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The Kármán line (or von Kármán line ) is an attempt to define a boundary between
Earth's atmosphere The atmosphere of Earth is the layer of gases, known collectively as air, retained by Earth's gravity that surrounds the planet and forms its planetary atmosphere. The atmosphere of Earth protects life on Earth by creating pressure allowing fo ...
and
outer space Outer space, commonly shortened to space, is the expanse that exists beyond Earth and its atmosphere and between celestial bodies. Outer space is not completely empty—it is a near-perfect vacuum containing a low density of particles, pred ...
, and offers a specific definition set by the Fédération aéronautique internationale (FAI), an international record-keeping body for aeronautics. Defining the edge of space is important for legal and regulatory purposes since
aircraft An aircraft is a vehicle that is able to flight, fly by gaining support from the Atmosphere of Earth, air. It counters the force of gravity by using either Buoyancy, static lift or by using the Lift (force), dynamic lift of an airfoil, or in ...
and
spacecraft A spacecraft is a vehicle or machine designed to fly in outer space. A type of artificial satellite, spacecraft are used for a variety of purposes, including communications, Earth observation, meteorology, navigation, space colonization, ...
fall under different jurisdictions and are subject to different treaties.
International law International law (also known as public international law and the law of nations) is the set of rules, norms, and standards generally recognized as binding between states. It establishes normative guidelines and a common conceptual framework for ...
does not define the edge of space, or the limit of national airspace. The FAI defines the Kármán line as space beginning above
Earth Earth is the third planet from the Sun and the only astronomical object known to harbor life. While large volumes of water can be found throughout the Solar System, only Earth sustains liquid surface water. About 71% of Earth's sur ...
's
mean sea level There are several kinds of mean in mathematics, especially in statistics. Each mean serves to summarize a given group of data, often to better understand the overall value ( magnitude and sign) of a given data set. For a data set, the '' ...
. This number is well above the altitude reachable by a conventional airplane and is roughly where satellites, even on very eccentric trajectories, will decay before completing a single orbit. While experts disagree on exactly where the atmosphere ends and space begins, most regulatory agencies (including the United Nations) accept the FAI Kármán line definition or something close to it. As defined by the FAI, the Kármán line was established in the 1960s. Various countries and entities define space's boundary differently for various purposes. The Kármán line is named after Theodore von Kármán (1881–1963), a Hungarian American
engineer Engineers, as practitioners of engineering, are professionals who Invention, invent, design, analyze, build and test machines, complex systems, structures, gadgets and materials to fulfill functional objectives and requirements while considerin ...
and
physicist A physicist is a scientist who specializes in the field of physics, which encompasses the interactions of matter and energy at all length and time scales in the physical universe. Physicists generally are interested in the root or ultimate cau ...
who was active in aeronautics and astronautics. In 1957, he was the first person to attempt to calculate an altitude limit for airplanes.


Definition

The FAI uses the term Kármán line to define the boundary between aeronautics and astronautics:


