Temperatures are rising across the country and in Phoenix the heat keeps planes from taking off. Wired has a simple write up on the science of heat and flight!
Before you can understand how it can be too hot to fly, you have to understand how airplanes fly. Everyone likes to give a simple answer, like “It’s all about lift.” Yes, that is true, but it’s not terribly convincing. To really get at the physics involved here, you need to look at the momentum principle. The momentum principle says that the total force on an object is equal to the rate of change of momentum, where momentum is mass times velocity.
The increase in temperature causes the gas to expand. As the volume increases, the air density decreases.
Less air density generates less lift. And that’s the problem in Arizona. The air density is simply too low for some of those planes to take off.