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Why does an aircraft require less power when it is flying slower than the most efficient speed?

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While I understand the derivation of Power required,I fail to understand why minimum power required corresponds to a velocity that is lower than velocity corresponding to minimum thrust required.

My understanding is that Minimum Thrust is the most efficient speed an airplane should fly at and how can flying lower than that consume even lesser power.

Please correct my understanding if wrong.Introduction to flight 9th Edition

Edit: While the given explanations make sense thinking about Piston driven engines, where thrust decreases with increase in velocity. I am still having trouble understanding the concept with JET engines where thrust is fairly consistent with speed. Would really appreciate if somebody could clarify


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