Space Fleet - Evasion

Well, there are many topics to cover in Space Fleet combat, so I think I'll try to break my thoughts into posts of reasonable length.

Maneuver in Combat – Dodging or Voiding

Almost all aspects of combat stem from one dictum. Hit your opponent without getting hit in return. The part about not getting hit can often determine the form that combat and weaponry takes, pushing the warships to ever greater levels of defensive agility. The reason for this is that if you can come up with a way whereby your enemy can't ever hit you, yet you can hit in return, you always win. Not only do you always win, but you always win without even suffering any losses. For example, if you have mounted horse archers with bows powerful enough to penetrate a knight's armour, and the knights are stuck on foot, only carrying swords, the archers can win without suffering a single casualty. Archers firing from a castle are in the same position, as were our aircraft over Afghanistan. It means you can strike with impunity. So how do we make sure our future ships can avoid being hit? Well for one thing, they might have to be agile.

The act of avoiding an attack by moving to render it a miss was once called voiding, and in medieval swordplay we commonly say we void the enemy's attack and then counter. The more modern form of the word would be avoid, but this word also carries many other meanings, so I'll avoid using it, along with the more standard evasion. Both those words can imply that you're just not letting an opponent even take a shot at you, as if you were being elusive. So I'll reserve "void" or "dodge" to refer to the act of dodging an attack that is already launched. If you can't void the attack then you have to block, absorb, or otherwise engage it, and you might say that engaging the incoming weapon, or else getting hit by it, is unavoidable. The purpose of voiding is to turn your opponent's aimed or guided shots into clear misses. Ideally your void also leaves your attacker open to a counter-attack, and taken to perfection you simultaneously void while landing your own attack, all taken as a single motion, such as twisting out of the path of your opponent's blade while stabbing him in the face. So let's take a look at what it takes to void an attack.

Consider the flight time of unguided but aimed projectile versus a target's ability to change its own position within that flight time. If the target can deduce the flight path of the projectile and then move out of the projectile's path then it can dodge the projectile. This is exactly what you did when you played dodgeball, aside from the part of the game where you catch the ball. It's important to note that the act of dodging requires either acceleration or redistribution of your parts so that none of them are in the flight path. In the first case you either jump left or right, leap forward, or slow down suddenly. Since the attacker can observe your existing motion prior to throwing and adjust for it by leading you, simply maintaining a high constant velocity isn't necessarily buying you anything if your attacker can properly calculate the lead and put the projectile on an intercept course.

The alternative is to simply bend yourself so you're not touching the flight path, which can be useful for things like single-time rapier combat where you sometimes dodge your attacker's thrust by contorting yourself (looking like your playing a game of "Twister") while simultaneously making a thrust of your own. But since almost no craft are ever built with this type flexibility I'll ignore it from here on out, in reference to a targeted ship, except to note that my previous post on laser combat mentioned using multiple rotating hulls to defeat an attempt at laser penetration, and in essence the ship was moving the targeted hot spot to foil the enemy beam's progress.

As an aside, there's potentially a related trick that might be useful for enhancing the lethality of a very small high-velocity projectile trying to penetrate laser defenses. Connecting several small solid penetrators together with mechanical linkages to form a chaotic mechanical oscillator, much like a part of a car engine or crazy whirligig, violently jinks the exact positions of the masses and linkages. That "smears" each masses predictable future position, making targeting more difficult at longer ranges, where speed of light delays between observing and firing play a role in the targeting problem. This forces an anti-missile laser to target the broader "position cloud" and thus forces a waste of finite defensive laser power on stopping the shot. And if you can waste enough of the defender's defensive power, they run out of defenses. Simpler than this "whirligig" are oddly shaped projectiles that spin at high speed, yet that don’t have material occupying their own axis of rotation, such as a piece of metal bent like a boomerang viewed from above. These are little tricks that may or may not be significant, depending on how things works out.

