Recently, some students I've flown with were not clear on the effects of a head wind and the need to stay upwind of the field when flying near the airport. In this article, I'd like to clear up some mis-conceptions using only basic algebra. It is a companion to another article, Speeds to Fly. In the L23 polar below, it is useful to note that 100 feet per minute is very close to 1 knot (0.987 kts, to be exact).

An L23 at maximum gross weight has a published best L/D of 29:1 at 48 kts (the polar below [red lines] agrees :-) ).  The task is to fly from point A to point B and the distance between A and B is 1 nautical mile (nm). So, let's see what it takes to fly the task in various wind conditions. Note that we're ignoring sink and concentrating only on the effect of a headwind. We want to consider 3 scenarios for the task: the first, no wind; the second, a 48 knot head wind; and last, a 24 knot head wind.

If there is no wind and you fly at best glide speed (48 kts), it takes 60/48=1.25 minutes to go travel the distance. The sink rate at 48kts is 48/29=1.7kts=170fpm, and so the amount of altitude lost on task is 1.25x170=213 feet. Alternatively, a nautical mile is 6076 feet so altitude lost on course is 6076/29=210 ft.

For an extreme case, let's look at a 48 knot headwind on task. How long would it take to fly the task at best glide speed (48 kts)? It would take "forever" because you'd be stationary over the ground. Of course, in those conditions you wouldn't fly at 48 kts. We'll get back to that later.

Now, let's take something in the middle - a 24 knot head wind. At an airspeed of 48 kts, your speed over the ground would be cut in half, the time on task would be doubled, and so the altitude lost on task would be double that of the no wind flight or 213x2=426 feet.

When penetrating a headwind, the rule of thumb is to add half of the headwind speed to the best glide speed (See also http://home.att.net/~jdburch/polar.htm). With a 24 knot headwind, this would be 48+12=60 kts. From the polar below, the actual correct optimal speed speed in a 24 knot headwind is 58 knots (blue lines) so the rule of thumb is pretty close, I think. From the polar, at 58 knots the sink rate is about 2.4 knots (240fpm). At 58kts (airspeed), ground speed is 58-24=34kts and the time on course is 60/34=1.76 minutes,  and so the altitude lost on course is 1.76x240=422 feet - which is a little better than if you flew at the published best glide speed of 48 knots (426 ft altitude loss).

The conclusion is that you should always be aware of the wind speed and direction and to fly at the correct speed for the conditions. It really does make a difference, and on a hard day can mean the difference between making it home or landing out. Do look at the Speeds to Fly article to see how sink and other factors affect the best speed for the task at hand. If you have a headwind on task, even at the optimal speed to fly, you'll need more altitude to get the job done.

For a more mathematical explanation, see Helmut Reichmann "Cross Country Soaring".