Atomic Rockets

Introduction

With all this frightfulness flying at your ship, you'd want some kind of defense, besides just hoping they'll miss. Go to The Tough Guide to the Known Galaxy and read the entry "SHIELD".

As mentioned before, advances in effectiveness of weapon lethality and defensive protection are mainly focused on the targeting problem. That is, the weapons are generally already powerful enough for a one-hit kill. So the room for improvement lies in increasing the probability that the weapon actually hits the target.

And the room for improvement on the defensive side is to decrease the probability of a hit.

Weapons can be improved two ways: increase the precision of each shot (precision of fire), or keep the same precision but increase the number of shots fired (volume of fire).

Precision of fire is governed by

  1. the location of the target when the weapons fire arrives
  2. the flight path of the weapons fire given characteristic of the shot and the environment though which the shot passes
  3. the weapon's aiming precision

Volume of fire is governed by

  1. the weapon's rate of fire
  2. the lethality of a given shot

A defense can interfere with the [a] location of the target by evasive maneuvers.

There isn't really a way to interfere with [b] the characteristics of a shot, short of inserting a saboteur into the crew of the firing ship. A defense can interfere with the environment through which the shot passes by such things as jamming the weapon's homing frequencies or clouds of anti-laser sand (which may work in the Traveller universe, but not in reality).

There isn't really a way to directly interfere with [c] the weapon's aiming precision (again short of a saboteur), though one can indirectly do so by decreasing the target's signature, increasing the range or jamming the firing ship's targeting sensors and degrade their targeting solution.

Finally, while one cannot do much about the [d] weapon's rate of fire, the [e] lethality of a given shot can be effectively reduced by rendering harmless shots that actually hit. This is done by armor, point defense, and science-fictional force fields.

Evasive Maneuvers

The first rule of fighting is: Don't get hit.

If you can complicate your opponent's firing solution enough (i.e., dodge enough so all the shots miss), you do not need all that heavy bulky armor. Of course, if a shot does hit, you are up doo-doo pulsar without a gravity generator.

With fighter aircraft: weapon speeds, aircraft speeds, and target ranges are such that the main targeting problem is the large angular changes the undertaken by the target (you cannot slew the gun around quick enough). With spacecraft, however, the problem is light-speed lag and weapon lag. Light-speed lag means if your target is at a range of one light-second, you are seeing it where it was located one second ago, not where it is now. Weapon lag means you have to lead your target so that your plodding weapon shot will intercept it (the technical term is "deflection").

The attacker can try to minimize this by reducing the range, or using homing weapons that guide themselves to the target. The defender will try to open the range, and use various counter-measures to confuse the weapon's guidance system.

Naturally, if the target moves at a constant velocity with no course changes, light-speed lag and weapon lag cease to be a problem. Attackers love a target wtih a perfectly predictable course. Therefore, a target that wishes to live had better dodge and jink as much as possible.

Light speed lag and weapon lag will put an upper limit on the maximum probablity that an unguided weapon will strike the target. If you dare, you can calculate it with an equation I cobbled together all by myself (which means you had better double-check it first as I have been known to make childish mistakes in algebra).

H = Cm / (0.7854 * a2 * ((Dm / 299,792,458) + (Dm / Wv))4)

where:

  • H = maximum percent chance to hit target given light-speed lag (0.0 - 1.0 with 1.0 = 100%)
  • Cm = target ship's mean cross section (m2, for a purely convex object this is approximately 1/4 of the surface area)
  • a = target's acceleration (m/s, where 9.81 = 1 g)
  • Dm = range to target (m)
  • Wv = weapon velocity (m/s)
  • 299,792,458 = meters in one light-second
  • 0.7854 = π / 4

Cm is the average target cross section. The target will be trying to orient itself so it presents the minimum possible cross section to the attacker, but the requirements of its propulsion system and other factors will interfere.

Since laser weapons travel at lightspeed (Wv = 299,792,458), for them the formula simplifies to:

H = Cm / (0.7854 * a2 * ((Dm + Dm) / 299,792,458)4)

Please note that this equation does not work if the target's acceleration is zero (since dividing by zero is mathematically undefined). In that case the target's official status is Sitting Duck and H = 1.0 or 100%. Neither does the equation work if the range is zero, in which the target's official status is At Point Blank Range or Eating The Gun Muzzle, and again H = 1.0 (Thanks to Eric Henry for pointing this out). Just remember that H cannot go over 1.0 and you'll be fine.

How was this equation derived? (just wait until you get a load of my assumptions...) Well, if H is chance to hit, a is acceleration in m/s, Dm is range in meters, and Cm is target's mean cross section:

Scircle = π * Rcircle2

where:

  • Scircle = surface area of a circle
  • Rcircle = radius of the circle
  • π = Pi = 3.14159...

H = Cm / (π * displacement2)

where:

  • displacement = maximum distance perpendicular to line of fire that the target can move in time between a shot being fired and the shot arriving at target

In other words, take the cross section surface area of the target, divide it by the surface area of the circle the target can move to, and you have your maximum hit chance. e.g., if the target has a surface area of 1, and it can displace anywhere into a circle of surface area 3, then the maximum hit chance is 1/3.

d = 0.5 * a * t2

where:

  • d = distance (m)
  • a = acceleration (m/s2)
  • t = duration of acceleration (s)

which is the classic acceleration equation, assuming a starting velocity of zero. We can assume zero because all we care about is the change in the target's current velocity, that is, the jinking

Now, to use acceleration equation to calculate displacement:

t = (Dm / 299,792,458) + (Dm / Wv)

where:

  • t = time it takes light from target to travel to targeting sensors plus time it takes weapon to travel to target (s)
  • t = time target has to jink before weapon arrives
  • Dm = range to target (m)
  • Wv = weapon velocity (m/s)
  • 299,792,458 = meters in one light-second
  • Dm / 299,792,458 = time it takes light from target to travel to targeting sensors (s)
  • Dm / Wv = time it takes weapon to travel to target (s)

d = 0.5 * a * t2

replace t with jink time

displacement = 0.5 * a * ((Dm / 299,792,458) + (Dm / Wv))2

Inserting displacement equation into hit chance equation and simplifying:

H = Cm / (π * displacement2)

H = Cm / (π * (0.5 * a * ((Dm / 299,792,458) + (Dm / Wv))2)2)

H = Cm / (π * 0.25 * a2 * ((Dm / 299,792,458) + (Dm / Wv))4)

H = Cm / (0.7854 * a2 * ((Dm / 299,792,458) + (Dm / Wv))4)

Note this equation only calculates the percentage chance of missing due to light-speed lag. There are many other factors that can contribute to a miss. However, most of these are not under control of the target.

