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May 23, 2004

Space Fleet - Missile Versus Laser

Now I'd like to write a bit about the game of anti-ship missile versus laser defenses and some of the interesting information it reveals. I covered some aspects of this in Space Fleet - Lasers. This post is just going to be a rough analysis, though sometimes delving into the details, to get a feel for the new game you get when you combine missiles and optics together, looking to see if equations and tactics pops out. So as Steven Den Beste often states, don't lose the forest for the trees. We're not trying to write a grant proposal here, we're just hypothesizing on space fleet combat, and fortunately telescopes and missiles are two of my hobbies.

I'll start by noting that a missile in space must maneuver only with rocket thrust, which is unlike our usual conceptions gleaned from looking at Sidewinders and other atmospheric missiles, which are steered with guidance fins. Our basic space missile has two components, a thrust motor that gets it up to high velocity, so it can minimize its flight time through the enemy defenses, and a maneuver motor so it can track the target by moving side-to-side. Our SDI program produced some missiles with just these features, under the program called "Brilliant Pebbles".

Let's assume that once the boost engine has gotten the missile up to speed, it's already got more than sufficient closing velocity to destroy the target. At this point the boost motor is just dead weight, which would be a detriment to agility during the closing phase of the missile's attack. So we'll use the boost motor as the first stage of a two stage missile. The second stage doesn't have only a single motor, but multiple ones aimed perpendicular to the missile's flight path, so that it can jink, dodge, or track a target. Odd as it may seem, our final missile doesn't have a motor in the back propelling it forward, it has little motors that push it side-to-side. You could use a single motor in the back and steer it conventionally, but then most of your thrust is being applied along an axis where you've already got sufficient velocity for the kill, instead of along an axis that you desperately need to maneuver in to intercept the target. So that basic type of missile will be the basis for the rest of this particular post.

Now in terms of what the missile must accomplish, I'll go back my earlier equations from Space Fleet – Evasion to see what our missile has to accomplish. We have a missile traveling at velocity Vm and would like to destroy a ship with it. The ship is going to maneuver along some path with an acceleration As, and the ship length along this path (probably the ship's shortest dimension) is L. Our missile is probably going to have its guidance abilities destroyed at some point along the path, but if we can get it close enough and fast enough we can still guarantee a kill on the ship. If we can keep our missile, traveling at velocity Vm alive and on course to within range Rkill=sqrt(Vm2L/As) we guarantee a kill on the enemy ship, if the enemy ship can't directly stop the missile.

Note that the faster the missile the greater the range where we can have the missile's guidance knocked out and still guarantee that our path should result in a kill. Also note that if the ship can't accelerate the kill range goes to infinity, meaning we could in theory guarantee a hit from extreme ranges, just like NASA probles heading for non-maneuvering planets. I'm assuming a kinetic kill weapon for the simple reason that it's a highly efficient method when missiles are moving at extreme velocities. For example, in an earlier post I ran some calculations for a missile traveling at Vm=19359 m/sec = 63,515 fps = 43,300 mph = 12 miles per second. If it slammed to a stop the energy released would be 76.3 megajoules, which is equivalent to 17 kg of TNT. Just because of the impact velocity our missile potentially possesses 17 times more energy than it would if the whole thing was made out of high explosives. All they need to do is make a hit.

Laser Weapons

I posted earlier on laser weapons, and now I'd like to mention some fundamental physics that come into play. Optical systems are generally "diffraction limited", meaning that the wave nature of light puts a limit on focusing, which means there's also a limit on how finely a system can direct a beam. The reason is that below about a quarter of a wavelength electromagnetic radiation isn't further affected very much by the precision of the reflecting or refracting surface, and this is why astronomical mirrors are often only finished to "1/8 wave". They're not perfect, just good enough to where adding more surface perfection doesn't keep increasing the performance.

There may be a bizarre way around this problem using materials with a negative index of refraction, and although it sounds strange we're actually able to do just that, but I don't know if a telescope could make use of the effect. I'll ignore such potential tricks and see how a laser would perform if we were to build it like we would either now or in the near future.

So we're talking about diffraction limited optics, and the key formula is also very common to astronomy.

Dspot = 2.44 Rl / Dlens

Dspot is the diameter of the spot that contains 84% of the transmitted light.

R is the range (in meters)

l is the wavelength of light

     If the light is visible it will be from 410x10-9 meters (violet) to 680x10-9 meters (red).

