From OSR

F

• [#nuke Nukes In Space]
  • [#boom Explosion size table]
• [#laser Laser Cannon]
• [#particle Particle Beam]
• [#kinetic Kinetic Kill]
  • [#hypervelocity Hypervelocity Weapons]
• [#missile Missiles]
• [#weird Far-Out Weapons]
  • [#antimatter Antimatter]
  • [#rbomb Relativistic Weapons]
  • [#bugs Space Bugs]
  • [#hackers Space Hackers]
  • [#ebomb E-Bombs]
  • [#propulsion Propulsion Systems]
  • [#fighters Space Fighters]
  • [#alien Alien Technology]
  • [#plasma Plasma Weapons]
  • [#tractor Tractor Beams]
  • [#medusa Medusa Weapons]
• [#classification Weapon Classifications]

When it comes to weapons, it looks like three main types: beam weapons, kinetic weapons, and missiles. Beam weapons are lasers and particle beams. Kinetic weapons are coilguns, railguns, and shrapnel weapons. Missiles are, well, missiles. Ken Burnside compared it to a policeperson armed with a service revolver, a shotgun, and a police dog. The revolver (beam weapon) cannot be dodged or outrun, but can miss. The shotgun (kinetic weapon) is more likely to hit, but with reduced lethality. The dog (missile) can be dodged or outrun (or shot, that would correspond to [rocket3y.html#pointdefense point defense]), but the blasted thing will chase you, and will always hit unless you actively prevent it. (Holger Bjerre begs to differ. He points out that kinetic weapons are less likely to hit since it can be dodged, beam weapons lose lethality with range just like shotguns, and kinetic weapons do not lose lethality with range just like revolvers. Well, no analogy is perfect...) Dave Bryant has his own analysis of spacecraft weaponry here. I'm not sure I agree with all of it, so do your own research.

Artwork by Malcolm Smith, Imagination Magazine, October 1953

From Space Dreadnoughts edited by David Drake.

One of the problems with figuring out how ships are going to fight in space (assuming that we have ships in space, which isn't as likely as I wish; and, that we're still fighting when we get there, which is unfortunately more probable) is that there are a lot of maritime models to choose from.

It's also true that some of the maritime models came from very specialized sets of circumstances; and a few of them weren't particularly good ideas even in their own time.

And it's also true that some of the writers applying the models have a better grasp of the essentials than others. For example, I recall two essays which were originally published about fifty years ago in Astounding.

In the first of the essays ("Space War", Astounding Science-Fiction, Aug 1939), Willy Ley, a very knowledgeable man who had been involved with the German rocket program, proved to my satisfaction that warships in space would carry guns, not missiles, because, over a certain small number of rounds, the weight of a gun and its ammunition was less than the weight of the same number of complete missiles. The essay was illustrated with graphs of pressure curves, and was based on the actual performance of nineteenth-century British rocket artillery ("the rockets' red glare" of Francis Scott Key).

As I say, the essay was perfectly convincing ... until I read the [rocket3z.html#jameson paired piece] by Malcolm Jameson ("Space War Tactics", Astounding Science-Fiction, Nov 1939).

Jameson's qualifications were relatively meager. Before throat cancer force him to retire, he'd been a United States naval officer -- but he was a mustang, risen from the rank, rather than an officer with the benefit of an Annapolis education. For that matter, Jameson had been a submariner rather than a surface-ship sailor during much of his career. That was a dangerous specialty -- certainly as dangerous a career track as any in the peacetime navy -- but it had limited obvious bearing on war in vacuum.

Jameson's advantage was common sense. He pointed out (very gently) that at interplanetary velocities, a target would move something on the order of three miles between the time a gun was fired and the time the projectile reached the end of the barrel.

The rest of Jameson's essay discussed tactics for missile-launching spaceships -- which were possible, as the laws of physics proved gun-laying spaceships were not. Ley could have done that math just as easily. It simply hadn't occurred to him to ask the necessary questions.

(Ed note: Malcolm Jameson wrote another essay with the intriguing name "Space-War Strategy" in Super Science Novels Magazine, March 1941. )

From Manna by Lee Correy (G. Harry Stine) 1983:

"This is a training flight to trans-lunar space with landing at Dianaport. Request permission to pass within five kilometers of you."

"Training flight? Hah!" Omer exclaimed. "Chung has give us an escort!"

"Yes, but why?" I wanted to know. "What's going on dirtside that we should know about?"

Omer shrugged. "Let Chinese escort us. It will discourage more hassle."

If the Chinese cosmolorcha wanted to escort us, there was nothing we could do about it. It was armed. Cis-lunar space is no place to get whanged; it's a long time to anywhere.

"Permission granted, Heavenly Lighting," I replied. "Be advised you are within our zone of damage if we should have a catastrophic failure." The last was pure bluff, but nobody wanted to be near a space vehicle if it catoed, regardless whether it was due to an internal or external cause.

Nukes In Space

As you should know, there are two types of nuclear weapons. An "atomic bomb" is a weapon with a war-head powered by nuclear fission. An "H-bomb" or "hydrogen bomb" is a weapon with more powerful warhead powered by nuclear fusion.

You can read all about the (unclassified) details of their internal construction and mechanism here.

Occasionally you will find a fusion weapon referred to as a "Solar-Phoenix" or a "Bethe-cycle" weapon. This is a reference to the nuclear scientist Hans Bethe and the Bethe-Weizsäcker or carbon-nitrogen cycle which powers the fusion reaction in the heart of stars heavier than Sol.

A "neutron bomb" is what you call an "enhanced radiation bomb". They are specially constructed so more of the bomb's energy is emitted as neutrons instead of x-rays. This means there is far less blast to damage the buildings, but far more lethal neutron radiation to kill the enemy troops.

You will also occasionally find references to a nasty weapon called a "cobalt bomb". This is technically termed a "salted bomb". It is not used for spacecraft to spacecraft combat, it is only used for planetary bombardment. They are enhanced-fallout weapons, with blankets of cobalt or zinc to make large quantities of deadly radioactive dust.

For missiles, consider the US Trident missile. Approximately a cylinder 13.41 m in length by 1.055 m in radius, which makes it about 47 cubic meters. Mass of 58,500 kg, giving it a density of 1250 kg/m³. The mass includes eight warheads of approximately 160 kg each.

Wildly extrapolating far beyond the available data, one could naively divide the missile mass by the number of warheads, and divide the result by the mass of an individual warhead. The bottom line would be that a warhead of mass X kilograms would require a missile of mass 45 * X kilograms, and a volume of 0.036 * X cubic meters (0.036 = 45 / 1250). Again futuristic technology would reduce this somewhat.

Nuclear weapons will destroy a ship if they detonate exceedingly close to it. But if it is further away than about a kilometer, it won't do much more than singe the paintjob and blind a few sensors. And in space a kilometer is pretty close range.

Eric Rozier has an on-line calculator for nuclear weapons.

George William Herbert says a nuke going off on [rocket3Notes.html#terra Terra] has most of the x-ray emission is absorbed by the atmosphere, and is transformed into the first fireball and the blast wave. There ain't no atmosphere in space so the nuclear explosion is light on blast and heavy on x-rays. In fact, almost 90% of the bomb energy will appear as x-rays behaving as if they are from a point source (specifically 80% soft X-rays and 10% gamma), and subject to the good old inverse square law (i.e., the intensity will fall off very quickly with range). The remaining 10% will be neutrons. There won't be any EMP, unless there is a Terra strength magnetic field and a tenuous atmosphere present.

Well, maybe a small EMP from x-rays interacting with the hull of the ship. Please, do NOT confuse EMP (electromagnetic Pulse) with EM (electromagnetic Radiation). An EMP can travel through airless space just fine, but it cannot be generated by a nuclear detonation where no atmosphere is present. Note that an EMP can be created in airless space by an [#ebomb e-Bomb], which uses chemical explosives and an armature.

For an enhanced radiation weapon (AKA "Neutron Bomb") figures are harder to come by. The best guess figure I've managed to find was up to a maximum of 80% neutrons and 20% x-rays.

A one kiloton nuclear detonation produces 4.19e12 joules of energy. One kilometer away from the detonation point defines a sphere with a surface area of about 12,600,000 square meters (the increase in surface area with the radius of the sphere is another way of stating the Inverse Square law). Dividing reveals that at this range the energy density is approximately 300 kilojoules per square meter. Under ideal conditions this would be enough energy to vaporize 25 grams or 10 cubic centimeters of aluminum (in reality it won't be this much due to conduction and other factors).

1e8 watts per square centimeter for about a microsecond will melt part of the surface of a sheet of aluminum. 1e9 W/cm² for a microsecond will vaporize the surface, and 1e11 W/cm² for a microsecond will cause enough vaporization to create impulsive shock damage (i.e., the surface layer of the material is vaporized at a rate exceeding the speed of sound). The one kiloton bomb at one kilometer only does about 3.3e7 W/cm² for a microsecond.

One megaton at one kilometer will do 3.3e10 W/cm², enough to vaporize but not quite enough for impulsive shock. At 100 meters our one meg bomb will do 3.3e12 W/cm², or about 33 times more energy than is required for impulsive shock. The maximum range for impulsive shock is about 570 meters.

Luke Campbell wonders if 1e11 W/cm² is a bit high as the minimum irradiation to create impulsive shock damage. With lasers in the visible light and infrared range, 1e9 W/cm² to 1e10 W/cm² is enough. But he allows that matters might be different for x-rays and gamma rays due to their extra penetration.

As to the effects of impulsive damage, Luke Campbell had this to say:

First, consider a uniform slab of material subject to uniform irradiation sufficient to cause an impulsive shock. A thin layer will be vaporized and a planar shock will propagate into the material. Assuming that the shock is not too intense (i.e., not enough heat is dumped into the slab to vaporize or melt it) there will be no material damage because of the planar symmetry. However, as the shock reaches the back side of the slab, it will be reflected. This will set up stresses on the rear surface, which tends to cause pieces of the rear surface to break off and fly away at velocities close to the shock wave velocity (somewhat reduced, of course, due to the binding energy of all those chemical bonds you need to break in order to spall off that piece). This spallation can cause significant problems to objects that don't have anything separating them from the hull. Modern combat vehicles take pains to protect against spallation for just this reason (using an inner layer of kevlar or some such).

Now, if the material or irradiance is non-uniform, there will be stresses set up inside the hull material. If these exceed the strength of the material, the hull will deform or crack. This can cause crumpling, rupturing, denting (really big dents), or shattering depending on the material and the shock intensity.

For a sufficiently intense shock, shock heating will melt or vaporize the hull material, with obvious catastrophic results. At higher intensities, the speed of radiation diffusion of the nuke x-rays can exceed the shock speed, and the x-rays will vaporize the hull before the shock can even start. Roughly speaking, any parts of the hull within the diameter of an atmospheric fireball will be subject to this effect.

In any event, visually you would see a bright flash from the surface material that is heated to incandescence. The flash would be sudden, only if the shock is so intense as to cause significant heating would you see any extra light for more than one frame of the animation (if the hull material is heated, you can show it glowing cherry red or yellow hot or what have you). The nuke itself would create a similar instant flash. There would probably be something of an afterglow from the vaporized remains of the nuke and delivery system, but it will be expanding in a spherical cloud so quickly I doubt you would be able to see it. Shocks in rigid materials tend to travel at something like 10 km/s, shock induced damage would likewise be immediate. Slower effects could occur as the air pressure inside blasts apart the weakened hull or blows out the shattered chunks, or as transient waves propagate through the ship's structure, or when structural elements are loaded so as to shatter normally rather than through the shock. Escaping air could cause faintly visible jets as moisture condenses/freezes out - these would form streamers shooting away from the spacecraft at close to the speed of sound in air - NO billowing clouds.

Dr. John Schilling describes the visual appearance of a nuclear strike on a spacecraft.

First off, the weapon itself. A nuclear explosion in space, will look pretty much like a Very Very Bright flashbulb going off. The effects are instantaneous or nearly so. There is no fireball. The gaseous remains of the weapon may be incandescent, but they are also expanding at about a thousand kilometers per second, so one frame after detonation they will have dissipated to the point of invisibility. Just a flash.

The effects on the ship itself, those are a bit more visible. If you're getting impulsive shock damage, you will by definition see hot gas boiling off from the surface. Again, the effect is instantaneous, but this time the vapor will expand at maybe one kilometer per second, so depending on the scale you might be able to see some of this action. But don't blink; it will be quick.

Next is spallation - shocks will bounce back and forth through the skin of the target, probably tearing chunks off both sides. Some of these may come off at mere hundreds of meters per second. And they will be hot, red- or maybe even white-hot depending on the material.

To envision the appearance of this part, a thought experiment. Or, heck, go ahead and actually perform it. Start with a big piece of sheet metal, covered in a fine layer of flour and glitter. Shine a spotlight on it, in an otherwise-dark room. Then whack the thing with a sledgehammer, hard enough for the recoil to knock the flour and glitter into the air.

The haze of brightly-lit flour is your vaporized hull material, and the bits of glitter are the spallation. Scale up the velocities as needed, and ignore the bit where air resistance and gravity brings everything to a halt.

Next, the exposed hull is going to be quite hot, probably close to the melting point. So, dull red even for aluminum, brilliant white for steel or titanium or most ceramics or composites. The seriously hot layer will only be a millimeter or so thick, so it can cool fairly quickly - a second or two for a thick metallic hull that can cool by internal conduction, possibly as long as a minute for something thin and/or insulating that has to cool by radiation.

After this, if the shock is strong enough, the hull is going to be materially deformed. For this, take the sledgehammer from your last thought experiment and give a whack to some tin cans. Depending on how hard you hit them, and whether they are full or empty, you can get effects ranging from mild denting at weak points, crushing and tearing, all the way to complete obliteration with bits of tin-can remnant and tin-can contents splattered across the landscape.

