I'll save the gory numerical details for an updated Clavius page at some future date.
Note how Bob and I discussed gas trapped
between the ascent and descent stage. Najak's conceptual error was assuming that was limited to what was happening only beneath the nozzle. When I hinted that you had to think outside the box when integrating
𝐹=∫ 𝑃𝑥 𝑑𝐴,
what I mean is that you have to integrate 𝑃
𝑥 over the entire underside of the ascent stage. I doubt it would be uniform, but the point is that there's a whole lot of 𝐴 for it to act against. Now his thrust model is all kinds of wrong too, but the reason you want to know the thermodynamics of the exhaust from first principles and the initial gap through which it's escaping (i.e., the "leak-rate" in my conversation with Bob) is that this gives you a basis for estimating the initial static pressure of the entire region of gas that's semi-trapped between the stages—not just under the nozzle. The photographs of the shock wave during ascent testing assure us that enough of a "bubble" of exhaust gas remains at a density sufficient to support wave propagation during the one second or so following ignition. It's not just immediately disappearing into vacuum. It's easy to hand wave the rest and say that's just a quantification exercise. But in fact that quantification is the aforementioned "nasty integral" and will take a fairly fun bit of math(s).
With apologies to Bob and to the world, I think we'll have to take ignition transient off the table. The more carefully I watch the ascent video, the more convinced I am that the APS engine has reached "steady state" by the time the ascent stage is cut loose. I add the cautionary quote marks because it's questionable whether any sort of nominal steady state operation is possible with the ascent stage engine that close to the descent stage deck. I originally estimated the ignition transient for this motor at about 350 ms, and the design requirements give the standard 90%-thrust deadline as something like 450 ms. (It's generally okay if a transient spike greater than 100% occurs later, so long as once having reached 90% thrust by the required time, the thrust does not then fall below 90%.) It looks like the ascent stage might be still attached through all those ballpark timings.
Also to that point, I've found the documentation for the launch sequencing up in my attic. When I get some time, I can sit down and map out the sequence and timings from APS valve actuation to the pyrotechnical let-go. Contrary to Najak's believe, no, there is never any one concise document that by itself answers some question that someone might come up with. But from watching what looks like transient exhaust plumes in the videos, I won't be surprised if the sequencing confirms that any thrust spikes due to ignition occur before the ascent stage is cut loose.