Dlens is the diameter of the mirror

For a bit more on high power lasers try this link, which details some of our advances at cleaning up atmospheric distortion so we can retain tight focus when targeting orbiting satellites with ground-based laser weapons. This link discusses some pros and cons of chemical lasers, and also mentions that laser weapons operate at the very margins where any flaw in reflectivity results in sudden destruction of the mirror surface. Yet that the laser weapon designer knows exactly how perfect his coatings have to be and where, and can use active cooling on hot spots. The defender has none of these advantages, and the slightest flaw in his coating will result in a heated region where his coating suffers catastrophic and expanding failure. In short, mirroring your craft might protect against generalized heating but won't succeed in stopping an extremely intense, tight beam. Another use for high-powered lasers is transmitting energy, and this link points out the potential application of powering a lunar base through the lunar night by beaming laser energy up from earth to the same photovoltaic solar array that the base uses throughout the lunar day.

So, we want to stop an incoming missile with a laser, yet the missile designer, if he so chooses, can coat his missile with a reflector every bit as good as the laser's mirror, which gets us to a crucial range equation. Let's assume the laser makes a single reflection of the primary mirror (the big one) and is driving the primary mirror's reflective surface to the very limits of self-destruction. If the missile uses the same coating technology as the laser's mirror then we'd have to hit the missile with at least this much energy density to destroy the reflective coating on the missile, and until this is done 99% to 99.9% of the laser energy is just reflecting away instead of heating. And a missile is certainly still intact if its thin, delicate reflective coating is.

Now the primary mirror is coated with full knowledge of the laser's frequency, so we can have its reflective layer tuned for maximum reflectivity in a narrow band. At present, this might mean that instead of a broadband reflector at 99% reflectivity, we might have 99.8% reflectivity. These numbers will improve somewhat, because optics is a very fast paced field and massive amounts of dollars and physicists are involved in it, and we certainly would never choose a reflector that's worse than what we have available now. For a small example look here or just Google up "mirror reflectors" or "reflective coatings mirror laser".

The defender might or might not have prior knowledge of our laser's frequency, but we must assume that he does. Since both sides are going to be using the best available coating technologies, if they're at all competent, and since I'm assuming some scientific and technical information was being shared prior to hostilities, I'll say that both sides are just as good at reflective coatings.

The formula given above tells the size of the spot that contains 84% of the laser's energy. Since this means our spot is a little bit diffuse, and since we need a spot that's even more intense than what's bouncing off our primary mirror if we're to destroy a similar coating elsewhere, then we need the area of the target spot to be less than 84% of the area of the primary mirror, which means the diameter of the spot has to be less than 91.7% of the diameter of the lens. So our formula for the closest point where we can possibly blow off a technically optimal reflector becomes this.

0.917 Dlens = 2.44 Rl / Dlens

R = 0.376 Dlens2 / l

For violet (410 nm) light this comes to R (km) = 917 Dlens2 (meters)

or R (miles) = 14.47 Dlens2 (inches).

Note that a little 10" mirror has a possibly useful anti-missile range of 145 miles. I've ground and polished an 8 inch and 10 inch mirror by hand, and it's a common size for an amateur telescope. As you get into Hubble sizes the range starts pushing out to almost 1500 miles. At a closing velocity of 12 miles per second (mach 57), you'd have about two minutes to intercept the missile. But of course it won't be alone. But in truth these ranges are going to be much smaller, because there are some very interesting optical tricks the missile designer will definitely use, but more on that a bit later.

Frontal Area of Missiles

Against a solitary enemy ship we might first go with a cylindrical missile, long and thin, to keep the frontal area minimal. If we can keep the nose aimed directly at the targeted ship then the defense lasers are striking the minimal area on the missile. Further, we're probably at the longest range where the laser could just manage to blow off that super reflective coating on our nose, which means the laser's beam size is still pretty large. As calculated previously, the laser probably can't damage our nose reflector till its beam size is less than 91% of its mirror diameter. If we're talking about a 100 inch diameter mirror means that we're at the point where 84% of the laser energy is in a 91 inch diameter circle. If our missile is only 8 inches in diameter then the area being heated by the laser only represents 0.77% of the central beam area. Note that we have a transmitted beam 91 inches in diameter, but only an 8 inch object there to catch the light.

Considering that the 91 inch central beam is only 84% of the total beam energy, this means that only 0.65% of our beam energy is even hitting the missile. That means the beam is 99.35% wasted. As a missile designer trying to penetrate their defenses, I really like that number. They defending ship would surely love to focus the beam tighter and reduce that value, but the diffraction limit on their optics means there's nothing they can do. But also note that if I'd sent in a monster 10 foot diameter super missile then that same beam would put nearly 100% of its energy on target. Small targets at extreme range are not an efficient way for a defending ship to expend its power. If we wait till this small missile has traveled three fourths of the way to the ship then our beam diameter is only 22.75 inches, and 10.4% of our beam energy is hitting it, a sixteen-fold improvement.