Again, this will be much faster in reality than in the thought experiment. And note that a spacecraft will have many weak points to be dented, fragile bits to be torn off, and they all get hit at once. If the hull is of isogrid construction, which is pretty common, you might see an intact triangular lattice with shallow dents in between. Bits of antenna and whatnot, tumbling away.

Finally, secondary effects. Part of your ship is likely to be pressurized, either habitat space or propellant tank. Coolant and drinking water and whatnot, as well. With serious damage, that stuff is going to vent to space. You can probably see this happening (air and water and some propellants will freeze into snow as they escape, BTW). You'll also see the reaction force try to tumble the spacecraft, and if the spacecraft's attitude control systems are working you'll see them try to fight back.

You might see fires, if reactive materials are escaping. But not convection flames, of course. Diffuse jets of flame, or possibly surface reactions. Maybe secondary explosions if concentrations of reactive gasses are building up in enclosed (more or less) spaces.

Boom Table

Note in the table below, there is some controversy over the exact values of some of these figures. Note also that the largest SI prefix is "yotta-" which is 1 x 10²⁴. For TNT equivalent, the energy of one gram of TNT was arbitrarily standardized by scientists to exactly 4184 joules (1000 thermochemical calories).

• 0.0 x 10⁰⁰ Joules: Big Bang (interpretation one)
• 1.0 x 10⁰² J: Firecracker
• 1.4 x 10⁰³ J: kinetic energy of a 3.5 g AK-74 bullet fired at 900 m/s
• 3.3 x 10⁰³ J: kinetic energy of a 9.33 g NATO rifle cartridge fired at 838 m/s
• 4.184 x 10⁰³ J: 1 gram TNT equivalent = 1 microton of TNT
• 1.3 x 10⁰⁵ J: Anti-personnel land mine (31 grams TNT charge)
• 2.1 x 10⁰⁵ J: Single round of depleted uranium from an A-10 Warthog's GAU-8 rotating cannon (1,800 rpm) = 50 grams TNT equivalent
• 8.4 x 10⁰⁵ J: 1 stick TNT (200 grams)
• 9.5 x 10⁰⁵ J: Hand grenade (226 grams of TNT charge)
• 4.184 x 10⁰⁶ J: 1 kilogram TNT equivalent = 1 milliton of TNT
• 6.1 x 10⁰⁶ J: 120mm Tank Gun KE Ammunition (KEW-A1) = 1.4 kilogram TNT equivalent
• 2.1 x 10⁰⁷ J: Anti-tank mine (5 kg TNT charge)
• 3.9 x 10⁰⁷ J: Impact energy of proposed Navy 64 megajoule railgun
• 1.2 x 10⁰⁸ J: 1 gallon of gasoline = 28 kilograms TNT equivalent
• 1.8 x 10⁰⁸ J: 1 microgram of antimatter + 1 microgram of matter = 43 kilograms TNT equivalent
• 5.3 x 10⁰⁸ J: Battleship Iowa 16 inch shell with 54 kg high explosive charge = 127 kilograms TNT equivalent
• 1.9 x 10⁰⁹ J: Tomahawk cruise missile (TLAM-C) = 454 kilograms TNT equivalent
• 4.184 x 10⁰⁹ J: 1 ton TNT equivalent
• 8.4 x 10⁰⁹ J: Oklahoma City bombing = 0.002 kiloton = 2 tons TNT equivalent
• 2.0 x 10¹⁰ J: Average lightning bolt = 4.8 tons TNT equivalent
• 3.6 x 10¹⁰ J: Average tornado = 8.6 TNT equivalent
• 4.2 x 10¹⁰ J: Davy Crockett tactical nuclear weapon = 0.01 kiloton = 10 tons TNT equivalent
• 5.0 x 10¹⁰ J: yield energy of a MOAB (Massive Ordnance Air Blast) bomb, the most powerful non-nuclear weapon ever designed = 12 tons TNT
• 1.8 x 10¹¹ J: 1 milligram of antimatter + 1 milligram of matter = 43 tons TNT equivalent
• 4.184 x 10¹² J: 1 kiloton
• 3.6 x 10¹³ J: energy released by an average thunderstorm = 9 kilotons
• 4.6 x 10¹³ J: [#rbomb Relativistic weapon]: 1 gram at 75% c = 11 kilotons
• 6.3 x 10¹³ J: 1 Hiroshima "Little Boy" = 15 kilotons
• 8.8 x 10¹³ J: Nagasaki "Fat Man" = 21 kilotons
• 1.2 x 10¹⁴ J: [#rbomb Relativistic weapon]: 1 gram at 90% c = 29 kilotons
• 1.8 x 10¹⁴ J: 1 gram of antimatter + 1 gram of matter = 43 kilotons
• 4.2 x 10¹⁴ J: W76 warhead = 100 kilotons
• 5.5 x 10¹⁴ J: [#rbomb Relativistic weapon]: 1 gram at 99% c = 132 kilotons
• 6.0 x 10¹⁴ J: energy released by an average hurricane in one second = 143 kilotons/sec
• 1.3 x 10¹⁵ J: W87 warhead = 300 kilotons
• 1.4 x 10¹⁵ J: Earthquake 6.9 on the Richter scale = 338 kilotons
• 1.9 x 10¹⁵ J: [#rbomb Relativistic weapon]: 1 gram at 99.9% c = 454 kilotons
• 2.0 x 10¹⁵ J: W88 warhead = 475 kilotons
• 2.0 x 10¹⁵ J: Earthquake 7.0 on the Richter scale = 477 kilotons
• 2.1 x 10¹⁵ J: Ivy King device = 500 kilotons (largest pure fission device ever made)
• 4.184 x 10¹⁵ J: 1 megaton = 67 Hiroshimas
• 5.0 x 10¹⁵ J: B83 nuclear bomb = up to 1.2 megatons (most powerful U.S. weapon in active service)
• 6.3 x 10¹⁵ J: [#rbomb Relativistic weapon]: 1 gram at 99.99% c = 1.5 megatons
• 1.5 x 10¹⁶ J: 1 Barringer Meteor Crater = 3.5 megatons
• 3.8 x 10¹⁶ J: B53 nuclear bomb = 9 megatons (most powerful US warhead; no longer in active service)
• 4.4 x 10¹⁶ J: Eniwetok = 10.4 megatons
• 4.6 x 10¹⁶ J: [#rbomb Relativistic weapon]: 1 kilogram at 75% c = 11 megatons
• 6.3 x 10¹⁶ J: Castle Bravo device (Bikini Atoll) = 15 megatons (most powerful US test)
• 6.3 x 10¹⁶ J: 1 Tunguska event = 15 megatons = 4.3 Barringer Meteor Craters
• 6.3 x 10¹⁶ J: Earthquake 8.0 on the Richter scale = 15 megatons
• 1.1 x 10¹⁷ J: 1 "city killer" = 25 megatons
• 1.1 x 10¹⁷ J: B41 bomb = up to 25 megatons (most powerful US bomb; no longer in active service)
• 1.1 x 10¹⁷ J: Mount St. Helens = 25 megatons = 1.6 Tunguskas
• 1.2 x 10¹⁷ J: [#rbomb Relativistic weapon]: 1 kilogram at 90% c = 29 megatons
• 1.3 x 10¹⁷ J: energy released by an average hurricane in one day = 31 megatons/day
• 1.7 x 10¹⁷ J: total energy from the Sun that strikes the face of the Earth each second = 42 megatons/sec
• 1.8 x 10¹⁷ J: 1 kilogram of antimatter + 1 kilogram of matter = 43 megatons
• 2.1 x 10¹⁷ J: Tsar Bomba device = 50 megatons (USSR, most powerful nuclear test ever)
• 2.7 x 10¹⁷ J: Star Trek photon torpedo = 1.5 kg antimatter + 1.5 kg matter = 64.3 megatons
• 3.6 x 10¹⁷ J: Earthquake 8.5 on the Richter scale = 85 megatons
• 5.0 x 10¹⁷ J: Earthquake 8.6 on the Richter scale = 120 megatons
• 5.5 x 10¹⁷ J: [#rbomb Relativistic weapon]: 1 kilogram at 99% c = 132 megatons
• 6.3 x 10¹⁷ J: 1 Krakatoa = 150 megatons = 6 Mount St. Helens
• 7.1 x 10¹⁷ J: Earthquake 8.7 on the Richter scale = 120 megatons
• 1.0 x 10¹⁸ J: Earthquake 8.8 on the Richter scale = 239 megatons
• 1.9 x 10¹⁸ J: [#rbomb Relativistic weapon]: 1 kilogram at 99.9% c = 454 megatons
• 2.0 x 10¹⁸ J: Earthquake 9.0 on the Richter scale = 477 megatons
• 2.5 x 10¹⁸ J: 1 Thera = 600 megatons = 6 Krakatoas
• 2.8 x 10¹⁸ J: Earthquake 9.1 on the Richter scale = 674 megatons
• 4.0 x 10¹⁸ J: Earthquake 9.2 on the Richter scale = 952 megatons
• 4.0 x 10¹⁸ J: energy released by the 2004 Indian Ocean earthquake (between 9.1 and 9.3 on the Richter scale)
• 4.184 x 10¹⁸ J: 1 gigaton = 1000 megatons
• 6.3 x 10¹⁸ J: [#rbomb Relativistic weapon]: 1 kilogram at 99.99% c = 1.5 gigatons
• 1.1 x 10¹⁹ J: Earthquake 9.5 on the Richter scale = 3 gigatons
• 1.8 x 10²⁰ J: 1 metric ton of antimatter + 1 metric ton of matter = 43 gigatons
• 4.184 x 10²¹ J: 1 teraton = 1000 gigatons = 1e6 megatons
• 1.5 x 10²² J: total energy from the Sun that strikes the face of the Earth each day = 4 teratons/day
• 2.5 x 10²² J: 1 Shoemaker-Levy = 6 teratons = 10,000 Theras
• 2.0 x 10²³ J: Solar flare = 48 teratons
• 3.4 x 10²³ J: 1 Dinosaur Killer = 8e7 megatons = 80,000 gigatons = 80 teratons = 13 Shoemaker-Levys
• 5.0 x 10²³ J: 1 Chicxulub Crater = 120 teratons = 20 Shoemaker-Levys
• 3.0 x 10²⁴ J: 1 Wilkes Land crater = 720 teratons = 6 Chicxulub Craters
• 4.184 x 10²⁴ J: 1 petaton = 1000 teratons
• 5.5 x 10²⁴ J: total energy from the Sun that strikes the face of the Earth each year = 1 petaton/year
• 3.2 x 10²⁶ J: Energy required blow off Terra's atmosphere = 77 petatons
• 3.9 x 10²⁶ J: total energy output of the Sun each second = 92 petatons/sec
• 6.6 x 10²⁶ J: Energy required to heat all the oceans of Terra to boiling = 158 petatons
• 4.184 x 10²⁷ J: 1 exaton = 1000 petatons
• 4.5 x 10²⁷ J: Energy required to vaporize all the oceans of Terra = 1 exaton
• 7.0 x 10²⁷ J: Energy required to vaporize all the oceans of Terra and dehydrate the crust = 2 exatons
• 2.9 x 10²⁸ J: Energy required to melt the (dry) crust of Terra = 7 exatons
• 1.0 x 10²⁹ J: Energy required blow off Terra's oceans = 24 exatons
• 2.1 x 10²⁹ J: Earth's rotational energy = 50 exatons
• 1.5 x 10³⁰ J: Energy required blow off Terra's crust = 359 exatons
• 4.184 x 10³⁰ J: 1 zettaton = 1000 exatons
• 2.9 x 10³¹ J: Energy required to blow up Terra (reduce to gravel orbiting the sun) = 7 zettatons
• 3.3 x 10³¹ J: total energy output of the Sun each day = 8 zettatons/day
• 5.9 x 10³¹ J: Energy required to blow up Terra (reduce to gravel flying out of former orbit) = 14 zettatons
• 2.9 x 10³² J: Energy required to blow up Terra (reduce to gravel and move pieces to infinity) = 69 zettatons
• 4.184 x 10³³ J: 1 yottaton = 1000 zettatons
• 1.2 x 10³⁴ J: total energy output of the Sun each year = 3 yottatons/year
• 4.184 x 10³⁶ J: 1 x 10²⁷ tons = 1000 yottatons
• 6.0 x 10³⁷ J: Nova Persei = 1.4 x 10²⁸ tons
• 1.2 x 10³⁸ J: total energy output of the Sun in ten thousand years = 2.9 x 10²⁸ tons/deca-millenium
• 4.184 x 10³⁹ J: 1 x 10³⁰ tons = 1,000,000 yottatons
• 1.0 x 10⁴⁰ J: one second's worth of output from a quasar = 2.0 x 10³⁰ tons/sec
• 1.0 x 10⁴² J: Energy in photons from a type I supernova = 0.01 foe = 2.7 x 10³² tons
• 4.184 x 10⁴² J: 1 x 10³³ tons = 1,000,000,000 yottatons
• 3.0 x 10⁴³ J: Energy needed to make the [rocket3aj.html#bubble local superbubble] (Supernova Geminga) = 0.3 foe = 7.0 x 10³³ tons
• 1.0 x 10⁴⁴ J: 1 Foe (ten to the Fifty-One Ergs, unit of supernova strength)
• 1.0 x 10⁴⁴ J: Energy in neutrinos from a type I supernova = 1 foe = 2.4 x 10³⁴ tons
• 1.3 x 10⁴⁴ J: Total radiant energy from the Sun (approximately ten billion years worth) = 3.1 x 10³⁴ tons/solar lifetime
• 3.0 x 10⁴⁴ J: Energy in photons from a type II supernova = 1.3 foes = 7.2 x 10³⁴ tons
• 1.0 x 10⁴⁵ J: Gamma-ray burster = 10 foes = 2.4 x 10³⁵ tons
• 4.184 x 10⁴⁵ J: 1 x 10³⁶ tons = 1,000,000,000,000 yottatons = 41.84 foes
• 1.0 x 10⁴⁶ J: Energy in photons from a hypernova = 100 foes = 2.0 x 10³⁶ tons
• 3.0 x 10⁴⁶ J: Energy in neutrinos from a type II supernova = 300 foes = 7.0 x 10³⁶ tons
• 1.0 x 10⁴⁸ J: Energy in neutrinos from a hypernova = 10,000 foes = 2.4 x 10³⁸ tons
• 4.184 x 10⁴⁸ J: 1 x 10³⁹ tons = 1,000,000,000,000,000 yottatons = 41,840 foes
• 3.0 x 10⁶⁹ J: Big Bang (interpretation two)

where:
 Fn = Neutron fluence (neutrons/cm2)
 Y = weapon yield (kilotons)
 R = range from ground zero (kilometers)

For bomb blasts on the surface of the Earth or other planet with an atmosphere, you can use the handy-dandy Nuclear Bomb Effects Computer, found online here. But if you really want to do it in 1950's Atomic Rocket Retro style, make your own do-it-yourself Nuclear Bomb Slide Rule!

