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Take the weight on the axle, divide by 2.
Take that number and divide it into the maximum load rating of the tire(on sidewall).
take that result and multiply it by the maximum tire pressure on the sidewall.
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Sorry, mdocod, but the maximum pressure listed on the sidewall of a tire may or may be be connected to the maximum load also listed there. This is a common misconception. The good news is that the method will yield a result that can carry more load than indicated by the method.
EXCEPT!!!
There isn't anything in the method to account for:
1) asymetrical loading (Differences from side to side)
2) Extra capacity - Good engineering design practice is to always overestimate the loads, then underutilize the component based on its capacity.
There are also several other errors in the posting.
In the example of the Rodeo:
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Here's an example of a rodeo:
I've figured with my tools and a passenger or 3 and a full tank of gas, I'm sitting at around 4500lbs on average, with around 2100lbs in the rear, and about 2400lbs in the front.(aprox) My door-panel sticker says 245/70-16 tires, 29PSI.
example: BF AT KO 245/70-R16, load range "D", 65PSI max, 2535lbs max.
front: 2400/2=1200, 1200/2535=0.473, 0.475x65=~31PSI
rear: 2100/2=1050, 1050/2535=0.414, 0.414x65=~27PSI
31+27=58(taking average of 2 here), 58/2=29PSI (the recommended PSI on my door), coincidence?
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Yes, it is a coincidence.
There is a mixing of P metric and LT metric tires in the example.
A P245/70R16 has a maximum load carrying capacity of 2094 # at 35 psi, but at 29 psi the capacity is 1940 #. Now since this is a "multi-purpose vehicle, truck, bus, or trailer" (quote from the Tire and Rim yearbook), these loads have to be reduced by 10%. So the rated load carrying capacity at 29 psi is really is 1763 #.
An LT245/70R16 - as stated - has a maximum load carrying capacity of 2535 at 65 psi, but at 29 psi, the capacity is 1428 # (my estimate - the chart doesn't go that low).
Bottomline: I think the methodology is faulty.