inches. Then I lifted the load of blocks and measured again and got 20+1/8 inches. So the tire compressed 3/8 of an inch under the load. Using Pi run out to 32 decimal places, it looked like this: 22 ½ equaled 64.42 inches circumference and 22 1/8 worked out to 63.25 inches. A difference of minus 1.17 inches circumference under a load.
Now the interesting part: I measured the actual circumference with a very flexible tape, being careful to stay in the center of the tread. The numbers look like this:
1)With the tire lifted off the ground 65 + 18/32 inches.
2)Tire on the ground carrying the weight of the tractor but not the FEL, again 65 + 18/32
3)Tire on the ground with the FEL load lifted, 65+17/32.
The actual difference in circumference was 1/32 of an inch, despite the tire losing 3/8 of an inch in height with the load.
So it appears that with radial tires, when the sidewall bulges under a load, it is simply laying more of the tread on the ground, and losing almost no actual circumference. How would this relate to bias ply tires? I am not sure, but common wisdom in the tire business is that bias ply tires tend to ‘squirm’ under a load. That would seem to indicate the bias ply tire is trying to lay more tread on the road also, but the sidewalls are not controlling the direction of the tread as well as a radial sidewall might. Input and comments, as always, are welcomed. Mark




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Changes in tire circumference under a load

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Art White
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2002-06-22          39749


Mark, the tires outer distance won't change. The length and width of the flat spot on the bottom is what will get you into trouble with gearing. ....


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Changes in tire circumference under a load

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TomG
Join Date: Feb 2002
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2002-06-22          39751


Mark: Lots for me to think through on the Board today and I can't do it this morning. I'm always much more interested in real observations than 'pat answers.' It's very good that you did the experiment.

I can say that somewhere in the older archives here I think is a method for calculating tire rolling circumference. It is more complicated than might be imagined and I don't know if the method allowed for different loads. Rolling circumference and tire circumference is somewhat different, and rolling circumference is what is speced for axle lead. I think that typical specs are for front axles to lead by several percent. It may not take huge differences to through a tractor out of spec.

Seems like the question of how load affects tire profile and rolling circumference has good potential here for another very interesting subject. Thanks for introducing the subject.
....


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Changes in tire circumference under a load

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Billy
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2002-06-22          39755


The radius of an under inflated tire is less, thus will change the tracking speed. To get a true figure, you need to measure the radius from center of axle to ground. In other words the radius from axle up will be greater than from axle down.

Billy ....


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DRankin
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2002-06-22          39757


Art, now I am really confused. Clearly the tire footprint changes and therefore so must the amount of traction generated. So I reckon we have to consider there is some more work energy required to overcome that drag, but if the tire still takes 65.5625 inches to complete a revolution on the ground, how does this effect a change in relative gearing between front and rear axles?
Maybe what is happening is this: Because the front axle is set up to turn a bit faster by a couple of percent, when we increase the loading/footprint/traction profile the front axle has more trouble generating the slippage that is necessary to relieve itself of the extra rpm’s built into the system, and therefore can bind at the ring and pinion interface even though it has the same circumference as a rounder, less loaded tire.
Are you tracking with me? Or am I hopelessly lost in a cosmic cul-de-sac of ethereal vapors? Wait! There’s Tom G. He’s up here with me. Someone please find the strings to our balloons and pull us back to earth!
....


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dsg
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2002-06-22          39764


Mark,
You have WAY too much time on your hands :))

David ....


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TomG
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2002-06-23          39773


Yes, and I think it's time well spent--a luxury to have time to figure out how something works. I’m never too happy black-boxing things.

I started out thinking that the main thing about axle lead was that the tread surfaces of the front and back tires should have about the same speeds. The explanation was real basic. The surfaces of big circles move faster than those of smaller when rotated at the same RPM. So, the rear axles have to have lower RPM's than the front axles.