Although it occurs to me that the jet of supersonic plasma escaping from the hole being drilled could have the combined effect of a blowtorch and grenade on anyone standing too close to the point of incidence, even if they are not directly in the beam. The effect would probably be similar to the arc flash you can get in high power, high voltage electrical systems, where jets of superheated plasma can cause severe burns from contact with the plasma, blast damage from the shock waves, blindness from the intense light produced, and flash burns from the radiated heat.

A continuous beam could have enough scattered and radiant heat to cause flash burns to those near the point of incidence, along with blinding those who are looking at the point of incidence when the beam burns through. If it burns a wide hole, people die quickly when the compartment explosively decompresses, throwing everyone into deep space. If it burns a narrow hole, the survivors who can see can just slap a patch over the hole to prevent the escape of their air.

Anthony Jackson:

Luke Campbell said: "Although it occurs to me that the jet of supersonic plasma escaping from the hole being drilled could have the combined effect of a blowtorch and grenade..."

Well, it really depends on what you're standing next to, and on how wide the beam is. The energy release at any point along the beam path will be equal to the energy required to drill through the object (so you'll get pulses of heat from each object hit), and it won't really be explosive. Flash burns is the most likely consequence.

Flash burns start at about 5 J/cm² on exposed skin, and can go above 100 J/cm² with reasonable protection. At a range of 1 meter, that requires an energy release of 0.63MJ, and once the beam is substantially inside the object, most of the flash will be deposited on the rest of the inside of the object, so it's really only object shells we need to worry about.

If the beam has an area of 50 square centimeters ( AV:T scale) to emit a total of 630 kJ it must be emitting 12.6 kJ/cm². About the same amount is probably consumed drilling through the object. 1mm of steel requires about 6 kJ/cm², so anything with a casing of at least 2mm steel, or anything comparable, will cause flash burns within 1 meter.

This is not particularly terrifying, unless of course the beam drills through something like a high pressure steam line, at which point it's suddenly very exciting, though not because of the laser per se.

Luke Campbell:

Anthony Jackson said: "so you'll get pulses of heat from each object hit, and it won't really be explosive"

My thought was that the shocks could coalesce. All shocks are supersonic to the material they have not gone through, and subsonic to the material they have traveled through. As a consequence, a second shock will catch up to a previous shock until they merge into a single, stronger shock. If the beam is pulsed at a high rate (say, a MHz or so) a good number of the individual blasts could coalesce within a short distance to create a more potent blast that might cause significant problems.

The physics of shocks is tricky, and for spherically expanding shocks you get into issues of rarefaction and backflow, which should limit the number of shocks that can coalesce. While I have a highly recommended text on shock physics, I've not had the time to look through it yet, so I don't have a good idea yet on the limits and possibilities of this mechanism.

There's also the issue that iron heated to 10,000 K, for example, will expand in volume about 150,000 times from its solid phase. So burning a 10 cm wide hole through a 1 cm steel bulkhead would produce a cloud of iron vapor with a volume of about a cubic meter if the final temperature was 10,000 K (note that if the iron was converted to a singly ionized plasma, the temperature would be ten times that much, and you would get ten times the volume). Getting caught in that incandescent cloud simply cannot be healthy.

There's also the ozone and nitrogen oxides and reactive chemicals produced as a consequence of incomplete combustion, which will not be healthy to breathe, but I expect that would be secondary.

Anthony Jackson:

Luke Campbell said: "My thought was that the shocks could coalesce."

They could if the drilling speed is supersonic. Usually it won't be.

H = C_m / (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

Now, to use acceleration equation to calculate displacement:
a = 10 * A (10 is approximately how many m/s² in one g)
t = 2 * D_L (time it takes light from target to travel to laser cannon's targeting sensors plus time it takes for laser beam to travel from laser cannon to target) where D_L = range to target (light-seconds)
d = 0.5 * a * t²
displacement = 0.5 * 10*A * 2*D_L²
displacement = 5*A * 2*D_L²

Inserting displacement equation into hit chance equation and simplifying:
H = C_m / (π * displacement²)
H = C_m / (π * (5*A * (2*D_L)²)²)
H = C_m / (78.54 * A² * (2*D_L)⁴)
Converting range in light-seconds into range in kilometers:
H = C_m/(78.54 * A² * (D_k/150,000)⁴)

Note this equation only calculates the percentage chance of missing due to light-speed lag. There are [#lasermiss many other factors] that can contribute to a miss.

where:
 RT = beam radius at target (m)
 D = distance from laser emitter to target (m)
 L = wavelength of laser beam (m, see table below)
 RL = radius of laser lens or reflector (m)

Note that frequencies below 200 nanometers are absorbed by Terra's atmosphere (so they are sometimes called "Vacuum frequencies") and anything below 10 nanometers is considered "ionizing radiation" (i.e., what the an average person on the street calls "atomic radiation"). Vacuum frequencies will be worthless for a laser in orbit attempting to shoot at ground targets protected by the atmosphere.

More to the point is the intensity of the beam at the target. First we calculate the beam divergence angle θ

θ = 1.22 L/R_L

where:
θ = beam divergence angle (radians)
L = wavelength of laser beam (m, see table above)
R_L = radius of laser lens or reflector (m)

Note that this is the theoretical minimum size of the divergence angle, it will be larger with inferior lasers.

Next we decide upon the beam power B_P, then calculate the beam intensity at the target (the beam "brightness"):

B_PT = B_P/(π * (D * tan(θ/2))²)

where:
B_PT = Beam intensity at target (megawatts per square meter)
B_P = Beam Power at laser aperture (megawatts)
D = range to target (meters)
θ = Theta = Beam divergence angle (radians or degrees depending on your Tan() function)
π = Pi = 3.14159...

There are a few notes on laser firing rates and power requirements [rocket3as.html#laserCannon here].

When figuring the tangent, remember that θ from the beam divergence angle equation is in radians, not degrees (Divide radians by 0.0174532925 to get degrees).

What this means is if you are calculating the Beam Intensity equation with a pocket calculator or the Windows calculator program, the calculator is generally set to degrees and it expects you to punch in the angle in degrees before you hit the TAN key. If you punch in the angle in radians you will get the wrong answer.

If instead you are calculating the Beam Intensity equation with a computer spreadsheet or with a computer program you are writing from scratch, the TAN() function wants the input angle to be in radians.

For comparison purposes, the average beam intensity of sunlight on your skin is about 0.0014 MW/m².

Please note that the amount of beam power deposited on the target is still B_P, the intensity just measures how tightly it is focused. It's like using sunlight through a magnifying glass to burn a hole in a piece of paper (or to incinerate ants if you were one of those evil children). The amount of beam power hitting the paper does not change, it is always B_P. But if the magnifying glass is so close that the spot size is large, the paper will just get warm. If you move the glass so the spot focuses down to a tiny dot, the intensity increases and the paper spot starts to burn.

Also note that a laser cannon might have lens/mirror which is larger than strictly required for the desired spot size, due to the fact that otherwise the mirror would melt. The larger the mirror, the more surface area to dilute the beam across, and the less the thermal stress on the mirror.

In the game Attack Vector: Tactical, the smallest laser lens is three meters in diameter, the frequency of various models of cannon is from 0.0000024 meters (2400 nanometer) to 0.0000002 meters (200 nanometer) and the efficiency varies from 20% down to 1.5%

Example: Say you have an ultraviolet (20 nanometer) laser cannon with a 3.2 meter lens. Your hapless target spacecraft is at a range of 12,900 kilometers (12,900,000 meters). The [#beamradius Beam Radius equation] says that the beam radius at the target will be about 4 centimeters (0.04 meters), so the beam will be irradiating about 50 cm² of the target's skin ([rocket3n.html#scircle area of circle] with radius of 4 centimeters). If the hapless target spacecraft had a hull of steel armor, the armor has a heat of vaporization of about 60 kiloJoules/cm³. Say the armor is 12.5 cm thick. So for the laser cannon to punch a hole in the armor it will have to remove about 625 cm³ of steel ([rocket3n.html#vcylinder volume of cylinder] with radius of 4 cm and height of 12.5 cm). 625 * 60 = 37,500 kiloJoules. If the laser pulse is one second, this means the beam requires a power level of 37,500 watts or 38 megawatts at the target.

In practice, a series of small pulses might be more efficient, causing a shattering effect and driving chips of armor out of the hole, which of course requires less energy than actually vaporizing the armor.

where:
 We = Waste power percentage
 Ce = Efficiency of Laser Cannon

where:
 CP = Laser Cannon total power (megawatts)
 BP = Beam Power at laser aperture (megawatts)
 We = Waste power percentage

where:
 WP = Waste Power (megawatts)
 CP = Laser Cannon total power (megawatts)
 BP = Beam Power at laser aperture (megawatts)

Getting rid of the waste heat from a laser is a problem if you don't dare extend your heat radiators because you are [rocket3y.html#radiators afraid they will be shot off]. A strictly limited solution is storing the waste in a heat sink, like a huge block of ice. "Limited" because the ice can only absorb so much until it melts and starts to boil. If your radiator is retracted and your heat sink is full, firing your laser will do more damage to you than to the target.

Eric Rozier has this analysis of heat sink mass:

One common mistake people make is assuming that lasers are infinite fire weapons. With proper radiators extended, this is true, but with them drawn in, to avoid being shot off, we're limited by the heat capacity of our sinking material, as you well know.

An interesting question to ask is: "Without radiators, how many shots can I get off for some mass of coolant and some sort of laser?"

Given single laser of Bp megawatts at aperture, and an efficiency of eff, duty cycle of dc, and firing time of Tf, we get the waste heat Wh (in MWseconds) as:

Wh = Tf * (Bp/eff * dc) * (1 - eff)

Wh is then the waste heat generated by a single blast from our lasers. To figure out how many times we can fire our lasers we need to perform some calculations based on our coolant, the data of interest is:

Mass of coolant dedicated to lasers (Mc) in kg
Atomic mass of coolant (Ma) in g/mol
Heat capacity of coolant (Hc) in J/(mol * K)
Melting point of coolant (Km) in K
Boiling point of coolant (Kb) in K

Given this, we can find the number of shots we can fire (S) as follows:

S = ((Mc / Ma) * Hc * (Km - Kb)) / 1000 / Wh

If you do not have the atomic mass of coolant or heat capacity of coolant, you can instead use the specific Heat capacity of coolant. This is useful if the coolant is a compound instead of an element in the periodic table.

Specific Heat capacity of coolant (Hck) in J/(kg K)
Energy Capacity of coolant in MW seconds (or MegaJoules if you prefer)

Ec = (Mc * HcK * (Km - Kb)) / 1000000

S = Ec / Wh

There is an online calculator for this here.

This assumes the coolant is just melted before firing the laser, and just boiling after firing all available shots. In reality, you want to set Kb at some level below the real boiling point, and Km at some level above the melting point.

As a worked example, a 100MW laser with efficiency of 0.2, 0.5 duty cycle, and 0.1s firing time generates 20 MWseconds of waste heat each time it fires. 1000kg of Lithium, (with about 1140K between melting and boiling) can contain enough heat to fire the laser roughly 204 times.

This, I think, helps show some of the heat limitations of lasers, and constrains them (especially as point defense weapons). You end up having to lug a lot of lithium around if you want to fire them often.

I think this is most interesting when thinking about [rocket3y.html#pointdefense point defense]. Lasers fielded as a CIWS are pretty scary, and if you could fire them infinitely often, they probably keep missiles from hitting you. So in order to constrain you from using lasers for point defense, I simply pull into laser range, threatening your radiators, and forcing you to withdraw them. As such, you can no longer afford to use a laser CIWS, and have to switch to something projectile/missile based, which is liable to be less effective.

What about a laser turret? It can be so inconvenient to have to move the entire ship in order to aim the blasted beam. As it turns out, the US Air Force has a solution created for their Airborne Laser project.

The key to preventing the laser beam from slicing the turret into pieces is to feed the beam into each rotating segment along the axis of rotation. So the olive ball has to be fed the laser beam along the pitch axis, and the black spoons fed along the roll axis.

The giant primary mirror will contain adaptive optics (i.e., it will be a "rubber mirror"). This will allow the mirror to change its focus to accommodate the range to target. In diagram "a" above, the flexible mirror is laid over a slab of piezoelectric material that changes shape as power is applied to the electrodes. In diagram "b" individual actuators are used. The image on the right is a 19-actuator deformable mirror built by Rockwell International. The mirror is only 40 cm in diameter. The actuator density is about 150 actuators per square meter, so the 1.5 meter ABL mirror would require about 270. (surface area of a circular 1.5 meter mirror is about 1.8 square meters, times 150 actuators per square meters give 270 total actuators)

[Scope4.JPG Image:Scope4THMB.jpg] [Scope3.JPG Image:Scope3THMB.jpg] [Scope2.JPG Image:Scope2THMB.jpg] [Scope5.JPG Image:Scope5THMB.jpg] [Scope6.JPG Image:Scope6THMB.jpg] [Scope7.JPG Image:Scope7THMB.jpg] [Scope8.JPG Image:Scope8THMB.jpg] [Scope9.JPG Image:Scope9THMB.jpg] [Scope10.JPG Image:Scope10THMB.jpg] [Scope11.JPG Image:Scope11THMB.jpg] [Scope12.JPG Image:Scope12THMB.jpg] [Scope13.JPG Image:Scope13THMB.jpg] [Focus1-f1E4.JPG Image:Focus1-f1E4THMB.jpg] [Focus1-f30.JPG Image:Focus1-f30THMB.jpg]

Luke Campbell has his own design for a laser turret. Cararra 5 was used to create the 3D mesh and to render the images.