This effect creates another range equation that takes into account the target size. For targets that look circular we get a range beyond which the laser beam widens to the point where the beam is fatter than the target, and past which the delivered energy goes down with an inverse square law. I'll denote this range as the energy efficient range, Ree.

Ree = Dmissile Dlens / 2.44l

For violet (410 nm) light this comes to R (km) = 1000 Dmissile Dlens (meters)

and Ree (miles) = 0.401 Dmissile Dlens (inches)

Since the energy efficiency of the defenses drops with an inverse square law past this range, the offensive-missile designer can reduce the frontal area of his missiles to both shrink the defenders energy efficient defensive range or to force him to fight less efficiently at the longer ranges. These equations aren't completely exact, since they're based on that 84% number from the diffraction equations, but the actual values aren't off by much.

Missile Heating

So, we've blown off the super-reflective surface protecting the nose of the incoming missile. Now we need to apply heat to disable, melt, and even vaporize it. Obviously if the missile is has nothing between the reflective nose and the fuel it will immediately explode, since the 0.1 to 1% of absorbed laser intensity, which just blew off the nose reflector, is really going to chew up a fuel tank or guidance system with energy absorptions that are 50 times higher or more. Additionally, the reflectivity of metals drops under high intensity illumination as they melt and vaporize, and will probably be reflecting roughly half the energy instead of 99% of it. So we need to stick some thermal "armor" behind that reflector. As a first attempt, I'll suggest a heavy high-temperature metal, though this may not be nearly a good a choice as some type of high-temperature ceramic.

We're going to go through a couple iterations of missile improvements and see where we end up. First off, suppose I put a slug of uranium up at the nose. I'm using uranium mostly because it makes an incredibly good penetrator in the event we actually hit the enemy ship. Here are some really rough stats on 1 kg of uranium. The final numbers are exact since specific heat varies a bit with temperature, but they're good enough for our purposes.

molecular weight 238.029 - density 18.9 g/cm^3 - 1 kg = 4.2011 moles
Specific heat 0.12 kJ/kgK
Melts at 1405K (So it takes 168 kJ/kg to raise the temperature of 1 kg from 5K to 1405K)
Boils at 4203K (So it takes 336 kJ/kg to raise the temperature from 1405K to 4203K)
Heat of fusion 8.520 kJ/mol (So it takes 35.79 kJ to melt 1 kg)
Heat of vaporization 477.0 kJ/mole (So it takes 2004 kJ to vaporize 1 kg)

It takes 203 kJ/kg to melt 1 kg
It takes 2340 additional kJ/kg to vaporize 1 kg of liquid U

Our 8 inch diameter missile could have a tip that's of course 8 inches across and 6.4 inches thick, which would weigh 100 kg. If it was 50% absorptive of laser energy, it would take about 40 mega joules to melt it, and about 500 mega joules to vaporize it, neglecting that fact that boiling hot uranium will also be radiating some heat back into space. Now some of you may not exactly recall what a Joule is, so I'll mention that it's simply a Watt-second. A 100 Watt light bulb uses 100 Joules per second, so our 40 mega joules could come from a 0.1 second burst from a 400 megawatt laser, or a 10 second burst from a 4 megawatt laser. Considering that the target will be radiating some of the applied energy away as heat (the target will be glowing) it's a bit more efficient to use the bigger laser for a shorter time.

Now obviously, a heavier missile is going to take more energy to melt, disable, or vaporize, and here we get into the frontal area effect again. If I make missile heavier by fattening it, say going to a 16" diameter missile with the same 6.4 inch thick nose, and arbitrarily treat the nose as the payload for rocket equation purposes, then to maintain the same mass ratio (and thus achieve the same speeds), the entire missile becomes four times heavier. But also note that beyond the energy efficient defensive range, Ree, this fat missile is getting heated up by the defending laser four times as efficiently because it's got four times the frontal area. So the new fat boy missile is no better able to survive long enough to get inside Ree than the old missile, yet the attacker can only carry a fourth as many of them for the same payload weight. That's a dramatic step backwards. The attacker is better off using four of the smaller missiles, or even better, just make his missile longer and thinner, to provide more frontal area that has to be melted prior to killing the missile.

Now also note that as long as you guarantee that your attacker can't disable your missile before it crosses the "sure kill" range, given earlier as Rkill=sqrt(Vm2L/As), the question is simply whether the defensive lasers can completely vaporize your missile, because it's going to hit the attacking ship if he doesn't, unless his point defenses (guns, metal plates, or armor) can stop it.

So the design of missile versus laser goes round and round as we figure out that we need more insulation between the nose and the guidance, rocket fuel, and engines, because melting uranium is really freaking hot. You can plug through the basic rocketry equations to try and optimize your missile velocity versus warhead mass, and go through many other design exercises, but keep in mind we're still only talking about missiles optimized against a solitary target.

