Guys, this is all pretty vanilla aerodynamics. The same physics principles apply as for any aircraft: Thrust balances drag => constant speed, lift balances weight=> constant altitude.
In the case of a quad, energy is being used directly for both lift and forward thrust as the single thrust vector from each prop.
The reason there is an optimal speed for distance efficiency is for two reasons:
1) Energy is being used to simply maintain altitude. Because of this, at very low speeds energy consumption is distance inefficient -- most of the energy is being consumed hovering. Obviously the degenerate case -- simply hovering without moving for the entire battery -- is most inefficient in terms of distance traveled per unit Ah consumed... ZERO. So obviously efficiency increases as you go faster -- you'll end up with a higher efficiency figure for ft/Ah running an entire battery moving along at 0.025mph; even better at 1mph; 2mph; and on and on. All of these runs would take about the same time, because the energy going into horizontal translation is trivial -- all of it's essentially going into hovering.
If you gather a ton of experimental data doing careful runs incrementing 1mph each time, you'd find that at first the increase in efficiency vs. speed would be linear, up to the point thrust going to forward motion was below 3 or 4 percent. At that point, more and more thrust is going to forward motion in addition to what's being consumed hovering, so the curve starts to bend toward flattening as speed increases.
2) Air resistance (drag) increases as the square of speed. Because of this, the curve starts to bend downward, with efficiency actually decreasing with higher speed. This is because to go twice as fast requires 4x the forward thrust to overcome the increased by squared drag. Obviously, at very low speed changes (1 mph to 2mph) the double of drag (from 0.1oz to 0.2oz) is completely inconsequential compared to the total forces the aircraft is countering with thrust -- basically the weight of the aircraft.
Now, lets go 15mph. Drag is 2lbs. double to 30mph, now drag is 4lbs. A lot more power (energy/time) is needed to push against this drag.
The knee of the curve -- the point of peak efficiency -- will not be at the aircraft's maximum speed, because aircraft always have much more power than just that necessary to fly at peak efficiency -- it's a necessary safety margin.