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.)

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 *f*_{fuel} 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 *εf*_{fuel}/
(*c*_{d}*f*_{A})^{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 (CH_{2})_{n}.

Jet fuel has a calorific value of *C* = 40 MJ per kg. The distance associated

with jet fuel is

(C.33)