The key physical aspect about dodging is that from the time you detect the object and deduce the flight path, or see a potential flight path, you have to be able to maneuver out of that path. So you must accelerate in some given direction, and most craft aren't able to accelerate equally in all directions. Some attack angles make it harder to dodge than others, and a good attacker tries to exploit the fact. A fighter plane, for example, can use its wings to accelerate at many G's up or down, relative to the pilot's orientation, but the engines will generally only accelerate it at about 1 G or less forward, and the plane has almost no ability to accelerate to the sides. They can slow down pretty quickly, but at lower airspeeds the wings can't generate as much lift, which reduces what's available for further accelerations, and thus the plane's subsequent ability to maneuver is reduced. As Col. John Body showed with his energy-maneuverability theory, being able to retain your maneuverability is the key to winning a dogfight. But also note that if the attacker's ability to change his aim is limited, as for example a fighter plane that can only fire forwards, then dodging also encompasses the act of maneuvering to stay out of the potential path of projectiles.

The size of the vehicles tremendously affects the ability to dodge a shot, since a larger ship has to accelerate faster than a smaller one if it's going to clear a given projectile flight-path in some given amount of time. For instance, if a projectile was going to hit dead center on two different ships, a fifty footer and a five-hundred footer, the smaller ship must accelerate so that it moves 25 feet prior to the predicted impact, whereas the larger ship must accelerate so that it moves 250 feet. Given that the time allowed for this acceleration is some constant time T, and the distance cleared is given as s=1/2*A*T^2, the amount of required acceleration goes up in proportion to the linear size of the ship. And of course any ship would best dodge by moving in the direction that allows it to clear the projectile path in the least amount of time. Also note how sensitive that equation is to the time. If the ranges stay the same but the projectile speeds double, then the ships have to accelerate four times as fast to be able to successfully dodge. Likewise, if the attacker can slip in twice as close the effect is the same, since the flight time is again cut in half. You know this intuitively from your days playing dodgeball, noting that close range throws result in easy kills whereas long range ones are just a waste of effort.

This brings up another point on ship design. We're probably used to imagining that a ship will travel along its long axis, just like a naval ship. However, this means that the thrust is applied along the long axis, which is absolutely the worst direction for entirely clearing your previous position in the least time. The other problem with long ships is that the moment of inertia, the resistance of the object to rotation by applied torques, goes up with the square of the length. For a long uniform object the moment of inertia about the center is m*L^2/12, where m is the object's mass and L is the length. Since it follows a square law, doubling a ships length (while keeping the weight the same) makes it four times harder to rotate (or steer), which means it's not necessarily very agile. On top of this, if you did apply enough force to wrestle it around, the people or equipment near the ends will be getting beat to death as the walls slam into them during all the jinking and dodging. Even though there aren't any serious structural restrictions on building a space vessel miles long, there are very good reasons not to if the ship is ever going to maneuver.

It would make more physical sense, although perhaps less structural sense, if a ship had its thrust aligned along the shortest axis, which would require less total acceleration to clear its previous position. The reason ocean going ships don't do this is that plowing through water creates a bow wave that robs energy, and the effect creates a "natural" boat speed that goes up with the square root of a boat's waterline length. Exceeding the natural boat speed for a given hull length creates a large drag penalty for the ship, and the only way to overcome it is to provide far more power so the boat can begin to plane. Aerodynamics plays a similar role in shaping how aircraft are built. As an aside, both subjects are given an excellent treatment in "The Aero-Hydrodynamics of Sailing", which I highly recommend and which necessarily covers both topics in depth, because both are vital to making a high-performance sailing craft. Unfortunately, sailing craft are rather obsolete for the question at hand.

