## Airships

This chapter has emphasized that planes can't be made more energy-efficient by slowing them down, because any benefit from reduced airresistance is more than cancelled by having to chuck air down harder. Can this problem be solved by switching strategy: not throwing air down, but being as light as air instead? An airship, blimp, zeppelin, or dirigible uses an enormous helium-filled balloon, which is lighter than air, to counteract the weight of its little cabin. The disadvantage of this strategy is that the enormous balloon greatly increases the air resistance of the vehicle.

The way to keep the energy cost of an airship (per weight, per distance) low is to move slowly, to be fish-shaped, and to be very large and long. Let's work out a cartoon of the energy required by an idealized airship.

I'll assume the balloon is ellipsoidal, with cross-sectional area A and length L. The volume is V = lAL. If the airship floats stably in air of density p, the total mass of the airship, including its cargo and its helium, must be mtotal = pV. If it moves at speed v, the force of air resistance is

where cd is the drag coefficient, which, based on aeroplanes, we might expect to be about 0.03. The energy expended, per unit distance, is equal to F divided by the efficiency e of the engines. So the gross transport cost - the energy used per unit distance per unit mass - is Figure C.14. The 239m-long USS Akron (ZRS-4) flying over Manhattan. It weighed 1001 and could carry 831. Its engines had a total power of 3.4 MW, and it could transport 89 personnel and a stack of weapons at 93 km/h. It was also used as an aircraft carrier.

Figure C.15. An ellipsoidal airship.

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