I haven't got much more to explain other than the title of the question itself. This question was written down in my notes that I took while studying Principles of Flight for my EASA commercial license.
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2 Answers
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Ideally it would not. With increasing Mach number the lift curve slope of the vertical tail goes up proportional to the Prandtl-Glauert factor $\frac{1}{\sqrt{1-Ma^2}}$ while the destabilising fuselage as a slender body is mainly unaffected by Mach effects. But that is only theory which assumes a perfectly rigid body.
In reality, elasticity decreases the effectivity of the vertical tail. Higher loads lead to higher deformations which in turn decrease the loads and with them the stabilising moments. What happens in detail depends on the structure: A light aircraft will experience decreasing directional stability as dynamic pressure increases.
At supersonic speed, fin effectivity is further reduced by the now again decreasing lift curve slope as Mach increases further. Now even the rigid aircraft experiences decreasing directional stability and elasticity will reduce stability further.
Directional stability over Mach, from Ray Whitford's Fundamentals of Fighter Design
answered Oct 30, 2016 at 14:11
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$\begingroup$ @mns: I have only those figures, and they have no units. It is a qualitative measure of directional stability, that's all I know. British nomenclature is odd at times. $\endgroup$ Commented Oct 30, 2016 at 20:27
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It depends- there are two things in play here and the net effect would be dependent on their interaction.
The most important contributor to lateral stability is dihedral effect, $C_{l_{\beta}}$, which is not usually affected by high Mach numbers. However, in case of a highly effective vertical tail (which would be improving the lateral stability by introducing a rolling moment), the increase in lift curve slope of the vertical tail increases in its contribution, which would improve lateral stability.
However, lateral stability would degrade if the lift distribution over the wing is affected by shock wave formation. The net effect would depend on the magnitude of these things.
Change in lateral stability derivatives with Mach number, from Chapter on lateral-directional stability from USAF test pilots school.
It can be seen that the $C_{l_{\beta}}$ decreases in transonic regime, which improves lateral stability. However, at these speeds, aeroelastic considerations become important, leading to effects like aileron reversal and reduction in lateral control effectiveness due to flow separation as a result of shock formation.
answered Oct 30, 2016 at 15:33