I've always understood that Vx & Vy and Vxse & Vyse meet at the absolute ceiling for AEO or 1 inop, respectively. So how is it that a single, 65kts, figure is given for those four speeds even though the aircraft still has a large performance reserve?
I agree Tinstaafl. I don't think it's possible. To see this, it needs a little algebra.
Let T(v) be the
excess thust (i.e. thrust available - thrust required, not the usual convention for T).
For max rate of climb, T is maximum and so dT/dv = T'(v) = 0. So T'(Vx) = 0.
Now look at excess power, which is v*T(v). For max rate of climb, v*T is maximum and so d(v*T)/dv = 0
So v*T'(v) + T(v) = 0.
Under normal circumstances this is satisfied at v = -T(v)/T'(v), which gives Vy. But in this case we know T'(Vx) = 0. So it can only be satisfied at v = Vx if T(v) = 0 also. That means no excess thrust, i.e. you're at the absolute ceiling.
Note that I've made no assumptions about the shape of T(v), so this applies equally to props and jets.
If you prefer thinking about curves, note that Vy is the minimum the excess power curve, where it's flat. Thus if you go to Vy minus a little, the excess power changes hardly at all (2nd order), while the distance travelled decreases a little (1st order). Thus the angle of climb must increase.
The only thing I can think of is that Vx has to be greater than a minimum value for other reasons. For example, is the "book" Vx required to be a certain percentage above the stall?