Before we get into the theory of operating aircraft from a ship, we need to cover some basics of aviation. Fixed-wing aircraft work by moving through the air, and using that movement to create higher pressure on the bottom of their wings, creating a force we call lift. To stay in the air, the plane needs to generate lift to match its weight. The faster the plane moves, the more lift is created, so there is a speed below which the plane will fall out of the sky, known as the "stall speed". One of the key tasks of the pilot involves making sure it never goes below stall speed, at least when you are close to things you don't want to hit, like the ground or the sea.
Forces on an aircraft, a graphic I am legally required to use at this point
For land-based aircraft, this means the task of taking off and landing is simple enough. Get a long, flat piece of ground, put some asphalt on it, and make sure you have a safe margin above stall speed when you don't have wheels on it. Because there's a lot of ground, it doesn't matter too much if the required distance is several thousand feet. But it's annoying to build a ship much over a thousand feet long, so if you want to fly fixed-wing aircraft from ships, you'll need to be clever. First, it's important to realize that the airplane can't tell the difference between air moving past the wings because it's moving through the air, and air moving past the wings because the air is moving past it. If you had an airplane with a stall speed of, say, 30 kts, and there was a 30 kt wind, you could simply point it into the wind and take off straight up without using the engine. Now, land-based aircraft can take advantage of this, but it would take a lot of land to be able to align with the local winds no matter which way they were blowing, so the people building airports generally just figure out which way they usually blow and build the runways accordingly, with some acceptance of crosswinds. But ships can move, and thus can both align their runways with the prevailing winds and use their speed to add to the natural wind. This is important because every knot of what is known as "wind over deck" is a knot of airspeed the plane doesn't need to gain before it runs out of deck and falls into the ocean.
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