Max q

The max q, or maximum dynamic pressure, condition is the point when an aerospace vehicle's atmospheric flight reaches the maximum difference between the fluid dynamics total pressure and the ambient static pressure. For an airplane, this occurs at the maximum speed at minimum altitude corner of the flight envelope. For a space vehicle launch, this occurs at the crossover point between dynamic pressure increasing with speed and static pressure decreasing with increasing altitude. This is an important design factor of aerospace vehicles, since the aerodynamic structural load on the vehicle is proportional to dynamic pressure. Dynamic pressure q is defined in incompressible fluid dynamics as where ρ is the local air density, and v is the vehicle's velocity. The dynamic pressure can be thought of as the kinetic energy density of the air with respect to the vehicle, and for incompressible flow equals the difference between total pressure and static pressure. This quantity appears notably in the lift and drag equations. For a car traveling at at sea level (where the air density is about ,) the dynamic pressure on the front of the car is , about 0.38% of the static pressure ( at sea level). For an airliner cruising at at an altitude of (where the air density is about ), the dynamic pressure on the front of the plane is , about 41% of the static pressure (). For a launch of a space vehicle from the ground, dynamic pressure is: zero at lift-off, when the air density ρ is high but the vehicle's speed v = 0; zero outside the atmosphere, where the speed v is high, but the air density ρ = 0; always non-negative, given the quantities involved. During the launch, the vehicle speed increases but the air density decreases as the vehicle rises. Therefore, by Rolle's theorem, there is a point where the dynamic pressure is maximal. In other words, before reaching max q, the dynamic pressure increase due to increasing velocity is greater than the dynamic pressure decrease due to decreasing air density such that the net dynamic pressure (opposing kinetic energy) acting on the craft continues to increase.