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My thoughts:
Go for as large a diameter as you think the rest of the drive line can handle. Large diameter gives you a longer footprint (once aired down), without increasing the 'uphill' aspect of sand too much - akin to tank tracks.
Go for width as a secondary option, it does help float, but I've seen and experienced a larger benefit from diamter rather than width on sand.
Larger diameter will also give other benefits - clearance, better angles, blah blah. It'll also help you on those tracks that others have been cutting up due to large tyres+poor suspension+poor driving.
T
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My experiences with tyres on the sand are road tyres are best in smaller (stock) sizes because they are softer typically and belly out more, but as soon as you start heading up to 32in etc the muddies are great as the deeper tread starts to act like paddle keeping you moving where the road tyres seem to just spin alot more.
As for diameter V width, the taller skinnier tyres are great, once you start going wider you need more power to get the best results from them, as the wider you go the harder your engine has to work to cut through the sand.
Best tyres i have ever driven on the sand with are 37x12.5x15 MTRs at about 6psi... i drive it hard at that pressure and have done more sand kays then most will in a life time on them and never once poped a bead.
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I have driven in the Sahara as part of an expedition from Sudan to Morocco over some 40 days. The most interesting sand driving was in the deep deserts of Libya and Tunisia.
As has been mentioned, sand is not all the same, with grains ranging from 3-5mm down to talcum powder-like stuff called fesh fesh.
When I first saw the rather beat-up vehicles used by our local guides and handlers, I felt sorry for them, thought they were too poor to buy decent tyres. All their vehicles on near-bald, skinny Michelins.
They taught us foreigners to lower pressure to 1bar (about 14psi) for "normal" dune driving, and lower to 0.5bar if car starts to bog. Their skinny, bald tyred cars went everywhere and got bogged a lot less than our MT-shod rigs.
In fesh fesh, the advice is to keep going, don't stop for buddy vehicles that bog, reach hard ground, park, and walk back with shovels to help. Stopping would only mean 2 stuck trucks instead of one.
Tunisian sand is generally much finer since prevailing winds blow from east to west, and the heavier grains fall first. As a result, Tunisian dunes are much smaller. Bigger grains can pile up higher.
Anywhere, point is, you don't need treads on sand. If tyres can claw, they will and only dig away sand under your tyres. There is no hard bottom to reach.
Traction is not really an issue since it's like driving on sandpaper. What's needed is a gentle right foot and, for climbing slopes, momentum.
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(not about sand driving, just tyres)
255/85 is a good size for a defender, and you can get BTG MT KM/2s in them. They fit on a defender without mods and are not too wide for a 33" tyre.
