Why isn't Vy lower than the speeds for best L/D ratio and best glide ratio in an airplane with a piston engine and a variable-speed prop? This answer to a related question implies that if the power available were constant regardless of airspeed, Vy would occur at approximately the angle-of-attack that yields the minimum sink rate with power idle, which occurs near the airspeed for the max ratio of lift coefficient cubed / drag coefficient squared, slower than the airspeed for max L/D ratio.  The airspeed for best glide ratio should be only a little slower than the airspeed for max L/D ratio, to minimize the extra drag from the stationary or windmilling prop.  

Therefore it would seem that in an aircraft with a piston engine and a constant-speed propeller, Vy should be slower than the best glide speed.  Yet this manual for a Cessna 182 gives the best glide speed as 70 KIAS, and gives Vy as 78 KIAS at sea level and 72 KIAS at 10,000' MSL (page 4-14.)  So why is Vy faster than the best glide speed in this aircraft?  Why isn't Vy slower than the best glide speed?

In essence, this is a question about what the power-available curve looks like for an aircraft with a piston engine and a variable-speed prop, plus a question about what other factors may be at play here.  

Is less power available at lower airspeed?  If so, does that imply that less manifold pressure is available at lower airspeed?  Presumably the throttle would be fully open in a climb at Vy -- is the engine unable to turn at the optimum RPM for maximum power when climbing at Vy?  

Does the answer have to do with the fact that even with a constant speed prop, at most airspeeds, the pilot cannot simultaneously optimize the RPM of the engine and the angle-of-attack of the prop?  And thus the power available (given that RPM and manifold pressure are kept within safe limits) is not constant as the airspeed varies?  Since there is no variable transmission (variable gearing) between the engine and the prop, it would seem that this would be an accurate description of the situation.

(Naturally, the designer of the prop can simultaneously optimize the angle-of-attack of the prop and the RPM of the engine by selecting the appropriate prop diameter, chord width, blade twist, etc, but it would seem that this optimization might be only valid at one particular airspeed, even with a variable-pitch or constant-rpm prop.)

It would seem that in an aircraft like a Cessna 182, the maximum achievable steady-state climb angle would be shallow enough that the "unloading" of the wing during the climb is not very significant, so that essentially the same correlation between angle-of-attack and airspeed exists in climb, horizontal flight, and gliding flight.

Here are some other related ASE questions and answers--

Why is best angle/rate of climb indicated in airspeed? -- informative, but it is unclear whether the graphs are meant to represent the case of a fixed-pitch prop or a variable-speed prop.

Does a windmilling propeller create more drag than a stopped propeller in an engine out scenario? -- informative, but it is unclear whether the "best glide" airspeed in a typical pilot's operating handbook would represent a stopped prop or a windmilling prop.

Is Vy closer to Vbg with a variable pitch prop -- closely related to the current question, but the actual body of the question is phrased entirely in terms of a fixed-pitch prop.
It's because climbing at Vy the engine only has to overcome the airframe drag minus the prop, on top of the thrust lift component reduction in induced drag you mentioned in your answer to another post.  

It's as if you took the prop off and towed the plane with a tow line glider style (this was done on a Wittman Tailwind back in the early 60s for some gliding drag studies to learn the plane's true L/D, with the tow line connected to the engine prop hub; the Tailwind turned out to be an extremely efficient airplane, square corners, stubby little wings and all).

Best glide has to take into account the substantial drag of the windmilling prop, so the best L/D is achieved at a lower speed.  I'm pretty sure the POH numbers are based on the worst case of the prop windmilling at flat pitch (where it goes if you are climbing at Max RPM and the engine quits), where the drag is so massive it's like you deployed a speed brake.  

You can improve this a lot by pulling the prop to Min RPM when the power is removed to try to get the governor to drive the blades to full coarse pitch. This gets you at least part way to being feathered, and helps quite a lot in the glide.