# Air mattress pressure question regarding partial inflation

1. Nov 3, 2015

### elegysix

so last night I get on a sleep number bed and the remote reads 35 (unitless - I am assuming this number is related to pressure.) I click it down once to 30 and it deflates nearly completely. I get off the mattress, the reading drops to 5 or 10 and the mattress begins to inflate to 30.

So this got me thinking.

if we have a partially inflated air mattress, without any mass on it, I'd expect the pressure inside to be slightly above 1 atm. Then if we put a mass, m, on this mattress, I'd expect the pressure to roughly rise to mg/A, where A is the inner surface area of the barrier. (the mattress being inflated enough so that the mass does not rest on the floor.)

Now here's where it gets interesting - if the air mattress is more inflated than before, but still only partially inflated (without the mass), is the overall pressure after the mass is added still approximately mg/A ?

If there is ~constant pressure during partial inflation based on the mass, it would explain the poor response from the mattress (assuming the reading is based on pressure).

What do you think?
thanks

2. Nov 4, 2015

### BvU

So the remote isn't for the TV but for the matress .

If we make a small simplification: the contact area between mass and matress is the same in the various scenarios, then the pressures will also be the same: pressure times area must offset mg and that's a constant.

So I think you have the right picture in mind !

Sleep well !

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3. Nov 4, 2015

### elegysix

Thanks! I'd overlooked that the contact area was important... that makes complete sense. I was thinking surface area of the mattress for whatever reason.
So this means that as it inflates and deflates, a changing contact area means a changing pressure.

That means my stupid air mattress shouldn't have had a problem. Oh well.