Aiming Problems

During WW-I early attempts at aerial combat involved scouts taking pot-shots at each other with rifles, and this proved highly ineffective. Correctly leading a running man is hard enough, but shooting at targets that are moving far faster than highway speeds is incredibly difficult, especially if you're just guessing at the range. That's why we started using anti-aircraft machine guns with a large circular grid in the sight picture to help gunners get close to the correct leads, which still didn't produce a very high hit ratio. What Von Richthofen and some others came up with instead was to just fly right up the enemy's ass and open up on him point blank, which proved highly effective. Instead of doing endless math the Red Barron cut the Gordian knot.

So a human's inability to exactly judge the range, range rate (the closing velocity), angular rate (how many degrees per second the target seems to be moving), and the rate of change of these rates has greatly shaped aspects of combat in the past. However, in any scenario about future space combat we'll have radar and laser range finders coupled to targeting computers, so I don't think there's much that can be done to keep the enemy from correctly aiming, in terms of confusion about proper lead angles. So let's set aside any thoughts that dodging and jinking at human capable speeds, merely to confuse another human's limited ability to aim, will play a major role in shaping future space combat. However, jinking fast enough to take advantage of speed-of-light delays might prove somewhat useful, at least for small objects at extreme range.

Counters to Voiding

To defeat the enemy's ability to dodge an aimed projectile you can do several things. The most obvious is to either move to closer ranges before attacking, or to use faster projectiles. The next obvious is to make exploding projectiles that still damage even when they miss. But the usefulness of this is limited to situations where your opponent can barely dodge the attack, where miss distances are no larger than the effective blast radius of a warhead. For example, if your target can manage to clear your solid shots, but clear them only by half a boat length, then your explosive charge needs to have a half boat-length effective blast radius. As more agile craft are designed it, relative to the agility of the incoming missile, it will takes a larger blast radius to guarantee a hit. This might create a design race between more maneuverable craft versus larger warheads.

Yet larger warheads are just that, larger, and thus fewer can be carried, making salvo fire or repeated follow-up shots less likely. If you totally maximize your incoming attack speed (faster missiles) and blast radius (bigger warheads) compared to a target's ability to maneuver you end up with something equivalent to firing a short range nuclear missile at a naval vessel, where the ship's maneuverability is irrelevant. However, the utility of nuclear warheads in space is not nearly what you'd think, since most of their damage on earth is from overpressure wave in the pre-existing air, whereas space is a vacuum. Likewise the thermal effects that torch wooden houses aren't nearly so good against a thick titanium hull. I'll go through the math in another post, but if you're using 1 megaton warheads I'd recommend getting them within 50 to 100 meters of the enemy ship if you really want to guarantee a kill. A nuclear warhead is great in an atmosphere against essentially naked people and their matchstick houses, much like dropping a fire cracker into an aquarium full of guppies, but might not be that useful against a tough warship in space, just as the same firecracker is pretty useless as a near miss against a turtle in a vacuum chamber. Likewise, if the ships are given armor thick enough to serve as radiation shielding against the space environment, which is going to be titanium or steel a couple feet thick, simple high-explosive fragmentation weapons would likewise be pretty useless, because normal fragments just don't have enough velocity to penetrate these kinds of armor.

Another extreme is to use weapons that travel at such extreme speeds that dodging at all but the most incredibly ranges is pointless, such as lasers. If the combatants use turreted lasers that can track and fire at anything, and the aim can't be spoofed, then dodging by rapid maneuvering or jinking is pointless. If you put laser turrets on our modern fighters, the close-in knife fight requirements would probably go away, and everyone would be working to maximize the lethal ranges of their lasers instead of trying to optimize aircraft for a phase of combat that both aircraft won't survive long enough to engage in.

Guided Shots

The next obvious counter to dodging is to use a guided projectile, which is the currently favored solution. When the Sidewinder was first developed it wasn't something the design group was authorized to be working on. They were supposed to limit their efforts to improved proximity fuses, so they just called it a proximity fuse with a tendency to reduce dispersion. In effect, that's what a seeker head is, just a trick to make sure the missile doesn’t tend to miss very badly. At first blush it looks like the ability of the missile to follow the target's jinks renders maneuver irrelevant, again changing the air combat problem back to one of capital ships launching their missiles at extreme range and then opening the distance back up to avoid return fire. The design game becomes one of making the fastest plane with the longest range missile systems. We stayed in this rut for a while before the Col. Boyd who also developed Energy-Maneuverability theory, showed that it's possible to outmaneuver a missile. But during this period many thought that manned aircraft had been rendered obsolete, and the British went from a strong manned fighter program to almost none at all.

