%MAC, to be fair I was using piston engine curves for the Vx/Vy comparison with sink rate/glide range. I shouldn't have done that.
However, now that I have
, the engine's power & thrust curves are irrelevent because we're also referring to a no-engine scenario.
This means that we have to consider airframe drag/thrust/power requirement curves only and not the more usual 'greatest difference between available & required' ie maximum excess which is governed by the powerplant type.
We're talking about two different measurements - one involving
angle of descent as a function, the other involving
rate of descent. Rate includes a
time factor.
The appropriate curves for each of these is the drag curve (for range) and the power required curve (for duration). Power is is appropriate for duration (min. sink rate) because power is a
rate ie includes time as an element.
Best range (as far as the airframe is concerned) is achieved by flying at min drag and provides the best L/D ratio. I think of this as the least cost in D to achieve the lift, hence the range effect ie if drag was zero we'd be fly S&L indefinitely and if D=L then we'd be descending vertically.
This is also the same as flying at a tangent to the power required curve but by using this method we've effectively introduced a distance parameter into the situation (the tangent commences from the graph's origin). Handy if you know the headwind or tailwind component because you can adjust the tangent's commencing point to find the Best range speed for that wind component.
Best endurance (ie min sink) will be found by flying at the min. power required. This is slightly slower than L/D. This I think of as the least cost in
energy and hence its effect on duration.
Bear in mind that this spiel is done entirely from memory and I could be wrong.