Isaac Kuo has some interesting observations on the placement of turrets:

There's an interesting question of what the ideal number of turrets is. One thing that's counterintuitive is that the number of turrets has little effect on total firepower. Your laser engine(s) can fire the beam down a central corridor, with mirrors to select a branch toward any of the laser turrets. No matter how many turrets you have, you can concentrate all laser firepower through one turret.

I tend to favor two turrets on opposite sides. Besides providing all around coverage and some redundancy, it also allows use of a "hunter-killer" tactic. While one turret fires the laser to kill a target, the other turret can be scanning to "hunt" for the next target. This allows a near instantaneous switch from one target to the next, minimizing down time for the laser engine.

More importantly, this has a big tactical effect on the enemy's options. Suppose each of your ships only had one laser turret, and the enemy knows this. Then the enemy knows it takes some time for you to switch from the current targets to new targets. If the enemy notices that all of your ships are firing on particular targets, he can take advantage of this to open up sensitive sensors or radiators onboard the non-targeted ships. He knows that if you want to fire on a different target, he's got enough time to close protective "shutters". In contrast, with two turrets per ship nowhere is safe from being targeted.

Rick Robinson has a more serious concern. You know how it is a very bad idea to look through a telescope at the Sun? Well, for the same reason it is bad to unshutter your laser cannon optics and point them at a hostile ship which might zap you with its laser. Your cannon's optics would funnel their beam right down into the delicate interior of your cannon. The optics would also concentrate their beam to 10x or 100x the intensity. This means that if your lasers are unshuttered and your opponents are shuttered, you have the drop on them. The instant you detect their shutters trembling you give them a zap. Their shutters will still be opening when your bolt scrags their laser.

However, Ken Burnside says:

I will point out that the likeliest result of "shooting down the barrel of a laser" is to destroy one of the mirror elements on the focal array. Since those elements are likely to be used with adaptive optics, this won't even hurt the laser that much. It's only if the mirrors are hit at exactly the right angle that they'll direct energy back into the Free Electron Laser itself.

Anthony Jackson has another messy solution. One can design a laser cannon without a mirror or lens, if one uses a phased array. Currently we can create phased arrays for microwaves and radars, but have no idea how to do it with visible light. It would take a major technological break-through, but it is not actually forbidden by the laws of physics. Another nifty effect of phased array emitters is that they're flat and can fire at any angle (range will suffer at extreme angles), without requiring a turret assembly.

Dr. Yo came to the horrified realization that the logical acronym for PHased Array laSER was ... aiieee!

Eric Henry prefers that particular name for Free-electron laSER.

Bomb-pumped lasers do not use lenses or mirrors (because there ain't no such thing as an x-ray mirror). To calculate their beam divergence angle, use the following:

θ = 2 * (w / l)

where:
θ = beam divergence angle (radians)
w = width of lasing rod (meters)
l = length of lasing rod (meters)

A practical maximum length of a single laser rod is no more than five meters. Making the rod thinner decreases the divergence angle, but this is limited by diffraction, just like in more conventional lasers. Make the rod too narrow and diffraction actually makes the divergence angle larger. The width limit is:

(1.22*L) / w = w / l

where:
L = wavelength of laser beam (meters)
w = width of lasing rod (meters)
l = length of lasing rod (meters)

For an x-ray laser rod of one nanometer wavelength and rod length of five meters, the optimum rod width is 0.06 millimeters. The beam divergence angle will be 20 microradians.

There is a variant on the bomb-pumped laser in Larry Niven and Jerry Pournelle's classic novel Footfall, which is arguably the best "alien invasion" novel ever written. They noticed that bomb-pumped lasers is a concept that merges seamlessly with [rocket3c2.html#orion Orion drive] spacecraft. In this case the submunitions do not need a bomb. They are thrown below the pusher plate, they take aim at the enemy, then the next propulsion bomb pushes the ship and simultaneously pumps the submunitions. There is a diagram of the ship from Footfall here.

Laser guru Luke Campbell thinks it not impossible to make an x-ray laser which does NOT require a nuclear device to pump it. In theory a Free Electron laser can produce any wavelength. And while there ain't no such thing as an x-ray mirror, it is possible approximate an x-ray lens by having the rays make glancing blows off dense materials.

Bottom line is an x-ray laser is technologically very challenging, but if you manage to make one you have an Unstoppable Death Ray of Stupendous Range.

Luke Campbell:

Let's take a 10 MW ERC pumped FEL at just above the lead K-edge. This particular wavelength is used because lead is pretty much the heaviest non-radioactive element you can get, and at just above the highest core level absorption for a material you can get total external reflection at grazing angles - so no absorption or heating of a lead grazing incidence mirror. We will use a 1 meter diameter mirror. The Pb K-edge x-ray transition radiates at 1.4E-11 m. This gives us a divergence angle of 1.4E-11 radians. At 1 light second, we get a spot size of 5 mm, and an intensity of 5E11 W/m².

Looking at the NIST table of x-ray attenuation coefficients, and noting that 1.4E-11 m is a 88 keV photon, we find an attenuation coefficient of about 0.5 cm²/g for iron (we'll use this for steel), 0.15 cm²/g for graphite (we'll use this for high tech carbon materials) and 0.18 cm²/g for borosilicate glass (a very rough approximation for ceramics). Since graphite has a density of 1.7 g/cm³, we get a 1/e falloff distance (attenuation length) of 4 cm. Iron, with a density of 7.9 g/cm³, has an attenuation length of 0.25 cm. Glass, density 2.2 g/cm³, has an attenuation length of 2.5 cm.

At 1 light second, therefore, the beam is depositing 2E12 W/cm³ in iron at the surface and 7E11 W/cm³ at 0.25 cm depth; 1.2E11 W/cm³ in graphite at the surface and 5E10 W/cm³ at 4 cm depth; and 2E11 W/cm³ in glass at the surface and 7E10 W/cm³ at 2.5 cm depth. Using 6E4 J/cm3 to vaporize iron initially at 300 K, we find that iron flashes to vapor within a microsecond to a depth of 0.9 cm. The glass, assumed to take 4.5E4 J/cm³ to vaporize (roughly appropriate for quartz) will flash to vapor within a microsecond to a depth of 4 cm within a microsecond. Graphite, at 1E5 J/cm³ for vaporization, will flash to vapor to a depth of 0.7 cm within a microsecond (the laser performs better if we let it dwell on graphite for a bit longer, we get a vaporization depth of 10 cm after ten microseconds).

Net conclusion - ravening death beam at one light second.

Now lets look at one light minute. The beam is now 30 cm across. This is much deeper than the attenuation length in all cases, so we will just find the radiant intensity and the equilibrium black body temperature of that intensity. We have an area of 7E-2 m², and an intensity of 1.4E8 W/m². You need to reach 7000 K before the irradiated surface is radiating as much energy away as heat as it is receiving as coherent x-rays. The boiling point of iron is 3023 K, the boiling point of quartz is 2503 K, and the sublimation temperature of graphite is 3640 K. All of these will be vaporized long before they stop gaining heat. At this range, the iron is subject to 5.6E8 W/cm³ at the surface, the graphite to 3.3E7 W/cm³ at the surface, and the glass to 5.6E7 W/cm³ at the surface. Using the above values for energy of vaporization, we get about 0.1 milliseconds before the iron starts to vaporize, 0.8 milliseconds before the glass starts to vaporize, and 3 milliseconds before the graphite begins to vaporize (because of its long attenuation length, once it begins to sublimate, graphite sublimates rapidly to a deep depth, while you essentially have to remove the iron layer by layer).

Net conclusion - still a ravening death beam at one light minute.

What about at one light hour? The beam is 18 meters across. The equilibrium black body temperature is 900 K. This is well below the melting point of most structural materials. Ten megawatts, however, is a lot of ionizing radiation. Any unhardened vehicle will be radiation killed at these ranges.

However, he goes on to note that in order to boost electrons to the velocities required for an X-ray free electron laser, you will need an acceleration ring approximately one kilometer in diameter. So this X-ray laser would only be suitable for exceedingly huge warships, orbital fortresses, and Death Stars.

A more scientifically plausible but much less dramatic laser weapon is the combat mirror. In this scheme, the spacecraft doesn't have a laser, just a large parabolic mirror. The laser is several million miles away, on a freaking huge solar power array orbiting your home planet. You aim the mirror so it will do a bank shot from the distant laser to your target and tell the laser crew to let'er rip. About fifteen minutes later the diffuse laser beam arrives, and your parabolic mirror focuses it down to a megaJoule pinpoint on your target.

They have a disadvantage of possessing a much shorter range. The beam tends to expand the further it travels, reducing the damage density ("electrostatic bloom"). This is because all the particles in the beam have the same charge, and like charges repel, remember? Self-repulsion severely limits the density of the beam, and thus its power.

They also can be deflected by charged fields, unlike lasers. Whether the fields are natural ones around planets or artificial defense fields around spacecraft, the same fields used to accelerate the particles in the weapon can be used to fend them off.

Particle beams can be generated by linear accelerators or circular accelerators (AKA "cyclotrons"). Circular accelerators are more compact, but require massive magnets to bend the beam into a circle. This is a liability on a spacecraft where every gram counts. Linear accelerators do not require such magnets, but they can be inconveniently long.

Another challenge of producing a viable particle beam weapon is that the accelerator requires both high current and high energy. We are talking current on the order of thousand of amperes and energy on the order of gigawatts. About 1e11 to 1e12 watts over a period of 100 nanoseconds. The short time scale probably means quick power from a slowly charged capacitor bank, similar to the arrangement in a typical camera strobe. You want a very thin beam with a very high particle density, the thinner the better and the more particles the better. The faster the particles move the more particles will be in the beam over a given time, i.e., the higher the "beam particle current" and the faster this current flows, the more energy the beam will contain.

The power density is such that the accelerator would probably burn out if operated in continuous mode. It will probably be used in nanosecond pulses.

Protons are 1836 times more massive than electrons, so proton beams expand only 1/1836 times as fast as electron beams and are 1836 times harder to deflect with charged fields. Of course they also require 1836 times as much power to accelerate the protons to the same velocity as the electrons.

It is possible to neutralize the beam by adding electrons to accelerated nuclei, or subtracting electrons from negative ions. While this will eliminate electrostatic bloom, the neutralization process will also defocus the beam (to a lesser extent). As a rough guess, maximum particle beam range will be about the same as a very short-ranged laser cannon.

For a neutral particle beam, the divergence angle is influenced by: traverse motion induced by accelerator, focusing magnets operating differently on particles of different energies, and glancing collision occurring during the neutralization process. The first two can be controlled, the last cannot (due to Heisenberg's Uncertainty Principle). The divergence angle will be from one to four microradians, compared to 0.2 for conventional lasers and 20 for bomb-pumped lasers.

The source of the particles for the beam come from sophisticated gadgets with weird names like "autoresonantors", "inertial homopolar generators", and "Dundnikov surface plasma negative ion sources".

Dr. Geoffrey A. Landis had this to say:

Particle beams disperse for a lot more reasons than laser beams, unfortunately, so it's harder to give a simple formula. It will depend on things like magnetic and electric fields in the region between the source and the target (if the particles have spin, for example, they will couple to the magnetic field gradient even if they are neutral).

However, for a neutral particle beam traversing empty, field-free space, the dispersion is proportional to the temperature of the beam. Using, for the sake of a simple example, a mercury ion beam (dispersion decreases proportional to square root of atomic mass, and mercury is a convenient high-mass atom that ionizes easily), the lateral (spreading rate) velocity of the beam is:

V = 1.4 SQRT(T) m/sec, for T in Kelvins

To calculate the actual angular spread of the beam, you need to know the beam velocity. For a quick calculation, you could say it's no more than the speed of light, 300,000,000 m/sec. So the dispersion in nano-radians is 5 SQRT(T).

So, for a beam with an effective temperature of, say, 1000K, dispersion for mercury is 150 nR, or 0.15 micro-radians. Dispersion at a distance of 100,000 km would be 0.015 km, or 15 meters. A hydrogen beam would disperse SQRT(80)= 9 times more.

[note that if the beam is actually relativistic, you have to apply a relativistic correction, which I'll ignore here.]

I'm not sure I have this correct, but to put this in useful form:

θ = (5e-9 * Sqrt[B_T]) * Sqrt[80/B_n]

where:
B_T = beam temperature (Kelvin)
B_n = atomic number of element composing the beam (Uranium = 92, Mercury = 80, Zirconium = 30, Calcium = 20, Neon = 10, Hydrogen = 1)
θ = Beam divergence angle (radians)

R_T = Tan(θ) * D

where:
D = distance from particle beam emitter to target (m)
R_T = radius of beam at target (m)

...making sure that Tan() is set to handle radians, not degrees. Or as one big ugly unified equation:

R_T = Tan((5e-9 * Sqrt[B_T]) * Sqrt[80/B_n]) * D

...again making sure that Tan() is set to handle radians, not degrees. I must stress I derived this equation myself, so there is a chance it is incorrect. Use at your own risk.

While particles cannot travel at the speed of light, they can get close enough that it is hard to tell the difference. Unfortunately, particle beams do obey the inverse-square law.

