C   Planes II

What we need to do is to look at how you make air travel more energy efficient, how you develop the new fuels that will allow us to burn less energy and emit less.

Tony Blair

Hoping for the best is not a policy, it is a delusion.

Emily Armistead, Greenpeace

What are the fundamental limits of travel by flying? Does the physics of
flight require an unavoidable use of a certain amount of energy, per ton,
per kilometre flown? What’s the maximum distance a 300-ton Boeing 747
can fly? What about a 1-kg bar-tailed godwit or a 100-gram Arctic tern?

Just as Chapter 3, in which we estimated consumption by cars, was
followed by Chapter A, offering a model of where the energy goes in cars,
this chapter fills out Chapter 5, discussing where the energy goes in planes.
The only physics required is Newton’s laws of motion, which I’ll describe
when they’re needed.

This discussion will allow us to answer questions such as “would air
travel consume much less energy if we travelled in slower propellor-driven
planes?” There’s a lot of equations ahead: I hope you enjoy them!

How to fly

Planes (and birds) move through air, so, just like cars and trains, they
experience a drag force, and much of the energy guzzled by a plane goes
into pushing the plane along against this force. Additionally, unlike cars
and trains, planes have to expend energy in order to stay up.

Planes stay up by throwing air down. When the plane pushes down
on air, the air pushes up on the plane (because Newton’s third law tells
it to). As long as this upward push, which is called lift, is big enough to
balance the downward weight of the plane, the plane avoids plummeting

When the plane throws air down, it gives that air kinetic energy. So
creating lift requires energy. The total power required by the plane is
the sum of the power required to create lift and the power required to
overcome ordinary drag. (The power required to create lift is usually called
“induced drag,” by the way. But I’ll call it the lift power, Plift.)

The two equations we’ll need, in order to work out a theory of flight,
are Newton’s second law:

force = rate of change of momentum

Figure C.1. Birds: two Arctic terns, a bar-tailed godwit, and a Boeing 747.