The vis-viva equation models the motion of an orbiting body and it applies when the only force acting on the body is it's own weight.

So is it correct to apply this equation to an airplane that flies in a straight line at the Kármán line?

If it's correct, please explain why and if it's not, why not?

I ask this question because I'm puzzled by this question from @uhoh about the Kármán plane where the orbital velocity is used to determine the look of the Kármán plane.

v = 4 km/sec --> wing loading = 0,635

v = 3 km/sec --> ,, ,, = 0,31

v = 5 km/sec --> ,, ,, = 1,24

v = 6 km/sec --> ,, ,, = 2,53

v = 7 km/sec --> ,, ,, = 6,97

  • $\begingroup$ @uhoh Isn't the airplane in the question an example ? $\endgroup$ – Conelisinspace Dec 18 '18 at 13:35
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    $\begingroup$ @uhoh i've added a link to your question about the Kármán plane $\endgroup$ – Conelisinspace Dec 18 '18 at 14:18

In the example given in the question (my question) I use the vis-viva equation to calculate the magnitude of orbital velocity. That's what the equation does, and "orbital velocity" is the term specified and used in definitions of the Karman line. So without reinventing the Karman line, one can use the vis-viva equation to address the Karman line as it is currently known.

As I say there in the first sentence:

...the Kármán line is roughly the altitude where a "Kármán plane's" upward lift force at the orbital velocity for that altitude would be equal in magnitude to the gravitational downward force.

To get that velocity at that altitude, you can correctly use the vis-viva equation.

There's nothing about this scenario that says that the object is actually in orbit. It only calls for the velocity that an object that happened to be in orbit at that altitude would have.

The problem may be that this is a definition, not reality. Definitions can be as hypothetical and unrealistic as they want to be.

Peruse Johnathan McDowell's paper discussed in this answer for a more thorough mathematical discussion of an "improved definition" of a Karman-like line, which uses the vis-viva equation quite nicely, even though drag and lift are invoked within the definition as well.

  • $\begingroup$ Clear answer, it revealed to me the difference between definition and reality. But that definition on Wiki, where does it come from, on who's authoroty ? $\endgroup$ – Conelisinspace Dec 18 '18 at 14:51
  • $\begingroup$ Someone asked him to come up with a definition, so he did it. Nobody needs authority to come up with a definition. Authority is only needed to enforce it somehow. For example, anyone can define what "impaired" by alcohol could mean (for example ability to walk in a straight line without flying), but in some countries a blood alcohol level of 0.08% is enforced by a very powerful authority. $\endgroup$ – uhoh Dec 18 '18 at 14:56
  • $\begingroup$ Is there any written evidence that Von Kármán did not use the centrifugal force for his calculations ? Because in his comments he compares aerodynamic lift with centrifugal force, i think it's very likely he did ! $\endgroup$ – Conelisinspace Dec 18 '18 at 15:50
  • $\begingroup$ @Conelisinspace That's a whole different discussion on one or more other questions already. $\endgroup$ – uhoh Dec 18 '18 at 15:54
  • $\begingroup$ I think everybody that comes up with a definition on Wikipedia needs some authority, according to Wiktionary: "a person accepted as a source of reliable information on a subject ". $\endgroup$ – Conelisinspace Dec 19 '18 at 15:12

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