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I saw this question on a closed Facebook group, generating wildly differing answers. So I thought I would ask it here.

You're in a C172 flying straight and level at 5000 feet and 100 knots IAS. You apply full power and go into a sustained climb maintaining this airspeed.

Has the angle of attack increased, decreased, or remained the same?

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    $\begingroup$ This question needs a more specific scope or you'll be trolled by people who will be like, "well by the time you climb into space you will probably start to stall from the increase in angle of attack needed to compensate for the reduced air density." What I think you want to know is: not really. At first it increases due to initial acceleration upward, then the angle of attack will probably decrease to a lower angle than at level flight due to the vertical thrust vector making some of the work from the wings be done by the engine's thrust vector... until the air gradually gets too thin. $\endgroup$ – Ryan Mortensen Nov 23 '16 at 3:45
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    $\begingroup$ This is a trick question. At 5000 and 100 KIAS a C172 is already at full power. Well, almost ;) $\endgroup$ – J Walters Nov 23 '16 at 14:42
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We have seen that

A climbing aircraft needs less aerodynamic lift than in horizontal flight, not more.

this means that if we keep constant airspeed and if we do not alter the configuration, the angle of attack will be (slightly) smaller, at least until the air density does not change.

As your assumption is that

You apply full power

to enter the sustained climb, you will have even more thrust during the climb, and this will reduce even more the needed lift. This, together with the fact that you are slightly accelerating, reduces even more the angle of attack.

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