In-game reentry trajectory compared to formulae

[Jonfliesgoats]

Has anyone run the reentry formulae for a given BC body and compared that to the performance we see in the game?

[Plusck]

I'm not sure I understand the question, really.

To start with, what are the "reentry formulae"? I didn't know there were any set formulae for that.

Sure, there are the formulae for orbital mechanics, and the drag equation, so if you combine them you end up with a set of rules telling you whether you'll reenter or just sail though the atmosphere and emerge the other side (assuming no lift). Or they'll tell you the maximum g-forces or heating effects experienced during reentry. And if you integrate lift into the equations for orbital mechanics, you'll also be able to know whether a "skipping" reentry is possible.

However, those formulae are necessarily based on the density of air at different altitudes, so I think what your question comes down to is "how well is the Earth's atmosphere modelled on Kerbin", and "how lifelike is the game's drag model", since the game is essentially simulating all that in real time.
And I suppose the answer to both those questions is "getting better with each release".

In the end, Kerbin's atmosphere cannot be equivalent to Earth's because the planet is so much smaller. On Kerbin, you can dive into the atmosphere and come out the other side in a couple of minutes. The planet is smaller and the atmosphere is much more "round". Therefore you have a lot more room to maneuvre (missing your target altitude by 0.5% of the orbit's radius is probably not going to be fatal on Kerbin, but would very definitely be fatal on Earth).

So, I don't know whether this answers your question, because I don't know what the reentry formulae are to start with. As for "has anybody run them", well the game is essentially running the relevant equations all the time. As to whether they do so faithfully to real life, I couldn't say.