Somewhere along the way I also picked up the impression that load affects axle lead, and in my experience that seems to be true. I guess I'm guilty of black boxing this and I usually need my explanations. The main thing that seems to change with load is tire shape, and I don't have a ready explanation for how changing the shape changes the tread speed. It's probably pretty basic but I'm just not using the right set of concepts to try and come up with an explanation.
....


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Stan
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2002-06-23          39775


OK, at the risk of having to think this through the rest of the way with you guys, I'll just throw out a comment and run.

The circumference of the tire can't change (OK, it can stretch a little, but not substantially.

And the surface speed has to be the same, all 4 tires are attached to the tractor and the ground - (again, if you have slip in the mud, it changes a little.)

What does change is the effective diameter which - with a nice serving of pi for everyone - changes the rpm.

So, at "X" rpm out of the transfer case, through the front differential should give you "Y" rpm, and on the proper size tire with another serving of pi, gives you the ground speed that matches the speed of the rear wheels (w/in whatever lead the manfacturer built in). If the tire has a smaller diameter (squished or mismatched) it is trying to go at a different "ground speed", which it can't, so things start to "lock up".

Anyway - that's my off the cuff analysis - I'm sure I'm pretty close, but I don't know if I explained it all that well. Hope I have made a positive contribution to the thread - its nice to stretch the brain now and then.





....


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Stan
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2002-06-23          39777


...and somehow I missed the short post from Billy P - who is heading to the same place. ....


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DRankin
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2002-06-23          39782


Before I lowered a tire with a load on a tape measure, I would have agreed with Billy and Stan. The question I was trying to answer was this: If the tire gets shorter (which it does) where does the extra tread go? The answer is it flattens out on the ground and creates more traction, or turning resistance, or drag or whatever you want to call it.
Picture a tank or a dozer track. With nearly half of it on the ground it creates tremendous traction and in doing so absorbs huge amounts of horsepower, which in turn limits the ground speed of the machine. If you could construct a giant set of spokes and turn the track into a wheel, would you have the same amount of traction? I think not. But, as the traction/resistance/drag decreases, could you then expect to turn it thing faster (given the same horsepower)? I think so.
If we were dealing with rigid wheels, like a spoke wheel from a 18th century wagon or the steel wheels from a 1920’s tractor it would be a different story. With no flexibility built into the wheel it has no choice but to sink into the earth under a heavy load.
That is the circumstance Art was describing. He described a set of tires where the rears flattened out on the ground with a load, but the fronts were so rigid that they acted like a wagon wheel and sunk into the earth. If both ends had the same amount of flexibility (or lack thereof) in the tread then the problem would not have manifested as it did.
Here is another facet of the same issue most owners of four-wheel drives know. When you get stuck in the mud, many times you can get your self out by letting most of the air out of the tires. Why does that work? Maybe you are turning your wagon wheel into a sort of a modified tank track.
My tape measure is telling me that the rolling circumference of my tires is not changing with a big load even though the tire gets measurably shorter. So I think it is acting like a tank track and laying more rubber flat on the road. More rubber on the road will certainly increase traction and reduce slippage. By reducing the slippage, the drive train is not able to rid itself of the lead built into the front axle as easily and begins to bind the gears, especially on paved surfaces.
....


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BillMullens
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2002-06-24          39786


Mark,

I've seen a discussion somewhere before about contact patch and tire pressure. The claim was that you can figure contact patch (area of tire in contact with the ground) given tire pressure (psi) and load on the tire. If the tire has 10 psi, and has a load of 500 pounds on it, then it would have a contact area of 50 sq. inches. I guess this ignores the stiffess of the tire sidewall. Also, the idea of letting air out of a tire works on pavement. I've done a little bit of drag racing (1/8 mile) with my Dakota, the difference in traction between 34 psi and 20 psi in the rear tires is amazing.
Bill ....


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TomG
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2002-06-24          39787


I did some searching in the archives here and elsewhere but couldn't find a thread I recall. I am starting to remember some things though. A couple of comments:

First is that tractor axles, and the wheels along with them, do rotate at different RPM's. They have to because the front and back tires sizes are different. I think the final axle gear ratio is speced in one of my Ford manuals.

