If you're in a plane and steering around a circle, the centripetal force comes from leaning into a curve, just like a cyclist leans into a bend.
Steering involves banking, where the plane tilts to one side causing the one wing to dip. The plane's overall lift is tilted at an angle, making some of the lift act sideways. This sideways part of the lift provides the centripetal force that makes the plane go around in a circle. But turning the plane in a circle will make it lose lift and altitude, unless the pilot uses the elevators to increase the angle of attack to cause lift again.
Planes can fly quite easily without engines, as gliders (planes without engines), paper planes, and gliding birds show us.
A plane's engine is designed to move the plane forward at high speed. The wings move a plane upward. At high speed, the air flows fast over the wings and throws the air down toward the ground, generating an upward force, or lift. The upward force overcomes the plane's weight and keeps it in the sky.
A plane throws the air down behind it by making a spinning vortex - a kind of mini-tornado.
Most of the vortex is moving downward, but not all. There's a huge draft of air moving down in the center, but the air also swirls upward on either side of the wingtips, reducing lift.
Wings make lift by changing the direction and pressure of the air that the plane comes into contact with as the engines push the planes through the sky.
Air that flows at a certain angle (generally 15 deg) over the top and bottom of a wing follows the curve of the wing surfaces very closely. But as the angle increases (the angle of attack), the smooth airflow behind the wing becomes more turbulent and reduces the lift.
Another way to look at steering is to think of it as stopping something from going in a straight line and going in a circle. That means you have to give it a centripetal force.
Things that move in a circle always have something acting on them to give them a centripetal force. For example, if you're on a skateboard, you can tilt the deck and lean over, so your weight helps to provide centripetal force.
Most aeroplane wings are curved on the upper surface and flatter on the lower surface, making a sectional shape, named an airfoil.
When you change something's direction of travel, you change its velocity - the speed it has in a particular direction. A change in direction always means a change in velocity and acceleration.
Newton's laws of motion state that you can only change the speed of something or change its direction of travel by applying a force to it.
You steer something flying through the air at high speed by making the air flow in a different way past the wings.
Planes are moved up and down, steered from side to side, and made to stop by a complex collection of moving flaps called control surfaces on the leading and trailing edges of the wings and tail. They are called ailerons, elevators, rudders, spoilers, and air brakes.
The second aspect of making lift:
The pressure difference that a wing creates and the downwash of the air behind it generate the same effect: The angled airfoil wing creates a pressure difference that causes a downwash and produces lift.
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