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Afterburners are much less efficient than turbine engines at converting fuel into thrust, so AFAIK no jet will engage afterburner unless it is already at full throttle on the turbine.

But what if an afterburner were used at less than full throttle? How, if at all, is the efficiency of an afterburner related to the thrust of the engine feeding it?

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Normally, what is throttled back is the afterburner. The principle of reheating an already hot gas is so inefficient that partial wet thrust is achieved by running the engine at full power and using less than full afterburner.

The efficiency of the afterburner is proportional to the ratio of gas temperatures (peak to entry temperature), but at partial jet thrust the pressure level and volume flow in the jet exhaust is also diminished, so the available thrust increase from the afterburner will also decline sharply. To produce the same thrust, it will be much more efficient to run the jet at full speed and to throttle the afterburner.

The Tornado attack aircraft, designed for nap-of-the-earth flight, was so inefficient at higher altitudes that during the Bosnian war of the mid-Nineties it had to run one engine in partial afterburner in order to keep up with the tanker aircraft. For inexperienced crews which used most of their allotted time for coupling with the tanker, the tank stop could result in a negative fuel gain because so much was needed to keep up with the tanker.

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