# what are the different grades of helium? Answered

how do the different grades affect lift capacity?

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Lifting ability depends on the difference in density between the lifting gas and the atmosphere gas.

For example, suppose you've got a V sized balloon of some gas.  There's an upward buoyant force equal the weight of the air displaced, and there's a downward force equal to the weight of the lifting gas.

ΣF   =       ρatm*g*V - ρlift*g*V

ΣF   =       g*V(ρatm - ρlift)

You can simplify this further by assuming that both the lifting gas and the atmosphere gas, are ideal gasses at the same temperature, so that they have the same mol density (P/R*T) = (1 mol/22.4 L).  The trick here is that now calculate that lifting force just based on a difference in molecular weights.

(ΣF)/(g*V) = (P/R*T)*(matm - mlift)
= (1 mol/22.4 L)*(14.4g/mol - mlift

Then you can use that formula to make a little table for some of your popular lifting gasses.

gas,    mol weight,  lifting ability,  relative to vacuum
vacuum,   m=0,        0.64286 g/L,    1.000,
H2,         m=2,        0.55357 g/L,    0.861,
He-3,     m=3,         0.50893 g/L,    0.792,
He-4,     m=4,        0.46429 g/L,    0.722,

Here I am assuming the most bad-ass lifting gas possible would be a super-engineered (magical really) balloon that could somehow hold vacuum without collapsing. Or maybe its a magic photon gas or something. You know: it exerts pressure, but doesn't have any weight.

So as you can see from the table, helium-3 is a little bit better lifting gas than helium-4, but molecular hydrogen (H2), is a little bit better than both of those.

The trouble with helium-3 though, is that its really expensive.  They have to mine it on the Moon, because it is not abundant on Earth.  I think its used in some fusion reactors, and you can look into that, but I expect isotopically pure He-3 will be very hard to find.

That's why I recommend using H2.  It's cheaper than both 'topes of helium, and you can make it yourself from tap water.
https://www.instructables.com/pages/search/search.jsp?q=make+hydrogen

Uh... wait a minute. It looks like was using the using the wrong number for the average molecular weight of air. It's N2 and O2. So I should have used matm=28.8 g/mol, and that changes that whole table:

gas,    mol weight, lifting ability, relative to vacuum
vacuum,   m=0,    1.2857 g/L,     1.000,
H2,            m=2,    1.1964 g/L,     0.931,
He-3,        m=3,    1.1518 g/L,     0.896,
He-4,        m=4,    1.1071 g/L,     0.861,

Sorry, 'bout that.  But the trend's still the same.  H2 is a little  better lifter than He-3, and He-3 is a little better lifter than He-4.