The key to outmaneuvering a missile is they're limited in their total energy, don't have good sustained turning performance, and are thus limited in how they can maneuver before slowing down. With such tiny fins a slow missile can't pull many G's. Contrary to what you see in many bad movies, a fighter plane doesn't get involved in a neck-and-neck race with a missile, since in most cases our missile's motors burn for less than 10 seconds. After that it's a guided dart and can't keep maneuvering forever. The target aircraft can sustain its own thrust and use its more efficient wings to maintain turning accelerations that the missile can't always follow. Fighter pilots and engineers look at curves of the performance envelopes to spot such weaknesses, devising maneuvers to use against them. If your maneuver envelope can extend past the missile's own then you can move yourself into a velocity and position that the missile can't reach. But in space, aerodynamics are out, and the question of evasion depends entirely on total achievable delta-V, in other words the efficiency of the missile and warship, considered purely as rockets, and the maximum acceleration they can achieve.

Stripped of the concept of missile and ship, the game can be seen as a simple game of tag, with a pursuer and an evader. These are generally classed as pursuit-evasion games, and we watch these type of games every time we watch American football, where you can learn some simple lessons about it. If the evader has a higher instantaneous acceleration than the attacker he can use his higher accelerations during the close-in phases and dodge the attack. These are your Heisman trophy winners who maneuver through swarms of assaulting linemen to pop burst through clear and unscathed. If you can reach a higher velocity than your attacker in some particular direction, especially perpendicular or along the same line as the attack then he likewise can't reach you. These are the players whose world class sprinting leaves linemen in the dust, unable to close the distance. In both cases evading the attacks requires either a higher acceleration or greater total delta-V, which is the maximum change in velocity, or taken from a standing start, a greater final velocity, but in some particular plane.

This point is important enough to re-emphasize. If your ship can always out accelerate an incoming missile, perpendicular to the missile's flight path, the ship can always dodge a single shot, as long as the ship starts accelerating soon enough. It has to clear its entire hull from the projectile's path, plus clear any fragments the projectile might release, which is exactly the same as playing tag, where you have to make sure your entire body moves outside your pursuer's maximum reach.

If you can't out accelerate an incoming missile then you have to either somehow destroy its ability to maneuver while it's still some distance out, or you have to be able to achieve a greater total delta-V than the missile. This second option requires starting your acceleration very early, because you've just set up a game of a distance runner versus a sprinter. The sprinter always can win in the short term, but if you put enough distance behind you he can't catch back up. I suppose this game might get a bit interesting in that an attacking ship will send a missile cruising toward your current position, forcing you to being your acceleration, and then the attacking ship will try to shadow you in while closing the range, so that it can get close enough so that another of the "sprinters" it has on board can be launched directly into the end-game, where the sprinter has the advantage.

But this gets us into ship on ship maneuvering, which brings up another point. Different planes, in our 3 dimensional reference system, are important to understanding voiding, since your attacker must be able to intercept you in all three planes to intersect your path. A missile might be launched along some x-axis with incredible acceleration and a high final velocity, but if it can't match your acceleration, or your change in velocity, along the y-axis and z-axis as it crosses your position in the x-axis then it simply can't hit you. Unless you can flat outrun the incoming missile then your best option is probably to move perpendicular to its trajectory, only noting its closing velocity to calculate the time till it crosses your position.

