If in an emergency and a modern passenger aircraft had to glide, will it make a big difference if the aircraft had a headwind rather than having to glide downwind to nearest airport?
The only way I can think to characterize a "big difference" for an airplane which has lost its engines is "Can the plane make it to the runway in time?"
If that's the question, then the answer has to do with the plane's glide polar.
The way to read the below chart is that the airspeed is on the x-axis and the sink rate is on the y-axis. You'll notice that as airspeed decreases, sink rate decreases; up until that sharp hook, which is when the plane starts stalling.
The best glide range occurs when the straight line is tangent to the L/D curve. (green curve in the below picture)
The straight line's starting point is determined by the atmospheric conditions:
- Calm air: the starting point is the origin (red line)
- Sinking air: the starting point moves up the y-axis (yellow line)
- Rising air: the starting point moves down the y-axis (not shown)
- Tailwind: the starting point moves back the x-axis (black line).
- Headwind: the starting point moves forward on the x-axis (purple line)
So the question of how much of a difference it makes comes down to how far the headwind vs tailwind moves the tangent line's starting point. You can see that the stronger the headwind, the steeper the tangent line. You can also see that a headwind has a very similar effect to sinking air, only the difference is that you never fly out of the sink.
As a results, a headwind has a surprisingly large impact on glide ratio. How much is dependent on how far the plane needs to fly and how much of a headwind it has vs. its glide polar.
Unfortunately, as is the way of these things, a headwind hurts much more than a tailwind helps. From my experience in gliders, I'd hazard a guess that a headwind which is only 10% of the best glide speed will have a >20% impact on range. 10% of an airliner's speed is quite fast, but it's not crazy fast and if it were flying in or near the jet-stream the plane could easily be fighting headwinds much stronger than that.
One last consideration in determining the glide range is how winds will change in both heading and direction as the plane descends. Check out the altitude slider at www.windy.com to get a feel for how the global winds vary with altitude.