A beam of neutrons does not suffer from electrostatic bloom since they have no charge, nor could they be deflected by charged fields. However, this also means it is difficult to accelerate the neutrons in the first place (and if you discovered a new way to do it, chances are it too could be used as a defense). Without electrostatic bloom neutron beams are only limited by "thermal bloom". Brett Evill says this will give a neutron beam an effective range of 10,000 km, but he doesn't mention the details of this estimate. Nelson Navarro is of the opinion that a science fictional heavy neutron beam could be produced by a science fictionally efficient method of breaking up deuterium nuclei.

Another problem is one shared by ion drives, the "space charge." If you keep shooting off electron beams you will build up a strong positive charge on your ship. At some point the charge will become strong enough to bend the beam. And the moment your ship tries to dock with another it will be similar to scuffing your shoes on the rug and touching the doorknob. Except instead of a tiny spark it will be a huge arc that will blow all your circuit breakers and spot-weld the ships together.

Don't try to neutralize the charge by firing off positively charged proton beams. John Schilling warns that space is filled with an extremely low-density, but conductive, plasma. You try to eject charge from your ship, and the ship itself becomes part of a current loop. Not only is the current flowing through the hull (or trying to) likely to cause problems, but all those electrons or protons being sucked in produce X-rays on hitting the hull.

Anthony Jackson says if you crank up your particles to a few GeV per nucleon they will be in the soft end of the spectrum of primary cosmic rays. Each particle will be highly penetrating, and you no longer need to actually focus the beam. Just apply a couple megajoules per square meter and everything dies (unless it's behind a huge amount of shielding or is basically operating at pre-microchip levels of automation. Neither is an option for a surface mounted weapon turret.). We are talking about a surface radiation level of over 500 grays. Such a cosmic ray beam would require armor with a [#TVT TVT] (for radiation purposes) peaking at 200-300 g/cm².

Also note that if the particles are moving a relativistic velocities higher than, say, 90% c, you will have about the same energy release if the particles are matter or antimatter. In other words, it is pointless for relativistic particle beam weapons to use antimatter, with all the added complexity due to antimatter manufacture and storage.

Ships that expect to be fired upon by particle beam weapons would be well advised to add a layer of paraffin or other [rocket3ah.html#radarmor particle radiation armor] on the outside of their metal hull, to prevent the beam from generating Bremsstrahlung with the hull.

K_e = 0.5 * M * V²

where:
K_e = kinetic energy (Joules)
M = mass of projectile (kg)
V = velocity of projectile relative to target (m/s)

W_p = K_e * (1 / W_e)

where:
W_p = power required by weapon to fire one projectile (Joules)
K_e = kinetic energy of one weapon projectile (Joules)
W_e = efficiency of the weapon (0.0 = 0%, 1.0 = 100%)

Rick Robinson's First Law of Space Combat states that "An object impacting at 3 km/sec delivers kinetic energy equal to its mass in TNT." In other words there are 4,500,000 joules in one kilogram of TNT (3,000²m/s * 0.5 = 4.5e6). This means a stupid bolder traveling at 2,000 km/sec relative has about 400 kilo-Ricks of damage (i.e., each ton of rock will do the damage equivalent of 2e12 / 4.5e6 = 400 kilotons of TNT or about 20 Hiroshima bombs combined).

Ricks = (0.5 * V²) / 4.5e6

where:
V = velocity of projectile relative to target (m/s)
Ricks = kilograms of TNT worth of kinetic energy per kilogram of projectile

So a projectile moving at 200 km/sec (20,000 m/s) would have about 4,000 Ricks (4 kilo-Ricks) of damage, approximately the same as a standard one-kiloton-yield nuclear weapon. By that I mean it has the same damage per kilogram as a nuke, counting all the nuke's framework, electronics, fissionable material, and whatnot. (for the projectile to do the same damage as a standard nuke, it would need to be the same mass as a standard nuke, about 250 kilograms) A projectile moving at 3,500 km/sec would have about one mega-Rick, which is the same damage per kilogram as the ultra-compact 475-kiloton-yield W-88 nuclear warhead.

As a rule of thumb, anything with more than 100 Ricks (i.e., over 30 km/sec relative) does weapons-grade levels of damage.

And if you are thinking in terms of bombarding your enemy with asteroids, as a rule of thumb an asteroid's mass will be:

M_a = 1.47e4 * (R_a³)

where:
M_a = mass of asteroid (kg) R_a = radius of asteroid (m)

Example: The wet navy battleship Iowa had 16-inch guns. They fired shells which massed about 2000 pounds (907 kg), carried a charge of 145 pounds (54 kg) of high explosive, and traveled at about 820 meters per second. By the kinetic equation above, they contained about 3.0e8 joules of kinetic energy. There are about 4.184e6 joules per kilogram of TNT (which is different from the value used in Rick Robinson's equation, if this annoys you, take it up with him) so the explosive charge contains about 2.3e8 joules of energy.

This means one 16-inch shell does about 3.0e8+2.3e8 = 5.3e8 joules of damage.

Floyd has spent the last 8.6 boring months in the good scoutship Peek-A-Boo, traveling from Mars to Earth in a hohmann orbit. Suddenly he notices a convoy raider from the Asteroid Revolutionary Navy accelerating from low Earth orbit into a Martian hohmann transfer orbit.

Unfortunately for Floyd, scoutships are unarmed. But since the two ships are traveling in opposite directions at a fair speed, anything Floyd can throw at the raider will be good for quite a few Ricks. How massive an object will Floyd have to hurl in order to inflict the same damage as a 16-inch shell?

For the raider to leave LEO and enter Earth Escape orbit takes about 3.17 km/s. To leave Earth Escape and enter Mars Hohmann orbit takes 2.95 km/s. So the raider has about 6.12 km/s relative to Earth.

therefore

In AV:T are kinetic weapons called "Kirklin mines" (invented by Kirk Spencer). They are dirt cheap chemical fueled anti-missile weapons, specifically anti-Torch missile weapons. The ideas is that they cost a fraction of the price of a missile, yet can scrag it. Using the magic of relative velocity, all they have to do is get in the way (this is why they are used against torch missiles, if the relative velocity isn't large enough the mine might not do enough damage to mission-kill the missile).

Launched at the proper time a Kirklin mine can either take out the incoming missile while it is too far away to damage the targeted ship, or force the missile to miss the ship entirely in the process of avoiding the mine (if the mine is launched too soon the missile has enough time to zig-zag around it and still kill the ship). Since they are cheaper, a given spacecraft can carry several mines for every missile their equivalent opponent ship has.

The current thinking is the only way a torch missile can avoid being neutralized by Kirklin mines is by becoming a bus carrying sub-missiles and decoys. Of course for a modest increase in cost the mines can become buses as well...

Hypervelocity Weapons

A special type of kinetic weapon is the hypervelocity weapon. These come in two types: rail guns and coil guns.

However, once the speed of the projectile surpasses about 14% the speed of light (42,000 kilometers per second), it is no longer a strict hypervelocity weapon, it has become a [#rbomb relativistic weapon].

Advantages are simple construction, disadvantage is the severe rail erosion each projectile causes, requiring frequent replacement of rails (some prototypes required replacement after each use). The rails need massive braces, since they are under tremendous force trying to repel the rails from each other.

I tried to derive some values for the above weapons system and produced the following analysis. It turned out to be totally wrong, I reproduce it here so you can see my mistakes:

225 nautical miles in six minutes is an average velocity of 463 meters per second. The best estimate I could find in a five minute Google search for the mass of a Ford Taurus is 3111 pounds or about 1400 kg. 3111 pounds at 380 mph is 1400 kg at 170 m/s. K_e = 0.5 * M * V² so the Ford Taurus will hit with about 2e7 joules or 20 megajoules. About the equivalent of 4.5 kilograms of TNT (170 m/s is about 0.003 Ricks of damage). I guess the other 44 megajoules are lost due to wind resistance.

Working the other way, we can take the 463 m/s average velocity and the 64 megajoule power consumption. K_e = 0.5 * M * V² therefore M = K_e / (0.5 * V²). This means the projectile mass is around 600 kg.

As I said, the above analysis is incorrect. Lucky for me, a gentleman named Thomas Rigby appeared and set matters straight:

Thomas Rigby:

I noticed some deficiencies in your analysis of the Navy's proposed 64 MJ railgun system, particularly in your derived velocity. The M1 Abrams main gun fires a FSAPDA round somewhere between 1200 and 1800 m/s (can�t remember exactly), so why would the Navy put so much unto a system that only fires at a third the velocity?

I also remember reading a Popular Science article on the new features of the DD(X) project, one of which is the railgun. According to the article the railgun would fire a 40 pound projectile (about 18.2 kg) with a Mach 8 muzzle velocity and Mach 7 velocity at the target. A quick calculation (setting speed of sound a 343 m/s):

KE = ½ (18.2 kg) (2401 m/s)² = 52.46 MJ

KE = ½ (18.2 kg) (2744 m/s)² = 68.52 MJ

Which compares much more favorably as a weapon system. Derived values can easily be obtain close to these numbers

We�ll take the average range, 225 nmi, for the calculations. Of course we can�t just convert 225 straight to meters, since a nautical mile is a bit over 15% longer than a standard mile (about 6076 feet). After converting to miles we can go to meters (or go straight from nmi to meters, if your calculator has a bunch of built-in conversion factors):

1nmi = 1.151mi

225nmi (1.151nmi / mi) = 258.975mi

1mi = 1.609km = 1609m

x = (258.975mi) (1609m / mi) = 416690.775m

Real Value: 416700 m

Dividing by the time (6 min / 360 sec):

V_x = 416700m / 360s = 1157.5 m/s

Which s a far more appropriate velocity for a kinetic kill weapon. However, this is only part of the velocity. The railgun fires in a parabolic arc, getting almost 95 miles up. Assuming the Earth is flat, and the projectile is launched and lands at the same height, this part of the velocity component is easy to calculate. In theory the projectile reaches its maximum height half way through the journey, or at 3 min - 180 s. We can put this into the gravity-displacement equation to determine the speed. A height of 95 miles (500,000 feet) is about 152400 m.

h = -4.9t² + vt ⇒ v = (h / t) + 4.9t

V_y = (152400m / 180s) + (4.9 m/s²)(180s) = 1728.67 m/s

Now we can combine the two velocity components to determine the actual velocity, by Pythagorean Theorem.

V_T = √(1157.5² + 1728.67²) = 2080.41 m/s

Which is much closer to the Mach 7 value that the Navy claims the projectile hits at. Using this value to calculate the kinetic energy:

KE = ½ (18.2 kg) (2080 m/s)² ≈ 39 MJ

Ken Burnside notes how difficult it is to calculate the damage caused by a solid shell:

In terms of how ships survive taking damage, there is also the matter of rate of deposition to the target and area of deposition.

Basically, you're poking holes in a compartmentalized object. Unlike an aircraft, or a submarine, the outside environment isn't that hazardous. It doesn't take much damage to make a jet fighter unflyable at air combat speeds. Getting hit with a torpedo in a sub can cause the hull to collapse.

Hitting a spaceship won't cause it to pop like a balloon. There's likely a swath of compartments that are uninhabitable at this point...but the ship can still fight.

For example, an M1A2's main gun is about a 5" naval gun -- firing an armor piercing round, at a target that wouldn't quite actually be a full sized Naval compartment. Very rarely does it leave an exit wound in the back of an enemy tank, which is the indicator of what it would do to the NEXT compartment of a ship. It WILL destroy everything in that compartment, unless its blunted by hitting an engine in the way (like the Merkava design of the IDF).

For point of reference, an M1A2's round has a velocity of about 1600-1700 m/s. Mass between 3.5 and 4 kg, diameter about 2.5 cm.

Quite simply, there isn't a lot known about the interaction dynamics of objects impacting at 1.5+ kips. One field says that they'll turn into a plasma spray (more or less what happens when a tank round hits a tank...), which limits their damage to the compartment hit. Another says they'll get a plasma sheathe and go through multiple compartments shedding a bit of energy (but far less than the total carried by the round) in each, and exit the back of the ship.

Either of these makes for a more interesting fight than "gee, one hit, one kill, no stealth."

Isaac Kuo is of the opinion that hypervelocity weapons will have limited penetration. He notes that a projectile has both kinetic energy and momentum. Momentum is what keeps the projectile moving in its direction of motion.

Now, if you look at the equations for kinetic energy and momentum, you will note that as the velocity rises the kinetic energy goes up much faster than momentum (1/2 velocity squared vs just plain velocity).

K_e = 0.5 * M * V²

p = M * V

So Mr. Kuo figures that the greater your ratio of kinetic energy to momentum, the more spherical the resulting explosion and the less penetration into the interior you will get. This means hypervelocity weapons can be stopped (for a while) by a Whipple shield (until it is shot full of holes). Whipple shields are set at some distance from the hull, if the spacing is larger than the radius of the explosion, the shield takes damage but the hull does not.

I'm still looking for more details on this, especially the mathematical relationship between the ratio and the explosion sphericality.

3D artist Scott Halls has made an amazing website illustrating technical information about Peter F. Hamilton's Night's Dawn trilogy. Above are the "Combat Wasps", which are a sort of armed drone. Left to right are the Kinetic Harpoon, Electronic Warfare, Fusion Torpedo, and Particle Beam Cannon Wasps. You can read all the details here.

Once more, to get some idea of the amount of damage represented by a given amount of Joules, refer to the [#boom Boom Table]

If you are interested, 42961.6 is from (9.0e16 * 2) / 4.184e12 where 9.0e16 = c², 4.184e12 = joules in a kiloton, 2 = 1 unit of matter + 1 unit of antimatter.

You may get close to 100% of the antimatter reacting if you, say, drop the antimatter chunk onto a planet, but getting that efficiency with a warhead exploding in the matter-less depths of deep space is much more difficult. You may be lucky to get 10%. Naturally as the state-of-the-art of antimatter warhead design advances, this percentage will rise.

The second problem is that not all the energy from the blast is dangerous. Some of it is in the form of neutrinos, which are utterly harmless (you know, those slippery little customers who can fly through one light year of solid lead like nothing is there).

