Front to Rear tire raito

[Blake13]

I want to put some wider tires on my 2610d to get better flotation. I figured I would check the front to rear ratio so that I can make sure I am keeping the front tire rolling circumference lead perfect, as opposed to simply using the current tire ratio and getting something close. I'm going to include a long-winded explanation below the summary: 1, so anyone can check my work, 2, in case anyone is interested.

I will say, I am very surprised by the result, so PLEASE correct me if my methods are off.

Summary (quick, no math):
I jacked up the tractor and put a blocks down as a zero axis marker. I put a piece of tape on each tire at the block, engaged both axles in gear and recorded it on my phone for about a minute. Refer to pics at bottom. I counted revolutions to determine front to rear ratio of 1:0.6082. Using stock tire size rolling circumference and the experimentally determined ratio, it is calculated that the front tires lead by 9.5%. Based on this, a 13.6-24 tire would be better suited over the stock 11.2-24 rear tire. This is very surprising, so I question my methods.

One potential problem with my method; I locked the rear diff lock just in case, but with the front open differential could the spider gears be spinning slightly allowing the front two axles spin at different rates? Since there is no resistance i was assuming both front axles spin at the same exact rate. If this happens then it would obviously produce inaccurate result.

Update:
Jacking the entire tractor proved to be an unreliable method because while the front axle is suspended in the air, left and right sides will likely rotate at non equivalent rates (however proportional rates). Jacking the tractor from the side, forcing one side of each front and rear axle to remain in contact with the ground, stationary, ensures suspended axles are representative of gear ratio. Using this method the front:rear ratio 1:0.6341 was measured. This ratio is much closer to what was expected, showing the factory tire size have a 5.7% front lead.

Below is the trial using the first method, although not reliable, the methods and calculations are still useful.
_______________________________________

Long winded explanation with math:

After recording the wheels rotating, I watched the video and individually counted (double checked!) the number of revolutions for front and rear wheels. After exactly 17 rear revolutions the front turned almost 28. The tire lugs make a good measurement scale for this. It was shy (about 85%) of a lug-to-lug distance from turning a full 28. See "end" picture at bottom. The end picture is the video frame where rear tire hits revolution 17.
There are 17 lugs on the tire (don't confuse the 17 tire lugs with 17 rear tire revolutions, unrelated):
0.85 x 1/17 rev = .05 revs
1 - .05 revs = .95 revs
27 revs + .95 revs = 27.95 revs

So, the front tire does approximately 27.95 revolutions when the rear does 17.

And if you are thinking that my estimation of the front tire revs is not accurate enough, my accuracy is within 0.2%. This is because for certain, my observation is within one lug-to-lug distance. There are 17 tire lugs so 1/17th of a revolution over 28 revolutions . You can also see how the accuracy is dependent on how long the wheels spin, as revs go up percent error goes down.

(1/17) / 27.95 = 0.00210 = 0.2% error or 99.8% accurate
Or said another way, the front tire spins 27.95 +/- 0.03 revs (between 27.92 and 27.98 revs) for every 17 rear revs.

Now we can write this a few ways:
27.95:17 front to rear
1.644:1 front to rear
1:.6082 front to rear

Up until this point tire circumference was irrelevant. Now we can use this gear ratio to determine information like front tire lead for the factory tire set up. The factory tire arrangement is 7-16 front 11.2-24 rear. Carlisle literature for their Farm Specialist 7-16 lists a rolling circumference of 86.8 inches. The Farm Specialist 11.2-24 rolling circumference is 129.1 inches.

86.8" (front tire R.C.) x 1.644 (gear ratio) = 142.7" (theoretical matching rear tire R.C)
Rear tire must decrease by 5% R.C to give 5% lead to front tire
142.7" x 0.95 = 135.6" (theoretical rear tire R.C. to achieve 5% front tire lead)
So, acceptable stock rear tire R.C. range with 7-16 front tire: 135.6" to 142.7"

BUT the 11.2-24 is 129.1" R.C.
129.1" / 142.7" = .905 = 90.5%
This means the REAR tire is lagging by 9.5% with the factory tire size.

