A question about nuclear-tipped ICBM's and physics

Thankfully not ‘need answer fast’.

Anyway, random question but something that popped into my head today. Just prior to detonation the re-entry vehicle of an air-burst ICBM is moving at speeds we scientists like to term as ‘really frikken fast’ (I’ve seen estimates of between 7.5 and 9.5 kilometers per second)

When the warhead detonates does the expanding fireball also continue to move along the projected path towards the ground or is the kinetic speed also converted into fire/blast/radiation etc

Basically if the device detonates at say 10’000 feet does the center of the expanding fireball remain at that height or does it continue towards the ground?

Knowing this could be really, really, important someday.

It seems to me that the total momentum of the warhead and the air around it before the explosion has to be equal to the total momentum of the fireball after the explosion. Since the fireball is much more massive, it must have a much lower speed for the momenta to match. So yes the fireball moves forward but much more slowly than the warhead was moving.

Off the top of my head, I’m thinking a cubic km of air. Assuming 1.2 km/m3, that’s a total mass of 1,200,000,000 kg compared to, say, 120 kg for the warhead. That’s a ratio of 10 million to 1. So if the warhead was moving 8,000 m/s I’d expect the fireball to be moving at .0008 m/s which is negligible compared to whatever light breeze was blowing before the warhead showed up.

The “fireball” that results from the atmospheric detonation of a nuclear weapon is almost entirely due to heating of the atmosphere by x-rays and is essentially stationary initially (expanding out and up due to thermal effects). The actual weapon mass is almost inconsequential by comparison, and the detonation so quick (about 3 to 10 “shakes” or 30 to 100 nanoseconds) that its momentum doesn’t make any measureable difference compared to a stationary weapon.

Stranger

May I ask a tangential question?

Now that there is a rocket scientist around…

How do MIRVs redirect their reentry vehicles? Anything I have read about them indicates that there is a “bus” that the warheads sit on, and as the bus is hurtling along through space, it drops off the warheads at predetermined spaces, like a school bus letting off children.

The image I have always had is of a single MIRV hitting different cities with nukes, like this illustration.

But… doesn’t the whole bus assembly have an absolutely huge amount of momentum and wouldn’t it take a massive amount of energy to divert the point of landing? In my mind I can’t imagine how they could land much further apart than a few football fields, and this photo of a test seems to show all landing within sight of each other.

Imagine this device traveling at several miles per second on its brief trip between the US and USSR, and somewhere along the way a little rocket fires to move the trajectory a bit. Even if the little rocket manages to add several hundreds of miles per hour velocity orthogonal to the trajectory, that won’t mean much over the few minutes left in the flight, so I can’t see how they can get any decent spread. (and I’m certain the physics don’t work that way, but still the forces seem to great to go anywhere off the original trajectory)

From what I understand, a MIRV has a very high trajectory*, above 1000KMs and the individual warheads are deploy at/near apoapsis where small differences in velocity and vector can matter a lot.

Also, the Wiki page you link to mentions airfoils.
In addition, I know that the Russian return pods are built in an asymmetrical way such that rolling movement will give them lift in a particular direction. Wouldn’t be difficult to get the same effect in a warhead.

*Some BMs can have a shallow trajectory but I doubt they’re MIRVs.

The picture you linked to was of a Minuteman III, and links to the Wikipedia article, which says:

The article on MIRV says:

It also says that the purpose of MIRV is to:

So the answer to your question is that there is a limit, but it’s not that bad, and it’s not really the point anyway.

Nuclear ballistic delivery systems with multiple independently targeted reentry vehicles (MIRV) have a maneuvering rocket engine (along with attitude control engines) which is attached to the guidance section and warhead bus. The engine, guidance can and bus are collectively generically referred to as the post-boost vehicle (PBV). Some PBVs that carry only a few RVs such as the LGM-30G ‘Minuteman III’ that carried three Mk-12A or one to two Mk-21 RVs have only a small PBV; others with more numerous payloads such as the LGM-118A ‘Peacekeeper’ or the Russian R-36M and R-36UTTh (NATO reporting name SS-18 ‘Satan’ Mod-2 and Mod-4) have much more capable PBV engines. With the highly precise inertial guidance systems (ring laser gyroscopes and fiber optic gyroscopes) used in modern ICBMs and SLBMs allow for terminal trajectory errors that are statistically much smaller than the blast radius of the weapon itself.

