A blog dedicated to helping writers and worldbuilders create consistent, plausible Science Fiction.

Tuesday, 23 August 2016

Space Warship Design II: Guns and Shields

We will continue looking at the vital systems you need to design to complete your space warship.
Weapons 

The most important system on a warship, bar none. Since we do not want a 'weapons monoculture', that is, a setting where a single weapons system dominates all others, we will try to make lasers and missiles equally useful.

In an all-guns monoculture, we end up with the largest possible battleships equipped with the largest number of the biggest guns possible. Pictured, the Scharnhorst.
Lasers, because they are able to hit targets up to 300000km away without worrying much about lightspeed lag, will be the weapon of choice in space battles. Whether they do damage at those ranges depends on how much the warship invests in the weapon. Tactically, they will be the weapon which determines the distance at which warships will be considered 'in combat' or not. They will determine how ship classes are classified, between those that can withstand laser fire and those that can run outside of effective range. They also give us a duration for battles. We should aim for about an hour between ships entering combat range and leaving with one side destroyed.
THAAD laser missile test.
Missiles are the anti-thesis to lasers. They allow a small spaceship with insignificant power supply and poor acceleration to punch well above their weight. Due to the levels of kinetic energy involved and mass of armor required to protect against kinetic strikes, warships will invariably be vulnerable to missiles. The issue is actually getting the missiles to their target. Whether it is through stealth drops or massed strikes, the solutions devised will make the battle unpredictable and prevent stale attrition wars. 
Lasers

Lasers have three main components: Pump source, laser medium and optical resonator. To turn it into a weapon, you add a cooling system and optics. 

Simple flash-pumped laser configuration.
In low temperature, low power applications, lasers can produce high quality beams, called diffraction limited or Gaussian beams. The familiar '0.61*D*L/R' equation describes such a perfect beam. However, real lasers cannot focus their beam so well. The ratio between the actual beam's spot radius and a diffraction-limited radius is determined by the M^2 factor. The M^2, or Beam Quality Factor, rises rapidly with the temperature of the laser medium. Modern high-powered conventional lasers have an M^2 of over 1000, so their ability to focus energy is restricted at long ranges. In this realistic setting, we must take advantage of the decades of laser research into solving this problem.
M^2 has an X- and Y-component.
The biggest element of a conventional laser to affect the M^2 factor is the laser medium. As it heats up, it creates a thermal lensing effect that spreads out the beam. A laser that does not have a laser medium would therefore excellent for our setting. 

An example of such a laser would be the Free Electron Laser. They are already being developed as a modern day weapons technology, so they are a suitably 'hard' technology. However, data on high-powered FELs is scarce, and omits much of the numbers we need, such as specific power, mass, wallplug-to-beam efficiency and so on. Instead, we will use their less extreme cousins, the Gyrotrons.
A megawatt Gyrotron producing Microwaves. The beam collector can be looped into the electron gun to recover the beam's energy and increase efficiency.
The Gyrotron operates similarly to FELs, but only reaches microwaves as the shortest wavelength it can produce. They have been developed extensively in many high-energy applications, such as fusion ignition, and as a result, we can find a wealth of information on their performance. The first interesting point is their ability to produce megawatt beams for durations of up to 10 seconds on end. The second is their high operating temperature, which helps with cooling. Third, if we recycle the electron beam, we can reach very high efficiencies, building on the current 55-60% figures. 

Of course, Gyrotrons are not very useful as weapons. They produce very poor quality beams (M^2 of 5000 to 10000) due to their operating temperatures, especially at the diamond window. Microwaves suffer greatly from diffraction on top of that. Another type of laser fares much better: VECSELs. 

Laser-pumped VECSEL configuration
VECSELs are not very powerful, but they produce beams of excellent quality. Their thinness and ability to be mounted on large plates means they are very easily cooled. Alone, they are not useful as weapons either, as pumping them electrically gives them very poor specific power. Pumping them optically is much more appropriate, turning them into efficienct converters. Efficiency is poor if you rely on conventional means (flashlamps or arc lights), but the overall efficiency of a two-stage Gyrotron+VECSEL system can rise to an excellent 50%. 
 
