Edit: this question is about making clear that the Wikipedia's article about the Kármán line is an interpretation, not the definition !

Why not consider the Kármán line as a curved boundary that follows the curvature of the Earth ?

According to Wikipedia's article about the Kármán line:

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 )………………………………………………………………………………………………………………...The Kármán 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.

Note: this is an interpretation of the writer of the article, not the real definition !

The FAI (Fédération Aéronautiqe Internationale) that adopted the definition, doesn't mention any straight line in this article about the 100km altitude boundary for astronautics

So would not the definition of the Kármán line be better explained by an airplane in orbit around the Earth, rather than by an airplane flying in a straight line ?

  • 1
    $\begingroup$ but to what benefit? It's easy to define the speed needed for orbit at an altitude, harder to calculate to calculate the lift generated at an air pressure and speed. Why introduce a requirement to calculate an intermediate speed? $\endgroup$
    – user20636
    Oct 19 '18 at 19:36
  • $\begingroup$ @JCRM These calculations are just done to show that the Kármán line, now defined for an unrealistic straight line, can also be defined as a realistic curved line around the Earth with a realistic centrifugal force. $\endgroup$
    – Cornelis
    Oct 19 '18 at 20:41
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    $\begingroup$ Normally Wikipedia articles don't contain original research, so I expect one of the sources to mention this. Karman's autobiography is available online: ntrs.nasa.gov/… $\endgroup$
    – Hobbes
    Oct 23 '18 at 9:43
  • 1
    $\begingroup$ Interesting paper: sciencedirect.com/science/article/pii/S0094576518308221 $\endgroup$
    – Hobbes
    Oct 23 '18 at 12:47
  • 1
    $\begingroup$ @Conelisinspace I have closed this question because the scope has been changed multiple times. Please see the related meta discussion: space.meta.stackexchange.com/q/1074/58 $\endgroup$
    – called2voyage
    Oct 23 '18 at 12:50

Why not? Because the people who started using the Karman line didn't see the need for a more refined definition (e.g. because nobody was going to attempt aerodynamic flight in this region).

The Karman line is an approximation anyway. It depends on the lift coefficient and the state of the atmosphere, both of which are variables. Karman's calculations didn't arrive at 100 km exactly.

The Karman line is used for two things:

  1. to legally separate the airspace above a country (over which the country has jurisdiction) from space (over which the country has no jurisdiction).
  2. to determine who has been "in space" and gets to be called an astronaut.

For both, an arbitrary number suffices. The USA uses a different number for 2. (50 miles instead of 100 km)

  • $\begingroup$ ...especially that they rounded the actual value up by some 8%, to a neat 100km... Nah, the origin of the definition is aerodynamic, but currently it's an arbitrary 100km. Similarly how a meter was 1/10000 the distance from the equator to the pole, and kilogram was a cubic decimeter of water. They aren't anymore and nobody bothers to make the old definitions better. $\endgroup$
    – SF.
    Oct 19 '18 at 20:11
  • $\begingroup$ @uhoh There won't be another line, because the line in this new definition has the same height , but will be a realistic one because it is curved around the Earth, while the present Kármán line is a straight one. $\endgroup$
    – Cornelis
    Oct 20 '18 at 11:41
  • $\begingroup$ I've changed the question somewhat to make it clear that it is about a realistic, curved line that is subject to a centrifugal force. $\endgroup$
    – Cornelis
    Oct 20 '18 at 12:16
  • 1
    $\begingroup$ Despite all the changes in your question, the answer remains the same. $\endgroup$
    – Hobbes
    Oct 21 '18 at 10:56

There's no such thing as centrifugal force in this case.

The only real forces in this problem that are vertical (normal to the local surface of the Earth) are gravity and lift. "Centrifugal force" is a fictitious force which people sometimes invoke to solve problems more quickly in in certain cases.

If you write a set of equations or write a program to calculate a trajectory of an airplane or a spacecraft in an inertial (i.e. non-rotating) frame, and you include all of the real forces correctly, you get the right answer without ever adding a "centrifugal" term.

If you leave something out, or you start injecting a non-inertial, rotating frame of reference (whether or not you realize you are doing it), only then does the centrifugal monster raise it's ugly head and start to mess with yours.

To address the terminology, the Karman line is not literally a line, it is an altitude.

That altitude is now 100 km. Trying to use a literal interpretation of "line" and asking if it is curved or straight, or ask about how a plane would fly along this line is only playing with semantics. It's simply an altitude of 100 km.

  • $\begingroup$ Then what are the forces with a satellite in orbit ? There must be some reaction to the gravitational one. $\endgroup$
    – Cornelis
    Oct 23 '18 at 15:03
  • 2
    $\begingroup$ Satellites are falling due to Earth's gravity. They are falling around the Earth. They orbit Earth. $\endgroup$
    – user27822
    Oct 28 '18 at 18:21

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