First off, a particle will only annihilate with the corresponding anti-particle. This means if an electron hits an anti-proton, they will just bounce off each other (actually, protons and antineutrons sometime annihilate, and vice versa).

The good news for antimatter bomb makers is that electron-positron annihilations create flaming death in the form of a pair of deadly gamma rays. However, this is tempered by the unfortunate fact that electrons and positrons are approximately 1/1836 the mass of protons and other nucleons, and there are about 2.5 times as many nucleons as electrons. This means we can more or less ignore the energy contribution from electron-positron annihilation.

The trouble is with proton-antiproton annihilations. This produces (on average) two neutral and three charged pions. The neutral pions cooperate by almost instantly decaying into gamma rays.

The charged pions though, are a pain in the posterior, er, ah, behave most inconveniently. Assuming that they are zipping along at about 0.94c, they will on average only make it to about 21 meters from ground zero before decaying into mostly harmless muons and neutrinos. If the intended target is farther away than that, the blast energy that is composed of charged pions is totally wasted. Accurate figures are hard to come by, but from what I've managed to dig up, something like 30% of the energy from proton-antiproton annihilation is going to be wasted as harmless muons and neutrinos. At worst, 4/9ths of the energy (44.4%) will be deadly (3/9ths are the helpful neutral pions decaying into gamma rays, 1/9th are muons decaying into electrons). At best, 100% of the energy will be deadly. My expert said that the deadly energy percent will normally be over 70%. So conservatively one can take 70% as the deadly percent, or optimistically take 85% (the average of 70% and 100%) as the percent. You can read all the gory details here.

Putting it all together, our new (conservative) formulae will be:

E_ktB = M * 42961.6 * 0.7 * R_f
or
E_ktB = M * 30073.1 * R_f

E_mtB = M * 43.0 * 0.7 * R_f
or
E_mtB = M * 30.1 * R_f
where:
E_ktB = deadly blast energy (kilotons)
E_mtB = deadly blast energy (megatons)
M = mass of antimatter (kilograms)
R_f = reaction factor, percentage of the matter and antimatter that manages to annihilate before the rest is blown apart. 1.0 if you are an optimist, 0.1 if you are a pessimist, or a point in between that varies according to the technological level of the bomb-maker.

Example: Given a warhead with one gram of antimatter, an optimist will say it will blow up with a force of 0.001 * 30073.1 * 1.0 = 30.1 kilotons and a pessimist will say 0.001 * 30073.1 * 0.1 = 3.0 kilotons.

Also note that, for the most part, antimatter particle beam weapons are a [#antiparticlebeam waste of good antimatter].

The gamma-ray flux from an antimatter annihilation can be strong enough to transmute some elements into radioactive isotopes. This happens by the photoneutron process. The cross-section of this is quite low, but the gamma-ray flux can be quite high. And I am also informed that the charged pions may be short-lived, but they have a high cross-section and will do all sorts of interesting things to atomic nuclei. Apparently the higher the mass of the element transmuted, the longer lived it is as a radioisotope. I will get back to you when I manage to find some hard numbers.

As a side note, electron-positron annihilation produces two gamma rays with precisely an energy of 511 keV. Which means this is a dead giveaway for antimatter use. As you zip along in your antimatter powered rocket, everybody within a couple of light-years will be able to see a fool broadcasting the fact that their rocket contains militarily significant amounts of antimatter. If you head towards an alien race's home planet, you may inadvertently frighten them into giving you a very [rocket3aa.html#killingstar hot reception].

If you are using your ball of antimatter as a fuel source instead of a bomb, Dr. Forward suggests extracting antimatter fuel from the chamber by using ultraviolet lasers. The lasers ionize a bit of anti-hydrogen from the snowball, which is captured by tailored electrostatic fields and piped to the engine. To insure the snowball's mass is not removed asymmetrically (which would destabilize the magnetic levitation), it is spun on its axis while under the laser.

Current particle accelerators are horribly inefficient at generating antimatter, but Dr. Forward says this is because they were designed by physicists, not industrial engineers. He is of the opinion that a dedicated antimatter factory built with current technology could approach 0.01% efficiency (which isn't good but is still about 6000 times better than Fermilab). The theoretical maximum is 50% efficiency due to the pesky Law of Baryon Number Conservation (which demands that when turning energy into matter, equal amounts of matter and antimatter must be created).

At such speeds, the [#kequation kinetic kill equation] is no longer accurate. Instead, the following equation is used. Remember that this not only tells how much kinetic damage the projectile will do to the target, it is also the minimum amount of energy the weapon will consume when it fires a round.

Again, to get some idea of the amount of damage represented by a given amount of Joules, refer to the [#boom Boom Table]

where:
 Ker = relativistic kinetic energy (Joules)
 M = mass of projectile (kg)
 V = velocity of projectile relative to target (m/s)
 P = velocity of projectile relative to target (percentage of c, e.g., three quarters lightspeed = 0.75)
 C = speed of light in m/s = 3e8

And as before

W_p = K_er * (1 / W_e)

where:
W_p = power required by weapon to fire one projectile (Joules)
K_er = kinetic energy of one weapon projectile (Joules)
W_e = efficiency of the weapon (0.0 = 0%, 1.0 = 100%)

Example: How much damage would the 7 kilograms of used kitty litter from Sneaky the cat's litterbox inflict if it was traveling at a velocity of 90% c?

K_er = ((1/sqrt(1 - P²)) - 1) * M * 9e16
K_er = ((1/sqrt(1 - 0.9²)) - 1) * 7 * 9e16
K_er = 8.2e17 Joules, about 195 megatons.

Not bad, for kitty litter.

But a civilization that does gain the ability to create relativistic kinetic-kill weapons becomes a [rocket3aa.html#killingstar deadly threat] to any and all alien civilizations in range.

Iain Paterson did some calculations which produced some surprising results.

I had this image of putting a relatively small payload on top of a bloody massive conventional booster and firing it of -- the poor mans R-bomb i guess -- but after looking at some calculations this doesn�t look likely.

From the kinetic energy equation and Tsiolkovsky�s equation you get:

E = 1/2 * Mpayload * (Vexhaust * ln(R))²

E = 1/2 * (Mtotal / R) * (Vexhaust * ln(R))²

Differentiating with respect to R and setting equal to zero gives the mass ratio that gives the maximum energy. Canceling terms gives that:

R = E * 2

Vfinal_Ideal = 2 * Vexhaust

This is rather surprising to me though I suppose it makes sense: at higher velocities there is a greater kinetic energy per mass but it requires a huge amount of fuel to get to that velocity. After reaching this velocity any additional acceleration REDUCES the energy impacted on the target so you might as well shut off the engines and let it coast.

I worked it out for other cases as well, for 2 ships that are approaching each other before one fires a missile you get

R = e^(2-γ)

where γ (gamma) is the ratio of the approach velocity to the exhaust velocity although this again gives that the missile should impact with a relative velocity of twice its exhaust velocity.

The final case is for relativistic velocities (although being fired from ships that are stationary with respect to each other otherwise the maths is really nasty!) and you get:

R = ((c + Vexhaust) / (c - Vexhaust))²

Vfinal_ideal = 2 * Vexhaust / (1 + (Vexhaust / c)²)

note that for V«c, Vf = 2 * Vexhaust. And for V~c, Vf = c.

So is it just me or does this completely defy the concept of the poor-mans R-bomb so that instead it requires some sort of some handwavium total-conversion drive?

Also this shows that to be effective a kinetic-missile must have a high exhaust velocity, not just a lot of fuel. While I suppose in order to evade point defense they need to be going faster but every extra second of thrust would reduce the damage inflicted to the target.

Isaac Kuo agrees:

Mr. Paterson is optimizing a more plausible scenario. His "poor man's R-bomb" is constrained by a particular exhaust velocity, and the question is how to squeeze the maximum kinetic energy into the payload. I'm not sure whether his analysis is correct, but it seems plausible.

The optimum energy efficiency would actually be reached at an terminal velocity equal to the exhaust velocity. But that doesn't seem to be the objective of the poor man's R-bomb. The poor man's R-bomb seems to be limited by loaded mass rather than energy budget. You don't use any sacrificial propellant at all, you just use pure fuel at the maximum exhaust velocity you can manage all the way.

Mr. Paterson writes: So is it just me or does this completely defy the concept of the poor-mans R-bomb so that instead it requires some sort of some handwavium total-conversion drive?

His conclusion is essentially correct, if we assume the poor man's R-bomb must be internally powered.

Still, this is nothing new to those of us who have seriously considered the problem of fast interstellar propulsion. We gave up on the idea of internal power for fast interstellar propulsion years ago, on the pretty obvious grounds that no fuel has a sufficient (usable) energy density. If you want to reach high relativistic speeds, you should use external power--either in the form of a laser beam or particle beam or "runway" track or relativistic kinetic impactors.

From The Killing Star by Charles Pelligrino and George Zebrowski (you really should read this book):

All the energy put into achieving that velocity had transformed the Intruder into a kinetic storage device of nightmarish design. If it struck a world, every gram of the vessel�s substance would be received by that world as the target in a linear accelerator receives a spray of relativistic buckshot. Someone, somewhere, had built and was putting to use a relativistic bomb -- a giant, roving atom smasher aimed at worlds...

The gamma-ray shine of the decelerating half was also detectable, but it made no difference. One of the iron rules of relativistic bombardment was that if you could see something approaching at 92 percent of light speed, it was never where you saw it when you saw it, but was practically upon you...

In the forests below, lakes caught the first rays of the rising Sun and threw them back into space. Abandoning the two-dimensional sprawl of twentieth-century cities, Sri Lanka Tower, and others like it, had been erected in the world�s rain forests and farmlands, leaving the countryside virtually uninhabited. Even in Africa, where more than a hundred city arcologies had risen, nature was beginning to renew itself. It was a good day to be alive, she told herself, taking in the peace of the garden. Then, looking east, she saw it coming -- at least her eyes began to register it -- but her optic nerves did not last long enough to transmit what the eyes had seen.

It was quite small for what it could do -- small enough to fit into an average-sized living room -- but it was moving at 92 percent of light speed when it touched Earth�s atmosphere. A spear point of light appeared, so intense that the air below snapped away from it, creating a low-density tunnel through which the object descended. The walls of the tunnel were a plasma boundary layer, six and a half kilometers wide and more than 160 deep -- the flaming spear that Virginia�s eyes began to register -- with every square foot of its surface radiating a trillion watts, and still its destructive potential was but fractionally spent.

Thirty-three kilometers above the Indian Ocean, the point began to encounter too much air. It tunneled down only eight kilometers more, then stalled and detonated, less than two-thousandths of a second after crossing the orbits of Earth�s nearest artificial satellites.

Virginia was more than three hundred kilometers away when the light burst toward her. Every nerve ending in her body began to record a strange, prickling sensation -- the sheer pressure of photons trying to push her backward. No shadows were cast anywhere in the tower, so bright was the glare. It pierced walls, ceramic beams, notepads, and people -- four hundred thousand people. The maglev terminal connecting Sri Lanka Tower to London and Sydney, the waste treatment centers that sustained the lakes and farms, all the shops, theaters, and apartments liquefied instantly. The structure began to slip and crash like a giant waterfall, but gravity could not yank it down fast enough. The Tower became vapor before it could fall half a meter. At the vanished city�s feet, the trees of the forest were no longer able to cast shadows; they had themselves become long shadows of carbonized dust on the ground.

In Kandy and Columbo, where sidewalks steamed, the relativistic onslaught was unfinished. The electromagnetic pulse alone killed every living thing as far away as Bombay and the Maldives. All of India south of the Godavari River became an instant microwave oven. Nearer the epicenter, Demon Rock glowed with a fierce red heat, then fractured down its center, as if to herald the second coming of the tyrant it memorialized. The air blast followed, surging out of the Indian Ocean -- faster than sound -- flattening whatever still stood. As it slashed north through Jaffna and Madurai, the wave front was met and overpowered by shocks rushing out from strikes in central and southern India.

Across the face of the planet, without warning, thousands of flaming swords pierced the sky...

Then out of no where -- out of the deep impersonal nowhere -- came a bombardment that even the science fiction writers had failed to entertain.

Just nine days short of America�s tricentennial celebrations, every inhabited planetary surface in the solar system had been wiped clean by relativistic bombs. Research centers on Mars, Europa, and Ganymede were silent; even tiny Phobos and Moo-kau were silent. Port Chaffee was silent. New York, Colombo, Wellington, the Mercury Power Project and the Asimov Array. Silent. Silent. Silent.

A Valkyrie rocket�s transmission of Mercury�s surface had revealed thousands of saucer-shaped depressions where only hours before had existed a planet-spanning carpet of solar panels. The transmission had lasted only a few seconds -- just long enough for Isak to realize there would be no more of the self-replicating robots that had built the array of panels and accelerators, just long enough for him to understand that humanity no longer possessed a fuel source for its antimatter rockets -- and then the transmission had ceased abruptly as the Valkyrie disappeared in a silent white glare.

Presently, most of the station�s scopes and spectrographs were turning Earthward, and Isak found it impossible to believe what they revealed. The Moon rising over Africa from behind Earth was peppered with new fields of craters. The planet below looked like a ball of cotton stained grayish yellow. The top five meters of ocean had boiled off under the assault, and sea level air was three times denser than the day before -- and twice as hot...

The sobering truth is that relativistic civilizations are a potential nightmare to anyone living within range of them. The problem is that objects traveling at an appreciable fraction of light speed are never where you see them when you see them (i.e., light-speed lag). Relativistic rockets, if their owners turn out to be less than benevolent, are both totally unstoppable and totally destructive. A starship weighing in at 1,500 tons (approximately the weight of a fully fueled space shuttle sitting on the launchpad) impacting an earthlike planet at "only" 30 percent of lightspeed will release 1.5 million megatons of energy -- an explosive force equivalent to 150 times today's global nuclear arsenal... (ed note: this means the freaking thing has about nine hundred [#firstlaw mega-Ricks] of damage!)

