the thrust of a cruising 747 is 200 kN, just 50% more than our cartoon
suggested. Our cartoon is a little bit off because our estimate of the drag-
to-lift ratio was a little bit low.

This thrust can be used directly to deduce the transport efficiency
achieved by any plane. We can work out two sorts of transport efficiency:
the energy cost of moving weight around, measured in kWh per
ton-kilometre; and the energy cost of moving people, measured in kWh
per 100 passenger-kilometres.

Efficiency in weight terms

Thrust is a force, and a force is an energy per unit distance. The total
energy used per unit distance is bigger by a factor (1/ε), where ε is the
efficiency of the engine, which we’ll take to be 1/3.

Here’s the gross transport cost, defined to be the energy per unit weight
(of the entire craft) per unit distance:


So the transport cost is just a dimensionless quantity (related to a plane’s
shape and its engine’s efficiency), multiplied by g, the acceleration due
to gravity. Notice that this gross transport cost applies to all planes, but
depends only on three simple properties of the plane: its drag coefficient,
the shape of the plane, and its engine efficiency. It doesn’t depend on the
size of the plane, nor on its weight, nor on the density of air. If we plug in
ε = 1/3 and assume a lift-to-drag ratio of 20 we find the gross transport
cost of any plane, according to our cartoon, is

0.15 g


0.4 kWh/ton-km.

Can planes be improved?

If engine efficiency can be boosted only a tiny bit by technological progress,
and if the shape of the plane has already been essentially perfected, then
there is little that can be done about the dimensionless quantity. The trans-
port efficiency is close to its physical limit. The aerodynamics community
say that the shape of planes could be improved a little by a switch
to blended-wing bodies, and that the drag coefficient could be reduced a

Figure C.9. Cessna 310N: 60 kWh per 100 passenger-km. A Cessna 310 Turbo carries 6 passengers (including 1 pilot) at a speed of 370 km/h. Photograph by Adrian Pingstone.