Necessary air pressure in flexible vessel to lift a certain mass I have the following situation in mind:  
A big airtight bag of arbitrary shape with a person standing on it. The bag gets inflated with air to lift the person.
Assuming that the bag is much larger than the persons footprint, how do I find the minimal overpressure in the bag that I need to lift the person of the ground?
I was thinking of just dividing the normal force of the standing person by the footprint area, but I am not sure on that approach 
$$F_n = 80×9.81 = 784\text{ N}$$  $$P_n = \frac{784}{0.2×0.3} = 13066\text{ Pa}$$
I have the feeling that the bag dimensions play a role as well, as intuitively I would say that to do this, a small bag would work better than a big bag, but again I'm not sure...
 A: It is just as simple as you suggest. At the moment my feet are exerting a pressure on the ground of my weight divided by whatever the area of my shoes is and the pressure exerted by the ground on me is what keeps me stationary. Exactly the same applies to your air bag. once the air pressure is the same as the pressure you exert on the bag it will support you.
But there are a couple of extra things to consider. When you stand on the bag you will compress the air in it and you'll sink until the air is compressed enough to match the pressure of your shoes. So the initial pressure can be lower than your shoe pressure and the bag can still keep you off the ground.
You mention the bag size, it's probably easier to compress the gas a lot in a small bag than in a large bag, so a small bag would probably work better. There's nothing especially fundamental about this; it's just that a large bag allows more room for the air to move into as your feet compress it.
A: According to this website it is not recommended for the object being lifted to have only a small footprint on the inflating bag:

You can see that with a small (not recommended) footprint, the surface tension of the bag (which apparently is quite stiff) will contribute to the lifting of the object (the "sling effect" mentioned in the image).  These bags have multiple layers of rubber and are reinforced with either strong synthetic fibers (aramid) or steel cables.  
Your calculation of 13066 Pa is correct, but it will really be the upper limit to the true amount of pressure needed to lift the person.  Surface tension of the bag material will effectively increase the area that is supplying the lift and thus a lower pressure will be suffice.  The exact pressure needed is impossible to calculate without detailed knowledge about the bag material, it's properties and the height you want to lift the person.
