The engine was turned off at 1000m above sea level. If you ignore the landing pattern, how long can the runway be within a few kilometers of the landing to safely land? However, the wind is blowing at 72 km / h from behind.
I am really confused if the wind is blew from head or tail how it influence on range.
I'm going to assume that when you say 1000 meters above sea level, what you really mean is 1000 meters above ground level. 1000 m AMSL can be underground in many locations.
First, you need to understand that the airplane, once in the air, always moves together with the surrounding air. The surrounding air can be moving relative to the ground – what's usually referred to as wind – but assuming sufficient altitude above local ground, the airplane is largely unconcerned with what the ground is doing under it.
Second, every airplane has some glide ratio. The glide ratio tells you, for each amount of distance covered, how much altitude you will lose. Typical values for light motor fixed-wing airplanes might be around 10:1 to 12:1, while commercial airliners might get 15:1 to 20:1, and high-performance gliders can exceed 50:1. For simplicity, I'll assume a glide ratio of 10:1, which is pessimistic, but which should be achievable by most light motor airplanes. (User XRF pointed out in a comment that these values might actually be on the optimistic side, but I'm sticking with them because the point is to illustrate the principle, not to give an exact calculation.)
Typically, the glide ratio is quoted at speed and configuration of best glide, so your first course of action when losing the engine should be to configure the airplane for best glide, and re-trim to match.
What the 10:1 tells us is that, for each 1*X meters (or feet) of altitude that you lose in a glide, you will cover 10*X meters (or feet) of distance. Since you start out at 1000 meters above ground, this means that you can cover 10*1000 meters or 10 km of distance before your flight path intersects ground.
However, again, that's distance covered through the surrounding air mass.
To figure out how far you can travel along your ground track, you need to figure out the amount of time for which you can remain in the air. Let's say that the speed of best glide in your airplane is 100 km/h indicated airspeed. Since you can travel 10 km through the surrounding air mass, this means that your travel time after losing the engine is 10/100 of an hour, or six minutes.
In six minutes, the 72 km/h wind will push your airplane 7.2 km along the ground, because six minutes is 1/10 of an hour, and 1/10 * 72 = 7.2.
Therefore, if you maintain that tailwind, with this highly simplified example, the point where you reach ground level will be 7.2 + 6 = 13.2 km from where you lost engine power.
If you instead make a 180° turn to head straight into the wind, you now have a 72 km/h headwind and a 100 km/h indicated airspeed, for a ground speed of 100-72 = 28 km/h. You can still travel 10 km through the airmass before you reach the ground, and this still takes 6 minutes, but in those 6 minutes, your ground track distance is only 2.8 km.
The major advantage of turning into the wind is that when you reach ground, you will do so at a relative speed of 28 km/h, rather than 172 km/h, assuming an unchanged 100 km/h indicated airspeed. (This is why you always land into the wind.)
Therefore, with that wind, depending on which direction you turn into, your point of contact with ground, with these assumptions, will be somewhere between 2.8 km from where you lose engine power, and 13.2 km from where you lose engine power, expressed in terms of ground track distance.
In practice, however, if you lose the engine while in the air, this is all awfully academic. Rather, you'd pick out a nearby spot on the ground that looks reasonably even, level, and large enough to set down on; and head that way. There are virtually always ways to lose altitude, but without engines in an airplane not designed as a glider, very few ways to gain altitude. With experience, you might be able to quickly judge if you'll make it to the runway or not; but any controlled landing, even an outfield landing, is always better than a crash. You can always worry about getting the airplane back to the airport once you're safely on the ground.