If the PBV did not have propulsive capability the RVs would all essentially reenter along the same trajectory with only minor variations (a system that was used in the Polaris A-3 system to improve likelihood of target damage as the IMU was not sufficiently accurate to assure direct target impingement). When the PBV deploys an RV it releases it with some small delta-V (usually provided by retropropulsion), then turns and jets off in a different direction to release another. Interestingly, the SS-18 and SS-19 PBVs deploy their RVs “backward”, i.e. the engine is pointed in the same direction as the RVs, where the American systems are oriented “forward” (the engine is pointing away from the RVs), a fact I only learned last year when attending a Roskosmos presentation about microsat and nanosat deployment. The Soviet way of doing it seems counterintuitive at first as the PBV is fighting against the momentum imparted by the booster, but actually makes a lot of sense, with the longest reach targets being released first and the nearest ones last, presumably calculated to impact at nearly the same time. With the extra throw weight that Soviet launchers like the SS-18 had the loss of total impulse performance was probably inconsequential. The PBVs may also deploy countermeasures, e.g. balloons, chaff, dummy RVs, et cetera, to confuse sensors and complicate interception by anti-ballistic missile systems. Such countermeasures are almost trivial to deploy and difficult to discriminate, making the business of ballistic missile interception after RV deployment.

The photo you linked to is a Peacekeeper 8 RV reentry test off Kwajalein Island. I don’t remember the spread offhand but it was tens of miles apart between each, and only so confined to keep the impacts out in broad ocean area and away from shipping lanes. The apparent angles are also a bit misleading; the actual angle of attach was nearly the same on all RVs, but appears different because the RVs are entering at trajectories angled away from the photographer. (If you imagine standing under your own right hand with fingers spread as the RV trajectories, you’d be under the thumb looking out toward the fingers turned to the left.) Depending on the trajectory, it is possible to get spreads of hundreds of miles between RVs. A single Soviet ICBM like the SS-18 coming over the North Pole could conceivably send RVs to New York, Columbus, St. Louis, and potentially Charlotte. (Cities picked quasi-randomly from a map.) As the US has strategic sites and populations centers spread throughout the continental US the Soviet vehicles had to cover a lot of ground, versus Soviet facilities and cities which, with a few exceptions, were pretty clustered in the West and in the Warsaw Pact nations.

Stranger

Thanks folks. I’m certain that they work, and that it is my understanding that is faulty. I appreciate the comments on the photo of the test, clarifying how that was done. Likewise, I hadn’t spotted the actual numbers in the Wikipedia article.

(I’ll ask a few more questions and then let it go, as this isn’t my thread and I don’t want to annoy the folks taking time to answer.)

I am having a problem understanding how they can get a spread of hundreds of kilometers. Does the bus have a huge amount of propellant (e.g. >5% of the total propellant of the missile)? In other words, is the missile still undergoing great acceleration while the bus is doing its thing, or is it already in ballistic mode and just using small steering rockets to aim things?

It is my understanding that satellites can change orbital altitude fairly easily, but it costs great amounts of energy to change the plane of an orbit–does this match the mechanics of ballistic missile trajectories? I imagined a MIRV bus to be similar, and that it would be easier to have the RVs land in a line, but if one wants to target NY, DC, and STL at the same time that would require substantial energy to steer them away from the straight-line direction of the original launch.

Again, I’m sure they do just that, but somehow I am not understanding how a missile flying at several miles a second can accelerate enough to make a turn of several degrees without a prohibitively large supply of fuel.

At apoapsis, it isn’t going miles per second, at least with respect to the earth’s surface. It reaches zero vertical velocity.

So as you let go the warheads, they have to fall all the way back to the earth’s surface, and this will take a while. 10-20 minutes or so. Before releasing the warheads, if you gave them a small push, that push adds up over the entire falling period. It also changes the entry angle to the atmosphere which results in an even larger deflection.