VMD: the best-glide speed
The best glide angle needs the best L/D, and the drag lessons located it long ago: the aircraft flies its best lift-to-drag ratio at one particular angle of attack (where induced and parasite drag are equal), and, at a given weight, that α corresponds to one speed: VMD, the minimum-drag speed. Fly VMD and the aircraft is at its best-glide α automatically: minimum drag, maximum L/D, shallowest glide, greatest still-air range. Faster or slower both steepen the glide — slower is not safer here, it is shorter.
Wind, mass and configuration
Wind — the glide happens in the air, but the pilot cares about the ground. A headwind steepens the glide over the ground: less distance per metre of height, while the duration is unchanged (the air neither slows nor speeds the descent through itself). A tailwind flattens the path over the ground and stretches the distance, duration again untouched.
Mass, flown at VMD — the glide angle does not change: L/D belongs to the α, not the weight. But the heavier aircraft's VMD is higher (the same α needs more speed to carry more weight), so it flies the same path faster: same distance, higher rate of descent, shorter duration.
Mass, flown at the same airspeed — hold the old speed after adding weight and the aircraft now flies below its (raised) VMD: a different α, a worse L/D, a steeper glide and less distance. The angle is mass-independent only for the aircraft that adjusts its speed to stay at the best-glide α.
Configuration — gear and flap are pure L/D destroyers: extended, the glide steepens and both range and duration shrink. The engine-failure drill's 'clean up' items are this bullet in checklist form.
Gradient, rate and TAS
Two different questions hide in 'how fast am I going down'. The gradient says how much height each kilometre costs. The rate of descent says how much height each minute costs — and it is the gradient multiplied by the TAS (for the glide's shallow angles, sin γ and the gradient are effectively the same number): rate of descent = TAS × sin γ. The same gradient flown faster burns height faster; the same rate can belong to a shallow fast glide or a steep slow one. Keeping the two apart is half the marks on this topic.
VMP: minimum sink
If the aim is not distance but time, the answer changes. The rate of descent is drag times speed over weight (a power divided by a weight), so it is least where the power required is least: at VMP, the minimum-power speed, which sits below VMD. Fly VMP and the aircraft achieves its minimum rate of descent — the longest airborne time from the height in hand, though over a shorter distance than VMD would give. The choice (the syllabus asks for it):
minimum sink for time — waiting for a restart, working a thermal, delaying arrival.
best glide angle for distance — reaching the field.
And two cautions tilt the choice toward VMD in practice: below VMD the aircraft sits on the wrong side of the drag curve: speed-unstable, demanding constant attention exactly when attention is scarce; and whenever reaching somewhere matters at all, wind moves the best speed over the ground away from the still-air optimum (faster than VMD in a headwind, slower in a tailwind), so a headwind pushes the practical choice even further from VMP. (For a pure time task, wind changes nothing: sink rate and duration are air-referenced.)