With a rolling circumference of 140", a 13.6-24 tire would be much better matched for the 7-16 wheel on this tractor... very weird.
_______________________________________


To corroborate this I never did like using the front wheel assist on pavement because it seemed to wind up more than I wanted. Disengaging was a bit tough, but not too bad.

Also to note, this determined ratio is almost exactly the golden ratio (1:0.618)! This must explain why the tire size relationship on the tractor is so pleasing to our eye :laughing:

Here is the start and end video frame of the experiment. I didn't include the video because I figure I don't need to prove that I can count to 28

Start

End

 

[bmaverick]

Drain out the beet juice and fill with helium instead. There are tanks at the Dollar Tree for these mylar balloons.

It's almost 11pm and this is a math final exam to read.

 

[Blake13]

No ballast onboard!

I condensed the most important bits into a small summary towards the beginning of the post. Between that and the pic it should be obvious what I did. If there's mistake, my bet is that its in the test method not the calcs.

 

[npalen]

There have been several threads over the years for determining lead/lag between the front and rears. Your method seems accurate for determining the gear ratio but there are other variables in determining lead/lag.
I think that the most reliable is traveling a marked distance on a hard surface and noting the difference in revolutions of the front and rear tires with the 4WD engaged and then disengaged.

 

[winston1]

Do you have 7-16 tires on front. Picture looks like the front is jacked up. Not used to seeing that.

I am not very smart on tires, what is the difference between 11.2/24 and 11.2/10-24?

 

[WinterDeere]

Seems to me that in your math you are assuming the unloaded tire diameter or radius can be used to calculate rolling circumference, or did I miss that? Under the weight of the tractor, rolling circumference will not be simply pi x diameter, and because rear and front tires compress differently, this must be carefully measured. I dint think there’s a good way to do it with the tractor in the air.

 

[npalen]

BUT the 11.2-24 is 129.1" R.C.
142.7" / 129.1" = 1.105 = 111%
This means the REAR tire is LEADing by 11% with the factory tire size.

If I understand correctly, you are saying that the smaller REAR tire is leading. It would actually be lagging with its smaller diameter and the FRONT tires would be leading. Right?

 

[CoyPatton]

I want to put some wider tires on my 2610d to get better flotation. I figured I would check the front to rear ratio so that I can make sure I am keeping the front tire rolling circumference lead perfect, as opposed to simply using the current tire ratio and getting something close. I'm going to include a long-winded explanation below the summary: 1, so anyone can check my work, 2, in case anyone is interested.

I will say, I am very surprised by the result, so PLEASE correct me if my methods are off.

Summary (quick, no math):
I jacked up the tractor and put a blocks down as a zero axis marker. I put a piece of tape on each tire at the block, engaged both axles in gear and recorded it on my phone for about a minute. Refer to pics at bottom. I counted revolutions to determine front to rear ratio of 1.644:1. Using stock tire size rolling circumference and the experimentally determined ratio, it is calculated that the front tires lag, not lead, by 10%. Based on this, a 13.6-24 or even 14.9-24 tire would be better suited over the stock 11.2-24 rear tire. This is very surprising, so I question my methods.

One potential problem with my method; I locked the rear diff lock just in case, but with the front open differential could the spider gears be spinning slightly allowing the front two axles spin at different rates? Since there is no resistance i was assuming both front axles spin at the same exact rate. If this happens then it would obviously produce inaccurate result.

_______________________________________

Long winded explanation with math:

After recording the wheels rotating, I watched the video and individually counted (double checked!) the number of revolutions for front and rear wheels. After exactly 17 rear revolutions the front turned almost 28. The tire lugs make a good measurement scale for this. It was shy (about 85%) of a lug-to-lug distance from turning a full 28. See "end" picture at bottom. The end picture is the video frame where rear tire hits revolution 17.
There are 17 lugs on the tire (don't confuse the 17 tire lugs with 17 rear tire revolutions, unrelated):
0.85 x 1/17 rev = .05 revs
1 - .05 revs = .95 revs
27 revs + .95 revs = 27.95 revs

So, the front tire does approximately 27.95 revolutions when the rear does 17.