Conic Noses, or "Nose Cones"

Of course sometime in the first three days someone will point out the benefits of using a long cone for the nose of the missile, which obviously is just a nose-cone. Normally we use these to reduce drag, but in this case "drag" is irrelevant and we'll use it to better resist the defense lasers.

The energy being absorbed by the nose cone is just a function of the frontal area and the energy in the laser beam, while the actual surface area receiving this energy can be made vastly larger by having the beam strike it obliquely, meaning across the area of a long, thin cone or other shape. The energy striking the nose is just the energy density in the beam multiplied by the frontal area, or pi times the square of the missile radius. The area of our cone is pi * r * sqrt (r2+h2), where h is the length of the nose cone. Not only is the laser beam impinging less efficiently across the surface, probably allowing the initial reflector to stay intact much longer, but as this new nose heats up to glowing it has a much greater surface area to radiate the heat away. It's simply a more efficient design.

Grazing Angle Nose Cones

As the idea of continually lengthening the nose cone to radiate heat away more and more efficiently is pursued, eventually becoming a thin, rolled piece of metal, a startling thing happens. It stops absorbing laser energy altogether, instead reflecting 100.00% of the incident beam.

The reason for this is that the uranium on our nose has what's called a grazing angle, or critical angle, below which all of the light reflects. This only occurs at extremely shallow angles, however, so our missile is now looking more like a long, thin needle or the blade of a rapier. Grazing angle is also dependent on the wavelength of light, as a formula in the above link shows, so the warship could try and move into the UV and X-ray portion of the spectrum to try and take out the warhead. But wouldn't you know it, uranium also happens to be potentially the best grazing-angle reflector up into the X-ray band, at over 100 times the frequency of violet light.

Mutual Defense With Two Ships

So now our missiles are pretty much unstoppable by light emitted directly from the target, which has a profound effect on our fleet tactics. It means solitary ships are virtually defenseless if all they can rely on is lasers. Even our earlier simple cylindrical missile was very much more vulnerable from the side, indicating a clear need to have defending ships cover each other with interlocking fields of fire, and now that we have our new conical super missile the need has become a requirement. We simply have to have at least two ships, or at least two lasers, widely seperated and covering each other, since neither is capable of self-defense, only defense of the companion ship.

Against this arrangement the first thing an attacker will do is try to launch an attack long a line intersecting both defending ships, where neither ship is off angle enough to mount any defense. Yet the incoming missiles are coming from far away, and the ships can circle each other to always "get in formation" as long as they've sensed the incoming missiles at a sufficient range. And if we keep our ships moderately close together, you can picture them as being at the center of a circle, whereby the line intersecting them can be rotated around just by having the one ship move some small distance relative to the other, whereas the attack missile, much further away, would have to move around the much larger perimeter of the much larger circle marking its range. You can imagine the two ships as swordsmen surrounded by enemies, circling each other to avoid presenting an opening.

Multiple attacking ships might try to attack down various axes, but to guarantee success they need to attack from a complete hemisphere, since a line through two ships always has an intersection in any arbitrary hemisphere centered on one ship or the other. The line makes two intersections with a full sphere, but we only need the one angle to guarantee the correct tactical position. But so far using two ships for mutual protection has made sure the "magic" bullet is only magic if you can use a vast swarm of them. And then of course, even if you do launch a swarm, the defending ships will try and eliminate a zone of incoming missiles, then change their mutual positions to put their ship-to-ship axis along the zone they just cleared out, so they can work on the rest of the swarm. But if the two ships are widely separated and the flight times of the missiles is very small, they might not succeed. And if the attacker eliminates one of the defending ships the other is a freebie, because of the "magic" bullet we've developed to take out lone ships.

Missile That Defeats Two Ships

Then we introduce a new innovation, a missile that's almost a disk, or very flat cone, kind of like a squashed rice hat. It's not only taking advantage of grazing angles along a single line to its front, but along an entire plane. Suddenly all it has to do is keep level with the two defending ships so that they're both firing right on its rim. Now we have a magic bullet against pairs of ships, and the defenders have to add a third ship to their formations. That still leaves open the game of the three circling swordsmen, but if you add a forth ship you can arrange them in a tetrahedron and close off all possibility of a magic, unstoppable missile. We've just put the "fleet" in space fleet tactics.

Beyond this we'll have to look at how much energy the ships can dump into an incoming missile volley, because on this will hinge the next question. Obviously if the ships can't stop a single missile, either killing it far enough out for a dodge or vaporizing it directly, then they can't hope to stop a volley, and if they can't stop a single missile just through purely thermal means then they ships of course lose, and we don't have a space fleet, at least not for long. So let's assume that our ships can stop a single missile using purely energy weapons. Yet each missile has to be targeted and fired upon, which consumes a great deal of energy, and the ships only can produce energy at a finite rate. If we attack with one missile followed by another, knowing that the defending ships can stop single threats, then the attacker is losing because he's shedding mass (and money) to no effect against an adversary that's expending neither.

