So whereas lowering speed-limits for cars would reduce the energy con-
sumed per distance travelled, there is no point in considering speed-limits
for planes. Planes that are up in the air have optimal speeds, different for
each plane, depending on its weight, and they already go at their optimal
speeds. If you ordered a plane to go slower, its energy consumption would
increase. The only way to make a plane consume fuel more efficiently is to
put it on the ground and stop it. Planes have been fantastically optimized,
and there is no prospect of significant improvements in plane efficiency.
(See pages 37 and 132 for further discussion of the notion that new super-
jumbos are “far more efficient” than old jumbos; and p35 for discussion of
the notion that turboprops are “far more efficient” than jets.)

### Range

Another prediction we can make is, what’s the range of a plane or bird –
the biggest distance it can go without refuelling? You might think that
bigger planes have a bigger range, but the prediction of our model is
startlingly simple. The range of the plane, the maximum distance it can go
before refuelling, is proportional to its velocity and to the total energy of
the fuel, and inversely proportional to the rate at which it guzzles fuel:

(C.31)

Now, the total energy of fuel is the calorific value of the fuel, C (in joules
per kilogram), times its mass; and the mass of fuel is some fraction ffuel of
the total mass of the plane. So

(C.32)

It’s hard to imagine a simpler prediction: the range of any bird or plane is
the product of a dimensionless factor εffuel/ (cdfA)1/2 which takes into
account the engine efficiency, the drag coefficient, and the bird’s geometry,
with a fundamental distance,

 C , g

which is a property of the fuel and gravity, and nothing else. No bird size,
no bird mass, no bird length, no bird width; no dependence on the fluid
density.

So what is this magic length? It’s the same distance whether the fuel is
goose fat or jet fuel: both these fuels are essentially hydrocarbons (CH2)n.
Jet fuel has a calorific value of C = 40 MJ per kg. The distance associated
with jet fuel is

(C.33)
Figure C.11. Boeing 737-700: 30 kWh per 100 passenger-km. Photograph © Tom Collins.