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I've seen on numerous different constant-speed propeller aircraft and different pilots using different RPMs during the cruise phase on a propeller aircraft. What dictates the RPM used during normal cruise operations, and why is that the case? Often there are multiple possible throttle/RPM combinations that deliver the same power, so where would you pick one or the other?

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The POH has performance tables (random example: http://www.avsim.com/pages/0310/Carenado/Manual5.jpg) showing fuel burn, true air speed, and %hp, for a given altitude, RPM, and manifold pressure. The pilot selects a performance configuration based primarily on what speed they wish to cruise at, which in turn determines how much fuel they're going to use. Different pilots differ in how much speed they want to achieve, making things somewhat a matter of opinion, but regardless of selection it's standard that the more you pull from the engine, the more harm you do to the engine. Personally, I tend to aim for 65% to 75% maximum horsepower in order to neither overtax my engine, nor use more fuel than is needed.

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Note that it's % of maximum continuous power. Takeoff power is generally higher than that (the Katana I fly has a 104% as take-off power) –  falstro Feb 11 at 14:02
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"Dictate" is the wrong word. Within the ranges listed in the POH, the pilot may select rpm/MP settings as he pleases to meet other criteria.

Charles Lindbergh instructed many WWII pilots in a technique to extend range, by flying with low rpm and high manifold pressure. This extended range by reducing the "pumping losses" required to maintain low manifold pressure. Over long distances this technique did extend range considerably.

Secondly, lower rpm reduces noise - remember that the propeller is the largest contributor to a propeller-driven plane's noise signature. This is important in the terminal environment where the noise can affect the ground, but it also affects in-cockpit noise regardless of altitude.

This answer does not contradict the former answer, but it extends it to point out that there are other important factors that the pilot should consider in selection of engine operation parameters.

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As for noise in terminal environment, you will fly with high rpm there anyway, because high power is only possible with high rpm and you need the power on take off and need to have it available quickly on landing in case you need to go around. Of course you still don't want the noise during cruise for which low rpm is better. –  Jan Hudec Apr 10 at 7:54
    
Whereas you should indeed fly with the prop set for high rpm on takeoff, most noise abatement policies call for reduced rpm when you reach an altitude as low as 700 feet. Also on landing, the prop control is advanced when the power level has been reduced so that the rpm is limited by power developed not by rpm. Landing in this configuration permits rapid rpm increase if a go-around becomes necessary. –  Skip Miller Apr 10 at 20:05
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