I ran 31/10.50x15 Goodyears when I had my budget boost only. You will probably rub must on your control arms depending on what your rim offset is. This is only when you turn the wheel to the max either direction. That was the only problem I had. It's not a big deal.
I'm running 31x10.50 BFG A/T KO's right now under 1.75", stock saged springs, T/R front bumper (brings the front down an inch or so), and on the stock rims. They only rub on the control arms at full turn. Just put some washers under the steering stops.
Also, don't run Thornturds...they suck. Get some real swampers, or some Interco trXus..they're cheap, and they work. Thornturds are poser tires IMHO.
I'm a big fan of the TSL/SX myself, running them on the old CJ (33x15.50). Sidewall traction is great, especially when trying to turn through ruts and stuff, plus they don't tear as easily.
Wish they made 32x11.50 Boggers though, I'd love to run them on my Grand.
I believe that a 31" tire can be run witha budget boost with slight rubbing; however, i would also stay away from the Thornturds. Sure, they are pretty but to put it to you nicely...they suck. It is rare to see thornbirds with any tread. It almost seems like they come from Interco bald. If i had just the budget boost i would buy a set of 31x10.50 BFG or Pro-Comp Mud's. Both of these tires look good, pull well, and last.
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