Interpretations of the definition

The expressions "edge of space" or ″near space″ are often used (by, for instance, the FAI in some of their publications) to refer to a region below the boundary of Outer Space, which is often meant to include substantially lower regions as well. Thus, certain
balloon A balloon is a flexible bag that can be inflated with a gas, such as helium, hydrogen, nitrous oxide, oxygen, and air. For special tasks, balloons can be filled with smoke, liquid water, granular media (e.g. sand, flour or rice), or lig ...
or
airplane An airplane or aeroplane (informally plane) is a fixed-wing aircraft that is propelled forward by thrust from a jet engine, propeller, or rocket engine. Airplanes come in a variety of sizes, shapes, and wing configurations. The broad ...
flights might be described as "reaching the edge of space". In such statements, "reaching the edge of space" merely refers to going higher than average aeronautical vehicles commonly would. There is still no international legal definition of the demarcation between a country's air space and outer space. In 1963, Andrew G. Haley discussed the Kármán line in his book ''Space Law and Government''. Haley, Andrew G.; (1963) ''Space Law and Government'', Appleton-Century-Crofts In a chapter on the limits of national
sovereignty Sovereignty is the defining authority within individual consciousness, social construct, or territory. Sovereignty entails hierarchy within the state, as well as external autonomy for states. In any state, sovereignty is assigned to the perso ...
, he made a survey of major writers' views. He indicated the inherent imprecision of the Line:
The line represents a
mean There are several kinds of mean in mathematics, especially in statistics. Each mean serves to summarize a given group of data, often to better understand the overall value ( magnitude and sign) of a given data set. For a data set, the '' ar ...
or
median In statistics and probability theory, the median is the value separating the higher half from the lower half of a data sample, a population, or a probability distribution. For a data set, it may be thought of as "the middle" value. The basic f ...
measurement. It is comparable to such measures used in the law as
mean sea level There are several kinds of mean in mathematics, especially in statistics. Each mean serves to summarize a given group of data, often to better understand the overall value ( magnitude and sign) of a given data set. For a data set, the '' ...
,
meander A meander is one of a series of regular sinuous curves in the channel of a river or other watercourse. It is produced as a watercourse erodes the sediments of an outer, concave bank ( cut bank) and deposits sediments on an inner, convex ban ...
line,
tide Tides are the rise and fall of sea levels caused by the combined effects of the gravitational forces exerted by the Moon (and to a much lesser extent, the Sun) and are also caused by the Earth and Moon orbiting one another. Tide tables ...
line; but it is more complex than these. In arriving at the von Kármán jurisdictional line, myriad factors must be considered – other than the factor of aerodynamic lift. These factors have been discussed in a very large body of literature and by a score or more of commentators. They include the physical constitution of the air; the biological and physiological viability; and still other factors which logically join to establish a point at which air no longer exists and at which airspace ends.


Kármán's comments

In the final chapter of his autobiography, Kármán addresses the issue of the edge of
outer space Outer space, commonly shortened to space, is the expanse that exists beyond Earth and its atmosphere and between celestial bodies. Outer space is not completely empty—it is a near-perfect vacuum containing a low density of particles, pred ...
:
Where space begins ... can actually be determined by the speed of the space vehicle and its altitude above the Earth. Consider, for instance, the record flight of Captain Iven Carl Kincheloe Jr. in an X-2 rocket plane. Kincheloe flew 2000 miles per hour (3,200 km/h) at 126,000 feet (38,500 m), or 24 miles up. At this altitude and speed, aerodynamic lift still carries 98 percent of the weight of the plane, and only two percent is carried by inertia, or Kepler force, as space scientists call it. But at 300,000 feet (91,440 m) or 57 miles up, this relationship is reversed because there is no longer any air to contribute lift: only inertia prevails. This is certainly a physical boundary, where
aerodynamics Aerodynamics, from grc, ἀήρ ''aero'' (air) + grc, δυναμική (dynamics), is the study of the motion of air, particularly when affected by a solid object, such as an airplane wing. It involves topics covered in the field of fluid dy ...
stops and astronautics begins, and so I thought why should it not also be a jurisdictional boundary? Haley has kindly called it the Kármán Jurisdictional Line. Below this line, space belongs to each country. Above this level there would be free space.


