I have a new toy: it’s called HyperCFD and it calculates a number of interesting quantities for bodies of rotation that are moving faster than the speed of sound. I bought it because I was interested in the stability of the “reentry body” associated with the DF-2 which Jeffrey used to discuss the design (and weight!) of the DF-2’s nuclear warhead but I imagine I will find other uses for it. As it is, I was very surprised at what I found out.
But first, I needed to check its accuracy against some actual data. (After all, it says it’s for amateur rocket designers, which didn’t instill the faith that perhaps it should have in me.) It turns out to be pretty good! (This plot shows the pressure distribution along the reentry vehicle at a fixed speed (Mach 5.8 in this case. I wont bore you with such checks, but you can look at it if you like. I should note that this fairly blunt shape is one of the most stressing for Newtonian approximations in computational fluid dynamics and in the study I’ve quoted, the other shapes are even better simulated by HyperCFD.)
I picked this particular plot to check HyperCFD with because it’s closely related to the sum of all the pressure on the reentry body. It’s important because, when you add it all up, you can calculate the point on the hypersonic body where all the pressure effectively acts. The resulting point on the body is called the center of pressure and it had better be behind the center of mass of a body if the shape is going to be aerodynamically stable.
Image a weathervane. It, of course, pivots around its central pole, which can be thought of as the center of mass of a free rocket or reentry vehicle. To a very good approximation, all the torque or turning force of wind can be thought of as acting at a single point: the “center of pressure,” or Cp. If the Cp is behind the center of mass, the rocket is stable and turns into the “wind.” If the Cp is in front of the center of mass, then the rocket or reentry body will flip. Funny thing is, that might not be stable either since the aerodynamics will change completely if the reentry vehicle is going in “butt end first,” if you will.
Which brings us to the DF-2 warhead. Several readers of Jeffrey’s post commented on the position of the center of mass of the warhead, as indicated by the balance point of the jig that is lifting the warhead. It turns out that the center of mass is too far back for a nose-first reentry and too far forward for a butt-end-first reentry! (And, in fact, the butt-end-first becomes even less stable as it slows down. Oh, yes, before I forget, the calculated Cp’s are definitely on the symmetry axis of the body and I assume that the CG is also, though it doesn’t really have to be.) So what does that mean? It’s obvious, actually.
It doesn’t separate from its rocket body, or if it does, it separates much farther back from the nose. Perhaps an even more interesting question is why so many of us thought it must separate. My guess is that when you see a separated warhead, you assume it separates during flight.
What’s next for HyperCFD? Jeffrey got interested in this warhead because it was reported to be the same design sold to the Libyans. This program provides a little more information for trying to constrain the nuclear devices potential proliferators might try. So I think I want to “design” a nuclear warhead to fit in the Shahab-3 and Shahab-3B warheads. But that is going to be a little while from now.