One huge factor regarding lift is area: fact is, the more area exposed to the upward force, the better the lift.
Extending the flaps increases the surface area where lift can push up.
*Angling* the flaps increases resistance (and offsets lift), therefore when landing, flaps are extended and angled to help slow the plane down.
This is a bad assumption. Flaps don’t slow a plane down. Flaps simply allow a plane to fly at slower speeds by generating additional lift. Speed brakes are used to slow the plane down.
ETA:
Realized I don’t finish my answer. Flaps are used at takeoff because they generate additional lift at lower speeds allowing planes to takeoff at slower speeds which lessens the necessary runway length for take off
Because otherwise you would need to accelerate to VERY high speed to be able to take off, that causes tires to blow, or you need excessive angle of attack to lift off from the ground, which may not be geometrically possible since the tail would hit the ground.
After you lift off, ground effect diminishes, if you barely made it up, it would be time to drop like a rock now.
Flaps fix that by increasing wing surface area and curvature, allowing more lift generation at slower airspeeds and lower AoAs, at the cost of moderate increase in drag. The takeoff performance and wing design is calculated so that this trade-off is worthwhile.
There are commercial airliners permitting no-flap as a possible takeoff configuration given correct weights and altitude, but most Airbus/Boeing aircraft do not.
flaps may slow down the plane some but they also provide more surface area for lift to be generated. when the plane is running on the ground and there are frictional forces acting on the wheels, it may take a loooong time for the plane to reach the necessary speed to take off if there weren’t flaps.
so essentially flaps allow for planes to take off and land at lower speeds. they also allow for airports to have shorter runways.
Flaps don’t slow the plane down by themselves. They expand the size of the wing, which increases the amount of lift being generated and *allows* the plane to fly at slower speeds without stalling. That’s why they’re extended during takeoff. You want to maximize lift so that you can take off in a shorter distance. Among other reasons, this lowers the chance of overrunning the runway.
Some planes need a bit of extra lift to get off the runway and climb at the desired rate, but having the wing be that shape would negatively impact performance in other situations (like in cruise flight). So the plane is designed to have the flaps at a certain setting during takeoff which can then be retracted when that extra lift is not needed.
Creating lift does create extra drag but it depends on a lot of things like speed, angle of attack, and the shape of the wing.
Ultimately though to answer OPs question the flaps are lowered on some airplanes during takeoff because the benefits outweigh the cost.
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