The family of Shahab-3 warhead variants as compiled by Tal Inbar and Uzi Rubin. The NRV, the New Reentry Vehicle, is shown on the right. Note it’s a triconic design but with a larger base diameter than the Ghadr-1 warhead.
Wonk-friends Tal Inbar and Uzi Rubin are reporting a new warhead variant for the Shahab-3 family of missiles—and hypothesize that it will soon show up on the Sejiil solid-propellant missile. This new variant, also a so-called “triconic” design (why tri -conic? It has always struck me as “bi” conic.), got me wishing I had done a full aerodynamic analysis of “old” triconic warhead when it first appeared. Well, better late than never. Now I can compare all three designs: the conical warhead that appeared first on the Shahab-3, the “improved” warhead design that is often associated with the Ghadr-1 missile, and the New Reentry Vehicle (which Inbar and Rubin call the NRV, a naming convention I will adopt here).
The supersonic aerodynamics of these warheads are relatively easy to compare using the program HyperCFD, a program I tested and reported on in an earlier post. As expected, both triconic designs have larger drag coefficients than the simple conical design. This is because of the shock waves generated at the “breaks” in the aeroshell—where there is a discontinuity of the aeroshell’s form. What was surprising to me, however, was the relative positioning of the Ghadr-1 RV’s and NRV’s Cd (coefficient of drag). The NRV, with its more stubby appearance has a uniformly lower Cd. Perhaps I should have expected this: it is, after all, somehow “between” the two designs: the Ghadr-1 and the simple conical warhead. (Area, something vitally important to the actual drag of an object, has been removed from the calculation of the drag coefficient.)
The coefficient of drag, Cd, for the three warhead variants is shown here. Note that the first “triconic” design flown by Iran has the highest coefficient of drag, the new reentry vehicle (NRV) drag coefficient is slightly lower but still greater than the simple conic warhead.
As that first break approaches the rear of the warhead, any differences between the simple cone and the NRV should go away. That’s arguing purely on a continuity argument, which is perfectly valid but would have been more impressive if I had seen it before I ran the Cd calculations. On a perhaps more physical basis, it is possible that this decrease in Cd is related to the fact that the shock wave originating from the first break in the aeroshell is much closer to the shock wave originating from the second break. This proximity could reduce the amount of energy radiated in the shock waves, but I’m just guessing here. These differences in drag coefficient have only a very minor effect on the trajectory of the warhead as it reenters.
Let me emphasize that the “normal” triconic RV only matches the reentry velocity and acceleration profile so well because its base diameter—and hence its area—is considerably smaller than the other two base diameters. Refresh your memory of the design by looking at the graphic from Inbar and Rubin at that top of this post. When I take the same design and simply increase the flaring at the rear to fit the Shahab-3 rocket body (i.e. increase it to 1.25 m), then the triconic warhead slows down considerably. In fact, it nearly reaches terminal velocity and “gently floats” down to Earth. Well, if you consider 310 m/s floating.
Warhead Stability and Warhead Volume
As far as ascertaining the purpose of this evolution of warhead designs is concerned, the drag coefficient associated with each warhead variant is probably less important than the question of stability during reentry. Stability of any projectile using aerodynamic forces to achieve stability—either an guided rocket or a reentering warhead—is determined by the relative positions of the Center of Gravity (Cm) and the Center of Pressure (Cp). For any such object to remain stable, the center of gravity must remain in front of the center of pressure stability of a missile (either rocket or warhead) that relies on aerodynamics to keep on a straight path is determined by the relative positions of the center of pressure and thecenter of gravity. If the warhead is going to be stable in a “pointed end first” attitude as it reenters, the center of mass must be forward of the center of pressure. If it is not, the warhead will start to tumble.
The center of pressure is solely determined by the exterior shape of the warhead and can be easily calculated by the same program, HyperCFD, that I used to calculate the drag coefficient at supersonic velocities. Unfortunately, the center of mass is completely dependent on the arrangement of the mass inside the warhead and, as such, is not knowable to outside observers. However, we can still make some interesting calculations if we assume that the warhead is filled with a uniform material and fill it from the tip of the warhead back. In the calculations that follow, I use a density for this material of 1.8 g/cc, the theoretical density of RDX, a popular high explosive. I should note that this is considerably greater than the average density of the first plutonium weapon, the Fatman, which I calculate to be approximately 1.2 g/cc but much less than more advanced nuclear designs. What we will do is look at the relative positions of the Cp and Cm as we fill the warhead to various levels, always starting at the tip and filling backwards. (This is exactly what happens when you fill a SCUD warhead with conventional high explosive.) But first, let us fill each warhead right to its very end:
The positions of the Center of Pressure (Cp) and Center of Gravity (Cm) for the three Iranian warheads assuming a uniform fill from tip to back. Note that all three are unstable when completely filled because the Cp is in front of the Cm.
Since none of them can be totally filled, we can ask the question: which variant is capable of holding more mass as the variant just ceases being unstable? While the final answer is as we might have expected, I was surprised by the intermediate answer. So surprised that I almost did not post this analysis. (Perhaps some are wishing at this point into this every lengthening post that I did not!)
If we leave the rear portion of each warhead empty, we can calculate the position of the Cm for different total fills. This plot is shown below:
The position of the Center of Mass (shown along the Y-axis) of each warhead variant is shown when it is filled to different points along the warhead length. To compare the three variants (the NRV and the simple conic warheads are each 3.5 m long while the original “triconic” warhead is 2.75 m long), the level of fill is written normalized to each warhead’s overall length. (The triconic warhead appears to end earlier than one but that is an artifact of my plotting program, which stops at the last binned mass.)
Note that the vertical lines are the positions of neutral stability, where the positions of the Cp and Cm are equal. If we fill a warhead to less than its neutral stability point, than the warhead will be more stable on reentry. If we fill it past the point of neutral stability, it will be more unstable . Note that the simple conical warhead appears to be a better choice since its neutral stability point takes a fill that is closer to its rear. (This is the place I got stuck on and almost didn’t get past.) But this result is somewhat misleading. We need to look at the mass of the fill for the three warhead variants—and it turns out that the “central barrel” of the NRV makes all the difference.
The mass of each warhead variant as a function of the high explosive fill. The vertical lines are the lines of neutral stability for each warhead variant. Note that the NRV, while of necessity having a shorter fill length if it is going to be stable, is actually capable of carrying more mass than the simple conical warhead. (Also note that the weight of the nosecone skin is not included in this calculation.)
A Purely Conventional Warhead?
Truly understanding the reasons for the evolution of the warhead variants would require an understanding of what nuclear warhead designs Iran might use. However, the switch from the initial triconic warhead—which came out some what after the Shahab-3’s simple conical nosecone—to the NRV makes sense for a purely conventional warhead since it can carry considerably more high explosive even the simple cone. Furthermore, the differences in dimensions of the NRV and the simple cone seem rather minor and would clearly be very dependent of some unique feature of a hypothetical nuclear warhead design.