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Coffin corner (also known as the aerodynamic ceiling or Q corner) is the region of flight where a fast but subsonic
fixed-wing aircraft A fixed-wing aircraft is a heavier-than-air flying machine, such as an airplane, which is capable of flight using wings that generate lift caused by the aircraft's forward airspeed and the shape of the wings. Fixed-wing aircraft are distinc ...
's stall speed is near the
critical Mach number In aerodynamics, the critical Mach number (Mcr or M*) of an aircraft is the lowest Mach number at which the airflow over some point of the aircraft reaches the speed of sound, but does not exceed it.Clancy, L.J. ''Aerodynamics'', Section 11.6 At ...
, at a given gross
weight In science and engineering, the weight of an object is the force acting on the object due to gravity. Some standard textbooks define weight as a Euclidean vector, vector quantity, the gravitational force acting on the object. Others define weigh ...
and G-force loading. In this region of flight, it is very difficult to keep an airplane in stable flight. Because 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. Because 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 of a
flight envelope In aerodynamics, the flight envelope, service envelope, or performance envelope of an aircraft or spacecraft refers to the capabilities of a design in terms of airspeed and load factor or atmospheric density, often simplified to altitude. The t ...
chart where the stall speed and critical Mach number are within a few knots of each other. The "coffin" refers to the possible death in these kinds of stalls. The speed where they meet is the
ceiling A ceiling is an overhead interior surface that covers the upper limits of a room. It is not generally considered a structural element, but a finished surface concealing the underside of the roof structure or the floor of a story above. Ceilings ...
of the aircraft. This is distinct from the same term used for helicopters when outside the auto-rotation envelope as seen in the height-velocity diagram.


