Thanks for explaining singlet. That was pretty simple after all.

Re-stating: A crab angle is an angle that a pilot flies in order to acheive a desired ground track. It is systematically set by the pilot. Variations in crosswind component will of course necessitate variations in the crab angle. This is most easily seen immediately after rotation in a crosswind, and the reverse on landing. It goes without saying that crab angle is an integral feature of deduced-reckoning navigation, and any other form of course tracking with a crosswind.

From the FAA's Airplane Flying Handbook:
"CRAB—A flight condition in which
the nose of the airplane is pointed into
the wind a sufficient amount to counteract
a crosswind and maintain a
desired track over the ground."

Having written all that and possibly annoyed you, I understand that a change in crosswind component can result in a change in airplane heading proportional to the degree of yaw stability possessed by the airplane and the gust gradient. So, if you mean to argue that a change in crosswind necessitates a change in crab angle, I would have to agree, but we would not then be beyond the most basic of aeronautics, and we are NOT discussing stability yet. If on the other hand you want to link the airplane's crab angle, rather than it's sideslip angle, with it's response to a perturbation in yaw, I must strenously qualify that. Sideslip angle, and not crab, is a term in yaw stability calculation. Crab angle does not enter at all, though of course at any point in a yaw disturbance, the instantaneous crab angle could be calculated, if a crosswind existed at the time, though I don't understand what use that would be.

I think I understand your intent in the examples you gave (the parts I snipped). However, without placing a bunch of additional constraints on your final example, it cannot be said with certainty that the airplane will spin, since as far as we know, aurotation due to spinning requires at least a partial stall. Certainly, if no correction is applied, AND a stall ensued, a spin would likely occur, i.e. it depends on a lot of things that were not specified in your example. Departure due to yaw instability is not the same thing as spinning, especially not initially.

If you insist, I will allow the last sentence in the fourth paragraph to serve as a qualification to my statement about crab angles. Otherwise it stands un-rephrased.

<oops, rephrased first sentence of fourth paragraph>