Moment of Inertia

Roger M. Wilcox (creator of the indispensable Internet Stellar Database) spotted a major flaw with the above equation. In it, I assume that the target can instantly dodge in any desired direction. Bad assumption. Most rockets can only accelerate in the opposite direction of the main engine's thrust plume. True, a rocket can turn using its attitude control system so the plume is aimed in any desired direction, but this takes time. And it takes longer if the rocket is long and skinny like a pencil, instead of short and fat like an orange.

I was perusing your page wherein you calculate the probability for missing an accelerating target with a light-speed weapon at a distance of 1 light-second.

You carefully prefaced your equations with "Just wait'll you get a load of my assumptions" — but there's one additional assumption you were making that I think you might not be aware of. You assumed that the target's acceleration (a) could be applied in ANY randomly-chosen direction with equal ease.

This implies that the target is able to point its engine in any direction instantly, or nearly instantly. I did some calculations and discovered that it's much harder for a sizable spacecraft to rotate along its pitch or yaw axis than I thought.

Consider a modestly-sized 100 meter long spacecraft with a mass of 1000 tonnes, with a great big torch engine at the back capable of producing 20 million Newtons of thrust (enough for 2g of acceleration) and small attitude thrusters pointing sideways at its nose and tail. These attitude thrusters are what the spacecraft uses to rotate. We'll assume that the spacecraft is roughly rod shaped with its mass uniformly distributed along its length, so that its center of mass is at the 50 meter mark.

Let's say this spacecraft wants to start rotating. We want to apply a VERY MODEST angular acceleration of 1 radian per second squared — that is, after firing its attitude thrusters for 1 second continuously, its angular velocity will be 1 radian per second (it'll take 3.14 seconds to face the opposite direction at this angular speed). We fire the attitude thruster on one side of the nose, and simultaneously fire the attitude thruster on the opposite side of the tail.

How hard will each those attitude thrusters have to push?

For a rod-shaped object, the Moment of Inertia. (I) is 1/12*M*L2. Here, L = 100 meters, so I is 833 * 1,000,000 kg = 833 million. Our angular acceleration is 1 rad/s2. Thus, the total amount of TORQUE we need to apply to the spacecraft is 833 million meter-Newtons. Each of the 2 attitude thrusters will have to provide half this torque, or 416 mega-meter-Newtons each. Since each thruster is situated 50 meters from the center of mass, each will have to push with a FORCE of 416/50 = 8.33 million Newtons.

In other words, each of the ATTITUDE THRUSTERS has to produce enough thrust to accelerate the ENTIRE SPACECRAFT at 0.83 g !! The thrusters themselves would have to be torch drives!

And this is JUST to produce a very modest 1 radian/sec2 angular acceleration.

If you want to be able to point your nose in any direction in only, say, half a second, you'd need at least 12 radians/sec2 of acceleration — 24 rad/s2 if you wanted to angularly accelerate through half this angle and then angularly decelerate through the other half.

Oh, and the amount of attitude thrust force required works out to being proportional to your spacecraft's length as well as its mass. A 200 meter long 1000-tonne spacecraft would require 16.6 million Newtons from each thruster for 1 rad/s2 of angular acceleration. Note that I haven't increased the spacecraft's MASS there, JUST its length. A 200 meter long 2000-tonne spacecraft would require 33 million Newtons from each thruster.

As a side note, if a 100-meter long spacecraft WERE rotating at 1 radian/sec, everything in its nose and tail section would be pinned to the outer wall by a centripetal acceleration of 5g.

And if you keep making your spacecraft longer from nose-to-engines, there'll come a point where you can actually jink more rapidly by thrusting SIDEWAYS with your attitude thrusters than you will by rotating and using your main engine. (In my example, a 100 meter long spacecraft requires 0.83 g from its nose thruster and another 0.83g from its tail thruster to get 1 rad/s2 of angular acceleration. If you point both of those thrusters in the same direction, though, you'd get 1.66 g of acceleration sideways, which is almost as much as the 2g that its main engine can provide! You'd still have to ROLL the spacecraft to position those side thrusters onto the correct side, but rolling a rod-shaped spacecraft requires much less torque than pitching or yawing.)

Roger M. Wilcox

I too had no idea such huge amounts of torque were required (though I did know about the moment of inertia problem, having read Sir Arthur C. Clarke's short story "Hide and Seek"). Since torch drive attitude jets are highly unlikely, this drastically reduces the angle the ship's nose can be changed by, and thus drastically reduces the area the ship can dodge into. Instead of a sphere, it will be reduced to a cone sharing its long axis with the ship. The angular width of the cone will depend upon the target's moment of inertia, the torque produced by the target's attitude system, and the time it takes the weapon to fly to the target.

If your rocket exhaust is cool enough that material objects can actually survive being inserted into the exhaust plume, a possible solution to the dilemma is Cascade Vanes. So instead of making your attitude jets as big as your main engine, you actually use your main engine as an attitude jet. However, an exhaust that cool is probably way below torch rocket levels.

Excerpt from "Hide and Seek". Secret agent K-15 is being chased by enemy ship Doradus. If K-15 can survive a few hours, friendly spacecraft will come to his rescue. So to buy time, K-15 bails out of his ship in a spacesuit, and goes to ground on the tiny Martian moon of Phobos. The commander of the Doradus is most displeased.

To the layman, knowing nothing of the finer details of astronautics, the plan would have seemed quite suicidal. The Doradus was armed with the latest in ultra-scientific weapons: moreover, the twenty kilometers which separated her from her prey represented less than a second’s flight at maximum speed. But Commander Smith knew better, and was already feeling rather unhappy. He realized, only too well, that of all the machines of transport man has ever invented, a cruiser of space is far and away the least maneuverable. It was a simple fact that K-15 could make half a dozen circuits of his little world while her commander was persuading the Doradus to make even one.

