The Efficiency Paradox

Seems like everyone these days is obsessed with efficiency. Planes, trains, computers even fast food chains are getting faster. Electronics use less electricity than ever. Car engines are smaller than ever. Chevy is even advertising a remarkable 23 MPG on some of their cars! I guess no one told them the Honda had 41 MPG with their 1973 CVCC...(fail)

Even commercial airline suppliers are jumping onto the efficiency bandwagon. Namely, the crue group labeled Airbus and the company who put the B in 747, Boeing. Granted the two companies are approaching the solution in two opposite and unequal ways. Airbus, responsible for the behemoth A380, created flying cattle carriers bursting with 853 passengers per flight. (All aboard the fail plane!) I guess the idea was to cut back on the number of planes in the air, and therefore cut back on pollution. It's a valiant attempt.

Boeing's philosophy mimics that of auto manufacturers; make the new model more efficient. Apparently, the new B-787's incorporate the best aerodynamic designs and technology ever applied to commercial airliners. The fuselage is composed of all carbon fiber composite, sending the cost of carbon everywhere soaring. It also uses redesigned engines that are quieter and more efficient than any other. (Who'd have thought those wavy-things around the nozzle would work so well?)

Anyway, I really only care about the engine efficiency (η). See, there's this weird paradox when you start analyzing engine performance. Aircraft engines move by creating a force called thrust, essentially some amount of fast moving air (m_a) coming out of the engine at some speed (U_e). In simplest terms, that air pushes against the air in the atmosphere. Obviously, you have to account for the velocity of the engine itself (U), as it is attached to the flying plane. Complicated math makes the force of thrust look like this:

τ = m_a (U_e - U)

Efficiency is just the amount of power you get out of the amount of energy you put in. So If you divide that thrust equation by the rate at which you're creating that energy, you get this:

η = (2·U) / (U_e + U)

Now here's where it gets awesome. In order to maximize your efficiency, you need to have the smallest value on the bottom of that ratio, that means that the exhaust speed must equal the planes flying speed. BUT, and look at that thrust equation, if that's true, the most efficient engine is one that is making no thrust. (It's turned off!!)

Anyway, if you learn anything from this post it should be that Chevy is dumb, everyone should buy a Honda and the most fuel efficient engine is never going to get off the ground.


_ttk3