The most humbling feature of the relativistic bomb is that even if you happen to see it coming, its exact motion and position can never be determined; and given a technology even a hundred orders of magnitude above our own, you cannot hope to intercept one of these weapons. It often happens, in these discussions, that an expression from the old west arises: "God made some men bigger and stronger than others, but Mr. Colt made all men equal." Variations on Mr. Colt's weapon are still popular today, even in a society that possesses hydrogen bombs. Similarly, no matter how advanced civilizations grow, the relativistic bomb is not likely to go away...

From Giant's Star by James P. Hogan (1981)

The strain on the Command Deck of the Shapieron had been hovering around breaking point for days. Eesyan was standing in the center of the floor gazing up at the main display screen, where an enormous web of interconnected shapes and boxes annotated with symbols showed the road map into JEVEX that ZORAC had laboriously pieced together from statistical analyses and pattern correlations of the responses it had obtained to its probe signals. But ZORAC was not getting through to the nucleus of the system, which it would have to penetrate if it was going to disrupt JEVEX'S h-jamming capability. Its attempts had been repeatedly detected by JEVEX'S constantly running self-checking routines and thwarted by automatically initiated correction procedures. The big problem now was trying to decide how much longer they could allow ZORAC to try before the tables of fault-diagnostic data accumulating inside JEVEX alerted its supervisory functions that something very abnormal was happening. Opinions were more or less evenly divided between Eesyan's scientists from Thurien, who already wanted to call the whole thing off, and Garuth and his crew, who seemed willing to risk almost anything to pursue what was beginning to look, the more Eesyan saw of it, like some kind of death wish.

"Probe Three's function directive has been queried for the third time," one of the scientists announced from a nearby station. "Header response analysis indicates we've triggered a veto override again." He looked across at Eesyan and shook his head. "It's too dangerous. We'll have to suspend probing on this channel and resume regular traffic only."

"Activity pattern correlates with a new set of executive diagnostic indexes," another scientist called. "We've initiated a high-level malfunction check."

"We have to shut down on Three," another, standing by Ecsyan, pleaded. "We're too exposed as it is."

Eesyan stared grimly up at the main screen as a set of mnemonics unrolled down one side to confirm the warning.

"What's your verdict, ZORAC?" he asked.

"I've reduced interrogation priority, but the fault flags are still set. It's tight, but it's the nearest we've come so far. I can try it one more time and risk it, or back off and let the chance go. It's up to you."

Eesyan glanced across to where Garuth was watching tensely with Monchar and Shilohin. Garuth clamped his mouth tight and gave an almost imperceptible nod. Eesyan drew a long breath. "Give it a try, ZORAC," he instructed. A hush fell across the Command Deck, and all eyes turned upward toward the large screen.

In the next second or two a billion bits of information flew back and forth between ZORAC and a Jevienese communications relay hanging distantly in space. Then, suddenly, a new set of boxes appeared in the array. The symbols inside them were etched against bright red backgrounds that flashed rapidly. One of the scientists groaned in dismay.

"Alarm condition," ZORAC reported. "General supervisor alert triggered. I think we just blew it." It meant that JEVEX knew they were there.

Eesyan looked down at the floor. There was nothing to say. Garuth was shaking his head dazedly in mute protest as if refusing to accept that this could be happening. Shilohin moved a step nearer and rested a hand on his shoulder. "You tried," she said quietly. "You had to try. It was the only chance."

Garuth was staring around him as if he had just awakened from a dream. "What was I thinking?" he whispered. "I had no right to do this."

"It had to be done," Shilohin told him firmly.

"Two objects a hundred thousand miles out, coming this way fast," ZORAC reported. "Probably defensive weapons coming to check out this area." It was serious. The screen hiding the Shapieron would never stand up to probing at close range.

"How long before we register on their instruments?" Eesyan asked hoarsely.

"A couple of minutes at most," ZORAC replied...

..."So this is our ultimatum to you: either you withdraw from Thurien now, and agree to place your entire military command under our jurisdiction unconditionally, or the Thuriens will transfer through to Jevlen a combined Terran force that will blow you to stardust - you, your whole planet, and that laughable aggregation of scrap that you call a computer network."

Somewhere deep inside JEVEX something hiccupped. A million tasks that had been running inside the system froze in the confusion as directives coming down from the highest operating levels of the nucleus redefined the whole structure of priority assignments to force an emergency analysis of the new data. And in the middle of it all, the routines that had been scanning for inquisitive probes through h-space faltered. It was only for a few seconds, but...

..."It's busy," ZORAC's voice answered. "Don't ask me what's happened, but yes it was. Something deactivated the self-checking functions, and I've switched off the jamming routine. We're through to Thurien."

While ZORAC was speaking, VISAR decoded the access passwords into JEVEX's diagnostic subsystem, erased a set of data that it found there, substituted new data of its own, and reset the alarm indicators. Inside the Jevienese Defense Sector Five control center, a display screen changed to announce a false alarm caused by a malfunctioning remote communications relay. Far off in space, the two destroyers turned away to return to their stations and resume routine patrolling. Already VISAR was pouring volumes of information into JEVEX that it had not time to explain, not even to ZORAC. At the same time it broke its way into JEVEX's communications subsystem and gained control of the open channel to Earth.

From A Fire Upon the Deep by Vernor Vinge (1992)

And never lose sight of the reason for haste: the frigate. It had switched to rocket drive, blasting heedless away from the wallowing freighter. Somehow, these microbes knew they were rescuing more than themselves. The warship had the best navigation computers that the little minds could make. But it would be another three seconds before it could make its first ultradrive hop.

The new Power had no weapons on the ground, nothing but a comm laser. That could not even melt steel at the frigate's range. No matter, the laser was aimed, tuned civilly on the retreating warship's receiver. No acknowledgement. The humans knew what communication would bring. The laser light flickered here and there across the hull, lighting smoothness and inactive sensors, sliding across the ship's ultradrive spines. Searching, probing. The Power had never bothered to sabotage the external hull, but that was no problem. Even this crude machine had thousands of robot sensors scattered across its surface, reporting status and danger, driving utility programs. Most were shut down now, the ship fleeing nearly blind. They thought by not looking that they could be safe.

One more second and the frigate would attain interstellar safety.

The laser flickered on a failure sensor, a sensor that reported critical changes in one of the ultradrive spines. Its interrupts could not be ignored if the star jump were to succeed. Interrupt honored. Interrupt handler running, looking out, receiving more light from the laser far below... a backdoor into the ship's code, installed when the newborn had subverted the human's groundside equipment...

...and the Power was aboard, with milliseconds to spare. Its agents - not even human equivalent on this primitive hardware - raced through the ship's automation, shutting down, aborting. There would be no jump. Cameras in the ship's bridge showed widening of eyes, the beginning of a scream. The humans knew, to the extent that horror can live in a fraction of a second.

There would be no jump. Yet the ultradrive was already committed. There would be a jump attempt, without automatic control a doomed one. Less than five milliseconds till the jump discharge, a mechanical cascade that no software could finesse. The newborn's agents flitted everywhere across the ship's computers, futilely attempting a shutdown. Nearly a light-second away, under the gray rubble at High Lab, the Power could only watch. So. The frigate would be destroyed.

So slow and so fast. A fraction of a second. The fire spread out from the heart of the frigate, taking both peril and possibility.

Having said that, realize that as a general rule propulsion exhaust is poorly collimated, which means after a very short range it will have expanded and dissipated into harmlessness.

This is a more general concern. As propulsion systems get more powerful, the more energy they contain, and the worse the damage if an accident occurs. How would you like to have the captain of the Exxon Valdez skippering a tramp freighter with an antimatter drive? That brilliant mushroom cloud you see marks the former location of Clinton-Sherman spaceport. The more devastation a propulsion system can wreck, the shorter the leash the captains will be on. If they are too powerful, there won't be any colorful tramp freighters or similar vessels. This is known as [rocket3a.html#johnslaw Jon's Law].

Sometimes it works the other way. If you are attacking an [rocket3c2.html#orion Orion drive] spacecraft with nuclear warheads, they will just point their pusher plate at the missiles and laugh at you.

In The Outcasts of Heaven's Belt by Joan Vinge, warships attacking a visiting Bussard Ramjet starship get a rude surprise when the starship shows them its tail. The starship's fusion drive is quite deadly at close range. Things are more extreme in the anime Space Battleship Yamato (later watered down and made politically correct for viewers in the US under the name Star Blazers). The battleship's propulsion system is the incredibly powerful "wave-motion engine". But if attacked, the thrust is vectored out the nose of the ship to create the equally incredibly powerful "wave-motion cannon".

Being a spoil-sport, I said: "The question then becomes why doesn't the designers replace the minimal habitability crew space with some electronics and turn the fighter into a missile bus."

Mr. Robinson answered with: "What a rude question. {grin}". But then he got me, by invoking Burnside's [rocket3a.html#zerothlaw Zeroth Law] of Space Combat. SF fans don't want to read about the life and times of a nuclear missile, therefore space fighters will exist.

In the 1970's, DARPA was looking into a crude spacecraft called the "High Performance Spaceplane" that looked suspiciously like a space fighter, you can read about the details here and here.

Jack Staik has some further observations:

It is true that in a universe governed by hard-headed practicality and realism, a missile bus or an Honorverse-style missile pod would make more sense. However, there is one factor that would allow manned space fighters to proliferate and even prosper - Cultural Bias!

Practical and realistic concerns have often been swept aside in real life by cultural conditioning - look at Japan's centuries of refusal to modernize or adapt until the fact of their utter vulnerability was shoved down their throats by Admiral Perry.

An aristocratic culture with a leaning toward individual heroism (i.e. Arthurian or Samurai theme) would love the idea of manned space-fighters. Noble warriors with the blood of kings firing up their fighters to challenge the Evil Alien Hordes, one man's courage and missiles against the onslaught ... it's a primal image. The fighters themselves would probably be very individualistic, instead of mass-produced identical, to reflect their aristocratic pilot. And since the space-fighter would be the provenance of only the high-caste persons, the cultural conditioning could keep manned space-fighter a viable concept for generations in even a hyper-realistic scenario.

Of course, in time raw practicality will sweep aside the manned space-fighter, much as it did the armored knight on horseback, but the fighters will still be the emblem of a bygone age of chivalry and romance. And a Don Quixote-type character, pulling an ancestor's old space-fighter out of storage, to take up arms against a threat from the heavens, has lots of storytelling potential.

If you could build a TLAM that had the operational range of an F-18, you could probably get more of them packed onto a comparable size ship than a comparable mass of F-18s.

TLAMs require lots of data on the target and the terrain and have to fly "over the horizon". A lot of opposition to the TLAM was that it took away the offensive strike mission from carrier aviation.

In space, there's no horizon to hide behind.

On a later occasion, in a discussion on space combat game design, Mr. Burnside went into more detail:

The basic argument for fighters is that people think they're fun and cool.

The basic argument against fighters is horizon distance.

Fighters make sense in surface naval operations because a fighter can go to places where the carrier or cruiser can't. The fighter can also go to places where the big ships can't see, because of the curvature of the earth.

Unfortunately, there's no horizon for targets to hide behind in space. Even if you have something short of everyone sees everyone, it's hard(er) to justify fighters seeing things their carriers can't, just because carriers can carry bigger sensors, and space is a very sensor friendly environment.

Fighters do make sense in an orbital reference frame context, where, well, curvature of the earth matters, and where going into atmosphere matters. But this turns fighter carriers into "brown water" vessels that work in the tide pools of planetary gravity wells, which isn't the role you see them doing in fiction, which tends to take WWII carrier ops or modern USN carrier ops and apply an SFnal veneer.

Note that that's all mission specific, and only mildly tech related.

What do fighters do better than, or exclusively related to, larger ships? Answer this, and you get a reason for fighters in a setting.

In terms of pure offensive firepower, there's very little you can do with a fighter that a cruise missile can't do better in a space game context.

Of course, the best reason to have fighters is because they make your game more funnerer. But it does kind of help to figure out what mission they're doing.

Given the popularity of space fighters in such mass media shows as Star Wars, Battlestar Galactica, Buck Rogers in the 25th Century, Babylon 5, and others, they obviously appeal to people. I'm in the minority, but I think they are missing the point. Here's my reasoning:

It seems to me that the space fighter is nothing more that people taking a dramatic and comfortable metaphor (sea-going aircraft carriers and combat fighter aircraft) and transporting it intact into the outer space environment. But if you think about it, interplanetary combat is highly unlikely to be like anything that has occurred before.

Imagine a speculative fiction writer back in the Victorian era, such as Jules Verne. Say they wanted to write a novel about the far future, when heavier than air flight had been invented, and the age of Aerial Combat had arrived.

They might take the dramatic and comfortable metaphor of sea-going frigates and battleships and transporting it intact into the aerial environment. Held aloft by dozens of helicopter blades, the battleships of the air would ponderously maneuver, trying to "cross the T" with the enemy aerial dreadnoughts.

See how silly it sounds? Well, combat spacecraft behaving like fighter aircraft is just as silly. In both cases a metaphor is being forced into a situation where it does not work.

In reality, when the Wright brothers invented heavier-than-air flight and Fokker Triplanes started dog-fighting Sopwith Camels, it was totally unlike anything that had occurred before. Biplanes never ever tried to cross the T, and a sea-going battleship had never ever performed an Immelmann turn.

Therefore, by analogy, when interplanetary combat arrives, it too will be totally unlike anything that has occurred before.

As Ken Burnside puts it:

On the other hand - Winch's analogy to victorian era fiction about flying dreadnoughts and the "Who the hell thought of an Immelmann turn?" question sort of underscores why I want to model how space combat works using known physics as a gameable experience.

It won't be WWII in space. It won't be the Iraq war in space, it won't be subs in the North Atlantic in space. It will be its own unique thing.

To figure out what that unique thing is, you need to understand the environment of space, how it differs from a planetary environment, and once you have those differences modeled, you need to work out the tactics for this new environment, much the same way WWI biplane pilots had to work out the tactics of air to air combat.