Technical considerations

An atmosphere does not abruptly end at any given height but becomes progressively less dense with altitude. Also, depending on how the various layers that make up the space around the
Earth Earth is the third planet from the Sun and the only astronomical object known to harbor life. While large volumes of water can be found throughout the Solar System, only Earth sustains liquid surface water. About 71% of Earth's sur ...
are defined (and depending on whether these layers are considered part of the actual atmosphere), the definition of the edge of space could vary considerably: If one were to consider the thermosphere and exosphere part of the atmosphere and not of space, one might have to extend the boundary to space to at least above sea level. The Kármán line thus is an arbitrary definition based on some technical considerations. An aircraft can stay aloft only by constantly traveling forward relative to the air (rather than the ground), so that the wings can generate aerodynamic lift. The thinner the air, the faster the plane must go to generate enough lift to stay up. The amount of lift provided (which must equal the vehicle's weight in order to maintain level flight) is calculated by the lift equation: : L = \tfrac12 \rho v^2 S C_L, where : ''L'' is the lift force, : ''ρ'' is 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 ...
, : ''v'' is the aircraft's speed relative to the air, : ''S'' is the aircraft's
wing area A wing is a type of fin that produces lift while moving through air or some other fluid. Accordingly, wings have streamlined cross-sections that are subject to aerodynamic forces and act as airfoils. A wing's aerodynamic efficiency is express ...
, : ''C''''L'' is the lift coefficient. Lift (''L'') generated is directly proportional to the air density (''ρ''). An aircraft maintains altitude if the lift force equals the aircraft weight such that : L = mg where m is the aircraft mass, g is the acceleration due to gravity, and mg is the downward force due to gravity (weight). All other factors remaining unchanged, true airspeed (''v'') must increase to compensate for lower air density at higher altitudes. At very high speeds, centrifugal force (Kepler force) given by mv^2/R, where R is the distance to the center of the Earth, contributes to maintaining altitude. This is the virtual force that keeps satellites in circular orbit without any aerodynamic lift. An aircraft can maintain altitude at the outer reaches of the atmosphere if the sum of the aerodymanic lift force and centrigugal force equals the aircraft weight. : L + \fracR = mg As altitude increases and air density decreases, the speed to generate enough aerodynamic lift to support the aircraft weight increases until the speed becomes so high that the centrigual force contribution becomes significant. At a high enough altitude, the centrifugal force will dominate over the lift force and the aircraft would become effectively an orbiting spacecraft instead an aircraft supported by aerodynamic lift. In 1956, von Kármán presented a paper in which he discussed aerothermal limits to flight. The faster aircraft fly, the more heat they would generate due to aerodynamic heating from friction with the atmosphere and
adiabatic process In thermodynamics, an adiabatic process (Greek: ''adiábatos'', "impassable") is a type of thermodynamic process that occurs without transferring heat or mass between the thermodynamic system and its environment. Unlike an isothermal process, ...
es. Based on the current
state of the art The state of the art (sometimes cutting edge or leading edge) refers to the highest level of general development, as of a device, technique, or scientific field achieved at a particular time. However, in some contexts it can also refer to a level ...
, he calculated the speeds and altitudes at which continuous flight was possible – fast enough that enough lift would be generated and slow enough that the vehicle would not overheat. The chart included an inflection point at around , above which the minimum speed would place the vehicle into
orbit In celestial mechanics, an orbit is the curved trajectory of an object such as the trajectory of a planet around a star, or of a natural satellite around a planet, or of an artificial satellite around an object or position in space such as ...
. The term "Kármán line" was originally coined by Andrew G. Haley in a 1959 paper, based on von Kármán's 1956 paper, but Haley acknowledged that the limit was theoretical and would change as technology improved, as the minimum speed in von Kármán's calculations was based on the speed-to-weight ratio of current aircraft, namely the Bell X-2, and the maximum speed based on current cooling technologies and heat-resistant materials. Haley also cited other technical considerations for that altitude, as it was approximately the altitude limit for an
airbreathing jet engine An airbreathing jet engine (or ''ducted jet engine'') is a jet engine that ejects a propelling (reaction) jet of hot exhaust gases after first taking in atmospheric air, followed by compression, heating and expansion back to atmospheric pressure ...
based on current technology. In the same 1959 paper, Haley also referred to as the "von Kármán Line", which was the lowest altitude at which free-radical
atomic oxygen There are several known allotropes of oxygen. The most familiar is molecular oxygen (O2), present at significant levels in Earth's atmosphere and also known as dioxygen or triplet oxygen. Another is the highly reactive ozone (O3). Others are ...
occurred.