There is no need to go into technical details, but those who are still unconvinced might like to consider these elementary facts. A rocket-driven spaceship can, obviously, only accelerate along its major axis-that is, "forward." Any deviation from a straight course demands a physical turning of the ship, so that the motors can blast in another direction. Everyone knows that this is done by internal gyros or tangential steering jets, but very few people know just how long this simple maneuver takes. The average cruiser, fully fueled, has a mass of two or three thousand tons, which does not make for rapid footwork. But things are even worse than this, for it isn’t the mass, but the moment of inertia that matters here — and since a cruiser is a long, thin object, its moment of inertia is slightly colossal. The sad fact remains (though it is seldom mentioned by astronautical engineers) that it takes a good ten minutes to rotate a spaceship through 180 degrees, with gyros of any reasonable size. Control jets aren’t much quicker, and in any case their use is restricted because the rotation they produce is permanent and they are liable to leave the ship spinning like a slow-motion pinwheel, to the annoyance of all inside.

In the ordinary way, these disadvantages are not very grave. One has millions of kilometers and hundreds of hours in which to deal with such minor matters as a change in the ship’s orientation. It is definitely against the rules to move in ten-kilometer radius circles, and the commander of the Doradus felt distinctly aggrieved, K-15 wasn’t playing fair.

"Hide and Seek" by Sir. Arthur C. Clarke

Compartmentalization

If the pressurized habitable section of your warship was one single area, a hull breech would depressurize the entire ship (I was going to recount the ancient joke about "why is a virgin like a balloon", but luckily good sense intervened). A prudent warship design would use air tight bulkheads to divide the interior of the pressurized section into separate areas. This comes under the heading of "not keeping all your eggs in one basket". The keyword is redundancy.

For the same reason, you'd want back-up life-support systems, power plants, control rooms, and other vital components. And these duplicate systems should be located in widely separated parts of the ship. Otherwise a single lucky enemy weapon shot could take both of them out.

Even in the non-pressurized section, bulkheads can help contain destructive effects of hostile weapons fire. So an explosive warhead, with any luck, will merely damage the interior of one compartment, instead of gutting the entire interior of the ship.

Mark Temple says:

Recently at one of the RPG boards I visit, a discussion about "armor belts" and the durability of space warships has cropped up. This got me thinking about compartments and how they'd be an integral part of a ships survival.

Modern naval vessels are divided up into compartments to make them more survivable. Compare a naval frigate to a main battle tank. A tank is basically one compartment. Breach its (very thick) armor and you wreck the tank, since the hit will usually kill the entire crew and/or destroy the internal systems.

A frigate however has multiple compartments. Breach the hull of the frigate and while you might wreck one compartment, the entire ship will still float and will often still be able to fight. You have to wreck many compartments, or very specific compartments, in order to mission-kill the ship.

It seems to me this vital part of naval design would not be overlooked in space warship design. Beyond the obvious benefits of making it easier to control atmospheric leaks, a space warship built with many compartments that can be isolated would gains a structural benefit in combat.

Now, compartments would be worthless if one hit could completely disable vital systems like life support or command-and-control. Thus all these systems would be distributed all across the ship, with multiple redundancies. Thus if you lose a compartment with life support systems, you have others to fall back on. Having the main CiC compartment destroyed will not totally eliminate your ability to control the ship. This is standard for real world navy ships. Engine systems, command rooms (bridges, CiC's, etc.) would have secondary locations kept manned in battle in case the main compartments for them are destroyed.

This is also why those compartments would be buried as deep inside the ship as possible. No sense in making things easy for your enemy. True, on modern wet navey warships bridges are still mainly at the highest point of the ship, but that's mainly to facilitate visual tracking and identification. In space, you cannot see the enemy with the naked eye anyway, so you might as well put your command centers where the enemy has to destroy the entire ship to get at it.

In science fiction movies and television, we have never really seen all of these features at once. Ironically Star Trek managed to get the distributed systems part correct, we eventually even saw that Federation starships had "battle bridges" to provide emergency control should the main bridge be damaged. But Star Trek has utterly failed to put the bridge in defended positions, or show proper compartments in their designs (As David Gerrold noted, that silly bridge perched on the saucer top of the Starship Enterprise would have been shot off a long time ago). Apparently they rely on their handwavium deflector shields to do the job, which is great until you run out of power.

(New) Battlestar Galactica came pretty close, though. The ships systems are distributed, the ship itself compartmentalized, and it has a bridge buried deep in the hull. We just never see redundant engine rooms or command centers, which is probably more of a failing of the script writers than of design.

In novels we see this idea used properly, though. The Honorverse novels showcase the benefits of compartmentalization in a very obvious and graphic form, in nearly every novel.

Mark Temple

"There are six main classes of fighting machines. The great battleships are first, weighing in the neighborhood of one million five hundred thousand tons. A battleship is almost indestructible. Even when blown completely in two, it Is exceedingly dangerous, as it maintains maneuverability and fighting power... "

...Thirty great battleships formed the front, against twenty-nine whole Tefflan battleships, but there were no less than eleven half ships in action, and each of these was fully half as deadly as a full battleship...

...A battle between battleships of space is not like a sea battle, for the battleship of space never sinks, and every portion is capable of fighting until every man within is killed; a battle between space battleships is to the death of every individual...

From The Mightiest Machine by John W. Campbell jr. (1934)

Armor

Armor is a shell of strong material encasing and protecting your tinfoil spacecraft. Unfortunately as a general rule, armor is quite massive, so it really cuts into your payload allowance.

Basically, the energy requirement to damage a surface is measured in joules/cm2. If you exceed that value, you do damage, otherwise you fail. Keep in mind that a Joule is the same thing as a watt-second.

There are three ways that weapon energy damages a surface: thermal kill, impulse kill, and drilling.

Thermal kill destroys a surface by superheating it. Impulse kill destroys a surface by thermal shock. In the calculations for the SDI, the amount to thermal kill a flimsy Soviet missile is about 1 to 10 kilojoules/cm2 (100 MJ/m2) deposited over a period of a second. The same energy deposited over a millionth of a second is required for an impulse kill. Since the laser beam tends to be meters wide, the beam energy is in the hundreds of megaJoules.

