what exactly Vx and Vy for in gliding and powered descent(piston-prop aircraft)

Question

as i understood,for a prop-piston aricraft :

during a gliding, through the equation:

tanγ= D/W≈ 1/K

sink rate≈ VD/W≈ V/K

by which we get(theoretically):

Vx(Vmp) is the speed at which we get minimum sink rate

and Vy(Vmd) match up with minimum γ

but when it comes to a powered descent:

tanγ= △D/W

sink rate≈ V△D/W= -△P/W

then because at Vx(Vmp) the prop aircraft gets minimum excess drag gets minimum γ

at Vy(Vmd) gets minimum -excess power gets minimum sink rate

which does not add up, can't even make a graphic for powered descent.

what is wrong with that?

Answer 1

Vx (the speed of the steepest climb, ie. speed with most excess force) and Vy (the speed of the fastest climb, ie. speed with most excess power) are defined with climb power.

I don't really see they should play any role in descent, let alone in glide in which by definition there is no engine power. Vx and Vy are tightly defined by the engine properties and especially in a piston-prop where the engine thrust varies greatly with airspeed. They should not be mixed with by Vmp and Vmd even if they coincide.

Answer 2

This might be easier conceptually to look at thrust as negative drag.

A powered descent means a flatter angle of descent than an unpowered descent, you've just turned your Cessna 172 into a high performance glider!

So, to get maximum distance, you still want to be around Vbg to have optimal wing AoA for maximum Lift/to Drag.

Next you want to see at what speed your prop gives best efficiency at its AoA. Keep in mind a powered descent will be lower RPM than full throttle climbing Vy, so (for a fixed pitch) best prop efficiency will be at a lower airspeed.

The descent "Vy" will be near Vbg and V max prop efficiency. As far a descending "Vx", one may consider flaps (more drag) and no power for a steeper descent angle .