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My understanding on the relationship between stability and controllability has been that greater stability means less controllability and vice versa. This post confirms that. However, I've came across this paragraph from PHAK 5-43 today:

Generally, an aircraft becomes less controllable, especially at slow flight speeds, as the CG is moved further aft (my emphasis). An aircraft that cleanly recovers from a prolonged spin with the CG at one position may fail completely to respond to normal recovery attempts when the CG is moved aft by one or two inches.

Aft CG means less stability, so if I'm not mistaken, the phrase is basically saying less stability leads to less controllability. How should I understand this statement? Should I understand that, although controllability and stability are generally opposed to each other, when it comes to a stall or spin recovery, the opposite is true? Or is it simply an error?

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Your understanding of controllability and stability is correct, for the following definitions:

  • Controllability: the response of an aircraft in steady flight, on pilot control inputs. For instance deflecting the ailerons: a high resulting roll rate means a fast response.
  • Stability: the tendency of an aircraft air frame to return to trimmed position after a disturbance in air stream. Note that in this definition of stability, the airframe itself does all the work in getting back to neutral position, no pilot input required.

So the above is for steady, trimmed flight. The paragraph that you cite is about how to provide flight control inputs to recover from a spin. Now we need both control deflections and aerodynamic stability to recover. If the CoG is too far aft, there is not enough stability and the airframe may not recover even if the correct control inputs are given.

Use of the word Controllability is correct here, since it refers to controllability of recovery from a spin.

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  • $\begingroup$ Then does this inverted relationship between stability and controllability applies only to a spin recovery, or more generally slow flights (including level flight) as the paragraph seems to suggest as I see it? $\endgroup$ – lemonincider Oct 1 '17 at 0:59
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    $\begingroup$ Yes, there is less of an aerodynamic stabilising moment at slow flight. Response to flying control inputs is also sluggish, reducing controllability. $\endgroup$ – Koyovis Oct 2 '17 at 0:33

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