A kite stays in the air due to the difference in speed between the ground and the wind. Think about standing in the wind and feeling it push against you; a kite takes that push and directs the air down which turns the push into a force upward. Because it is tethered to the ground it can maintain this orientation and as it is let out rise higher into the sky.
The importance of the tail is to add drag, keeping the right side of the kite pointed into the wind. In order to fly it needs to have the leading edge higher into the wind than the tail so it pushes air down. If it turned around then the wind would tend to push it down and it would quickly stop flying.
The tail is not actually necessary – it’s just pretty to look at and can help estimate the air flow around your kite. Kites are basically just big sheets of paper/fabric that catch wind. If you grab a normal piece of paper from your desk and blow at it you’ll see it wants to move with the air flowing around it. The same happens with kites but on a bigger scale. We then create a skeleton for it to help it keep it’s shape and attach a string in the middle(ish) to help it stay in place and balanced.
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