Yet each fired missile requires the defender to expend energy to destroy it, and two missiles take twice the energy to destroy. Following this up, you can fire a volley that's going to require more energy to stop than the defender can produce and direct during the brief time those missiles are moving through the defended zone. So we know we can swamp his laser defenses given sufficient missiles. The question is whether the mass and cost of our missiles exceeds the mass of his ships, in which case we'd lose the game, if it was a battle of attrition.

But calculating all this is going to take a bit of math, and I'm sure I've probably exhausted your patience for now. So I'll just leave off here.

May 23, 2004 in Science | Permalink


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Excuse the optical ignorance behind the following questions: why not a missile armed with a nose cone laser of its own? Couldn't the pulsing of the missile's laser interfere with the laser fired from its target, or perhaps even damage its aperture? Or am I a total doober?

Terrific "futuretech" posts, by the way. Feel like I should be paying for this much entertainment and enlightenment. If my physics teacher was a fraction as fun as you are, I'd be building interstellar lightsails or something by now.

(Hey. Great future topic: solar sails and lightsails. I'm as fascinated as I am confused by those two subjects--and the seemingly "frail as Kleenex" materials science underlying them.)

Posted by: Dan at May 23, 2004 6:29:44 AM

Well Dan, you could put a laser on the missile, but I'm figuring that since the defending ships weigh far more than the missile, they're going to have a big advantage in optical power and beam resolution.

If the missile, which is expendable, weighed more than the target then the guy who launched the missile was probably a fool, because it's using the proverbial cruise missile to blow up camel.

However, the attacking ships might be using their volley to make the defenders respond with lasers so as to expose those very defending lasers to direct-counterfire. I haven't gone through the math on that yet, so I don't know the ranges at which it's going to occur, except that the same math about blowing off a reflector on a nosecone will apply to laser and counter-laser fire. And remember, if you can get your beam focused enough to concentrate on an enemy laser, the same optical laws indicate your telescope could also resolve it. "Target enemy weapons!" But even beyond these ranges a lasers targeting an enemy laser would be adding to its reflectors load, requiring it to reduce its power.

It may be, however, that with a fairly long tube to shield the mirror, maneuvering your ship so that the missiles in the foreground are no longer backlit by the enemy fleet, might prove a sound tactic. Not sure if the math is going to work out on that, though. It might require a tube that's longer than we'd want, or accelerations that are too high.

But since I've pointed out that missiles will work better in a volley than singly, and that the attacker is trying to use a volley that's putting stress on the defenders lasers, either in number of independently targetable beams (using their slew rate to keep them from being able to even aim at all the incoming missiles), deliverable short term power (not enough watts to deliver the required joules during the brief time available for intercept), or using multiple volleys to overwhelm the defender's thermal capacity.

Another thing I'll have to look at is that the ship need not stay at a sustainable thermal equilibrium to deliver the brief burst of power to survive the volley, and could possibly dump the excess heat into blocks of graphite or aluminum, which are then dumped overboard after that wave of the battle. Since the attacker is expending large amounts of mass in the attack, the defender probably has some leeway in pooping out some thermal waste. But I haven't gone through this math yet, either.

BTW, If you've noticed that my posting has been a bit slower lately, it's because I'm rolling this problem around quite a bit, often discussing it in LC Chat (link on the right, takes AOL Instant Messenger) with Russ Emerson from Tacjammer.

Posted by: George Turner at May 23, 2004 6:51:02 AM

Presumably, my spacecraft could have multiple lasers. Why am I using the same frequency for all of them? Why not have, say, four kinds of lasers mounted, each at a different frequency? It's much harder for him to create a coating for the missile that protects as a super-reflector against four frequencies, than for me to come up with three separate mirror coatings that each only have to work at high efficiency on one frequency. My mirrors will probably always be better than his missile coatings in that case.

Hmm. And why don't I use a bunch of small lasers, with computer coordnation so they strike the same portion of the target? That works around the difraction limit because each beam diffracts on its own, but now I have several aimed with a common center. (I'm not sure on the limits of this, but it would seem I could calibrate by test firings well enough to get the area down to less than the one-big-laser diffraction area.)

In fact, let's combine the two. Instead of one really big laser/mirror, I've got an array of, oh, forty-nine lasers at 1/49th the energy/size, each on a different frequency but targeted on the same spot (more-or-less). I think I've now radically reduced the amount of energy I need to output to get through his coating, and increased the range I can do it at.

