The Kármán line, or Karman line, lies at an altitude of 100 km
(62 mi; 330,000 ft) above Earth's sea level and commonly
represents the boundary between
Earth's atmosphere and outer space.
This definition is accepted by the Fédération Aéronautique
Internationale (FAI), which is an international standard-setting and
record-keeping body for aeronautics and astronautics.
The line is named after
Theodore von Kármán
Theodore von Kármán (1881–1963), a
Hungarian American engineer and physicist, who was active primarily in
aeronautics and astronautics. He was the first person to calculate
that the atmosphere around this altitude becomes too thin to support
aeronautical flight, since a vehicle at this altitude would have to
travel faster than orbital velocity to derive sufficient aerodynamic
lift to support itself. The line is approximately at the
turbopause, above which atmospheric gasses are not well-mixed. The
mesopause atmospheric temperature minimum has been measured to vary
from 85 to 100 km, which places the line at or near the bottom of
1 Kármán's comments
3 Interpretations of the definition
4 Alternatives to the definition
5 See also
7 External links
In the final chapter of his autobiography Kármán addresses the issue
of the edge of outer space:
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.
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 per cent of the weight of the plane,
and only two per cent is carried by centrifugal force, 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 centrifugal force prevails. This is
certainly a physical boundary, where aerodynamics 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.
An atmosphere does not abruptly end at any given height, but becomes
progressively thinner with altitude. Also, depending on how the
various layers that make up the space around the
Earth 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 10,000 km (6,200 mi) above sea
Kármán line thus is an arbitrary definition based on the
An aircraft only stays aloft if it constantly travels forward relative
to the air (airspeed is not dependent on speed relative to ground), so
that the wings can generate lift. The thinner the air, the faster the
plane must go to generate enough lift to stay up.
The amount of lift required at any given point can be calculated by
the lift equation:
displaystyle L= tfrac 1 2 rho v^ 2 SC_ L
L is the lift force
ρ is the air density
v is the aircraft's speed relative to the air
S is the aircraft's wing area,
CL is the lift coefficient.
Lift (L) generated is directly proportional to the air density (ρ).
All other factors remaining unchanged, true airspeed (v) must increase
to compensate for less air density (ρ) at higher altitudes.
An orbiting spacecraft only stays in the sky if the centrifugal
component of its movement around the
Earth is enough to balance the
downward pull of gravity. If it goes slower, the pull of gravity
gradually makes its altitude decrease. The required speed is called
orbital velocity, and it varies with the height of the orbit. For the
International Space Station, or a space shuttle in low
the orbital velocity is about 27,000 km per hour (17,000 miles
For an airplane flying higher and higher, the increasingly thin air
provides less and less lift, requiring increasingly higher speed to
create enough lift to hold the airplane up. It eventually reaches an
altitude where it must fly so fast to generate lift that it reaches
orbital velocity. The
Kármán line is the altitude where the speed
necessary to aerodynamically support the airplane's full weight equals
orbital velocity (assuming wing loading of a typical airplane). In
practice, supporting full weight wouldn't be necessary to maintain
altitude because the curvature of the
Earth adds centrifugal lift as
the airplane reaches orbital speed. However, the Karman line
definition ignores this effect because orbital velocity is implicitly
sufficient to maintain any altitude regardless of atmospheric density.
The Karman line is therefore the highest altitude at which orbital
speed provides sufficient aerodynamic lift to fly in a straight line
that doesn't follow the curvature of the Earth's surface.
Above 100 kilometers the air density is about 1/2,200,000 the density
on the surface. At the Karman line, the air density ρ is such that
displaystyle L= tfrac 1 2 rho v_ 0 ^ 2 SC_ L =mg
v0 is the speed of a circular orbit at the same altitude in vacuum
m is the mass of the aircraft
g is the acceleration due to gravity.
Although the calculated altitude was not exactly 100 km, Kármán
proposed that 100 km be the designated boundary to space, because the
round number is more memorable, and the calculated altitude varies
minutely as certain parameters are varied. An international committee
recommended the 100 km line to the FAI, and upon adoption, it became
widely accepted as the boundary to space for many purposes.
However, there is still no international legal definition of the
demarcation between a country's air space and outer space.
Another hurdle to strictly defining the boundary to space is the
dynamic nature of Earth's atmosphere. For example, at an altitude of
1,000 km (620 mi), the atmosphere's density can vary by a
factor of five, depending on the time of day, time of year, AP
magnetic index, and recent solar flux.
The FAI uses the
Kármán line to define the boundary between
aeronautics and astronautics:
Aeronautics — For FAI purposes, aerial activity, including all air
sports, within 100 kilometers of Earth's surface.
Astronautics — For FAI purposes, activity more than 100 kilometers
above Earth's surface.
