Dynamic Pressure
Dynamic pressure (q) is the kinetic energy per unit volume of a fluid in motion:
q = ½ρv²
where ρ is the fluid density and v is the flow velocity. Every aerodynamic force — lift, drag, side force — is proportional to dynamic pressure. The lift equation L = q × S × C_L and drag equation D = q × S × C_D both scale linearly with q. Double the dynamic pressure, double every aerodynamic force.
Dynamic pressure has units of pascals (Pa) or pounds per square foot (psf).
Max Q
In rocketry, “max Q” is the point during ascent where dynamic pressure reaches its maximum. At launch, velocity is low so q is low. As the rocket accelerates, q rises. But as altitude increases, atmospheric density ρ drops. The competition between rising velocity and falling density produces a maximum — max Q — typically occurring 60–90 seconds after launch at altitudes of 10–15 km.
Max Q is the point of maximum aerodynamic loading on the vehicle structure. Many rockets throttle down approaching max Q to limit structural loads, then throttle up after passing through it. The Space Shuttle’s main engines throttled from 104% to 67% thrust during the max Q period.
| Vehicle | Max Q (kPa) | Altitude at max Q | Time after launch |
|---|---|---|---|
| Saturn V | ~33 | ~13 km | ~80 s |
| Space Shuttle | ~32 | ~11 km | ~60 s |
| Falcon 9 | ~28 | ~12 km | ~75 s |
Incompressible vs. compressible
At low Mach numbers (M < 0.3), density is effectively constant and q = ½ρv² is exact. At higher Mach numbers, compressibility modifies the relationship — the “impact pressure” felt by a body differs from ½ρv² because the air compresses ahead of the body.
Related terms
- Mach Number — the compressibility parameter that determines when q needs compressibility corrections
- Wing Loading — weight per unit area, which together with q determines the lift coefficient a wing must produce