Benefits
The benefit of this setup is increased specific impulse over that of a rocket. For the same mass of fuel as a rocket motor, the overall output of the air turborocket is much higher. In addition, it provides thrust throughout a much wider speed range than a ramjet, yet is much cheaper and easier to control than a gas turbine engine. The air-turborocket fills a niche (in terms of cost, reliability, ruggedness, and duration of thrust) between the solid-fuel rocket motor and gas turbine engine for missile applications.
Read more about this topic: Air Turborocket
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