On Lighter-than-Air Craft

By P. Fobbington

To fly the stately airship again, ah, even to be but a passenger on such a vessel is a dream of many and represents flight in its true sense. No need to buzz loudly through the air just to stay aloft, one can float as they like. By some calculations an airship with a 1000 lb lift capacity would cost less than $5000 to build, but before one starts producing their own completely unlicensed and half-airworthy craft, one needs a little physics on their side to guide the design.

For lighter than air craft, no matter whether they use hot air or lifting gases such as hydrogen (or helium, that unexciting, expensive gas in limited availability), the mathematics all comes down to how the density of your lifting gas stacks up against the density of air. The principle of buoyancy holds sway here and it is worth stating formulaically that "The up- wards force on an object suspended in a medium (air, here) is equal to the weight of the volume of medium displaced by the object."

In the derivation given, two equations are presented-the first shows what maximum mass you can have for the structure of your airship's frame, including the material for the balloon, and passengers for a given lifting gas and volume of balloon. The second equation, just a rephrasing of the first, will tell you for a given mass of your craft how much lift you will get.

It is easy to see that if the density of the lifting gas were 0 (a vacuum balloon! …sadly not practical), you would have maximum lift. On the other hand, if your lifting gas was the exact same air as outside the balloon, your lift capacity would be equal to the mass of your balloon-downwards!-and you would obviously go nowhere . Tables are available on the inter- net and in chemistry and physics textbooks for the densities of various gases under different, commonly encountered temperatures and pressures. Please take a look at the example given, where the result calculated is that a cubic meter of hydrogen gas will lift about 1 .2 kg of payload.

Hopefully in times to come we can discuss the derivation of an equation that will let you find the density of any gas (or known mixture of gases) under any temperature and pressure conditions (so long as you have a periodic table handy), the effect of water vapour on gaseous densities, how to design lighter than air craft with lifting gases at higher working temperatures (i. e. hot air balloons. or hot hydrogen balloons!) and ultimately some explorations into more interesting unexplored designs.