Drag divergence Mach number
Encyclopedia
The drag divergence Mach number (not to be confused with critical Mach number
) is the Mach number
at which the aerodynamic drag
on an airfoil
or airframe
begins to increase rapidly as the Mach number continues to increase. This increase can cause the drag coefficient
to rise to more than ten times its low speed value.
The value of the drag divergence Mach number is typically greater than 0.6; therefore it is a transonic effect. The drag divergence Mach number is usually close to, and always greater than, the critical Mach number. Generally, the drag coefficient
peaks at Mach 1.0 and begins to decrease again after the transition into the supersonic regime above approximately Mach 1.2.
The large increase in drag is caused by the formation of a shock wave
on the upper surface of the airfoil, which can induce flow separation
and adverse pressure gradients on the aft portion of the wing. This effect requires that aircraft
intended to fly at supersonic
speeds have a large amount of thrust
. In early development of transonic
and supersonic
aircraft, a steep dive was often used to provide extra acceleration through the high drag region around Mach 1.0.
This steep increase in drag
gave rise to the popular false notion of an unbreakable sound barrier
, because it seemed that no aircraft technology in the foreseeable future would have enough propulsive force or control
authority to overcome it. Indeed, one of the popular analytical methods for calculating drag at high speeds, the Prandtl-Glauert rule, predicts an infinite
amount of drag at Mach 1.0.
Two of the important technological advancements that arose out of attempts to conquer the sound barrier were the Whitcomb area rule and the supercritical airfoil
. A supercritical airfoil
is shaped specifically to make the drag divergence Mach number as high as possible, allowing aircraft to fly with relatively lower drag at high subsonic and low transonic
speeds. These, along with other advancements including computational fluid dynamics
, have been able to reduce the factor of increase in drag to two or three for modern aircraft designs.
Critical Mach number
In aerodynamics, the critical Mach number of an aircraft is the lowest Mach number at which the airflow over any part of the aircraft reaches the speed of sound....
) is the Mach number
Mach number
Mach number is the speed of an object moving through air, or any other fluid substance, divided by the speed of sound as it is in that substance for its particular physical conditions, including those of temperature and pressure...
at which the aerodynamic drag
Drag (physics)
In fluid dynamics, drag refers to forces which act on a solid object in the direction of the relative fluid flow velocity...
on an airfoil
Airfoil
An airfoil or aerofoil is the shape of a wing or blade or sail as seen in cross-section....
or airframe
Airframe
The airframe of an aircraft is its mechanical structure. It is typically considered to include fuselage, wings and undercarriage and exclude the propulsion system...
begins to increase rapidly as the Mach number continues to increase. This increase can cause the drag coefficient
Drag coefficient
In fluid dynamics, the drag coefficient is a dimensionless quantity that is used to quantify the drag or resistance of an object in a fluid environment such as air or water. It is used in the drag equation, where a lower drag coefficient indicates the object will have less aerodynamic or...
to rise to more than ten times its low speed value.
The value of the drag divergence Mach number is typically greater than 0.6; therefore it is a transonic effect. The drag divergence Mach number is usually close to, and always greater than, the critical Mach number. Generally, the drag coefficient
Drag coefficient
In fluid dynamics, the drag coefficient is a dimensionless quantity that is used to quantify the drag or resistance of an object in a fluid environment such as air or water. It is used in the drag equation, where a lower drag coefficient indicates the object will have less aerodynamic or...
peaks at Mach 1.0 and begins to decrease again after the transition into the supersonic regime above approximately Mach 1.2.
The large increase in drag is caused by the formation of a shock wave
Shock wave
A shock wave is a type of propagating disturbance. Like an ordinary wave, it carries energy and can propagate through a medium or in some cases in the absence of a material medium, through a field such as the electromagnetic field...
on the upper surface of the airfoil, which can induce flow separation
Flow separation
All solid objects travelling through a fluid acquire a boundary layer of fluid around them where viscous forces occur in the layer of fluid close to the solid surface. Boundary layers can be either laminar or turbulent...
and adverse pressure gradients on the aft portion of the wing. This effect requires that aircraft
Aircraft
An aircraft is a vehicle that is able to fly by gaining support from the air, or, in general, the atmosphere of a planet. An aircraft counters the force of gravity by using either static lift or by using the dynamic lift of an airfoil, or in a few cases the downward thrust from jet engines.Although...
intended to fly at supersonic
Supersonic
Supersonic speed is a rate of travel of an object that exceeds the speed of sound . For objects traveling in dry air of a temperature of 20 °C this speed is approximately 343 m/s, 1,125 ft/s, 768 mph or 1,235 km/h. Speeds greater than five times the speed of sound are often...
speeds have a large amount of thrust
Thrust
Thrust is a reaction force described quantitatively by Newton's second and third laws. When a system expels or accelerates mass in one direction the accelerated mass will cause a force of equal magnitude but opposite direction on that system....