And you know what the neatest bit is? Now that it's through the coating, the laser is boiling off armor mass -- which is now acting as reaction mass to knock the missile off course. So now the missile needs to burn reaction mass to be able to hit the targetted ship. And it's going to be hard to judge how much reaction mass to use, because it's difficult to know how much mass was boiled off . . .

Posted by: Warmongering Lunatic at May 23, 2004 7:09:52 AM

Very good point, Warmongering Lunatic.

By maintaining a mix of lasers you can assure that an optimal missile coating can't be guaranteed. Even if you tried one to play the law of averages, the defender could probably fire a millisecond but intense burst at each of the incoming missiles, then observe their change in IR signature, then swap targets between its lasers, fire again, and use the data to tune each of its lasers to the individual targets.

You're multiple laser system doesn't actually "concentrate", it just puts more energy into the beam. Four 1-meter diameter lasers would work the same as a single 1 meter diameter laser that had four times the power, which might be possible if you come up with a more efficient emitter or a better reflector. However, if I'm stuck with the same refelctor material I can make my mirror area larger (by a factor of four), and then focus that energy to a spot size that's half the size.

However, even in regular telescopes it's been noted that the cost goes up dramatically with diameter (I haven't looked at this in a couple years, but I think it's somewhere between the third and fourth power of the diameter), so a few large mirror are going to hurt your budget (and also slew slower) than a bunch of small ones. So as you start looking at massively increasing you defenses at shorter ranges, the multiple small lasers are probably a better option, both for cost and mass. They also are more redundant and thus a single chance impact by a tiny piece of high-velocity scrap is less likely to seriously degrade your defense.

Just remember that unless you get your 49 small lasers into a coherent whole (like on multiple mirror telescopes) you've just got 49 blurry images. The photons are spread out say 7 times broader, but they're also 49 times more photons to contend with.

The boiling off reaction mass might be an interesting subject though. We'll have to figure up the velocity change induced in the target. The least efficient case would be a purely symetrical pattern caused by a laser hitting from dead ahead, in which case the missile might slow down a very small bit, but still follow the same basic course as before. Hitting the missile from the sides might really effect things, though.

And I haven't got deep into sub-munitions yet, but if your beam is much wider than the missile your energy delivery may be inefficient, but if the missile kicks out submunitions they'll likely get some flash heating before clearing the beam, and thus should show up clearly in the IR spectrum. This might be important because if your ship can see the individual submunitions it can concentrate on only targeting those that intersect it's intended evasion route.

Posted by: George Turner at May 23, 2004 7:36:15 AM

"...they're going to have a big advantage in optical power and beam resolution."

So I AM a doober. :/

I did entertain that honking weight advantage business after following the laser links you provided, but shrugged it off as party pooper. I guess I'd been assuming that the remarkable miniaturization and increasing efficiency apparently going on with SSHCL over at Livermore might be a reasonable predictor of "compactness to come": scaling those diode arrays and garnet crystals and so on down-down-down from Humvee to handsized to...god only knows what in future. But there's of course a limit on effective miniaturization somewhere, leaving bigger forever better.

One of the easiest mistakes to fall into (at least for me) when thinking about future technology is the temptation to overcomplicate things and reach for effects that mirror our C.G.I. imaginations. Bad habit.

You and SDB were prudent to have limited these space combat speculations to the plausible.

Now I get to muse over EM pulse missiles turning batteships into dead hulks--at least until you disabuse your readers of that cinematic old saw too. Sigh.

And don't worry about your "slow posting lately." Ha. You're friggin' FTL with new posts compared to most bloggers.

Posted by: Dan at May 23, 2004 7:50:12 AM

Too funny, Dan!

The EM topic you raise is interesting, though. Obviously there's a few tricks still up the sleeve when it comes to the diffaction limit (link up in the original there somewhere, and a very hot topic), but it's not unlikely that the tightness of beams will be a function of their frequency, although this bias comes from my having grown up understanding that this was the case. My dad was born in 1918 and was dealt with more than one thing he wouldn't have predicted either.

Anyway, our lasers a pretty darn efficient and have a tight beam, but at lower EM frequencies like far IR and microwave I'd guess the beam spread would be more diffuse. In terms of the efficiency of delivering energy to the target my basic math on target size versus beam size would apply. However, as you'll note when you compare the results of heating your Internet cables with a laser versus applying even a miniscule amount of noise shows, total delivered energy isn't the only thing to worry about.

Human military history is in part based on comprehending a defensive flaw and then exploiting it. For example, even if the incident laser light on the incoming missile rules out a like response, deeper in the heart of that mssile may lie a microwave, X-ray, or gamma ray generator that is unmolested. This may have practical applications, because the ship that launched the missle may be too far away to tightly focus low energy things like microwaves.

