Perhaps cd and fA are not quite the same as those of an optimized
aeroplane. But the remarkable thing about this theory is that it has no
dependence on the density of the fluid through which the wing is flying.
So our ballpark prediction is that the transport cost (energy-per-distance-
per-weight, including the vehicle weight) of a hydrofoil is the same as the
transport cost of an aeroplane! Namely, roughly 0.4 kWh per ton-km.
For vessels that skim the water surface, such as high-speed catamarans
and water-skiers, an accurate cartoon should also include the energy going
into making waves, but I’m tempted to guess that this hydrofoil theory is
still roughly right.
I’ve not yet found data on the transport-cost of a hydrofoil, but some
data for a passenger-carrying catamaran travelling at 41 km/h seem to
agree pretty well: it consumes roughly 1 kWh per ton-km.
It’s quite a surprise to me to learn that an island hopper who goes from
island to island by plane not only gets there faster than someone who hops
by boat – he quite probably uses less energy too.
This chapter has emphasized that planes can’t be made more energy-
efficient by slowing them down, because any benefit from reduced air-
resistance 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 = 2⁄3 AL. If the airship floats stably in air of
density ρ, the total mass of the airship, including its cargo and its helium,
must be mtotal = ρV. 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 ε of the engines. So the gross transport cost
– the energy used per unit distance per unit mass – is