However, neither thermal kill nor impulse kill works very well with armor. So we use the third method: drilling. The amount of energy required to drill through an object is within a factor of 2 or so of the heat of vaporization of that object. There are also two other limits: the maximum aspect ratio of the hole is usually less than 50:1, and the actual drilling speed, for efficient drilling, is limited to about 1 meter per second (depending on the material).

Therefore, the best anti-laser armor will be that material with the highest vaporization energy for its mass. The best candidate is some form of carbon, at 29.6 kilojoules/gram. You do not want a form that is soft or easily powdered, or the vapor action under laser impact will blow out flakes of armor, allowing the laser to penetrate much faster. Steel has a higher vaporization energy, but it masses more as well.

Under laboratory conditions, if an armor layer was 5 g/cm2 of carbon, burning through a 1 cm2 (1.12 cm diameter) spot of armor would take about 148 kilojoules and 20 milliseconds. An AV:T laser cannon with 50 megaJoules could burn through 330 such armor layers in a few seconds, under laboratory conditions (i.e., enough layers to burn through the entire ship the long way).

However, under combat conditions there is no way one could focus the laser down that tiny and keep it on the same spot on the target ship for multiple seconds.

It would be better to use a beam focused down to a larger 10 cm2 spot (11.2 cm diameter). Granted the beam power required to penetrate jumps from 148 kilojoules to 15 megaJoules, but now if we have an uncertainty in the target's velocity of up to 5 meters per second it doesn't matter.

Of course, if price is no object, you can do better than carbon. Boron has a vaporization energy of 45.3 kilojoules/gram and is only slightly denser than carbon. Expensive, though.

In a 1984 paper on strategic missile defense, it suggested that your average ICBM would require about 10 kilojoules/cm2 to kill it. This would rise to 20 to 30 kilojoules/cm2 with ablative armor, and it would be tripled if the ICBM was spinning on its long axis since the laser couldn't dwell on the same spot 100% of the time.

As a side note, a Whipple shield is very effective at stopping hypervelocity weapons. With kinetic weapons at closing velocities in excess of 10 km/sec, you're getting into the realm where armor is less important than blow-through. For armor, you want something that will resist being turned into a plasma for as long as is possible, followed by gaps made of vacuum to make it a Whipple shield.

Anti-radiation armor is discussed here.

Sandcasters

And you can forget about laser defenses like Traveller style Sandcasters. These fire clouds of magic "prismatic" dust that provide protection from hostile laser fire. In reality they would not work. There is no way that they can project a cloud dense enough to do any good.

In Frank Chadwick's starship combat game Star Cruiser, there are anti-laser fields.

Screens are not mysterious force fields that prevent enemy weapons from penetrating. Instead they are electromagnetic fields which hold reflective particles in suspension. When a laser hits the screen, the particles reflect a portion of the laser light and then vaporize, absorbing the rest of the laser's energy. Although some energy will penetrate the screen, often the screen absorbs or reflects enough energy that the remainder is insufficient to damage the ship.

From Star Cruiser by Frank Chadwick

However, the gang at rec.arts.sf.science are skeptical:

I don't remember that thread but the idea intrigues me. Why would a levitating cloud of metallic particles be any better at protecting a ship than the same metal used to make ordinary hull plating?

It sounds ike you are just wasting energy on maintaining armor with more holes in it than conventional armor. On the other hand there may be heat dissipation issues with conventional armor. On the third hand if you have a magnetically shaped armor you could concentrate the cloud on the side you are being attacked from so you don't have to create thick armor on all sides. This could cut the weight in half or more - but levitating plates instead of a cloud would seem better suited for the task.

Michael Grosberg

Seems to me it might even be worse. If you're talking about insanely powerful laser beams, when they hit the particles they'll just turn them into projectiles that will hit the ship. It doesn't seem to me like you could plausibly get a "shield" of magnetically-levitated particles in such a way that would give you any kind of real coverage -- especially if you're positing it being used in defense against superpowerful laser beams. The beams just knock the particles out of the way and fire straight through.

I would think it's because every little metallic particle would be exposed to the beam only a short time. Then more would fill in. Like having your hull plates jump in front of any hole. Sort of. That presumes particles circulating around in this levitating cloud.

: Seems to me it might even be worse.

Well... yes, there is that. Much easier to vaporize each particle, though it might be quite hard to get a particle to actually recoil and hit the ship. Hmmm. Anyways... yes, I suspect it wouldn't really work well, and you'd have to levitation a large, large: mass of particles.

Seems like most of the particles would hit the ship. To serve their purpose, after all, they are have to be between the beam and the ship. Whether that would be really dangerous to the ship depends on how thick the "shield" is and how big each particle is.

If we're granting superpowerful laser beams, it seems to me that the energy required to displace or even vaporize these particles will be much smaller than the amount of energy in the beam, which suggests, as you say, that such a "shield" won't be of much use unless it's very thick. At some point, it seems to me you're just better off having armor; you have to carry around the extra mass anyway. But without attaching numbers it's hard to be sure.

Put simply, a layer of sand is no more effective at stopping a laser beam than a similar areal density of monolithic armor (in fact, it's a bit less effective due to structural issues); you can simply shoot holes in a cloud of sand, just like you can shoot holes in armor. As such, why spend X tons of your mass budget on temporary armor when you can just spend the same X tons on permanent armor?

In addition, a cloud of sand

  1. needs to be somewhat larger than the ship it shields (reducing areal density, and thus armor value)
  2. cannot maneuver if the parent ship maneuvers (so if you deploy sand, you're stuck in your current position)
  3. without some form of containment will simply disperse in a time frame that's comparable to the deployment time (if the cloud can cover the entire ship in 10 seconds, after 20 seconds it will have expanded to twice the size of the ship, reducing protection by a factor of 4. You can improve this time somewhat by using multiple projectors)
Anthony Jackson

Creative Measuring Units

In his novel The Wellstone, Wil McCarthy proposes a unit called the TW or "train wreck". It is measure of impulsive acceleration (i.e., from a crash or explosion) equal to an inertial acceleration of 40 g. A human being can survive a 1 TW impulse lasting no more than a couple of seconds, while a 2 TW impulse of longer than a second is typically fatal. In The Hitch-Hiker's Guide To The Galaxy, Douglas Adams creates a tongue-in-cheek unit called the "hurt", with spacecraft weapons rated in "mega-hurts". Har-har.

