Coffin corner (aviation)
Encyclopedia
The coffin corner is the altitude at or near which a fast fixed-wing aircraft
's stall
speed is equal to the critical Mach number
, at a given gross weight
and G-force loading
. At this altitude the airplane becomes nearly impossible to keep in stable flight. Since the stall speed is the minimum speed required to maintain level flight, any reduction in speed will cause the airplane to stall and lose altitude. Since the critical Mach number is the maximum speed at which air can travel over the wings without losing lift due to flow separation and shock waves, any increase in speed will cause the airplane to lose lift, or to pitch heavily nose-down, and lose altitude. The "corner" refers to the triangular shape at the top right of a flight envelope
chart where the stall speed and critical Mach number lines come together.
shows that when a fixed-wing aircraft is in straight, level, flight at constant-airspeed
the lift
on the main wing is equal to its weight plus the downward force on the horizontal stabilizer; and its thrust
is equal to its drag
. In most circumstances this equilibrium can occur at a range of airspeeds. The minimum such speed is the stall speed, or VSO. The indicated airspeed
at which a fixed-wing aircraft stalls varies with the weight of the aircraft but does not vary significantly with altitude. At speeds close to the stall speed the aircraft's wings are at a high angle of attack
.
At higher altitude
s, the air density
is lower than at sea level. Because of the progressive reduction in air density, as the aircraft’s altitude increases its true airspeed
is progressively greater than its indicated airspeed. For example, the indicated airspeed at which an aircraft stalls can be considered constant, but the true airspeed at which it stalls increases with altitude.
Air conducts sound at a certain speed, the "speed of sound
". This becomes slower as the air becomes cooler. Since the temperature of the atmosphere generally decreases with altitude (until the tropopause
), the speed of sound also decreases with altitude. (See the International Standard Atmosphere
for more on temperature as a function of altitude.)
A given airspeed, divided by the speed of sound in that air, gives a ratio known as the Mach number
. A Mach number of 1.0 indicates an airspeed equal to the speed of sound in that air. Since the speed of sound increases with air temperature, and air temperature generally decreases with altitude, the true airspeed for a given Mach number generally decreases with altitude.
As an airplane moves through the air faster, the airflow over parts of the wing will reach speeds that approach Mach 1.0. At such speeds, shock waves
form in the air passing over the wings, drastically increasing the drag due to drag divergence
, causing Mach buffet, or drastically changing the center of pressure
, resulting in a nose-down moment
called "mach tuck
". The aircraft Mach number at which these effects appear is known as its critical Mach number
, or Mach CRIT. The true airspeed corresponding to the critical Mach number generally decreases with altitude.
The flight envelope
is a plot of various curves representing the limits of the aircraft's true airspeed and altitude. Generally, the top-left boundary of the envelope is the curve representing stall speed, which increases as altitude increases. The top-right boundary of the envelope is the curve representing critical Mach number in true airspeed terms, which decreases as altitude increases. These curves typically intersect at some altitude. This intersection is the coffin corner, or more formally the Q corner.
The above explanation is based on level, constant speed, flight with a given gross weight
and load factor of 1.0 G. The specific altitudes and speeds of the coffin corner will differ depending on weight, and the load factor increases caused by banking and pitching maneuvers. Similarly, the specific altitudes at which the stall speed meets the critical Mach number will differ depending on the actual atmospheric temperature.
"). The reason why the wing "stalls" when it exceeds its critical angle of attack is that the airflow over the top of the wing separates
.
When the airplane exceeds its critical Mach number (such as during stall prevention or recovery), then drag increases or Mach tuck occurs, which can cause the aircraft to upset, lose control, and lose altitude. In either case, as the airplane falls, it could gain speed and then structural failure
could occur, typically due to excessive g forces during the pullout phase of the recovery.
As an airplane approaches its coffin corner, the margin between stall speed and critical Mach number becomes smaller and smaller. Small changes could put one wing or the other above or below the limits. For instance, a turn causes the inner wing to have a lower airspeed, and the outer wing, a higher airspeed. The aircraft could exceed both limits at once. Or, turbulence
could cause the airspeed to change suddenly, to beyond the limits.
Aircraft capable of flying close to their critical Mach number usually carry a machmeter
, an instrument which indicates speed in Mach number terms. As part of certifying aircraft in the United States of America
, the Federal Aviation Administration
(FAA) certifies a Mach number for maximum operation, or MMO.
Some aircraft, such as the Lockheed U-2
, routinely operate in the "coffin corner", which demands great skill from their pilots. The FAA is concerned that as jet aircraft
become more common, less experienced pilots will be flying those aircraft closer to the altitude of their coffin corners, and that catastrophic accidents will occur as a result.
Fixed-wing aircraft
A fixed-wing aircraft is an aircraft capable of flight using wings that generate lift due to the vehicle's forward airspeed. Fixed-wing aircraft are distinct from rotary-wing aircraft in which wings rotate about a fixed mast and ornithopters in which lift is generated by flapping wings.A powered...
