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Old 16th February 2002 | 21:07
  #8 (permalink)  
Keith.Williams.
 
Joined: Aug 2001
Posts: 775
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From: Dorset
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Nick,

The basis of your question appears to be that "At low altitude the engines of a jet produce too much thrust, so have to run them at an inefficiently low RPM. By using fewer or less powerful engines, will we be able to run them at their optimum RPM at low altitude, thereby achieving the same level of fuel efficiency as we do at high altitude?". . . .The short answer to this question is no!

The speed at which an aircraft moves over the ground is proportional to TAS, whereas the drag it generates is proportional to CAS. At 4000 ft for example, . .the TAS is about twice the CAS. This means that by operating at 40000 ft we cover the ground at twice the speed, but pay no extra penalty in terms of drag. So the airframe is more aerodynamically efficient at high altitude. This in turn means that whatever we might achieve in terms of the fuel efficiency of the engines, a jet will always get more miles per gallon at high altitude that at low.

This does not however mean that your idea has no merit. It is commonly used when a high speed jet requires to loiter for long periods. In the case of maritime patrols for example, the NIMROD has 4 engines and is able to cruise at reasonably high speed at high altitude. But to loiter for 5 or 6 hours over a small area of ocean, 1 or 2 of its engines are shut down, thereby enabling the others to be operated closer to their optimum RPM. But this does not mean that the remaining engines are achieving the same fuel efficiency as they would at high altitude. The problem here is one of propulsive efficiency.

Propulsive efficiency is a measure of how efficiently the mechanical energy in the hot gas is transferred to the aircraft. 100% efficiency means that all of this energy is transferred to the aircraft and none of it is wasted in the exhaust. As explained by Checkboard in a previous post, propulsive efficiency is determined by the ratio of the TAS of the aircraft to the TAS of its jet plume (or prop wash). The closer these two speeds become, the greater will be the propulsive efficiency.

When the two speeds are equal, the exhaust gas will be laid down behind the aircraft as if it had never been disturbed. The air will have been given no mechanical energy, so propulsive efficiency will (according to the equation quoted by Checkboard) be 100% . Unfortunately this also means that the gas will not have been accelerated, so no thrust will be produced, so no energy will be given to the aircraft. This in turn means that propulsive efficiency will be zero. So 100% propulsive efficiency can never be achieved. But propulsive efficiency can still be maximised by keeping the aircraft TAS and exhaust TAS as close as possible. Jet engines produce thrust by taking a small mass of air and giving it a very large acceleration. So for maximum propulsive efficiency jet aircraft must fly at high speed.

So if we reduce the size or number of our jet engines to get high RPM and good thermal efficiency at low altitude, we will need to fly at very high TAS to achieve good propulsive efficiency. But at low altitudes the TAS is much closer to the CAS, and drag is proportional to CAS. So at low altitude, the high TAS required for high jet engine propulsive efficiency will incur very high drag forces. Power required is equal to drag x TAS, so this low altitude high TAS flight will require a great deal of power. So although the higher RPM will improve specific fuel consumption, this benefit will be lost due to the higher power requirement.

The most effective solution to this problem is to take our jet engines and fit propellers to them. This will increase the mass flow of air, enabling the same thrust to be generated using much lower acceleration rate. This in turn will give good propulsive efficiency at reasonably low airspeeds which will incur low drag and low power required. But then we will have turned them into turbo-props?
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