Force Fields

In the real world, defensive force fields do not exist. But if they did it would make things so much easier.

There are a couple of remotely possible real-world "force fields". Dr. Geoffrey Landis speaks of magnetic fields to ward off positively charged particle radiation. More on the fringe are cold plasmas, which could ward off microwaves and particle radiation. But they have a long way to go before they can stop weapon-grade particle beam weapons.

But there isn't anything like E.E."Doc" Smith's electromagnetic radiation stopping "ray-screens", nor his matter stopping "repellor screens."

There is a very good in-depth analysis of the science and issues of force fields at the alway authoritative Stardestroyer.net website here and here.

Considerations

As always when dealing with rubber science, the smart move is to nail down the ground rules for the item in question, think out all the logical consequences and implications, and stick to them.

If the force field blocks incoming laser fire, will it block your outgoing fire as well? In Isaac Asimov's "Black Friar of the Flame", a ship has to drop its field entirely in order to fire its weapons. This lead to chain reactions, ship A drops and fires, then it is hit by ship B who drops and fires, who is hit by ship C who drops and fires... In Larry Niven and Jerry Pournelle's The Mote in God's Eye, the Langston Field can have temporary holes opened to allow egress of your laser fire. In other novels, the field is on stroboscopically, that is, it flickers. It will be on, say, 80% of the time, and off for 20%. If your lasers flicker in synch with your field, 100% of their energy will penetrate. But since your opponent's lasers will probably not be in synch, only 20% of their energy will penetrate. However, if your opponent manages to match your synch rate, you'll be clobbered.

Does the force field block matter only (e.g., kinetic weapons), energy only (e.g., lasers), or both? Doc Smith had separate types of force fields for each ("repellors" and "ray-screens"), while the Langston Field would absorb both the kinetic energy of projectiles as well as the electromagnetic energy of lasers. The fields in "Black Friar of the Flame" only block energy, so the good guys get a bright idea from the Battle of Salamis.

Is the field a bubble around the ship, or flat planes that can be positioned? There was that throwaway line in the movie Star Wars, where Red Leader tells the Red Squadron X-Wing pilots to angle their deflector shields "double-front". Presumably this means rotating the rear shields to face forwards, so there is double the protection forwards and zero protection aft.

How fast can the field be charged up? The usual model is that energy is fed into the field, and each incoming shot reduces the energy in the field ("Deflector shields are down to 40%, Captain"). When the field energy reaches zero, the field goes down and the incoming weapons fire impacts directly on the ship. For dramatic reasons, it is desirable to have the rate of shield charging to be a fraction of the rate of shield reduction. Otherwise ship's shields will never go down.

Does the field obey the law of Conservation of Momentum? Say your force field generator is located in the Engineering deck. You put the force field around the ship, then quite by accident the ship crashes into an asteroid. One would expect that as the field hit the asteroid, the shock of impact would be transmitted to the field generator. You might wind up with the generator plowing through the hull and out the rear of the ship.

In Poul Anderson's novel Shield, the field has a sharp gradient on the outside, and a more gradual one on the inside. This means if you were running and collided with the shield it would feel like hitting a brick wall. But if you were inside the shield it would feel like hitting a mound of feather pillows.

Langston Field

In space combat it pretty much looks like the first to get a hit wins. This isn't really surprising; it's true of most combat these days (air combat, submarine combat, etc.). The weapons will be devastating enough that one hit will put a ship out of combat, if not vaporize it outright (i.e., they will have a very high Single Shot Kill Probability).

Larry Niven and Jerry Pournelle knew this, but wanted to write about dramatic extended space combat anyway. They contracted physicist Dr. Dan Alderson to design a self-consistent science-fictional gadget to allow this. He created the Langston Field.

In the SF trade, the Langston field is a "capacitor" or "tank" field. The field drinks up energy. It will absorb a laser beam, a nuclear blast or the kinetic energy in a coilgun shot. It then tries to radiate the energy away. However, the field cannot radiate away the energy as fast as the enemy can load the field with weapons fire. The field can only hold so much, and when the limit is reached, the field explodes, vaporizing the ship.

Also, the more destructive energy currently being held in the field, the more of the ship's own power that will be required to keep the field from exploding. If the field gets too full, the ship will not have energy to spare for movement or its own weapons.

A torpedo had penetrated her defensive fire to explode somewhere near the hull. The Langston Field, opaque to radiant energy, was able to absorb and redistribute the energy evenly throughout the field; but at cost. There had been been an overload at the place nearest the bomb: energy flaring inward...

All through Defiant nonessential systems died. It took power to maintain the Langston Field, and the more energy the Field had to contain the more internal power was needed to keep the Field from radiating inward. Local overloads produced burnthroughs, partial collapses sending bursts of energetic photons to punch holes in the hull. The Field moved toward full collapse, and when that happened, the energies it contained would vaporize Defiant. Total defeat in space is a clean death.

From "Reflex" by Larry Niven and Jerry Pournelle (the deleted first chapter of The Mote in God's Eye, collected in There Will Be War I)

Temporary "portals" or "holes" can be opened in the field to allow the ship's laser fire to hit enemy starships. Otherwise the laser beams will hit the underside of their own field. Of course the more energy being held in the field, the more difficult it is to open a hole.

Sensors are on booms so they can be extended outside of the field, otherwise the ship is blind. As the exposed sensors are blown away, the booms are retracted and fresh sensors are mounted. If the attack is ferocious enough, a ship can become blinded (i.e., all exposed sensors destroyed before any new ones can be deployed), and the enemy will quickly move out of the path of the ship's weapon fire while still pouring death and destruction into the blind ship's field. Then the blind ship frantically tries to deploy enough sensors so that at least one will last long enough to plot the position of the attacker.

Unfortunately, if the field becomes too full of energy, sensors or any other item being extended through the field will be fried or vaporized by the contained energy.

A hot field will also fry any object attempting to pass through the field en route to the ship inside (such as a shuttle containing a boarding party). Any object would also become embedded in the field, since the field also absorbs kinetic energy, unless is was moving really fast.

In a nod to E.E."Doc" Smith, when radiating, the field starts glowing red, then moves its way up the spectrum. The only thing a blinded ship can see is the color of the inside of its field.