Alternatives to the FAI definition

The
U.S. Armed Forces The United States Armed Forces are the military forces of the United States. The armed forces consists of six service branches: the Army, Marine Corps, Navy, Air Force, Space Force, and Coast Guard. The president of the United States is the ...
definition of an
astronaut An astronaut (from the Ancient Greek (), meaning 'star', and (), meaning 'sailor') is a person trained, equipped, and deployed by a human spaceflight program to serve as a commander or crew member aboard a spacecraft. Although generally r ...
is a person who has flown higher than
above mean sea level Height above mean sea level is a measure of the vertical distance ( height, elevation or altitude) of a location in reference to a historic mean sea level taken as a vertical datum. In geodesy, it is formalized as '' orthometric heights''. Th ...
, approximately the line between the mesosphere and the thermosphere.
NASA The National Aeronautics and Space Administration (NASA ) is an independent agency of the US federal government responsible for the civil space program, aeronautics research, and space research. NASA was established in 1958, succeedin ...
formerly used the FAI's figure, though this was changed in 2005, to eliminate any inconsistency between military personnel and civilians flying in the same vehicle, when three veteran NASA X-15 pilots ( John B. McKay, William H. Dana and Joseph Albert Walker) were retroactively (two
posthumously Posthumous may refer to: * Posthumous award - an award, prize or medal granted after the recipient's death * Posthumous publication Posthumous publication refers to material that is published after the author's death. This can be because the auth ...
) awarded their astronaut wings, as they had flown between and in the 1960s, but at the time had not been recognized as astronauts. The latter altitude, achieved twice by Walker, exceeds the modern international definition of the boundary of space. The United States
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 ...
also recognizes this line as a space boundary: Works by Jonathan McDowell (Harvard-Smithsonian Center for Astrophysics) and Thomas Gangale (University of Nebraska-Lincoln) in 2018 advocate that the demarcation of space should be at , citing as evidence von Kármán's original notes and calculations (which concluded the boundary should be 270,000 ft), confirmation that orbiting objects can survive multiple perigees at altitudes around 80 to 90 km, plus functional, cultural, physical, technological, mathematical, and historical factors. More precisely, the paper summarizes: These findings prompted the FAI to propose holding a joint conference with the
International Astronautical Federation The International Astronautical Federation (IAF) is an international space advocacy organization based in Paris, and founded in 1951 as a non-governmental organization to establish a dialogue between scientists around the world and to lay ...
(IAF) in 2019 to "fully explore" the issue. Another definition proposed in
international law International law (also known as public international law and the law of nations) is the set of rules, norms, and standards generally recognized as binding between states. It establishes normative guidelines and a common conceptual framework for ...
discussions defines the lower boundary of space as the lowest perigee attainable by an orbiting space vehicle, but does not specify an altitude. This is the definition adopted by the U.S. military. Due to atmospheric drag, the lowest altitude at which an object in a circular orbit can complete at least one full revolution without propulsion is approximately , whereas an object can maintain an elliptical orbit with perigee as low as about without propulsion. The U.S. is resisting regulatory movement on this front. A key consideration is the concept of free molecular flow. The essential property of outer space is in its being a realm where there is significant space between molecules –hence the name. Under free molecular flow, the path of molecules has transitioned to being straight lines, no longer continually bouncing off of each other. This condition of space can be artificially created in a vacuum chamber, or happens naturally at a high enough altitude. It has been known since at least as early as 1964 that the transition to free molecular flow happens at an altitude above “75–80 km”. So the USAF and NASA definitions are supported by this scientifically significant data that the realm of space is entered after the molecules in the atmosphere move in straight lines under free molecular flow, above 80 km (50 miles).


For other planets

While the Kármán line is defined for Earth only, if calculated for
Mars Mars is the fourth planet from the Sun and the second-smallest planet in the Solar System, only being larger than Mercury. In the English language, Mars is named for the Roman god of war. Mars is a terrestrial planet with a thin at ...
and
Venus Venus is the second planet from the Sun. It is sometimes called Earth's "sister" or "twin" planet as it is almost as large and has a similar composition. As an interior planet to Earth, Venus (like Mercury) appears in Earth's sky never f ...
it would be around and high respectively.Martínez, Isidoro
''Space Environment''
2021


See also

* * ** ** ** ** * * *


References


External links


Article on the Kármán line
at the FAI website


"The Kármán Line"
music video featuring NASA footage
Kármán line calculator
{{DEFAULTSORT:Karman line Aerospace Atmospheric boundaries Eponyms Outer space