Now, it's certain that I've got things wrong with the Attack Vector: Tactical model. When they get pointed out, I fix them. On the other hand, to the best of my knowledge and belief, it's the first serious attempt at trying to model what the tactical environment looks like.

World War II/Battleships/Fighters in space is about as likely to be an accurate model of space combat as, modeling jet air-to-air combat with pike square formations. Attack Vector: Tactical is probably akin to saying that jet fighters behave like World War I biplanes, only faster. It's still likely wrong, but it's probably much LESS wrong.

From Common Denominator by David Lewis (1972)

Night Killer II was not a beautiful vessel. Satarii fighters are sleek, polished for planetary re-entry, but a space-based interceptor need not be aesthetic. Had I attempted to land on Lot I would have reached the surface in ashes. Night Killer carried her missiles outside the hull in two cylindrical bundles. Radar sweeps and communication aerials were all exposed. Her drive was set on un-streamlined pylons spaced about her stern while the cockpit glass bulged beyond the curvature of her skin, ostensibly for wider vision with less distortion; the effect on the casual observer was that of a mutated hornet's head. And added to this were bundles of thrusters placed strategically about the hull to aid maneuvering. But regardless of her ungainliness, she remained an effective fighting unit, equal and in some ways more than equal to the darting black war craft of the Satarii.

As an analogy, imagine an 1850's Victorian Era scientist dismantling a live nuclear reactor trying to figure out how it works. Radioactivity hadn't been discovered yet, much less nuclear fission. So they would be at a loss trying to explain the disaster that happened after they removed all the nuclear damper rods for closer examination.

From Childhood's End by Arthur C. Clarke (1953)

Karellen paused, and the silence grew even deeper.

"There has been some complaint, among the younger and more romantic elements of your population, because outer space has been closed to you. We had a purpose in doing this: we do not impose bans for the pleasure of it. But have you ever stopped to consider -- if you will excuse a slightly unflattering analogy -- what a man from your Stone Age would have felt, if he suddenly found himself in a modern city?"

"Surely," protested the Herald Tribune, "there is a fundamental difference. We are accustomed to Science. On your world there are doubtless many things which we might not understand -- but they wouldn't seem magic to us."

"Are you quite sure of that?" said Karellen, so softly that it was hard to hear his words. "Only a hundred years lies between the age of electricity and the age of steam, but what would a Victorian engineer have made of a television set or an electronic computer. And how long would he have lived if he started to investigate their workings? The gulf between two technologies can easily become so great that it is -- lethal."

Anyway, Newtons says that if the starship Enterprise uses a tractor beam to reel in a Klingon battle cruiser, the Enterprise will also move towards the Klingon. Both will move towards the point called the Barycenter of the two ship system. In the same way if the Enterprise pushes away the Klingon, the Enterprise will also be pushed away from the barycenter.

The acceleration each ship will experience towards or away from the barycenter depends upon each ship's mass. Simply put: if ship Alfa has twice the mass of ship Bravo, it will be accelerated half as fast as ship Bravo. If an Imperial Star Destroyer tractors the Tantive IV, it will be accelerated about 1/110th as fast as the Tauntive. And if the Death Star tractors the Millenium Falcon, its acceleration will be so tiny as to be difficult to detect.

The actual equation is from Newton's Second Law:

a = F / m
where:
a = ship's acceleration (m/sec)
F = tractor beam energy (Newtons)
m = ship's mass (kg)

If you want relative acceleration, use 1 for F and measure m in terms of the other ship's mass. Example: If the ship in question has a mass of 3.5 times the mass of the other ship, it will experience an acceleration of 1 / 3.5 = 0.29 times as much as the other ship. If the ship has a mass of 1/4 times the mass of the other ship, it will experience an acceleration of 1 / (1/4) = 1 / 0.25 = 4 times as much as the other ship.

Step 1: Calculate each ship's x and y coordinate displacement:

V_1x = V₁ * cos(θ₁)
V_1y = V₁ * sin(θ₁)
V_2x = V₂ * cos(θ₂)
V_2y = V₂ * sin(θ₂)

Step 2: Calculate each ship's momentum:

O₁ = V₁ * M₁
O₂ = V₂ * M₂

Step 3: Calculate each ship's momentum in the x and y axes:

O_1x = O₁ * cos(θ₁)
O_1y = O₁ * sin(θ₁)
O_2x = O₂ * cos(θ₂)
O_2y = O₂ * sin(θ₂)

Step 4: Calculate the combined ship's momentum in the x and y axes:

O_fx = O_1x + O_2x
O_fy = O_1y + O_2y

Step 5: Calculate the combined ship's mass:

M_f = M₁ + M₂

Step 6: Calculate the combined ship's momentum:

O_f = sqrt( O_fx² * O_fy² )

Step 7: Calculate combined ships velocity:

V_f = O_f / M_f

Step 8: Calculate combined ships vector angle:

θ_f = arc tan( O_fx / O_fy )

Examples:

BLIT: In the story "Blit" and others by David Langford, some scientist, who should know better, invents a graphic pattern called a "basilisk" that will cause the viewer's brain to lock-up, killing the viewer instantly. It works much like a computer virus, crashing the brain's operatining system.

As the FAQ puts it: "...the human mind as a formal, deterministic computational system -- a system that, as predicted by a variant of Gödel's Theorem in mathematics, can be crashed by thoughts which the mind is physically or logically incapable of thinking. The Logical Imaging Technique presents such a thought in purely visual form as a basilisk image which our optic nerves can't help but accept. The result is disastrous, like a software stealth-virus smuggled into the brain."

An atomic rocketship of the valiant Space Patrol fires a warning shot across the bow of the sinister black spaceship belonging to the dreaded Necroscientist of Titan. A signal for parlay is sent, and the foolish Patrol captain accepts a videophone message from the Necroscientist in order to discuss terms. Everybody on the bridge within eyeshot of the videophone monitor keels over dead with the Parrot burned into their visual cortex, as the Necroscientist makes good his escape.

THE CASSINI DIVISION: In the novel by Ken MacLeod, one of the weapons is the so-called "Langford Visual Hack" (an obvious tip-of-the-hat to David Langford). As a defense, all computer monitors on the ship are designed to contain enough visual static to prevent the visual hack from working.

WAR AGAINST THE RULL: In the novel by A.E. van Vogt, the alien Rull can draw the "lines-that-could-seize-the-minds-of-men". Any human who looks at such a diagram is instantly hypnotized, and will just stand there in a trance.

THE BLACK CLOUD: In the novel by Fred Hoyle, a helpful intelligent interstellar nebula attempts to teach a human being its native language with remote controlled audio-visual equipment. This proved to be fatal the the person. The trouble is that humans know to be true too many things that actually are not true. They have to un-learn too much in order to learn the alien language, and the cognitive dissonance is fatal (it causes an inflammation of brain tissue).

MACROSCOPE: In the novel by Piers Anthony scientists discover an alien interstellar broadcast that is sort of a galactic library. Unfortunately for the scientists, the broadcast is overlayed with the "Destroyer Sequence." This is a visual sequence that forces the brain to think certain thoughts it is not able to think, which burns out the brain leaving the hapless victim mentally a vegetable.

KALEIDOSCOPE CENTURY: In the novel by John Barnes, a rogue artificial intelligence can call a person up on a telephone, then use rapidly changing audio signals to reprogram the person's brain, turning them into a brainwashed zombie.

BATTLEFLEET MARS: In the wargame by Redmond Simonsen, a top executive of the Ares corporation is assassinated by a sonic pulse over the telephone.

This scheme was created by Erik Max Francis, and contains some modifications by Isaac Kuo:

• I. Weapons systems.
  • A. Banks. Beams of directed particles fired at a target.
    • 1. Electromagnetic beams. Beams of photons (note this includes lasers, masers, xasers, gasers, etc.).
      • a. continuous
      • b. pulsed
      • c. single-shot submunition
    • 2. Particle beams. Beams of high-energy charged particles (such as protons).
      • a. continuous
      • b. pulsed
      • c. single-shot submunition
  • B. Cannon. Unguided projectiles directed at a ship target.
    • 1. Kinetics. Mere slugs fired at a target with no explosive capability.
    • 2. Shells. Unguided projectiles fired at a target which detonated with a proximity fuse and a conventional warhead.
  • C. Tubes. Guided projectiles directed at a ship target.
    • 1. Missiles. Guided projectiles with a proximity fuse. Has higher acceleration than average target ship.
    • 2. Torpedoes ([#AKV AKV]). Guided projectiles with a proximity fuse. Has lower acceleration than average target ship.
    • 3. Rockets. Dumbfire missiles, which only accelerate in the direction they were fired.
  • D. Releases. Guided projectiles directed at a planetary target.
    • 1. Atmospherics. Projectiles designed to reenter an atmosphere and detonate over a ground target.
    • 2. Biologics. Atmospherics with a biological warhead.
    • 3. Kinetics. No warhead. Does damage with kinetic energy, by large velocities or large mass, or both.
  • E. Layers. Latent projectiles merely dropped with only a slightly different speed from the firing ship.
    • 1. Mines. Conventional warheads which drift in orbit and a proximity fuse which then accelerate toward their target and detonate.

• II. Active defense systems.
  • A. Point defense. Smaller-sized kinetics, missiles, and beams directed at incoming weapons.
  • B. Minesweepers. Point defense designed to eliminate mines.
  • C. Charge dampener (?). Anticharge systems designed to reduce the damage caused by particle beams.
  • E. Nanotechnology dynamic armor repair.

• III. Passive defense systems.
  • A. Armor.
    • 1. Ablative armor.
    • 2. Reflective armor. Armor designed to deflect beam weapons, even as it is worn away.
  • B. Shields. [These are pretty hard to classify, since they're the only broad class of system that is hard to explain through current science.]
  • A. Electronic countermeasures. Electronic equipment designed to foil weapon targeting systems.
  • B. Decoys. Launched devices designed to foil incoming weapons with false signals.
    • 1. Electromagnetic decoys. Decoys which emit misleading electromagnetic signals.
  • C. Jammer. Electronic equipment designed to foil broadband electromagnetic signals.

This scheme was created by Timothy Miller (Cerebus), and contains some modifications by Erik Max Francis:

• 1 Deployment: How the weapons system is initially launched (fired). Note: Do not confuse this description with Guidance.
  • 1a Active: These weapons deploy themselves upon activation, with the propulsive mechanism integral to the unit; as a class, this includes commonly-termed missiles and torpedoes.
  • 1b Passive:These weapons are deployed by an external device, launcher or other means.
    • 1b1 Gun fired: Deployed by common explosives, as through an artillery piece.
    • 1b2 Railgun launched: Deployed by electromagnetic launcher, typically to much higher velocities than possible by Gun-fired or other methods; as such deserves a separate description.
    • 1b3 Dropped: Deployed by simply leaving the weapon behind you, without appreciable external impetus.
    • 1b4 Hand launched: Thrown, hurled, kicked or otherwise deployed by physical exertion.
  • 1c Lay in wait: These are fired passively, and activated when they in a given proximity to their target (i.e., "mines")
• 2 Guidance: Describes methods of an individual weapon achieving its objective.
  • 2a Dumb: No post-deployment guidance. Either you aimed right or you didn't.
  • 2b Smart: Capable of post-deployment guidance of any type (glide, thrust, etc.)
    • 2b1 External: Guided by external sensors and control.
      • 2b1a Wire guided: Guidance received through trailing wire. Limited in range, but not susceptible to interference.
      • 2b1b Signal guided: Less limited in range, but more susceptible to interference.
    • 2b2 Internal: Guided by internal sensors.
• 3 Kill Type: How the weapons system damages the target.
  • 3a Kinetic: These weapons carry no warheads, relying on impact energy alone to damage the target.
    • 3a1 Single warhead
    • 3a2 Scattershot: Weapon segments into shrapnel upon deployment. 3b1c types on the other hand delay segmentation until activation
  • 3b Explosive: These weapons carry explosives of varying types, and rely on on- or near-target detonation to damage the target.
    • 3b1 Chemical: Common (or uncommon) chemical explosives.
      • 3b1a Blast: Relies on blast effects.
      • 3b1b Armor piercing: Self-explanatory.
      • 3b1c Shrapnel: Weapons that intentionally shatter or otherwise scatter projectiles to incapacitate or kill. This can be anything from flechette-scattering missiles to hand grenades.
    • 3b2 Nuclear: Self-explanatory, includes both fission and fusion devices.
    • 3b3 Antimatter
  • 3c Directed Energy: These weapons transfer energy directly to the target, at range.
    • 3c1 Electromagnetic: Lasers and kin (masers, grasers, etc.)
      • 3c1a Submunitions: Bomb-pumped lasers
    • 3c2 Particle beam: Charged or neutral particles, not to be confused with small-sized railgun-fired projectiles. Typically limited to atomic or sub-atomic particles.
  • 3d Chemical: Anti-personnel weapons that attempt to poison the biological processes of the target to incapacitate or kill.
  • 3e Biological: Anti-personnel weapons that attempt to infect the target and incapacitate or kill.
  • 3f Radiological: Anti-personnel weapons that attempt to expose the target to incapacitating amounts of radiation.
• 4 Acquisition: Describes methods of an individual weapon detecting and targeting, its objective.
  • 4a Active: Weapon emits radiation to detect targets (e.g., radar).
  • 4b Passive: Weapon passively scans for target emissions (e.g., infrared)
  • 4c Illumination: Weapons passively scans for an illumination signature painted on target by a third object.
  • 4d Command : Weapon is issued an attack command by the controlling ship.
• 5 Trigger: Generally only for warheads, determines what causes weapon to detonate.
  • 5a Command: Detonated by command from controlling ship.
  • 5b Impact: Detonated by contact with target.
  • 5c Proximity: Detonates within predetermined range of the target.
  • 5d Timed: Detonates after a pre-determined time.
  • 5e Check-in: Detonates after the inability to contact a friendly ship after a predetermined period of time.