There are a few concepts at work here, so I will do my best to address them individually.
stumpy said:
how is it that, if inflated to equal tire pressure, i.e. 40 psi, a wide tire and a narrow tire can have different footprint AREAS? i understand they will have different SHAPES, that makes perfect sense. but area and shape are different.
Two tires of the same carcass construction, yet different widths will have different footprints with the same pressure. The shapes will also have very close to the same length. However, the wider tire will have a greater width dimension.
Let me try to explain this in different terms by removing the air component for a moment. Think of a solid rubber wheel: One that is 1" wide, and one that is 20" wide. The rubber is solid, and has no measurable deflection. The 20" wide wheel will have 20 times the area in contact with the ground compared to the 1".
Now lets reintroduce air, and go into detail on this: Air pressure inside the tire is only ONE component of what gives a tire shape and load capacity. The other is the tire itself. Have you ever tried deflating an E rated Super Swamper bias ply tire? On a light vehicle, the carcass wont even really start to deform until single digit numbers. This is the critical point. On that E rated Swamper, what is doing most of the job in supporting the Jeep? The carcass. Don't forget that the sidewalls are integral in supporting the weight of the vehicle. Where a passenger rated, single ply tire will start to deform much sooner as it relies more on air to support the vehicle.
Area and shape are different. A wide and narrow tire of the same construction must have different areas and different shapes.
Think again in the extreme. Do you believe that a 39x18 and 38x11 Bogger will have the same total area in contact with the ground? It is physically impossible, as they are within less than 10% of the load rating of each other, and within 5 psi of max pressure.
Pictures for reference:
18" width
11" width
stumpy said:
what does carcass strength have anything to do with anything?
Carcass strength and air pressure is what supports the load (vehicle and payload). Without the carcass, air has nothing to contain it.
Look at the side of a 255/85 and a 285/75. The sidewall is the same height. Now think of those tires without a rim; just resting against the garage wall. The tires maintain form because of the carcass construction. The heavier the load rating, the more they maintain form under load. Carcass' do not stretch (much), so if the air pressure in both is the same, and the only difference is width, why would the narrower tire elongate significantly more than the wide one? It wouldn't.
stumpy said:
ground pressure is ground pressure is ground pressure, isn't it?
Please elaborate, thanks.
stumpy said:
it doesnt make sense to me that sidewall strength can support more than the air pressure inside the tire. the air must support the tire at the same "strength" as the sidewall, otherwise there would be less ground pressure at the center of the tire, requiring the footprint to elongate.
Think of the example above. Just a naked tire carcass with no wheel and no pressure. It maintains its shape, and will even take a load on top of it without crushing. Once you combine a tire, a wheel (making a chamber) and air pressure the load capacity increases significantly. The narrower tire and wheel combo have the same internal pressure as the wide one, only the volume changes. So why would the narrower tire be subject to greater elongation than the wider one with the same load? It wouldn't.
stumpy said:
if, in the real world, a tire footprint does not have equal pressure across the entire area of the footprint, the total ground pressure would still have to be the integral of all the pressures on all the very small square inches.
Sorry, I don't quite follow you here. Please provide more detail, thanks
stumpy said:
assuming a constant internal air pressure for all four tires of either narrow or wide dimension, the ground pressure for a 5000 lb vehicle must still be 5000 lbs regardless of total footprint area and regardless of shape.
Yes, true. Vertical load is vertical load. What changes between narrow and wide tires is how much load there is per square inch.
stumpy said:
if the pressure on each square inch of tire changes, so must the area of the footprint.
The footprint will change, which will change the ground pressure for each square inch.
Hope this helps... I am off to dream of Diesel Troopy's (with narrow tires of course ;p )