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I was reading something about someone who was doing this and I'm intrigued, but I have no idea what you actually do to optimize the engine to be better at lower altitudes and lower speeds?

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    $\begingroup$ Why do you want to do that? That is, what do you want to achieve? Or in other words, what is not satisfactory in the existing solution - a turboprop? $\endgroup$
    – Zeus
    Nov 16 '18 at 0:13
  • $\begingroup$ He must know a good mechanic. Those Cyclone radials were pretty good on gas. $\endgroup$ Nov 16 '18 at 2:23
  • $\begingroup$ Welcome to the site @JustinHolderman, I think the answer may be "you don't". $\endgroup$
    – GdD
    Nov 16 '18 at 8:26
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As a summary, the engine generates thrust by changing the impulse (momentum) of the air. Please refer to this: NASA Genera Thrust Equation

So to optimize aircraft performance, the main options you can play with are that depend on your aircraft operation: V0: flight speed p0, r0: inlet pressure and density (function of altitude)

And the variables that depend on your engine design: Ve, pe, re: exhaust velocity pressure and density (depend on the thermal cycle and actual operating condition of the engine) A0, Ae: Inlet and nozzle areas (engine geometry, sizes derived from the design point)

Now what you need to see is that there is no single best option, aircraft design is an optimization problem, eg finding compromises. Flying lower and slower is actually an attractive option for greener aircraft, as it enables technologies that reduce drag, such as ultra high aspect ratio wings, laminar airfoils, boundary layer ingestion, electric propulsion and a few more.

Whether optimizing a turbofan for lower altitudes make sense can only be seen by comparing the wins against the losses, and it is hard to say absolute truths as it depends on many variables.

Now about the actual "how-to" optimize a gas turbine, essentially the key variable of the engine is the pressure ratio, PR, so how much it compresses the inlet air. For a given flight condition (thrust, speed and altitude) , there is an optimal pressure ratio. From that the number of compressor and turbine stages can be calculated (also if you need a multi-spool engine, do you use an intercooler, etc.), and also the geometrical dimensions of the engine. And this goes back to the comment I've made that it is a compromise. Building a very heavy, expensive, hard to maintain engine will not be a good choice as what you win by increased engine efficiency you will lose on the flight efficiency.

But suppose as an academic exercise you just want to alter an existing engine design to move its design point to a lower speed and altitude, then you need to change the design pressure ratio, and follow up with any internal changes (add/remove stages, change inlet, nozzle, etc.)

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