Note the implication. When a ship's field is ten seconds from detonation, the ship is near death. But nothing has been physically damaged. If the ship is left alone long enough the field will cool off and the ship is as good as new. This made surrender a tricky proposition. If you gave too much mercy to the surrendering ship, it would recover and you'd be right back where you started.

The solution was interesting. If a ship with hot fields surrendered to you, the captain asks for a volunteer from the midshipmen. If nobody volunteers, the captain shrugs and signals to destroy the enemy ship anyway. But if there is a volunteer, they get to strap on their chest a tactical nuclear weapon with a hand detonator (dead-man switch or other fail-deadly type). Under pain of destruction, the surrendering ship has to allow the midshipmen to board, and let the midshipmen go to the control room or other vulnerable spot. You can now allow the surrendering ship's field to cool off. If it doesn't do exactly what you say, the midshipmen will detonate the bomb (you hope).

A ship in Defiant's situation, her screens overloaded, bombarded by torpedoes and fired on by an enemy she cannot locate, is utterly helpless; but she has been damaged hardly at all. Given time she can radiate the screen energies to space. She can erect antennas to find her enemy. When the screens cool, she can move and she can shoot. Even when she has been damaged by partial collapses, her enemy cannot know that.

Thus, surrender is difficult and requires a precise ritual...

...Weapons in the hand of a defeated enemy are still dangerous. Indeed, the Scottish skean dhu is said to be carried in the stocking so that it may be reached as its owner kneels in supplication...

Defiant erected a simple antenna suitable only for radio signals. Any other form of sensor would have been a hostile act and would earn instant destruction. The Imperial captain observed and sent instructions.

Meanwhile, torpedoes were being maneuvered alongside Defiant. (Captain) Colvin couldn't see them. He knew they must be in place when the next signal came through. The Imperial ship was sending an officer to take command.

Colvin felt some of the tension go out of him. If no one had volunteered for the job, Defiant would have been destroyed.

Something massive thumped against the hull. A port had already been opened for the Imperial. He entered carrying a bulky object: a bomb.

"Midshipman Horst Staley, Imperial Battlecruiser MacArthur," the officer announced as he was conducted to the bridge. ... "I am to take command of this ship, sir."

Captain Colvin nodded. "I give her to you. You'll want this," he added, handing the boy the microphone. "Thank you for coming."

..."Midshipman Staley reporting, sir. I am on the bridge and the enemy has surrendered." He listened for a few seconds, then turned to Colvin. "I am to ask you to leave me alone on the bridge except for yourself, sir. And to tell you that if anyone else comes on the bridge before our Marines have secured the ship, I will detonate the bomb I carry. Will you comply?"

From "Reflex" by Larry Niven and Jerry Pournelle (the deleted first chapter of The Mote in God's Eye, collected in There Will Be War I)

For dramatic purposes, Dr. Alderson decreed that the Langston field was subject to "local burn-throughs". That is, a given weapon strike might be too intense to be absorbed all at once, so a fraction of the damage pokes through the field into the ship. This gives enough damage to the ship to be cinematically interesting, but not enough to vaporize the ship outright or something boring like that.

This had the intended side-effect of ensuring that the ship with the best damage control crew would win the battle.

The Langston field may be science fiction, but at least it is internally self-consistent. Niven and Pournelle used it in their novel "The Mote in God's Eye", which Heinlein said was "possibly the finest science fiction novel I have ever read." High praise indeed.

In principle Defiant was a better ship than she'd been when she left New Chicago. The engineers had automated all routine spacekeeping tasks, and no United Republic spacer needed to do a job that a robot could perform. Like all of New Chicago's ships, and like few of the Imperial Navy's, Defiant was as automated as a merchantman.

Colvin wondered. Merchantmen do not fight battles. A merchant captain need not worry about random holes punched through his hull. He can ignore the risk that any given piece of equipment will be smashed at any instant. He will never have only minutes to keep his ship fighting or see her destroyed in an instant of blinding heat.

No robot could cope with the complexity of decisions damage control could generate, and if there were such a robot it might easily be the first item destroyed in battle. Colvin had been a merchant captain and had seen no reason to object to the Republic's naval policies, but now that he had experience in warship command, he understood why the Imperials automated as little as possible and kept the crew in working routine tasks: washing down corridors and changing air filters, scrubbing pots and inspecting the hull. Imperial crews might grumble about the work, but they were never idle. After six months, Defiant was a better ship, but...

From "Reflex" by Larry Niven and Jerry Pournelle (the deleted first chapter of The Mote in God's Eye, collected in There Will Be War I)

Erickson's Model

And now for something totally different. Leonard Erickson came up with an interesting model for force fields: use the equation for gas pressure.

Best fit between real formulas and the desired behavior/model was one of the gas equations. The one that has Energy equaling pressure times volume times a constant. This works ok for a closed surface type field. And leads to some interesting performance issues.

P * V = k * E

where:

  • P = pressure
  • V = volume
  • E energy
  • k = constant

Assuming k=1, you get something like 42 joules for a 1 meter radius sphere with 1 atmosphere of pressure inside. If you make k smaller, the energy requirements go up.

It "makes sense" that the bigger the enclosed volume, the more energy it'll take. And likewise for higher pressure (i.e. "stronger") fields taking more energy. One unexpected, but nice detail is that the field doesn't "use" energy. It takes energy to set it up, but that energy is "stored" in the field. So, aside from losses, you don't need to keep pumping energy in.

On the other hand, when you start considering the strength or "resistance to penetration" of a force field in terms of "pressure" (i.e. force per unit area), you suddenly realize that while holding in air is cheap, stopping bullets is gonna cost.

Another nice thing is that it would seem likely that "puncturing" the field doesn't hurt it. On the other hand, this is little comfort to the user when he finds that it wasn't turned up high enough to stop that bullet.

Leonard Erickson

Potential Barrier

Yet another possibility is the system described in Poul Anderson's novel Shield.

"So what is your invisible screen? A potential barrier?"

Surprised, he nodded. "How did you guess?"