But an attacker may present a more complicated evasion problem by attack from multiple directions. For example, even if you can avoid an x-axis shot by accelerating strongly along the y-axis, that evasive maneuver may avail you nothing if another missile is traveling along that y-axis. This leaves the z-axis open but a third missile along that path can block the remaining escape route. So the target must maneuver along all three axes, where his total travel distance gets spread across all those axes, leaving him with a slightly less effective response than when he could maneuver strongly perpendicular to the single incoming shot. And a fourth shot along his new path will make him have to follow yet a different path. The more angles you can cover the better this type of attack becomes, and in the ideal you've got him surrounded in a sphere of incoming shots. Of course, if an attack is in a position to do this he's already got a position and possibly a fleet weight advantage on his opponent.

The defender still has maneuver options, though, since he's not just going to sit at the center or focus of the incoming missiles. He's going to maneuver against them, noting that the shots are just positions over time. The defender can maneuver toward some shots and away from others, shortening the intercept time of some missiles while lengthening that of others, and thus string out the massed attack into a series of smaller engagements. This is the same technique you might use when caught out alone and badly outnumbered by multiple opponents in hand-to-hand combat. You flee and force them to pursue, and if not well organized they get strung out based on how fast they can run. Then you unexpectedly turn and kill, flee some more, turn and kill. If you succeed against the first few, who by their faster pursuit are probably the most able, the rest might lose heart and let you flee unmolested. If not, they need sense enough to regroup before you turn and work your way down their strung-out line.

As a further example of this, suppose you are midway between two attackers who fire at you simultaneously. By charging toward one incoming shot you can encounter and defeat it first, while simultaneously stretching out the distance that the other shot must travel before reaching you. That allows you to deal individually with two shots that otherwise would've reached you simultaneously This corresponds to 16th century advice from George Silver on using a quarter staff against multiple opponents armed with rapiers. To nullify the staff's reach advantage the rapier men try to encircle to deliver a simultaneous attack from opposite sides, but in moving towards one or the other the man with the staff breaks apart their attack and forces sequential combats, each of which he can win.

In any event, to pull off this trick the defender can't wait until the missile swarm is upon him, closing with high velocity, because by then his own changes in velocity won't be able to signifcantly alter the intercept times.

Spoofing Incoming Missiles

Now one interesting way to look at spoofing is to note that a missile guidance system has certain things that it's looking for. As the guidance system of a missile become more and more advanced, you might eventually say that the missile senses its surroundings to create a mental model, or worldview. In trying to spoof the missile you're trying to mislead it about its observed reality, basically trying to alter its mental world into one where your true physical position, or even your very existence, is not a reflection of reality. In a physical sense, spoofing a missile is still dodging it, you're just creating the miss by moving the lighter object instead of the heavier. It's a shortcut to creating a miss.

We could of course use decoys and jammers to try and spoof a missile's guidance system. However, as missile computer power increases these tricks will become less and effective. In some future space combat spoofing will probably be very ineffective, since the target will present such a clear contrast against the blackness of space. The missiles will likely be very smart and equipped with multi-spectral sensors, including radar, infrared, and optical, and possibly laser guidance. Eventually we'll be at the point where this handy aphorism will apply

You can fool some of the sensors some of the time, but you can't fool all sensors all of the time.

But if you hit the missile with something like a massive EM pulse or a laser beam, you can blind it in the optical band, and eventually heat it till it fails, whether by exceeding the temperature tolerance of its electronics or simply melting them. Essentially, within some certain range a ship should be able to completely blind all incoming missiles in the optical and IR bands, unless they outnumber his blinding lasers, and can probably do a good job at spoofing any radar homers. I mean, we can already to that now. So the missile designer might do something clever, like have his missiles exchange information, so that the missile shot you thought was a stray, missing by 20 miles, might be the one that's telling his mates what's going on as they continue through your countermeasures.

When Dodging Fails

If you can't force the projectile to miss, you have to either destroy it or absorb the hit. To destroy the projectile you'll need to hit it with something, whether a projectile of your own, a laser, or some other energy source. If the projectile is guided you can probably destroy the seeker head, brain, or overheat the propulsion system much more easily than destroying the entire projectile, and by destroy I mean essentially vaporize.