's stall
Stall (flight)
In fluid dynamics, a stall is a reduction in the lift coefficient generated by a foil as angle of attack increases. This occurs when the critical angle of attack of the foil is exceeded...
speed is equal to the critical Mach number
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....
, at a given gross weight
Weight
In science and engineering, the weight of an object is the force on the object due to gravity. Its magnitude , often denoted by an italic letter W, is the product of the mass m of the object and the magnitude of the local gravitational acceleration g; thus:...
and G-force loading
G-force
The g-force associated with an object is its acceleration relative to free-fall. This acceleration experienced by an object is due to the vector sum of non-gravitational forces acting on an object free to move. The accelerations that are not produced by gravity are termed proper accelerations, and...
. At this altitude the airplane becomes nearly impossible to keep in stable flight. Since the stall speed is the minimum speed required to maintain level flight, any reduction in speed will cause the airplane to stall and lose altitude. Since the critical Mach number is the maximum speed at which air can travel over the wings without losing lift due to flow separation and shock waves, any increase in speed will cause the airplane to lose lift, or to pitch heavily nose-down, and lose altitude. The "corner" refers to the triangular shape at the top right of a flight envelope
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...
chart where the stall speed and critical Mach number lines come together.
Aerodynamic basis
Consideration of staticsStatics
Statics is the branch of mechanics concerned with the analysis of loads on physical systems in static equilibrium, that is, in a state where the relative positions of subsystems do not vary over time, or where components and structures are at a constant velocity...
shows that when a fixed-wing aircraft is in straight, level, flight at constant-airspeed
Airspeed
Airspeed is the speed of an aircraft relative to the air. Among the common conventions for qualifying airspeed are: indicated airspeed , calibrated airspeed , true airspeed , equivalent airspeed and density airspeed....
the lift
Lift (force)
A fluid flowing past the surface of a body exerts a surface force on it. Lift is the component of this force that is perpendicular to the oncoming flow direction. It contrasts with the drag force, which is the component of the surface force parallel to the flow direction...
on the main wing is equal to its weight plus the downward force on the horizontal stabilizer; and its 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....
is equal to its 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...
. In most circumstances this equilibrium can occur at a range of airspeeds. The minimum such speed is the stall speed, or VSO. The indicated airspeed
Indicated airspeed
Indicated airspeed is the airspeed read directly from the airspeed indicator on an aircraft, driven by the pitot-static system. IAS is directly related to calibrated airspeed , which is the IAS corrected for instrument and installation errors....
at which a fixed-wing aircraft stalls varies with the weight of the aircraft but does not vary significantly with altitude. At speeds close to the stall speed the aircraft's wings are at a high angle of attack
Angle of attack
Angle of attack is a term used in fluid dynamics to describe the angle between a reference line on a lifting body and the vector representing the relative motion between the lifting body and the fluid through which it is moving...
.
At higher altitude
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...
s, the air density
Density of air
The density of air, ρ , is the mass per unit volume of Earth's atmosphere, and is a useful value in aeronautics and other sciences. Air density decreases with increasing altitude, as does air pressure. It also changes with variances in temperature or humidity...
is lower than at sea level. Because of the progressive reduction in air density, as the aircraft’s altitude increases its true airspeed
True airspeed
True airspeed of an aircraft is the speed of the aircraft relative to the airmass in which it is flying. True airspeed is important information for accurate navigation of an aircraft.-Performance:...
is progressively greater than its indicated airspeed. For example, the indicated airspeed at which an aircraft stalls can be considered constant, but the true airspeed at which it stalls increases with altitude.
Air conducts sound at a certain speed, the "speed of sound
Speed of sound
The 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....
". This becomes slower as the air becomes cooler. Since the temperature of the atmosphere generally decreases with altitude (until the tropopause
Tropopause
The tropopause is the atmospheric boundary between the troposphere and the stratosphere.-Definition:Going upward from the surface, it is the point where air ceases to cool with height, and becomes almost completely dry...
), the speed of sound also decreases with altitude. (See the International Standard Atmosphere
International Standard Atmosphere
The International Standard Atmosphere is an atmospheric model of how the pressure, temperature, density, and viscosity of the Earth's atmosphere change over a wide range of altitudes. It has been established to provide a common reference for temperature and pressure and consists of tables of...
for more on temperature as a function of altitude.)
A given airspeed, divided by the speed of sound in that air, gives a ratio known as 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...
. A Mach number of 1.0 indicates an airspeed equal to the speed of sound in that air. Since the speed of sound increases with air temperature, and air temperature generally decreases with altitude, the true airspeed for a given Mach number generally decreases with altitude.
As an airplane moves through the air faster, the airflow over parts of the wing will reach speeds that approach Mach 1.0. At such speeds, shock waves
Shock Waves
Shock Waves, , is a 1977 horror movie written and directed by Ken Wiederhorn...
form in the air passing over the wings, drastically increasing the drag due to drag divergence
Drag divergence Mach number
The drag divergence 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...
, causing Mach buffet, or drastically changing the center of pressure
Center of pressure
The center of pressure is the point on a body where the total sum of a pressure field acts, causing a force and no moment about that point. The total force vector acting at the center of pressure is the value of the integrated vectorial pressure field. The resultant force and center of pressure...