Rolling circumference probably is less complicated than I thought. It is the outside diameter of the tire. However, a speced RC is for nominal pressures and loads. A more particular calculation would use loaded RC. Tire pressure at a given load does affect circumference somewhat. Shape of the tire under load may change length of the track but doesn't change the RC.

RC is sometimes used to determine an appropriate size tire when using something other than factory sets. Multiplying the front tire RC by the final axle ratio gives a zero lead RC for the rear tires. Several percent front axle lead is desirable. Axle lag can break things and may be dangerous.

Mark's method of driving on top of a tape measure should work OK for determining loaded RC. Now that I think about it, Mark's note that RC didn't change much under different loads shouldn't be too surprising. I believe that pressure increases under heavier loads, and greater pressure would tend to maintain the RC.

I believe that I've come to an understanding of Art's comment: 'It's the flat spots that'll kill you.' It seems like tire pressure may affect the axle lead somewhat but load may not have a great affect. Tires do deform under load and put more rubber on the ground more rubber should give more traction and less opportunity for the front tires to slip. Due to a built in front axle lead, they do have to slip. The added traction from weight plus tire flattening may be main factors here.

Mark: I believe that 'let the air out' to get out of mud works on tractors to an extent. It does increase traction since both length and width of the tract increases. However, at fairly low pressures, the centre tread starts cupping and the result is less traction. There's a NH farm tractor down the highway that's been converted into a snowmobile trail groomer. It has tracks that the tractor tires run in and an added set of passive wheels between the front and back tires. Tracks are used because they support the tractor in deep snow and provide good traction. I'll have to ask the guy if the tractor is operated in 4wd. I imagine that any front axle lead would give the tracks a hard time.
....


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Art White
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2002-06-24          39788


Mark, The outside of the tire will always be the same distance around except for wear. The size of the flat part on the bottom will get larger depending on load. That will give you a different lead lag ratio when useing the loader or depending what the tractor is carring and how. ....


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DRankin
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2002-06-24          39801


Art can say it in two sentences. It take a small book when I say it. ....


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Billy
Join Date: Oct 1999
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2002-06-24          39803


Hey Mark, here's a little experiment for you to do when you're not busy. It'll show you the difference in tire presures and distances traveled.

Park your truck on something hard that you can mark with chaulk. Adjust the tire presure in one tire to 35psi, mark the tire and ground at the middle where it sits on the pavement. Roll your truck until the mark makes one complete turn. Now adjust your tire presure to 20psi and roll it back one complete turn. You'll be able to see the difference 15 psi makes.

Although tire presure makes very little difference in circumference, it does in tracking speed (or distance).

When you have a bigger load, you have to increase tire presure to get your tracking ratio back.

Of course this only matters on 4wd.

You're right about letting the wir out for better traction. It puts more tread on the ground.

Billy ....


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TomG
Join Date: Feb 2002
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2002-06-25          39832


I've heard of a test similar to Billy's that is used to roughly estimate axle lead. Make a chalk mark at the bottom of both a front and rear wheel. Drive forward slowly in a straight line with somebody watching the tires until the rear tire turns one complete revolution. The front tire should turn the same number of times as the final axle drive ratio plus a bit.

I haven't thought it through, but the test probably is best to conduct on a hard surface in 2wd. The results should indicate if the loaded rolling circumferences of the front and rear tires are about right for the axle ration ratios. If the test is conducted in 4wd, there could be some slip between the front and rear tires, which is what axle wind-up does.

I wouldn't worry about writing books too much (got to say that since I end up producing books myself). It's about learning, which when done well, often is lengthy and messy stuff. But, a person has to go through this 'think through' stuff to make these ideas their own and actually come to know what's going on with a tractor. The alternative is to simply repeat what somebody else has said, and every time something a little different comes up, another question has to be asked. I'm happy enough that 'learning books' find some accommodation here with occasional reminders if the books become self-indulgent. Cripes, I almost wrote another one.
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