However, this raises another problem almost unique to space combat. Unless your defense absolutely destroys, then changes the flight path of the enemy projectile, its remnants will still be traveling on almost the exact path they had before the destruction. If you're not maneuvering, accelerating in one direction or another, then when "disabled" the projectile was probably on a direct ballistic path to your current position. If you don't get out of the way the projectile's parts are still going to hit you, and your intercept will probably not have appreciably changed the incoming projectile's mass. You may have turned a smart penetrator round into a dumb shotgun blast, but if the missiles are moving at extremely high velocities then the mass still carries tremendous kinetic energy and you still want to move out of the way.

When dodging is a useful attribute of a warship it puts a downward pressure on vehicle size. A battleship is a very poor choice for a sub-hunter that relies on depth-charge passes, just as it would do a poor job of dodging torpedoes. If dodging is next to impossible then you end up in slug fests. In the days of sail the slow maneuver speed and short projectile flight time rendered dodging impossible. The ineffectiveness of a single canon shot likewise made the first-shot/first-kill situation unworkable, so the battles were decided by slugging it out. The ships used guns to knock out the enemy guns with direct counter fire while also knocking out rigging and steering gear, which degraded the enemy's ability to change the relative position of the ships.

The only use for maneuver in such ships was to accomplish two goals. One was in closing and opening the range to exploit any relative advantage in mix and number of weapons, for example closing with the enemy if you had an advantage in raw short range throw weight or boarding parties, or opening the range if your ship held the advantage in long range gunnery. The other use was positioning a ship where the opponent couldn't bring effective counter fire to bear, such as sailing around the enemy's bow or stern faster than he could pivot, and then to fire raking broadsides down their bow or stern.

Anyway, I'll just leave off here, and finish with a bit of math.

Math - *gasp* - and Examples

The math on this is pretty simple, but feel free to skip this little section if you want. I'll use
As for the maximum acceleration of the ship
Am for the maximum acceleration of the missile
Vm for the missiles closing velocity relative to the ship
T0 for the initial time that the maneuvers begin
R for the initial range
Tm for the maneuver time before a potential impact

R=Vm*Tm, so Tm = R/Vm and we know exactly how many seconds we have to react. Assume that at the beginning of the maneuvers the missile traveling along a path to impact the ship at some point P, say dead-center of our ship of length L, and that if the missile didn't maneuver (say it had its seeker head or engine destroyed and has become merely a dumb shot, but a well aimed one, from the instant its brain or engine was disabled) the ship must move half a boat-length to get out of the way. We know we have to move distance L/2 in time Tm, relative to our initial motion. By s=1/2*a*t^2 we'd have to accelerate at As=2*(L/2)/(Tm^2), or just As=L/Tm^2.

Note that our required acceleration is indeed a linear function of boat length and inverse to the square of the unguided or "dumb" time of the missile's flight. If we can double the range R at which we fry the missile we only need to accelerate a fourth as hard to clear the path, whereas if the enemy can harden is missile to survive twice as long, or double its velocity as it comes within range R, he can require our ship to accelerate four times faster to ensure a miss. Obviously this too might become an arms design race, between longer range defenses, ship accelerations, missile hardening, and missile speed.

But what if we can't kill the missile at all, but can merely out accelerate it? Then the same equation applies, but you have to add the missile's maximum acceleration to that required for the ships to clear a "dumb" missile As=(L/Tm^2)+Am. Obviously if Am > As the ship always loses this game because the equation has no solutions for finite boat lengths. Unfortunately it's doubtful that a human crewed ship could out accelerate a missile in the end-stages of an intercept, since conventional solid rocket motors can generate staggeringly high thrust to weight ratios. Out accelerating a missile that had a zinc-sulfur motor for its final maneuver phase would require our ship to accelerate at levels that would not only crush the pilot, but his pet mouse George too.