, resulting in a nose-down moment
Moment (physics)
In physics, the term moment can refer to many different concepts:*Moment of force is the tendency of a force to twist or rotate an object; see the article torque for details. This is an important, basic concept in engineering and physics. A moment is valued mathematically as the product of the...
called "mach tuck
Mach tuck
Mach tuck is an aerodynamic effect, whereby the nose of an aircraft tends to pitch downwards as the airflow around the wing reaches supersonic speeds...
". The aircraft Mach number at which these effects appear is known as its critical Mach number
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....
, or Mach CRIT. The true airspeed corresponding to the critical Mach number generally decreases with altitude.
The flight envelope
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...
is a plot of various curves representing the limits of the aircraft's true airspeed and altitude. Generally, the top-left boundary of the envelope is the curve representing stall speed, which increases as altitude increases. The top-right boundary of the envelope is the curve representing critical Mach number in true airspeed terms, which decreases as altitude increases. These curves typically intersect at some altitude. This intersection is the coffin corner, or more formally the Q corner.
The above explanation is based on level, constant speed, flight with a given gross weight
Weight
In science and engineering, the weight of an object is the force on the object due to gravity. Its magnitude , often denoted by an italic letter W, is the product of the mass m of the object and the magnitude of the local gravitational acceleration g; thus:...
and load factor of 1.0 G. The specific altitudes and speeds of the coffin corner will differ depending on weight, and the load factor increases caused by banking and pitching maneuvers. Similarly, the specific altitudes at which the stall speed meets the critical Mach number will differ depending on the actual atmospheric temperature.
Consequences
When an aircraft slows to below its stall speed, it is unable to generate enough lift in order to cancel out the forces that act on the aircraft (such as weight and centrifugal force). This will cause the aircraft to sink (drop in altitude). The drop in altitude may cause the pilot to increase the angle of attack (the pilot pulls on the stick), because normally increasing the angle of attack (pulling up) puts the aircraft in a climb. When the wing however exceeds its critical angle of attack, an increase in Angle of Attack (pulling up) will lead to a loss of lift and a further loss of airspeed (the wing "stallsStall (flight)
In fluid dynamics, a stall is a reduction in the lift coefficient generated by a foil as angle of attack increases. This occurs when the critical angle of attack of the foil is exceeded...
"). The reason why the wing "stalls" when it exceeds its critical angle of attack is that the airflow over the top of the wing separates
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...
.
When the airplane exceeds its critical Mach number (such as during stall prevention or recovery), then drag increases or Mach tuck occurs, which can cause the aircraft to upset, lose control, and lose altitude. In either case, as the airplane falls, it could gain speed and then structural failure
Structural failure
Structural failure refers to loss of the load-carrying capacity of a component or member within a structure or of the structure itself. Structural failure is initiated when the material is stressed to its strength limit, thus causing fracture or excessive deformations...
could occur, typically due to excessive g forces during the pullout phase of the recovery.
As an airplane approaches its coffin corner, the margin between stall speed and critical Mach number becomes smaller and smaller. Small changes could put one wing or the other above or below the limits. For instance, a turn causes the inner wing to have a lower airspeed, and the outer wing, a higher airspeed. The aircraft could exceed both limits at once. Or, turbulence
Turbulence
In fluid dynamics, turbulence or turbulent flow is a flow regime characterized by chaotic and stochastic property changes. This includes low momentum diffusion, high momentum convection, and rapid variation of pressure and velocity in space and time...
could cause the airspeed to change suddenly, to beyond the limits.
Aircraft capable of flying close to their critical Mach number usually carry a machmeter
Machmeter
A Machmeter is an aircraft pitot-static system flight instrument thatshows the ratio of the true airspeed to the speed of sound,a dimensionless quantity called Mach number...
, an instrument which indicates speed in Mach number terms. As part of certifying aircraft in the United States of America
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
, the Federal Aviation Administration
Federal Aviation Administration
The Federal Aviation Administration is the national aviation authority of the United States. An agency of the United States Department of Transportation, it has authority to regulate and oversee all aspects of civil aviation in the U.S...
(FAA) certifies a Mach number for maximum operation, or MMO.
Some aircraft, such as the Lockheed U-2
Lockheed U-2
The Lockheed U-2, nicknamed "Dragon Lady", is a single-engine, very high-altitude reconnaissance aircraft operated by the United States Air Force and previously flown by the Central Intelligence Agency . It provides day and night, very high-altitude , all-weather intelligence gathering...
, routinely operate in the "coffin corner", which demands great skill from their pilots. The FAA is concerned that as jet aircraft
Jet aircraft
A jet aircraft is an aircraft propelled by jet engines. Jet aircraft generally fly much faster than propeller-powered aircraft and at higher altitudes – as high as . At these altitudes, jet engines achieve maximum efficiency over long distances. The engines in propeller-powered aircraft...
become more common, less experienced pilots will be flying those aircraft closer to the altitude of their coffin corners, and that catastrophic accidents will occur as a result.
External links
- Diagram for coffin corner-aviation (needs translation)