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How do you determine Tire size on a 4x4 tractor when going to Low Pro tires vs Factory tall ones?

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Like I said....Looking at a possible purchase..yep its 4x4.

When swapping from tall R1's to some Low pro Radials in a perfect world.

How do you know what size for front & Rear........I'm less than skeptical about trusting any of the current employees of Any tire store local to me.

I need to do this math myself w/Help of course.

It will be a spendy venture.....I don't think tractor Data lists gear ratio's for Front & Rear axlels.
Anyone know a source for this info...??

Heres the tractor..

Factory R1's
John Deere 5420 Tires
Ag front:7.50-16
Ag rear:16.9-30

This tells me not much.
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You need to find the distance traveled by the front and rear, per rotation, figure out the ratio of front to rear to ensure that any replacement tires are basically the same ratio to ensure that you're not introducing strain in the 4WD system. I'd be very suprised if there wasn't a published list of tires that can be run on that tractor.
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