. In early development of transonic
Transonic
Transonic speed is an aeronautics term referring to the condition of flight in which a range of velocities of airflow exist surrounding and flowing past an air vehicle or an airfoil that are concurrently below, at, and above the speed of sound in the range of Mach 0.8 to 1.2, i.e. 600–900 mph...
and supersonic
Supersonic
Supersonic speed is a rate of travel of an object that exceeds the speed of sound . For objects traveling in dry air of a temperature of 20 °C this speed is approximately 343 m/s, 1,125 ft/s, 768 mph or 1,235 km/h. Speeds greater than five times the speed of sound are often...
aircraft, a steep dive was often used to provide extra acceleration through the high drag region around Mach 1.0.
This steep increase in drag
Drag (physics)
In fluid dynamics, drag refers to forces which act on a solid object in the direction of the relative fluid flow velocity...
gave rise to the popular false notion of an unbreakable sound barrier
Sound barrier
The sound barrier, in aerodynamics, is the point at which an aircraft moves from transonic to supersonic speed. The term, which occasionally has other meanings, came into use during World War II, when a number of aircraft started to encounter the effects of compressibility, a collection of several...
, because it seemed that no aircraft technology in the foreseeable future would have enough propulsive force or control
Aircraft flight control systems
A conventional fixed-wing aircraft flight control system consists of flight control surfaces, the respective cockpit controls, connecting linkages, and the necessary operating mechanisms to control an aircraft's direction in flight...
authority to overcome it. Indeed, one of the popular analytical methods for calculating drag at high speeds, the Prandtl-Glauert rule, predicts an infinite
Infinity
Infinity is a concept in many fields, most predominantly mathematics and physics, that refers to a quantity without bound or end. People have developed various ideas throughout history about the nature of infinity...
amount of drag at Mach 1.0.
Two of the important technological advancements that arose out of attempts to conquer the sound barrier were the Whitcomb area rule and the supercritical airfoil
Supercritical airfoil
A supercritical airfoil is an airfoil designed, primarily, to delay the onset of wave drag in the transonic speed range. Supercritical airfoils are characterized by their flattened upper surface, highly cambered aft section, and greater leading edge radius compared with traditional airfoil shapes...
. A supercritical airfoil
Supercritical airfoil
A supercritical airfoil is an airfoil designed, primarily, to delay the onset of wave drag in the transonic speed range. Supercritical airfoils are characterized by their flattened upper surface, highly cambered aft section, and greater leading edge radius compared with traditional airfoil shapes...
is shaped specifically to make the drag divergence Mach number as high as possible, allowing aircraft to fly with relatively lower drag at high subsonic and low transonic
Transonic
Transonic speed is an aeronautics term referring to the condition of flight in which a range of velocities of airflow exist surrounding and flowing past an air vehicle or an airfoil that are concurrently below, at, and above the speed of sound in the range of Mach 0.8 to 1.2, i.e. 600–900 mph...
speeds. These, along with other advancements including computational fluid dynamics
Computational fluid dynamics
Computational fluid dynamics, usually abbreviated as CFD, is a branch of fluid mechanics that uses numerical methods and algorithms to solve and analyze problems that involve fluid flows. Computers are used to perform the calculations required to simulate the interaction of liquids and gases with...
, have been able to reduce the factor of increase in drag to two or three for modern aircraft designs.
See also
- wave dragWave dragIn aeronautics, wave drag is a component of the drag on aircraft, blade tips and projectiles moving at transonic and supersonic speeds, due to the presence of shock waves. Wave drag is independent of viscous effects.- Overview :...
- supercritical airfoilSupercritical airfoilA supercritical airfoil is an airfoil designed, primarily, to delay the onset of wave drag in the transonic speed range. Supercritical airfoils are characterized by their flattened upper surface, highly cambered aft section, and greater leading edge radius compared with traditional airfoil shapes...
- critical mach
- speed of soundSpeed of soundThe speed of sound is the distance travelled during a unit of time by a sound wave propagating through an elastic medium. In dry air at , the speed of sound is . This is , or about one kilometer in three seconds or approximately one mile in five seconds....
- sound barrierSound barrierThe sound barrier, in aerodynamics, is the point at which an aircraft moves from transonic to supersonic speed. The term, which occasionally has other meanings, came into use during World War II, when a number of aircraft started to encounter the effects of compressibility, a collection of several...