Max Q stands for “Maximum dynamic pressure.” It’s the moment in the launch when the rocket or shuttle is undergoing “maximum mechanical stress.” Which is just a way of saying the rocket is feeling a lot of physical pressure from going its way through all the air in the atmosphere at a really high speed. In fact, it’s going through the most physical stress it will feel during the entire launch.
Consider the situation similar to when you put your hand out from window in a fast moving car. You need to put some effort to keep your hands steady and not snapping back. That effort is to counter the pressure exerted by the wind. That pressure is known as the “dynamic pressure,” and the amount of that depends on two things. How fast your car is going, and how much air there is for your hand to push out of the way. That is, the thickness of the air, or the air density.
In case of a rocket launch, the rocket’s velocity keeps on increasing but the density of air, however, keeps decreasing with rise in altitude. Now, the formula of Dynamic Pressure is —
Where q is the dynamic pressure, ρ is the local air density and v is the rocket’s velocity (or air’s velocity in opposite direction). Because of the quadratic relationship, the dynamic pressure graph forms a parabola reaching a maximum point with increase in altitude and then decreasing because of decrease in pressure.
Once the rocket has crossed this region, there is a sense of relief as the mechanical pressure on the rocket, from thereafter will be less from the Max Q point. Almost in all webcasts of rocket launch you can see the Max Q point being highlighted prominently.