"Seemed reasonable. A two-way potential barrier, I suppose, analogous to a mountain ridge between the user and the rest of the world. But I've determined myself, today, that it builds from zero to maximum within the space of a few centimeters. Nothing gets through that hasn't the needful energy, sort of like the escape velocity needed to get off a planet. So a bullet which hits the screen can't get through, and falls to the ground. But what happens to the kinetic energy?"

"The field absorbs it," he said, "and stores it in the power pack from which the field is generated in the first place. If a bullet did travel fast enough to penetrate, it'd get back its speed as it passed through the inner half of the barrier. The field would push it, so to speak, drawing energy from the pack to do so. But penetration velocity for the unit I've got, at its present adjustment, is about fifteen miles per second."

She whistled. "Is that the limit?"

"No. You can push the potential barrier as high as you like, until you even exclude electromagnetic radiation. That would take a much larger energy storage capacity, of course. For a given capacity, such as my unit has, you can expand the surface of the barrier at the price of lowering its height. For instance, you could enclose an entire house in a sphere centered on my unit, but penetration velocity would be correspondingly less-maybe only one mile a second, though I'd have to calculate it out to be certain."

From Shield, by Poul Anderson's (1963)

Point Defense

Point Defense is a fancy name for all the short ranged weapons and anti-missile missiles used to shoot at incoming enemy missiles. They are analogous to anti-aircraft guns.

A low powered weapon would do for defense against nuclear warheads. John Schilling says that nuclear weapons are rather complex and fragile devices, and it doesn't take much to put them out of action. And they do not undergo sympathetic detonation, i.e., they don't go boom just because you hit them real hard. So if your point-defense system can score a solid hit, the nuke is effectively useless.

Kinetic PD

Eric Rozier has an on-line calculator here that does calculation of Kinetic point defense hit probabilities (i.e., a point defence using bullets).

Modeling kinetic point defense is no easy task, the simulation I've created is a discrete event simulator which simulates individual bullets fired from a Phalanx style weapons system. The initial parameters for the CIWS are equivalent to a Phalanx with a perfect targeting computer. You can increase the number of CIWS firing at an incoming missle by increasing the number of linked CIWS, it is not as simple as multiplying the probability.

Target parameters are set to those of an AIM-9 Sidewinder missle with "infinite fuel", i.e. it will accelerate continuously during the entire simulation, regardless of the distance.

The simulation begins firing at the given range to the target in meters, simulating each shot to the target, and calculating the percentage of a hit based on the apparent velocity of the missle (muzzle velocity + target velocity), and the acceleration capabilities of the target (much as in the laser calculations on your page, but with slower than light bullets).

During each time step (of length indicated by the intershot time), all of the linked CIWS simulate a firing and calculate a hit probability, the missle then accelerates to a new velocity, the distance is shortened and provided the missle hasn't closed to minimum targeting distance, the CIWS take another shot and the joint probability is recomputed.

Eric Rozier

Missile PD

The indefatigable Eric Rozier has an on-line calculator here that does calculation of Missile point defense hit probabilities (i.e., a point defence using anti-missile missiles).

Ok, I think I've got a pretty well justified CIWS missile system. It models anti-missile missile point defense, similar to the RAM system in development by the military.

Cm = (Rb + Rt)2 * π

  • Rb is the blast radius of the kill zone for the nuclear CIWS missile.
  • Rt is the radius of the missile we're attempting to kill.
  • Cm is the cross-sectional area we must hit to kill the missile.

Hp = Cm / (π * d2)

  • d is the displacement which can be achieved by the target missile
  • Hp is the hit probability

d = 0.5 * (9.8 * (At - (Ac * e)) * t2

  • At is the acceleration (in Gs) of the target missile
  • Ac is the acceleration (in Gs) of the CIWS missile
  • e is the effectiveness of the tracking system on the CIWS missile
  • t is the time to intercept

t is calculated in my model by approximating an integral which takes into account the increasing velocity due to acceleration of both the CIWS missile and the target missile.

The end model basically models the system by calculating when the two missiles will hit, and then calculating the possible displacement the missiles can achieve. Normally with a purely kinetic kill vehicle this is calculated by the acceleration potential of the target missile during the time it takes us to intercept. In this case since we can supply active thrust, we can cancel out some of this acceleration potential. Our ability to do so is modeled as our acceleration potential multiplied by an effectiveness of our tracking system. If we have a perfect tracking system, we match them move per move to the extent our acceleration allows (i.e. if At = Ac, we hit, if At > Ac we usually miss). If it is imperfect we only get a fraction of our acceleration, as a portion of the time we are correcting mistakes, (i.e. in general if At < Ac by a ratio proportional to effectiveness we hit, otherwise we usually miss).

Eric Rozier

Laser vs. Missile

When it comes to laser point defense vs incoming missiles, there is some controversy. This is the subject of a long-running "Purple/Green" debate on SFConSim-L.

Purple/Green?

The term "Purple/Green" comes from an episode of Babylon-5 called "The Geometry of Shadows". The episode involving the ritual Drazi civil war, where the sides are chosen by randomly choosing colored sashes from a barrel. It is a science-fictional version of Miller Lite partisans shouting "Tastes Great!" and "Less Filling!".

More specifcally, as Christopher Weuve explains:

"It's the SFConsim-L brevity phrase meaning 'an argument in which no actual agreement can be reached, usually (but not always) because it is dependent on going-in assumptions.'"

Anyway the argument is about what happens in the last hundred kilometers to the target ship.

For an in-depth look go to the Rocketpunk Manifesto and read Battle of Spherical War Cows: Purple vs Green and Further Battles of Spherical War Cows. For a brief summary, see below:

The laser gang asserts that they can zap a missile before it ever gets to kill range, even for a nuclear warhead. And do it every time, at least so much of the time that missiles aren't worth firing. Even if the missile fragments into 10,000 pieces of shrapnel (each with substantial killing power), tracking gear can determine the fragments that will hit, and zap them before they reach target.

The laser gang's theory is that lasers never miss. If you can paint the target with photons to see it, you can hit it with a laser. In addition: missiles, by definition, need to close on the target, which means there are some trigonometry tricks that will allow you to lock them up hard with lasers - they can't laterally juke in space without missiing the target, for example.

The missile gang contends that laser point defense can always be saturated. Fire a big enough missile, or a salvo of missiles, coming in fast enough, and there will just be more mosquitoes than the bug zappers can zap in the short time till impact.

