The flaps are extended to change the wing shape to make it bigger so it captures more wind. This causes the wing to generate more lift, which makes it easier to keep the plane in the air.
This is useful when the plane is flying slowly. When you move through the air slower, the wind isn’t pushing as hard on the wing, so you get less lift. The bigger wing surface helps you get more lift so you have enough to stay in the air.
This isn’t a problem when you’re cruising at full speed. You have plenty of wind. It’s better to make the wing smaller so you don’t have as much friction with the air (drag). That’s more fuel efficient.
The flaps are used during takeoff and landing because those are the times when the plane flies slower. It’s not safe to travel at full speed on the ground, so you have to liftoff and touchdown at a slower speed than you cruise at when at a higher altitude. Again, since you’re flying slower, you need that extra lift from the bigger wing surface, even though it uses more fuel to push the plane forward due to the added drag.
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