An airplane's best glide speed is at a specific angle-of-attack (AOA) and is the AOA for (L/D)max. At this specific AOA, the airspeed changes with weight to maintain this AOA. The heavier the weight, the faster the airspeed...the lighter the weight, the slower the airspeed. The distance covered will be the same, but the descent rate will increase for a faster airspeed and decrease with a slower airspeed. As for winds, this has no influence on the rate and angle of descent. However, the flight path gets shallower with a tailwind and steeper for a headwind. Consequently, the distance covered is greater with a tailwind than with a headwind, provided the best glide speed is maintained. A good book for this stuff is called, "Aerodynamics For Naval Aviators," by H. H. Hurt, Jr. It explains this aerodynamics without a lot of derivation of formulas. Hope this helps. Fly safe.
Although people don't use this method, it does work. If flying into a strong headwind, increase your KIAS so you can gain more ground for example, best glide is 62 and you are going into a 62 kt headwind you won't be going anywhere unless you increase your speed. Same goes for slower headwinds.
Now if you have a tailwind, slow your KIAS to take advantage of that nice tail wind. Maybe slow down to minumum sinkrate airspeed.
Nobody does these methods, but in extreme wind conditions, it could prove useful. If you have to stretch your glide to maximum maybe you should have picked a better field or airport?
Here some mathmatical apporaches to it, the rules of thumb apporach is at the bottem, if anyone knows any exact equations for L/D with tail winds and head winds, please post them, I can only find ones that are based on sink and thermals.
When it comes to weight and you want to find the best L/D (which happens at a spefic AoA) you can use this equations
V2 = V1 time the square root of(W2 over W1 )
This is where V2 is the speed that you want at weight W2
And V1 is the speed to keep that AoA with the weight W1
It works much better than using all those charts, they are often time consuming. This formula is proven out in most Aero. Engineering classes.
As far as and equation for Speed to Fly for L/D for head wings and tail winds couldn't find any in my soaring books (at least any that I could understand) but its has something to do with the tangent of the wind on a polar graph (thats about all I could gleam from it).
Thats the mathmatical apporach.
Rules of thumb:
Head wind = slower ground movement for every foot of altitude lost, so you would land shorter than the optimum distance.
Tail Wind = faster ground movement for every foot of altitude lost, more distance than usual L/D.
Heavy weight = faster flight at that angle of attack, so same L/D but you are doing it much faster (this is why a heavier gliders are better for flat out racing with no thermaling)
Lighter weight = slower flight for the same AoA, so same L/D, but you are going slower.