sacharlie wrote:In reference to air cushions.

If the bladder is 12x12=144 square inches.

At 1psi it will support 144lbs without deflection, right?

At 0.5psi it will support 72lbs without deflection, right?

For the above it makes no difference if the bladder is 1", 2" or 3" thick or cubic inches don't come in to play, right?

I ask cause I don't know what i don't know.

shirley_hkg wrote: Very true , provided that everything is static and evenly distributed.

As Shirley says, but that's not the case because air is compressible (and so, by definition, is your bladder). As you increase the pressure on the top surface the pressure inside will increase and therefore the volume will decrease. This relationship (at a constant temperature) is called the adiabatic relationship and is given by the formula:

- PSX_20190822_064628.jpg (13.96 KiB) Viewed 371 times

Where P is pressure, V is volume and gamma (the little y thing) is the adiabatic index, about 1.4 for air.

What this saying then is if pressure increases, volume decreases (at a constant temperature) given by:

p1 v1^1.4 = p2 v2^1.4

Or, rearranging

v2 = ((p1 v1^1.4)/p2)^(1/1.4)

You fill it with air at 1psi above atmospheric and seal it so no air can escape. Let's suppose your bladder is a box 12 x 12 x 2, a volume of 288cu in,

at that pressure. So every surface of your bladder experiences an internal pressure of ~15.7psi (this would be so much easier in sensible SI units). You now place your weight on top applying an extra 1psi to the gas which increases to 16.7psi. The volume of the air will then decrease from 288 to 275.6cu in.

Calculating the dimensional change will depend on the material & construction of the bladder and is too complex for now, but intuitively since top and bottom are dimensionally constrained the top surface drops and the side walls expand. But let's assume for now that the side walls are elastic vertically but rigid horizontally (treating the top as an unconstrained piston). Then the top surface drops to 275.6/144 = 1.9". Unless your side wall material expands significantly this will be a good approximation.