Can anyone explain this passage from page 11-5 of the PHAK: “ For example, if an aircraft in a steady flight condition at 100 knots is then accelerated to 200 knots, the parasite drag becomes four times as great, but the power required to overcome that drag is eight times the original value.” Would not the increase in power needed to overcome the added parasite drag be proportional to the amount of that added parasite drag? Why is the power needed 8 times the original value rather than 4?
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Drag is a force. Thrust is a force. The extra thrust needed to overcome the added parasite drag is proportional to the amount of that added parasite drag. But power is proportional to thrust times airspeed, and we've doubled the airspeed.