Ahh, the simplest questions always generate the most complex answers and vice-versa!
The efficiency of a heat engine is largely governed by the compression ratio. A heat engine is one that converts heat in a gas (added by a fuel) to do work. All combustion engines, like the Otto cycle (four stroke) engine, Diesel engine and Brayton Cycle (gas turbine) engine are heat engines.
How does the amount the air/fuel mix is compressed effect the efficiency? Imagine a piston travelling up a cylinder and compressing the gas in that cylinder (like pushing in the handle of a bike pump with your thumb over the exit hole). If released, the piston would now travel back down the cylinder until the pressure inside equalled the atmospheric pressure. The work done in compressing the gas is recovered as the piston moves back down the cylinder under the pressure of the compressed gas (less friction losses etc.)
If the piston compresses the gas to half its original volume, then it has a compression ratio of 2:1, as the piston recovers it can do work based on the compression it started with. The more the air is compressed, the more work can be done as it recovers. Otto cycle piston engines have a compression ratio of around 8:1.
Now lets introduce some combustion after the piston has compressed the air, as happens in an Otto cycle engine (a "suck, squeeze, bang, blow four stroke). If the charge was only compressed at a 2:1 ratio, then the effect of the combustion can only do work until the piston recovers to ambient pressure. The more the piston compresses the charge, the further away from ambient pressure it is and thus more work can be done by the piston as it recovers. So the higher the fuel/air mix is compressed, the more efficiently that fuel can expend its energy.
Why not compress the charge more in a four stroke, and get even better efficiency? Because as the charge is compressed it heats up, until at higher compressions it heats enough to explode at the wrong time ("known as "pinging", "knocking" or detonation) which may create enough pressure to exceed the strength of the engine components. Typically you put holes in pistons or cylinder heads - not considered a good thing.
Diesel engines actually take advantage of this effect and use "compression ignition" instead of a spark plug, so they can achieve double the compression of Otto engines and are consequentially more efficient. An aviation diesel engine, burning kerosene (Jet fuel) is being developed and should be available on the Socata Trinidad in a year or so. It is lighter, has less moving parts and burns less fuel with more power than your current Lycoming or Continental.
All this can be proved mathematically from first principles through the laws of
thermodynamics, a branch of Physics usually studied at second year degree level in Mechanical Engineering. I won't bore you with the proof, but if you are really interested you can
click here.
The same principle applies in gas turbine engines, although technically you don't talk about compression ratios, but rather cycle pressure ratios. Known as the
thermal efficiency, or
internal efficiency of the engine the higher the pressure ratios, the higher the efficiency of combustion. As the compressor is not a cylinder travelling a fixed distance, but a "fan blowing air into a small space" the pressure ratio is governed by the engine RPM.
So gas turbine engines like to run at high RPM.
Next you need to look at the
propulsive efficiency, or
external efficiency of the engine (the study in Physics known as
mechanics). The amount of thrust provided by an engine (propeller or jet) is related to the amount of air they throw out the back, and the speed at which they throw that air. In symbols, if
m kilograms is the mass of air affected per second, and if it is given an extra velocity of
v meters per second by the propulsion device, then the momentum given to the air per second is
mv, so
Thrust = mv (per second).
A propeller engine uses a large
m and a small
v, a gas turbine engine uses a small
m and a large
v. 10 kg of air given a velocity of 1 m/s has the same thrust as 1 kg/s of air given a velocity of 10 m/s. Which is most efficient? Well, the rate at which kinetic energy is given to the air (the work done) is
½mv² watts. So the first case requires 5 watts of work and the latter requires 50 watts of work. Clearly the piston is more efficient. Problems occur as the speed increases, and the propeller efficiency breaks down.
An easier way to think of it is by considering the waste energy in the flow. Stand behind a propeller engine at takeoff, and it will knock your hat off. Stand behind a jet giving the same thrust and it will knock you off your feet! Waste energy dissipated in the jet wake, which represents a loss, can be expressed as
[W(vj-V)²]÷2g (
W is the mass flow,
vj is the jet velocity,
V is the aircraft velocity, so
(vj-V) is the waste velocity). As the jet exhaust leaves the gas turbine at roughly the same speed whether it is standing still or moving, the faster the engine is moving the less waste energy lost. Assuming an aircraft speed of 375 mph and a jet velocity of 1,230 mph the efficiency of a turbo-jet is approx. 47%. At 600 mph the efficiency is approx. 66%. Propeller efficiency at these speeds is approx. 82% and 55% respectively.
So gas turbine engines like to fly at high TAS.
The problem is that at high RPM at sea level turbo-jets are sucking in very thick air, so when they add a heap of fuel and burn it they make tremendous amounts of thrust - good for take-off but way too much for level flight at low level (with the associated high IAS).
Aircraft generate too much drag at high Indicated Air Speed and keeping the engine turning at an efficiently high RPM at sea level would quickly exceed the aircraft speed limitations.
As you increase altitude, however, the amount of thrust the engine can produce reduces (as it is sucking in "thinner" air) even though it is still operating at high compression ratios (for good
thermal efficiency). Also you can have a high TAS (for good
propulsive efficiency) at a low IAS (for lower drag on the airframe). There are a few other advantages, like the cold temperature, which keeps the turbine temperatures down as well.
So jet engines like to fly at high power and at high TAS, while aeroplanes like a moderate IAS, and the regime were all this can be achieved together is at high altitude.
[This message has been edited by Checkboard (edited 04 July 2000).]