And if you are thinking that my estimation of the front tire revs is not accurate enough, my accuracy is within 0.2%. This is because for certain, my observation is within one lug-to-lug distance. There are 17 tire lugs so 1/17th of a revolution over 28 revolutions . You can also see how the accuracy is dependent on how long the wheels spin, as revs go up percent error goes down.

(1/17) / 27.95 = 0.00210 = 0.2% error or 99.8% accurate
Or said another way, the front tire spins 27.95 +/- 0.03 revs (between 27.92 and 27.98 revs) for every 17 rear revs.

Now we can write this a few ways:
27.95:17 front to rear
1.644:1 front to rear
1:.6082 front to rear

Up until this point tire circumference was irrelevant. Now we can use this gear ratio to determine information like front tire lead for the factory tire set up. The factory tire arrangement is 7-16 front 11.2-24 rear. Carlisle literature for their Farm Specialist 7-16 lists a rolling circumference of 86.8 inches. The Farm Specialist 11.2-24 rolling circumference is 129.1 inches.

86.8" (front tire R.C.) x 1.644 (gear ratio) = 142.7" (theoretical matching rear tire R.C)
Rear tire must increase by 5% R.C to give 5% lead to front tire
142.7" x 1.05 = 149.8" (theoretical rear tire R.C. to achieve 5% front tire lead)
So, acceptable stock rear tire R.C. range with 7-16 front tire: 142.7" - 149.8"

BUT the 11.2-24 is 129.1" R.C.
142.7" / 129.1" = 1.105 = 111%
This means the REAR tire is LEADing by 11% with the factory tire size.

With a rolling circumference of 149", a 14.9-24 tire would be much better matched for the 7-16 wheel on this tractor... very weird.
_______________________________________


To corroborate this I never did like using the front wheel assist on pavement because it seemed to wind up more than I wanted. Disengaging was a bit tough, but not too bad.

Also to note, this determined ratio is almost exactly the golden ratio (1:0.618)! This must explain why the tire size relationship on the tractor is so pleasing to our eye :laughing:

Here is the start and end video frame of the experiment. I didn't include the video because I figure I don't need to prove that I can count to 28

Start
View attachment 634385
End
View attachment 634384

I may well have misunderstood what you wrote, but as I read, you lacked about 85% of the 28th revolution of the front tire. But then you used 85% in your calculations. If I understood correctly, you should have used 15% in those calculations.
Additionally, I believe you have skewed your revolution counts by have unloaded/no resistance on your tires.

In my opinion, you need to get more math involved in your process. The marks in your tires are your starting point, but you should do rolling circumference measurements. You probably need several people to assistance (at least 3-1 to drive, 1 to watch front tires and 1 to watch rear tire).

 

[Blake13]

Do you have 7-16 tires on front. Picture looks like the front is jacked up. Not used to seeing that.

I am not very smart on tires, what is the difference between 11.2/24 and 11.2/10-24?

Yes, 7-16 on front. Both front and rear are jacked off ground to allow free rolling.
I am not a tire expert either, but I believe 11.2-24 is the current preferred notation for the tire size. 10-24 is the older convention for the same size. Because these two notations are for the same tire it can also be written, 11.2/10-24.

 

[Blake13]

Seems to me that in your math you are assuming the unloaded tire diameter or radius can be used to calculate rolling circumference, or did I miss that? Under the weight of the tractor, rolling circumference will not be simply pi x diameter, and because rear and front tires compress differently, this must be carefully measured. I dint think there’s a good way to do it with the tractor in the air.

Actually I never used the diameter or radius of the tire for any calculations. Every time I used the tire size, I used rolling circumference. This number was always taken from the manufacture's literature.

Carlisle literature for their Farm Specialist 7-16 lists a rolling circumference of 86.8 inches. The Farm Specialist 11.2-24 rolling circumference is 129.1 inches.