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I'd like to be able to say, "The Kármán line has been calculated to lie between ___ and ___ km."

The "accepted" altitude of the Kármán line is 100 km. In practice, the results of calculating the Karman line can vary wildly (e.g. different aircraft shapes, elliptical orbits, local variations of the gravitational field, effects of solar wind, etc ad nauseum).

To this end, what are largest and smallest calculated and published values for the Kármán altitude?

If a source uses a different mathematical model, it should still be in the spirit of the Kármán definition: the transition between flying and in orbit.

Related, perhaps helpful: Where does the definition of the Kármán line on Wikipedia come from?

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Philosophical approach

Teacher: Do not try to define the Kármán line, that's impossible. Instead, only try to realize the truth.

Student: What truth?

Teacher: There is no Kármán line

Student: There is no Kármán line?

Teacher: Then you'll see that it isn't Kármán who draws the line, it is only yourself.

Practical approach

I think your premise

The "accepted" altitude of the Kármán line is 100 km.

and that the line can be recalculated is incorrect. The Kármán line is defined to be exactly 100 km.

The aerodynamic justification is murky history, and even at the time was just hand-waving for space lawyers.

While I don't know where exactly the 100 kilometers is measured from (it could be from the local surface of the Earth, or a standard reference radius of 6378.137 km), it's just a fixed number. The history is messy and discussions here have been messier still but it's just a flat 100 km, no ifs, ands, or buts.

As far as Where does the definition of the Kármán line on Wikipedia come from? is concerned, that's not a definition. That's an internet explanation and not an authoritative source.

Theodore von Kármán was a great scientist, but discussions of the definition of the Kármán line is persona non grata here in Space Exploration Stack Exchange!

Until it isn't, see Why is FAI considering lowering the Karman Line to 80km?

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    $\begingroup$ Please answer the question in the context given. Kármán's definition leads to calculations, which lead to calculated results, which vary based on the assumptions used for the calculations. I'm not looking for the merits of one approach versus another, just the minimum and maximum. Some would claim that the Kármán calculations are meaningless; actually making the calculations and then showing they vary too much would support that premise. $\endgroup$ – DrSheldon May 8 '19 at 3:36
  • $\begingroup$ So if you're trying to stop Kármán discussions, answering this question would actually make the point that they are meaningless. $\endgroup$ – DrSheldon May 8 '19 at 3:38
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    $\begingroup$ My point is that there is no such thing as "Kármán's definition" other than the number 100 kilometers. There are some murky recounts of handwaving for space lawyers a half-century ago, but this has not been documented in a definitive way. Look for it, and I believe you will not find it. You are asking me to answer the question in the context of a fictional or hypothetical scenario. $\endgroup$ – uhoh May 8 '19 at 3:38
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    $\begingroup$ Kármán's autobiography says, "This is certainly a physical boundary, where aerodynamics stops and astronautics begins". That sounds like a definition, even if perhaps informal. Wikipedia makes a referenced claim that Kármán himself calculated the line to 83.6 km. It sounds to me that the calculation can be done, and has been published, and that this question can be answered. $\endgroup$ – DrSheldon May 8 '19 at 5:07
  • $\begingroup$ @DrSheldon it's mentioned in answers or comments to several of the questions linked here that the autobiography was written in part after Kármán died by a family member or friend, don't remember which. A Wiki-claim is a Wiki-cliam. Anyone can do a calculation, see What would a “Kármán plane” look like, a bird, or a plane? which preceded the era of Kármán unpleasantness. That the answer for the wing loading is a guess should suggest there is no published calculation. $\endgroup$ – uhoh May 8 '19 at 5:16

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