DynaSoar
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You also seem to have conflicting results from Rocksim. It no doubt is following some algorithm which may be quite different from either of these, and we've no reason to suppose it's any more correct than one or both of these. Unless of course each is "correct" based on its own assumptions which aren't shared.
I'm just thinking out loud here. Again, just working from concept, but I find that useful, particularly when confronted with a situation where an authoritative word finds itself in conflict with another.
I'm questioning the assumption of "tear drop shaped". Looks to me like that's derived from primarily from two dimensional airfoil theory and testing. I'm not convinced that it generalizes to 3 dimensions. A wing has parallel airflow over a surface. There's no parallel airflow in 3 dimensions over the nose or the tail of a rocket.
Nor am I convinced that an elongated trailing edge, intended to move the separation point, where the airflow breaks up into turbulence, the major factor in drag, as far back as possible applies either. There's to trailing point on a rocket, and there's going to be a flat or concave base of some size no matter what else you do, so optimization based on a separation point that never occurs may be misleading. If the point is to pull as much of the airflow back around behind the vehicle, and separation point is irrelevant, the proper shape may be more important than the dimensions.
The forward half of a motor nozzle compresses the flow. Turn it inside out and it pulls vacuum around itself. Half a nozzle has a cubic (S shaped) curve profile. The first half of that is a hyperbolic curve. What happens after the equivalent of a nozzle's curvature reversal on the aft end of a rocket is irrelevant because it doesn't exist, and is replaced by expanding gasses during boost and a slight concavity of the motor nozzle during coast (just thinking here of an Estes type motor, the complex shape of a composite's nozzle being another thing to confound the simple case).
Just going by conceptual stuff it just seems the shape as a truncated ogive, from body diameter to motor diameter, is going to be a more important factor than how long it is, within some fairly wide limits.
And I suspect that a tighter curve is going to be more effective on a finned rocket, due to the effect of the fins tending to direct airflow outward. An effective boat tail will have to fight that.
One of the more popular "common corrections" of science is the fact that a falling drop of water is not tear drop shaped, but rather spherical with a flattened bottom. Some of that (trailing half) shape is due to surface tension, but the rest to optimally fitting into the air flow. Less surface tension, or more airflow, and it'd elongate into an elliptical (you don't see that in a drop because it's at terminal velocity).
The best shape (amount of curvature and length) will depend on at what speed the boat tail most to reduces the effect of drag. That'd change with speed, but of course you can't easily change shape, so you optimize by choosing the one shape that contributes the most across the range of speeds and the amount of time spent within the smaller portion of that range where it helps the most, and regress that down with calculus to the optimum point.
I'm thinking that the best overall performance is going to be pretty much having the nose cone optimal for a rocket's intended profile (both shape and length/diameter ratio) on both ends, the aft truncated for the motor opening, and possibly a bit more blunt if the effect of the fins is to counter the vacuum being pulled by the tail.
That's what I'm thinking anyway. When it comes down to it I think it's going to be an empirical question. Here's what I'm thinking for that: a Baby Bertha sort of bird, built with the motor tube hanging down a ways so that with a boat tail added the end of the motor tube and the hole in the tail cone coincided. Launch it a sufficient number of times without the tail, then glue it on and launch it a sufficient number of times (sufficient N to be determined by the statistical power accumulating which will depend on the variance). Same motor every time of course. Measurement to be time from launch to landing. All flown on the same day to keep envoronmental stuff the same. Streamer instead of chute because chutes tend to foul and tangle, and might need to be replaced with another that even of the same size probably wouldn't have the same characteristics. All that would increase variance. Using the same bird will control for fin irregularity etc. I'd forego controlling for the added weight of the tail just to say that if there's any bias being introduced it'd be contrary to the experimental hypothesis (the tail cones gives higher flights, thus longer air times) rather than for it. Worst that could happen is that increases the N by 1 or 2. To get some generalizability, standardize very little across several designs except addition of a tail roughly like its nose.
Anybody want to do some rocket science? I'll do the stats.