This means that to ensure survival it is probable that any warship will have to use hard impacts, lasers, or EM to disable an incoming missile greater than some range R given by R=sqrt(Vm^2*L/As). If a warship let's a missile get inside this distance while on an intercept course then the ship has to completely destroy the missile with "AA" or it will get hit.

Examples

Suppose our enemy fires off a missile that uses a nuclear rocket such as we had in the 1960's. Its specific impulse is 950 seconds (strange units, but don't worry about it) so it's exhaust velocity c is 9310 meters/second. By the standard rocket equation its final velocity v is given by v = c * ln(M0/M1), where M0 is the missile's initial mass, and M1 is the missile's final mass. A mass ratio of 8 is easy to achieve, so the rockets final velocity is going to be ln(8), or 2.08 times faster than its exhaust velocity. That gives Vm=19359 m/sec = 63,515 fps = 43,300 mph. Down on earth that speed would be about mach 57, or 12 miles per second, and if we could kill it a 12 miles out we'd have only one second to get out of the way. By As=L/Tm^2 our boat length (in feet or meters) can't be bigger than our ship's maximum acceleration (in ft/sec^2 or m/sec^2).
So in this case, if ships were only good for 1G accelerations then they'd have to stay smaller than 32 feet, but if they could pull 7G's then they could get as big as 225 feet. But if you could disable the missile at 24 miles instead of 12, your ships can be twice as large.

On further problem pops up if the incoming missile tosses out a bunch of small uranium penetrators, because at those speeds a 10 pound hunk of metal has the same kinetic energy as a 16" battleship gun point blank. Note that using a high-explosive warhead really doesn't add that much to the kinetic energy of the incoming projectile, which already have enormous energy, and that the missile is already traveling far faster than even the detonation speed of a high explosive. Even if it hit and detonated on impact, the fragments would still just make an impact cone, making a little hole in the front and a big gaping exit wound. In this type of situation going back to the original concept of shrapnel is advantageous, and many people don't actually know what "Shrapnel" actually was, since it was abandoned during WW-I. As canon ranges increased the old anti-personel standby of using grape-shot was no longer effective. The little balls slow down to much and disperse too widely when you're trying to hit people miles away. So Shrapnel came up with the idea of keeping the grape shot in a can until right before impact, then using a tiny bursting charge to scatter the balls. It's just a delayed action shotgun blast, and the kinetic energy of the balls comes from the the original cannon shot, not the bursting charge. Since our missile in this case is going so fast that even a small ball has enormous kinetic energy (a 1 pound ball carrying about the same as an 8" artillery piece point blank), the best thing to do might be to toss out lots of small balls to get a greater hit probability.

One final thing I'd like to bring up about shrapnel is that a missile might have a good idea of when it's about to be destroyed, the current orientation of the target ship, and might be able to exploit the targeted ship's maneuver envelope to create a more efficient dispersion of shrapnel. For instance, if the enemy ship is rather conventional, with a rocket engine at one end and some small steering ability, the missile would know that the future positions of the ship lie in a limited area. This area is essentially a cone, like a trumpet. If the enemy captain does nothing his ship stays at the apex of the cone, whereas if he tries to evade by firing his sole engine he must follow a path in that trumpet, the shape of which is determines by the ship's maximum acceleration and maximum turning rate.

If I was a really smart missile I'd note I really should concentrate my shrapnel on four different points on that cone. The current position, in case the ship is already disabled or the captain is asleep, the maximum straight line position in case the captain bellows "all ahead full!" and the end points on the right and left of the cone, in case he adds "hard to port" or "hard to starboard". However, if we built a warship that had multiple engines the cone would be a sphere, and it would force the missile to disperse its submunitions over a much greater area. So there may be a big advantage to warships with all-around maneuvering capabilities.

Anyway, I hope this didn't put you all to sleep!