I am thinking about building a 1 or 2 man blimp. How many cubic feet of helium
is required to lift, say, 300 or 500 pounds?

Asked by: Kevin Petersen

Answer

So you want to build a blimp! OK the first principle we need to invoke is that of
buoyancy. Any object in a fluid feels an upward force equal to the weight of the fluid
displaced by the object. For example, if a boat's hull takes the place of 500 lbs of
water, then the water exerts an upward force of 500 lbs on the hull. Makes sense if you
imagine the water being pulled down by gravity and thus trying to push its way into the
spot the hull is occupying. Second we know that in order for the blimp to not accelerate
in the vertical direction (i.e. come crashing down) the sum of the vertical forces must be
zero. Gravity is supplying the downward force of the blimp's weight here, so the buoyant
force must be equal in magnitude to the weight, but in the upwards direction! The rest is
just math:

The weight you want to hold up is say, 500 lbs.
Add to that the weight of the He you will be using W(He). A good way to express the mass
is as the volume of gas you use, times the density of the gas, times the acceleration due
to gravity:

W(He) = V (He) x D (He) x g

The buoyant force is equal to the weight of fluid (in this case air) displaced and so is
given by the similar formula:

F (buoyant) = V(He)x D (air) x g

As stated above:

F (buoyant) = W(He) + 500 lbs

Solving for V we get :

V = 500 lbs / ([D(air)-D(He)] x g)

V comes out to be about 176,000 liters or 6,200 cubic feet.
Answered by: Rob Landolfi, Science Teacher, Washington, DC

'The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as in poetry.'