Also note that the missile might simply be trying to deliver a monstrous electrical charge through contact with a tiny submunition to cause problems for the defendng craft. EM sShields could possibly alleviate this problem, or possibly not, considering how they're having a missile's worth of potentially charged atoms blow passing through.

And a further point about those defending lasers is that they require extremely precise optics pointed to extreme accuracy, and as anyone who's ever used a telescope knows, telescopes tend to be extremely sensitive to vibration. If just a few little bits of projectile arrive early, they may be able to "ring" the defensive lasers for a few seconds.

Also note that to avoid having it's aimed defensive power used efficiently, the defending ship may have to avoid any significant accelerations or impacts.

Posted by: George Turner at May 23, 2004 9:00:10 AM

With the power ranges of the lasers being discussed, and the low weight of the warheads (no second stage), wouldn't a laser impact from the side affect the flightpath of the missle, in addition to possibly destroying the reaction mass?

Even a a fraction a degree in the flightpath miles out could gain the defenders meters of extra insurance. Especially if the target is flying away from the direction the missle is being pushed.

Posted by: Eric Sivula at May 23, 2004 5:27:29 PM

Re missle steering, there was (in 1975) a British anti-tank missle called Swingfire that steered itself by swivelling the propulsion rocket nozzle. This meant that you could have the launcher down behind an embankment, launch and turn the missle 90 degrees, making it very hard to spot the launch signature. I presume the technology would work equally well in space.

Posted by: SDN at May 23, 2004 11:18:34 PM

Eric Sivula:

I think George covered your tempting "laser impact from the side" tactic in his post above. i.e.: a narrow enough missile angled "head-on" would negate the debilitating potential of any such "side-on" attack until its proximity was truly alarming. (Assuming, as George mentioned, we're only modeling a single defending spacecraft. Add a fleet and most bets against side attacks are off, presumably.)

At least I think that's what George was saying.


I'm guessing that because the only "embankments" behind which to exploit such a deceptive launch signature tactic are solid bodies (and because solid bodies represent such a vanishingly small percentage of the space "theater") the British innovation you mentioned has a similarly limited potential.

Those are my quick and dirty impressions, anyway. (And I certainly may have missed something regarding both suggestions.)

Posted by: Dan at May 24, 2004 5:11:23 AM

I think you've got it exactly Dan, but I'll still need to see if I can grasp how much a side laser might knock the missile off target.

And a further thought. I've been assuming these missiles couldn't maintain a target lock because looking forward is death to anything other than high temperature materials. Then I thought "suppose we had a pinhole in the front, a hollow missile with a few guts, where we can star at the position of the bright spot coming through the pinhole?" If we spin the missile to make it a gyroscope aligned with some arbitrary X-axis aimed at the target, the previously centered bright spot is now making sweeping circles whose radius tells use the angle to the target. Normally the defending laser would stay centered, yet if the light coming through the pinhole started to drift off center, we'd have information to work with to maneuver our missile to match the evasions of our target.

Given the light intensity we'd be dealing with, this could probably act to engage thrusters to keep us locked for a kill. And I'm not talking computer brains, I'm talking heat sensitive valves cross plumbed so that getting raked by the off-target incoming laser allow thrust to flow to recenter the beam with the axis of the warhead.

And in terms of shedding reaction mass, perhaps the energy is being supplied by the very defense laser that is firing on our missile? The defending fleet is after all supplying tremendous energy which could possibly be used to heat to boil our fuel, as if our warehead could itself become a laser energized propulsion system. BTW: That's possibly a good long range offensive use of your defensive lasers, to supply shipboard energy to your offensive missile shots by heating a fuel.

With some given rotation rate and a staggeringly strong laser signal coming through a pinhole, you can almost envision a comletely mechanical means of controlling some valves to try and keep that pinhole image centered, much like a Sidewinder that can fly on seven vacuum tubes (The Russian missile designers, when first given the Sidewinder schematics by a spy, declared the man a missile genius).

But if the exterior of our missile is melting then the pinhole would probably clog, so how about this bizarre idea. Put a little backwards facing telescope on your warhead. It's shaded from all the light the defensive fleet is hurling, assuming your not going for deep penetration.

If during the boost phase or any stage of the missile's trajectory it emited iodine or some other gas, then once it came under fire the missile's rearward facing telescope would be seeing the shadow that the missile creates on that cloud. The cloud is of course illuminated to glowing by all the counter-missile laser radiation. Even though there will be multiple lasers hitting the missile, only one will probably be close enough to the missile's spin axis to create a lock.

If at the last point the missile was updated with real data, it had its X axis pointed directly on the target, and remembered what star field it had at that point, it could maneuver in Y and Z based on the angle between the star-field snapshot during target lock and the observed angle made with its own shadow that's created by the laser that's targeting it, lighting up the thin cloud of atoms in its wake.

