Air mattress pressure question regarding partial inflation

[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

 

[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 !

--

 

[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.