In aerospace engineering
Aerospace engineering is the primary branch of engineering concerned with the design, construction and science of aircraft and spacecraft. It is divided into two major and overlapping branches: aeronautical engineering and astronautical engineering...
, the maximum dynamic pressure
, often referred to as maximum Q
or max Q
, is the point at which aerodynamic stress on a vehicle in atmospheric flight is maximized. It is an important factor in the structural and mission design of rockets, missiles, and other aerospace vehicles which travel through an atmosphere
An atmosphere is a layer of gases that may surround a material body of sufficient mass, and that is held in place by the gravity of the body. An atmosphere may be retained for a longer duration, if the gravity is high and the atmosphere's temperature is low...
; the flight envelope
In aerodynamics, the flight envelope or performance envelope of an aircraft refers to the capabilities of a design in terms of airspeed and load factor or altitude. The term is somewhat loosely applied, and can also refer to other measurements such as maneuverability...
may be limited to reduce the total structural load on a vehicle near max Q.
Dynamic pressure, q
, is defined mathematically as
is the air density, and v
is the vehicle speed
In kinematics, the speed of an object is the magnitude of its velocity ; it is thus a scalar quantity. The average speed of an object in an interval of time is the distance traveled by the object divided by the duration of the interval; the instantaneous speed is the limit of the average speed as...
. For a typical launch of a rocket from the ground into space, 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
Therefore, there will always
In calculus, Rolle's theorem essentially states that a differentiable function which attains equal values at two distinct points must have a point somewhere between them where the first derivative is zero.-Standard version of the theorem:If a real-valued function ƒ is continuous on a closed...
be a point where the dynamic pressure is maximum. The point where that occurs is max Q.
In other words, below max Q, the effect of the vehicle acceleration
In physics, acceleration is the rate of change of velocity with time. In one dimension, acceleration is the rate at which something speeds up or slows down. However, since velocity is a vector, acceleration describes the rate of change of both the magnitude and the direction of velocity. ...
overcomes the decrease in air density so as to create more dynamic pressure (opposing kinetic energy) acting on the craft. Above max Q, the opposite is true. The dynamic pressure acting against the craft decreases as the air density decreases, ultimately reaching 0 when the air density becomes zero.
During a normal Space Shuttle
The Space Shuttle was a manned orbital rocket and spacecraft system operated by NASA on 135 missions from 1981 to 2011. The system combined rocket launch, orbital spacecraft, and re-entry spaceplane with modular add-ons...
launch, for example, max Q occurred at an altitude
Altitude or height is defined based on the context in which it is used . As a general definition, altitude is a distance measurement, usually in the vertical or "up" direction, between a reference datum and a point or object. The reference datum also often varies according to the context...
of approximately 11 km (35,000 ft). The three Space Shuttle Main Engine
The RS-25, otherwise known as the Space Shuttle Main Engine , is a reusable liquid-fuel rocket engine built by Pratt & Whitney Rocketdyne for the Space Shuttle, running on liquid hydrogen and oxygen. Each Space Shuttle was propelled by three SSMEs mated to one powerhead...
s are throttled back to about 70% of their rated thrust as the dynamic pressure approaches max Q; combined with the nozzle design of the solid rocket boosters
The Space Shuttle Solid Rocket Boosters were the pair of large solid rockets used by the United States' NASA Space Shuttle during the first two minutes of powered flight. Together they provided about 83% of liftoff thrust for the Space Shuttle. They were located on either side of the rusty or...
, which reduces the thrust at max Q by 1/3 after 50 sec of burn, the total stresses on the vehicle are kept to a safe level.
During a typical Apollo
The Apollo program was the spaceflight effort carried out by the United States' National Aeronautics and Space Administration , that landed the first humans on Earth's Moon. Conceived during the Presidency of Dwight D. Eisenhower, Apollo began in earnest after President John F...
mission, max Q occurred between 13 and 14 km of altitude (43,000–46,000 ft).
The point of max Q is a key milestone during a rocket launch, as it is the point at which the airframe undergoes maximum mechanical stress.
- Dynamic pressure
Pressure is the force per unit area applied in a direction perpendicular to the surface of an object. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure.- Definition :...
- Prandtl-Glauert singularity
The Prandtl–Glauert singularity is the prediction by the Prandtl–Glauert transformation that infinite pressure conditions would be experienced by an aircraft as it approaches the speed of sound. Because it is invalid to apply the transformation at these speeds, the predicted singularity does not...
- Ideal gas law
The ideal gas law is the equation of state of a hypothetical ideal gas. It is a good approximation to the behavior of many gases under many conditions, although it has several limitations. It was first stated by Émile Clapeyron in 1834 as a combination of Boyle's law and Charles's law...