Basically, you were aligned for intercept when staring backwards at some star field, say Cygnus 7, with the laser shadow centered, but now that shadow is drifting in Z. Apply thrust till the drift rate stops, keep it up until you drift back to having your shadow centered on Cygnus 7, then apply opposite thrust so you don't overshoot. You should have matched the target ship's Z axis position and velocity. The same thing is happening along the Y axis. Since you know you're closing along the X axis, if you can match up Y and Z you're guaranteed a hit. And I'm not talking serious brain power here. I'm talking about control systems that could run on a dozen vacuum tubes.

Combine this with using impinging energy to heat your rocket fuel and you might have something that can keep guiding itself longer than I had envisioned. To stop such a missile you might have to burn through its entire protective shell to fry whatever it is that keeps it maneuvering. The problem is that if you make the missile twice as heavy it takes twice the energy to kill it, so we might have to drop back and do the hard math on whether this is really going to change the game we're playing.

Of course, if your enemy had such mysteriously survivable weapons your first clue might be that the first ship to survive such an attack happens to be the one that had its defense system offline for a Windows bug fix, and the ship was just accelerating for all it was worth, flying on a wing and a prayer.

"How'd you survive?"
"I couldn't shoot back"
"Hmmm... Maybe they're homing in on our lasers somehow, seeing as that they're the brightest thing in the freakin' solar system."

Posted by: George Turner at May 24, 2004 6:02:45 AM

You've done such a job countering lasers here that I'm not at all clear they're the tool for the job. Three alternatives?

Have you looked at railguns, possibly some kind of railgun shotgun? Likely any substancial physical hit will be catastrophic for missle maneuvering...

What about some kind of physical barrier to block the missles? I'm not sure you could carry enough mass to destroy the missle with such a thing, assuming you want the fleet to carry it, but I'd want to do the math. What happens to a uranium-tipped missle when it hits a soap-bubble at 12 mps?

Alternately, how about using nukes for point defense? As you pointed out earlier, ships could likely survive them at a distance of a few hundred meters; a would a nuke launched into the path of a missle might well destroy/disable it, and others in the swarm as well...?

Posted by: mike earl at May 24, 2004 10:42:55 AM

Actually, Dan, the point of my post was that you wouldn't have to have BOTH propulsion and maneuver jets; a swivelling nozzle would do for both.

Posted by: SDN at May 29, 2004 3:02:35 PM

Well Mike,

My follow up post says our missile might not actually survive the lasers, but that option you mention of making the warhead suffer a collision is a good one.

The velocity at which our solid warhead could release enough energy to self-vaporize during a collision has likely been exceeded. If I add up the boiling point multiplied by the specific heat, then add the head of fusion and vaporization, I can calculate how many Joules it takes to vaporize a kg of a particular material. Running this through KE=1/2mv^2 lets me calculate a required change in velocity to accomplish this.

ele   m/sec
Be  8815
B  10383
C  11972
Al   5242
Ti    4682
Re  3095
Ir    2795
U   2256

If the warhead was moving at this speed and hits a very much heavier object it should vaporize. If it's moving at twice this speed I should be able to vaporize it with an equal sized object, with the resultant velocity dropping to half the original through conservation of momentum.

However, since the collision is taking place beyond the speed of sound in the material, the atoms in the armor don't self-support and only those in the path of the collision come into play, which is an obscure aspect of armor design, but probably relevant in this case. So if my armor has enough thickness and mass so that the atoms in direct line with the warhead can slow the warhead's own atoms down so that the change in energy is released as head, the blob coming out the backside of our armor plate has an average velocity given by conservation of momentum of the atoms involved in the collision.

On top of this I'd think that it's now a ball of high-temperature gas expanding at rate you'd expect from apply gas laws, so you might think of the collision as a spherical explosion of a fast moving warhead, which will produce a cone of vapor. Obviously if this was the hull of a ship things would suck pretty bad, but if your ship launched a piece of steerable plate out some distance from the real hull, then the ship would only have to survive the bombardment of the molecules of the gas at the calculated velocity. The parts of your armor plate that didn't get hit (sort of a safety factor) will kick back toward the ship at some velocity you could probably determine by figuring in the maximum supportable sheer forces around the impact hole through your plate.

However, the cute part is that we set up a warhead destruction much like a head-on train collision, but in this case the defender only had to move his train a little ways into the path of the high-speed express, so the attacker had to supply almost all of the energy to create the collision. The energy advantage goes to the defender.

Posted by: George Turner at May 29, 2004 4:01:09 PM

I hadn't really thought of it as antimissles (Get Smart, anyone?), but that might work. The missle has a high velocity, but it doesn't have much acceleration, especially laterally.

Posted by: mike earl at May 29, 2004 11:00:59 PM