Planes in the stratosphere

Having measured an aeroplane at 10km up the other week and having now learned about the stratosphere, the question becomes why do they fly so high. The answer is to do with the temperature inversion in that layer. Instead of the temperature falling as you go up, the temperature actually rises because the ozone absorbs ultra-violet radiation from the Sun. The heating is higher up in the stratosphere. Convection is difficult when the heating is at the top so there is less turbulence due to air currents. That's why planes fly up there.