Helium Lift Power
Date: 1999 - Revised May 2008
I would like to know the lifting power of Helium
eg: How much helium to lift 1kg
Any information would we great.
That depends on the density of air and the density of the helium. For
simplicity's sake, let's say the air and the helium are at the same
temperature and pressure. In that case, four grams of helium will occupy
about the same volume as 28.5 gm/mole of air. To lift an object, you need for
the mass of the object + the mass of the helium to be less than the mass of
the air it displaces. Since any object you want to lift will probably have
a much greater density than air or helium, let's neglect its volume for
simplicity's sake (in other words, we'll neglect the mass of the air
displaced by the object, because it will probably be only a small part of
the mass of the air displaced by the helium and the object together). Then
we can say that you need the mass of the object + helium to be less than
the mass of the air displaced by the helium.
M + Mh < Ma,
where M is the mass of the object, Mh is the mass of the helium, and Ma is
the mass of the air displaced. Our shortcut of neglecting the volume of
the object just says that
Ma = (28.5/4)Mh,
that is, a given mass of of helium will displace (28.5/4) times its mass of air.
Knowing that 4 grams of helium occupies that same volume as 28.5 grams of
air, we can see that four grams of helium will lift almost 25 grams:
M + Mh < Ma
M + Mh < (28.5/4)Mh
M < (28.5/4)Mh - Mh
M < Mh [(28.5/4) - 1]
M < Mh (7.125 - 1)
M < Mh (6.125)
M < 4g (6.125)
M < 24.5 g.
An easier way to look at this is to note that since four grams of helium displaces 28.5 grams of air, the "payload" for the helium is 28.5 g - 4 g = 24.5 g.
On a per gram basis, this means that one gram of helium will lift a payload (including the mass of the balloon) of (24.5 g payload)/(4 g helium) = 6.125 g payload /g helium. You can also see this in the above derivation if you just figure the mass of helium to be 1 g instead of 4 g.
So, to lift 1000 grams (1 kg), you need about 163 grams (~0.16 kg) of helium:
M < Mh (6.125)
M/(6.125) < Mh
Mh > (1000g)/ (6.125)
Mh > 163.3 g.
How much volume of helium is this? It depends on the temperature and
pressure. Neglecting the volume of the object to be lifted becomes a more
serious error as it becomes a larger fraction of the total volume. Under
normal conditions (ambient temperature and pressure), this is a small error.
Richard Barrans Jr., Ph.D.
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Update: June 2012