The missile gang's theory is that you can derive the number of missiles needed to overwhelm a given number of lasers by inputting some variables, like amount of energy per square cm needed to guarentee a kill on a missile, the wattage of output of the lasers, and the cycle/recharge time of the lasers. Lasers do require some time to recharge, and need some time to cool off.

The laser gang reply that lasers have the advantage in that they are reusable, unlike missiles. If lasers are dominant, it's also an offensive weapon to zap enemy ships, not a purely defensive one.

The missile gang retorts that the missile can be fired outside of laser range, and if it does penetrate point defense and smoke your ship, your laser is no longer reusable, now is it?

There is the cost effectiveness argument. Can you afford to carry point-defense lasers that can stop my missiles? Can I afford to carry missiles that can penetrate your point defense? Which is cheaper?

Can there be any tactics in a long-range duel between two missile armed ships? It comes down to whether you can afford to fire a missile on anything but a certain intercept, this is also ultimately a matter of cost.

Can there be any tactics in a long-range duel between two laser armed ships? It can be argued that it is the equivalent of two crack marksmen at opposite ends of a football field, shooting at each other with scope-equipped, tripod-mounted sniper rifles.

Given equal quality lasers, if I can zap you, you can zap me. Given laser ranges of at least a few hundred km, maybe a few thousand how can ships maneuver? If they are slow, it will take minutes to change position, meanwhile zapping away with multimegajoule lasers. If they are fast, they'll hurtle past each other in a drive-by, then take hours to swing around for another pass, unless they have science-fictional levels of acceleration. Possible solutions include long recharge and/or cooling-off times between laser volleys, and restricted firing arcs on the laser turrets.

The argument rages on, which probably means you can just pick which side appeals to you and be able to justify it. By carefully selecting, say, the proper minimum laser recycle time one can decide whether missiles are a viable weapon or not.

The Attack Vector: Tactical wargame adds an additional wrinkle. The laser recycle time is set such that missiles are viable. However, laser cannons have a limited number of "flash cooler" loads which can drastically cut the recycle time. But once you've used up your flash cooler loads, the laser is stuck at the standard recycle time.

Waste Heat

Radiators

The "Achilles Heel" of combat spacecraft are the heat radiators. Drives, power plants, and most weapons generate incredible amounts of waste heat. For unlimited operations, the heat has to be disposed of with radiators. However, since by their nature radiators are difficult or impossible to armor, radiators will probably be the first thing shot off by hostile weapons fire. Then you have about thirty seconds to scram the ship's reactor before the engineering section turns into a sea of molten metal. This is because shooting a hole in a spacecraft's radiator will have the same effect as shooting a hole in your automobile's radiator, except at a much higher temperature.

Droplet style heat radiators cannot be armored, but they are relatively immune to hostile weapons fire, since they are basically liquid sprays of coolant instead of physical panels. There are some notes on weapon radiators here. And before somebody mentions the "refrigerator laser" from David Brin's novel SUNDIVER, there appears to be certain theoretical reasons why it would not work. For one it probably violates the second law of thermodynamics.

And no, you cannot solve the problem by using a thermocouple to convert the heat into electricity.

Having said all that, Isaac Kuo is having second thoughts about the impossibility of armoring radiators.

The general wisdom, promulgated by the Atomic Rocket website, is that it's hard to armor a radiator and still have it be an efficient radiator.

Eric Henry

I know that's the general wisdom, and I used to believe in it...but I'm now skeptical of it. All you really need is for your armor material to be transparent to your desired operating frequency range. If diamond-like carbon is too rich for your tech, then try IR grade quartz. Either way, the basic idea is the same--your coolant fluid simply flows through tunnels in the transparent armor material. This actually makes for a more efficient radiator than the traditional design.

The traditional radiator involves coolant which conducts heat to the surrounding tubes, which then conduct heat to the radiator surface, which then radiates away heat. This armored radiator skips the conduction steps and simply radiates heat directly from the coolant.

Isaac Kuo

I tend to assume radiator wings will be lightly armored because they're big, and therefore heavy to armor. However, it doesn't seem that difficult to make radiators that are damage-tolerant enough to not be very tempting targets (the sails on age of sail ships weren't armored, but it wasn't terribly useful to shoot at them).

Anthony Jackson

Jens Bartmann disagrees with Anthony Jackson:

I beg to differ.

A sail, or more specific, the whole rigging was a very desirable target. Up to the point, special ammunition was created for bringing it down.

This is understandable, given that the rigging was the "motor" of a sailing vessel and bringing it down renders the opposing ship utterly helpless. While your opponent drifts along, you can attack at an angle where he cannot shoot back, or you can sail away if you so wish with no fear of persecution. (at least for the moment as damage control will try to set something up, Its all wood ropes and canvas after all and any self respecting ship had plenty of spares of that.)

For anti rigging weaponry have a look here around page 56. This should be somewhat similar to a spaceship with its radiators shot of, as it would be equally or even worse hampered in its abilities.

Jens Bartmann

Heat Sinks

In AV:T, ships going into battle retract their radiators into armored cubbies. They then rely upon internal heat sinks to dispose of waste heat. The good thing is that the heat sinks are armored. The bad news is that they can only store a few minutes worth of heat. This puts a severe time limit on the length of combat. Naturally a battleship will have a larger heat sink than a destroyer, but it will also have a higher waste heat level to dissipate.

If one's heat sink fills up too soon, the only option is to "strike the colors" and signal surrender to the enemy by extending the heat sinks (sort of like a dog in a dogfight surrendering by lying on its back and baring its throat). The alternative is being roasted alive as your ship melts.

Equations for heat sinks can be found here.

One concept for an orbital laser fort was to use a largish asteroid nudged into an appropriate orbit. The idea was to use the immense mass of the asteroid as a heat sink. During those long uneventful months the fort would use its radiators to cool down the asteroid as much as possible. When an attack occurs, all the fort's radiators are of course immediately retracted or are shot off by hostile fire. Both the fort and the hostiles will then commence lobbing laser beams at each other, and filling up their heat sinks with waste heat from laser cannon. However, when it comes to heat sinks, the internal sink of a warship is miniscule compared to the millions of tons of cold rock in an asteroid. It will require a fleet or two in order to even those odds.