Again returning to the real world, all the math can go stuff itself because what we really care about is stress on the axles and drivetrain. And that is easy enough to sense without any math or measurements. If after driving in 4wd you go to shift back into 2wd but the 4wd engagement lever seems stuck or difficult to shift out of 4wd then what you are feeling means there is too much stress on the drive train. Figure out what is going on, and don't do that! Or if you can't help avoid that situation then for sure don't carry a heavy load in 4wd on high traction surfaces. Remember, even if the ratio is near perfect, you still need for a tire to be able to slip to protect the drivetrain.
Of course if you enjoy a little bit of math and mechanics as I do, you'll be as glad as I was upon finding the old notes from 1999 when I was setting up the Yanmar 336D for new wheels and tires. But as we weave through specs and such, please keep in mind that rolling circumference is easy enough to measure exactly for any tractor with the paint blob technique.
Another interesting thing in the notes notes from back then is that I see that since most Yanmar tires were still in production I first went to the tire manufacturer's web site where rolling circumference was among the listed specs. I wonder if it still is? And then since real rolling circumference is dependent on the tire's age (elasticity), the psi, and the weight of the tractor I compared their specs to what I got on my own using the paint blob test. The manufacturer's spec is going to be less accurate than simply measuring it yourself. But to my surprise the deviation from spec to my experiment was less than 1%.
It turns out that the rolling circumference of a real tire on the ground will always be less than what one gets by arithmatically calculating the circumference of a circle from diameter times pi.
The reason the rolling circumference is smaller is because the tire is flat on the bottom, and therefore the distance from the center of rotation to the ground (called the "loaded radius") is less than the distance from the center of rotation to the top of the tire. A tire has multiple - and different - radiuses. That is why the rolling circumference differs from the circumference of a mathematically perfect circle where the radius is always half the diameter of a circle.
It's lots of fun to see how real engineering both relies on math but differs from it when we enter the physical world. And of course it is it is easier to just measure the rolling circumference if your interest runs to such extremes. When you do, you will find that the rolling circumference of a rear tire is around 93 to 95 percent of the number you would expect to get if the tire were indeed a mathematically true circle. For the front tire expect a rolling circumference to be in the 92 to 94 percent range. Yes, the front tire variation is slightly different from the rear tire's.
Still, the last word is not the arithmetic. It is how it performs in 4wd carrying your particular weight on your somewhat worn tires and especially over your own unique soil & traction. Rich, how does yours shift into and out of 4wd?
Enjoy!
rScotty
