Phoenix just provided another reason to hate flying: the heat. With temperatures there expected to hit 119 degrees Fahrenheit, airlines canceled more than 40 flights today.

Wait. What? Airplanes can't fly because it's too hot? That's crazy.

No, not really. According to news reports, the heat poses a particular problem for the Bombardier CRJ airliners, which have a maximum operating temperature of 118 degrees. Bigger planes from Airbus and Boeing can handle 126 degrees or so.

OK. But why?

How Does an Airplane Fly?

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.

At this point, you may be thinking about the change in momentum of the plane. Don't. Instead, consider the change in momentum of the air colliding with the plane. Imagine that each molecule of air is a tiny ball being hit by the airplane. This diagram I made for another post about flying might help:

The moving wing collides with the air balls (no, I won't call them air molecules). The air balls change momentum, which requires a force. Since forces always come in pairs, the force that the wing exerts on the balls is the same magnitude as the force the balls exert on the wing. This does two things. First, it provides an upward force that some people call lift. Second, it provides a backward force called drag. You can't achieve lift without drag.

Since the plane must move to generate lift, you need thrust to increase its speed. You also need thrust to balance the drag force once you are flying at the speed you want. Typically, a jet engine or propeller provide the thrust. I guess you could use a rocket engine if it made you happy, but whatever you use, this is how airplanes fly.

What Does This Have to do With Temperature?

If the wing just collides with one air ball, it won't get much lift. To generate more lift, you need more collisions with air balls. Several things can achieve this. ( If you want to play with an air ball simulator, check out this one.) The pilot can fly faster, increasing the rate at which the air balls come in contact with the wing. Engineers can design wings with greater surface area, because a bigger wing hits more air balls. Another way of increasing surface area is to use a greater angle of attack by tilting the wings. Finally, a plane can have more collisions with air balls if there are more air balls. In other words, increasing the air density increases the lift.

Which brings me to air temperature.

Think about all the air balls around you right now. They are moving in every possible direction and at different speeds. And they collide with stuff. As the temperature increases, the average ball speed increases, too. With a greater (average) speed, the air ball collisions have more of an impact on other air balls. The increase in temperature causes the gas to expand. As the volume increases, the air density decreases.

Remember what I said about higher air density generating more lift? Well, the opposite is true, too: 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.

I hear you saying, "Well, why not compensate for the decreased air density by increasing the speed?" How do you do that on the ground? You'd need a longer runway. And so those flights got canceled. At least the airport has air conditioning.