Aerodynamic basis

Consideration of
statics Statics is the branch of classical mechanics that is concerned with the analysis of force and torque (also called moment) acting on physical systems that do not experience an acceleration (''a''=0), but rather, are in static equilibrium with ...
shows that when a fixed-wing aircraft is in straight, level flight at constant-
airspeed In aviation, airspeed is the speed of an aircraft relative to the air. Among the common conventions for qualifying airspeed are: * Indicated airspeed ("IAS"), what is read on an airspeed gauge connected to a Pitot-static system; * Calibrated a ...
, the
lift Lift or LIFT may refer to: Physical devices * Elevator, or lift, a device used for raising and lowering people or goods ** Paternoster lift, a type of lift using a continuous chain of cars which do not stop ** Patient lift, or Hoyer lift, mobile ...
on the main wing plus the force (in the negative sense if downward) on the
horizontal stabilizer A tailplane, also known as a horizontal stabiliser, is a small lifting surface located on the tail (empennage) behind the main lifting surfaces of a fixed-wing aircraft as well as other non-fixed-wing aircraft such as helicopters and gyroplan ...
is equal to the aircraft's weight and its
thrust Thrust is a reaction force described quantitatively by Newton's third law. When a system expels or accelerates mass in one direction, the accelerated mass will cause a force of equal magnitude but opposite direction to be applied to that syst ...
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 Indicated airspeed (IAS) is the airspeed of an aircraft as measured by its pitot-static system and displayed by the airspeed indicator (ASI). This is the pilots' primary airspeed reference. This value is not corrected for installation error, inst ...
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 In fluid dynamics, angle of attack (AOA, α, or \alpha) is the angle between a reference line on a body (often the chord line of an airfoil) and the vector representing the relative motion between the body and the fluid through which it is m ...
. At higher
altitude Altitude or height (also sometimes known as depth) is a distance measurement, usually in the vertical or "up" direction, between a reference datum and a point or object. The exact definition and reference datum varies according to the context ...
s, the
air density The density of air or atmospheric density, denoted '' ρ'', is the mass per unit volume of Earth's atmosphere. Air density, like air pressure, decreases with increasing altitude. It also changes with variation in atmospheric pressure, temperature a ...
is lower than at sea level. Because of the progressive reduction in air density, as the aircraft's altitude increases its
true airspeed The true airspeed (TAS; also KTAS, for ''knots true airspeed'') of an aircraft is the speed of the aircraft relative to the air mass through which it is flying. The true airspeed is important information for accurate navigation of an aircraft. Tr ...
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 The speed of sound is the distance travelled per unit of time by a sound wave as it propagates through an elastic medium. At , the speed of sound in air is about , or one kilometre in or one mile in . It depends strongly on temperature as w ...
". This becomes slower as the air becomes cooler. Because the temperature of the atmosphere generally decreases with altitude (until the
tropopause The tropopause is the atmospheric boundary that demarcates the troposphere from the stratosphere; which are two of the five layers of the atmosphere of Earth. The tropopause is a thermodynamic gradient-stratification layer, that marks the end of ...
), the speed of sound also decreases with altitude. (See the
International Standard Atmosphere The International Standard Atmosphere (ISA) is a static atmospheric model of how the pressure, temperature, density, and viscosity of the Earth's atmosphere change over a wide range of altitudes or elevations. It has been established to provide a ...
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 (M or Ma) (; ) is a dimensionless quantity in fluid dynamics representing the ratio of flow velocity past a boundary to the local speed of sound. It is named after the Moravian physicist and philosopher Ernst Mach. : \mathrm = \frac ...
. A Mach number of 1.0 indicates an airspeed equal to the speed of sound in that air. Because 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 In physics, a shock wave (also spelled shockwave), or shock, is a type of propagating disturbance that moves faster than the local speed of sound in the medium. Like an ordinary wave, a shock wave carries energy and can propagate through a med ...
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 Moment or Moments may refer to: * Present time Music * The Moments, American R&B vocal group Albums * ''Moment'' (Dark Tranquillity album), 2020 * ''Moment'' (Speed album), 1998 * ''Moments'' (Darude album) * ''Moments'' (Christine Guldbrand ...
called "
mach tuck Mach tuck is an aerodynamic effect whereby the nose of an aircraft tends to pitch downward as the airflow around the wing reaches supersonic speeds. This diving tendency is also known as tuck under. The aircraft will first experience this effect ...
". The aircraft Mach number at which these effects appear is known as its
critical Mach number In aerodynamics, the critical Mach number (Mcr or M*) of an aircraft is the lowest Mach number at which the airflow over some point of the aircraft reaches the speed of sound, but does not exceed it.Clancy, L.J. ''Aerodynamics'', Section 11.6 At ...
, or MCRIT. The true airspeed corresponding to the critical Mach number generally decreases with altitude. The
flight envelope In aerodynamics, the flight envelope, service envelope, or performance envelope of an aircraft or spacecraft refers to the capabilities of a design in terms of airspeed and load factor or atmospheric density, often simplified to altitude. The t ...
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 higher than the maximum permitted altitude for the aircraft. 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 In science and engineering, the weight of an object is the force acting on the object due to gravity. Some standard textbooks define weight as a Euclidean vector, vector quantity, the gravitational force acting on the object. Others define weigh ...
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 centripetal force). This will cause the aircraft to drop in altitude. The drop in altitude may cause the pilot to increase the angle of attack by pulling back on the stick, because normally increasing the angle of attack puts the aircraft in a climb. However, when the wing exceeds its critical angle of attack, an increase in angle of attack will lead to a loss of lift and a further loss of airspeed – the wing stalls. 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 ''Separates'' is the second album by English punk rock band 999, released in 1978. ''Separates'' was released in the United States under the title ''High Energy Plan'', with a different cover and slightly altered track listing; on ''High Energ ...
. When the airplane exceeds its critical Mach number (such as during stall prevention or recovery), then drag increases or
Mach tuck Mach tuck is an aerodynamic effect whereby the nose of an aircraft tends to pitch downward as the airflow around the wing reaches supersonic speeds. This diving tendency is also known as tuck under. The aircraft will first experience this effect ...
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 integrity and failure is an aspect of engineering that deals with the ability of a structure to support a designed structural load (weight, force, etc.) without breaking and includes the study of past structural failures in order to ...
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 In fluid dynamics, turbulence or turbulent flow is fluid motion characterized by chaotic changes in pressure and flow velocity. It is in contrast to a laminar flow, which occurs when a fluid flows in parallel layers, with no disruption between ...
could cause the airspeed to change suddenly, to beyond the limits. Some aircraft, such as the
Lockheed U-2 The Lockheed U-2, nicknamed "''Dragon Lady''", is an American single-jet engine, high altitude reconnaissance aircraft operated by the United States Air Force (USAF) and previously flown by the Central Intelligence Agency (CIA). It provides day ...
, routinely operate in the "coffin corner". In the case of the U-2, the aircraft was equipped with an autopilot, though it was unreliable. The U-2's speed margin, at high altitude, between 1-G stall warning buffet and Mach buffet can be as small as 5 knots. Aircraft capable of flying close to their critical Mach number usually carry a
machmeter A Machmeter is an aircraft pitot-static system flight instrument that shows the ratio of the true airspeed to the speed of sound, a dimensionless quantity called Mach number. This is shown on a Machmeter as a decimal fraction. An aircraft flyin ...
, an instrument which indicates speed in Mach number terms. As part of certifying aircraft in the
United States of America The United States of America (U.S.A. or USA), commonly known as the United States (U.S. or US) or America, is a country primarily located in North America. It consists of 50 states, a federal district, five major unincorporated territo ...
, the
Federal Aviation Administration The Federal Aviation Administration (FAA) is the largest transportation agency of the U.S. government and regulates all aspects of civil aviation in the country as well as over surrounding international waters. Its powers include air traffic m ...
(FAA) certifies a maximum operational velocity in terms of Mach number, or MMO. Following a series of crashes of high performance aircraft operating at high altitudes to which no definite cause could be attributed, as the aircraft involved suffered near total destruction, the FAA published an Advisory Circular establishing guidelines for improved aircrew training in high altitude operations in high performance aircraft. The circular includes a comprehensive explanation of aerodynamic effects of, and operations near coffin corner. Due to the effects of greater Mach number at high-altitude flight, the expected flight characteristics of a given configuration can change significantly. This was pointed out by a report describing the effect of ice crystals on pitot-tube airspeed indications at high altitude: {{quote, " . . the ngle of attackAOA for buffet onset is considerably less than the stall AOA at low altitudes. For example, a flight test project conducted by the National Research Council of Canada titled “Aerodynamic Low-Speed Buffet Boundary Characteristics of a High-Speed Business Jet” and presented at the 24th International Congress of the Aeronautical Sciences involved an intermediate capacity, high-speed business jet with highly swept wings to conduct low-speed buffet testing. At an altitude of approximately 13,000 ft., the buffet onset AOA occurred at 16.84 deg. In contrast, in straight and level flight at FL 450 the buffet onset AOA was 6.95 deg. In other words, be wary of your pitch attitude while at high altitudes because of the limited range of AOA due to Mach effects."Veillette, Patrick, PhD. Business & Commercial Aviation
''Unreliable Airspeed Readings Made Worse by High Altitude Ice Crystals'' 22 April 2019 (accessed 24 April 2019)]


See also

* Height-velocity diagram for helicopters


References


External links

* :de:Datei:CoffinCorner.png, Diagram for coffin corner-aviation (needs translation) Aviation risks Aerodynamics