Interpretations of the definition
Some people[who?] (including the FAI in some of their
publications) also use the expression "edge of space" to refer to a
region below the conventional 100 km boundary to space, which is
often meant to include substantially lower regions as well. Thus,
certain balloon or airplane 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
Andrew G. Haley discussed the
Kármán line in his book Space
Law and Government. In a chapter on the limits of national
sovereignty, he made a survey of major writers’ views.:82–96
He indicated the inherent imprecision of the Line:
The line represents a mean or median measurement. It is comparable to
such measures used in the law as mean sea level, meander line, tide
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.:78,9
Alternatives to the definition
Air Force definition of an astronaut is a person who has
flown more than 50 miles (~80 km) above mean sea level,
approximately the line between the mesosphere and the thermosphere.
NASA uses the FAI's 100-kilometer figure. The United States does
not officially define a boundary of space. In 2005, three veteran NASA
X-15 pilots (John B. McKay,
William H. Dana
William H. Dana and Joseph Albert Walker)
were retroactively (two posthumously) awarded their astronaut wings,
as they had flown between 90 km (56 mi) and 108 km
(67 mi) in the 1960s, but at the time had not been recognized as
astronauts. The latter altitude exceeds the modern international
definition of the boundary of space.
Another definition proposed in international law discussions defines
the lower boundary of space as the lowest perigee attainable by an
orbiting space vehicle, but does not specify an altitude. 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 150 km (90 mi), whereas an object can maintain
an elliptical orbit with perigee as low as about 130 km
(80 mi) without propulsion. Above altitudes of approximately
160 km (100 mi) the sky is completely black.
Atmospheric gases scatter blue wavelengths of visible light more than
other wavelengths, giving the Earth’s visible edge a blue halo. The
Moon is seen behind the halo. At higher and higher altitudes, the
atmosphere becomes so thin that it essentially ceases to exist.
Gradually, the atmospheric halo fades into the blackness of space.
Atmosphere of Earth
V-2 rocket – the first human-built object to cross the Kármán line
^ Layers of the Atmosphere, National Weather Service JetStream –
Online School for Weather
^ Dr. S. Sanz Fernández de Córdoba (2004-06-24). "The 100 km
Boundary for Astronautics". Fédération Aéronautique Internationale.
Archived from the original on 2011-08-22. Retrieved 2014-05-07.
^ O'Leary, Beth Laura (2009). Ann Garrison Darrin, eds. Handbook of
space engineering, archaeology, and heritage. Advances in engineering.
CRC Press. p. 84. ISBN 1-4200-8431-3. CS1 maint: Uses
editors parameter (link)
Theodore von Kármán
Theodore von Kármán with Lee Edson (1967) The Wind and Beyond,
^ "Lift Coefficient". Wolfram Alpha Computational Knowledge Engine.
Wolfram Alpha LLC. Retrieved 2015-03-14.
^ Benson, Tom, ed. (2014-06-12). "The Lift Equation". Glenn Research
Aeronautics and Space Administration. Retrieved
^ "The Lift Coefficient". Glenn Research Center. NASA. Retrieved May
^ Squire, Tom (September 27, 2000), "U.S. Standard Atmosphere, 1976",
Thermal Protection Systems Expert and Material Properties Database,
NASA, archived from the original on October 15, 2011, retrieved
^ "Schneider walks the Walk [A word about the definition of space]".
NASA. 2005-10-21. Retrieved 2008-04-29.
^ International Law: A Dictionary, by Boleslaw Adam Boczek; Scarecrow
Press, 2005; page 239: "The issue whether it is possible or useful to
establish a legal boundary between airspace and outer space has been
debated in the doctrine for quite a long time. . . . no agreement
exists on a fixed airspace – outer space boundary . . ."
^ PDF on the FAI website Archived 2014-05-08 at the Wayback
Machine.[not in citation given]
^ a b c "A long-overdue tribute". NASA. 2005-10-21. Retrieved
^ "World Book @ NASA". NASA. Archived from the original on May 4,
2009. Retrieved 2006-10-18.
^ a b c
Andrew G. Haley (1963) Space Law and Government,
^ "Space Environment and Orbital Mechanics". United States Army.
Retrieved 24 April 2012.
Article on the
Kármán line at the FAI website
Layers of the Atmosphere – NOAA
The Kármán Line music video featuring
Kármán line calculator
Thermopause / Exobase
Extremes of motion
Land vehicle (rocket-based
production car (by speed / by acceleration)
production motorcycle (by speed / by acceleration)
Space (furthest spacecraft
furthest landing on another world
furthest travels on another world
closest spacecraft to the Sun)
Aircraft (furthest flight
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Space (most enduring spaceflight
most endurance on another world
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most enduring population of a spacecraft)