However, there is an additional concern: cooling temperature. If the weapon system operates at about 500K, then radiators will be forced to use this low temperature to get rid of hundreds of megawatts of waste heat, resulting in kilometers squared of radiator area. It is vital for a space warship to operate its radiators at much higher temperatures to reduce radiator area and overall mass.
Radiator Area in m^2, Temperature in K, for 1GW heat load at 90% emissivity

The solution is a heat pump. It would extract the waste heat at 500K and push it through a cooling system at 1500K. Doing so requires energy, but leads to an 81-fold reduction in radiator area. By moving the heat in 200K steps, we will require 1.25W input for each 1W moved. 
Instead of a ground source, we have a laser producing waste heat. Instead of water, we will be using a variety of gaseous and liquid coolants suited to each temperature step.

We can be satisfied from a worldbuilding point of view by the reliability of the data and the fact that the principal limit of this weapon system is cooling, not power. A Gyrotron-pumped Vertical-External-Cavity-Surface-Emitting-Laser could handle very high power loads, but would melt soon afterwards. In practice, it allows for thermal management to become a tactical decision. You can decide to 'snipe' with high-powered, high quality shots, giving the weapon time to cool in between shots to reduce M^2 values to a minimum. Or, you can dedicate most of your energy consumption to the heat pumps to allow for continuous shooting. An interesting dilemma is that sometimes, lower powered, low temperature shots can be more damaging than higher power shots pushed through an overheating weapon due to lower beam qulity. At short ranges, you can cut the VECSELs out of the loop and shoot directly with the Gyrotron's microwave beam.  
A solid-state laser producing higher M^2 as temperatures rise.
For lasers to penetrate substantial slabs of armor, it becomes essential that they keep their lasers cool, and their M^2 values low, over long periods of time. Flash coolants based on liquid hydrogen can quickly cool down a laser and restore perfect precision, but it is only a temporary solution, and carries a significant mass penalty. 


With all this information, we will settle on a Gyrotron efficency of 80%, using VECSELs to convert a poor quality microwave beam into a high quality, low wavelength blue (400nm) beam at 60% efficiency. The Gyrotron produces 10MW/ton. A rough guess for VECSEL specific power is 75-100MW/ton. High performance heat pumps based on stirling engines would move 2MW/ton of waste heat. 
A laser satellite venting hot gas.
Flash coolants will work by boiling off liquid hydrogen. It will take 445kJ of heat per kg. One ton of laser weapon at 500K will require between 200 and 600kg of flash coolant to reduce its temperature to 100K, so this is obviously unsustainable.

Another solution is to swap out the hottest components of a laser weapon, or at least, those that influence M^2 values the most. This advocates for switchable focusing elements and multiple main mirrors to spread the heat load. The mass of such a mirror will be 20kg/m^2, about 40kg/m^2 if we include actuators and adaptive optics. The same logic can be applied to flash coolants: they can be used exclusively on the hot diamond window of the gyrotron or the VECSELs, instead of the entire laser's mass, reducing requirements ten-fold per cooling cycle. 

Missiles and Kinetics

Lasers shooting down missiles - the eternal struggle.
In this setting, nuclear engines cannot be miniaturized to fit on missiles. We therefore rely on chemically fuelled rockets. This means that they will never reach the deltaV of a warship, so they have to out-accelerate their target and catch up before the relative velocity is brought to zero. This is problematic at long ranges, as they would need up to 10km/s of deltaV (mass ratio up to 12) to be effective (3000m/s+ impact) against a high acceleration warship (10m/s^2) at long range (4000km).

Without aerodynamics in play, and with chemical rockets being easily scaled, missiles could theoretically be any size, from as long as a bus to the size of a soda can. In the setting though, the size of a missile is determined by how combat plays out. The largest missiles are the most easily detected, and will be fired upon by lasers from extreme ranges. This means that they have to be armored, which reduces their performance. On the other hand, they might be large enough to mount compact, single-burst lasers or even the expensive and complex Casaba Howitzers. The smallest missiles, however, have a significant percentage of their mass taken up by essential compenents such as maneuvering thrusters, propellant pumps and onboard electronics. Again, this leads to low performance and in this case, high fragility to defensive fire. On the other hand, they can swarm laser defenses and deal enough kinetic damage to become significant threats.  


A chemical-fuelled missile with oversized maneuvering thrusters.
In all likelihood, the missile loadout will be varied and tailored for the mission. High velocity shrapnel-cloud missiles to catch fast accelerating targets, large and armored missiles that destroy high value targets from hundreds of kilometers away using lasers, or even staged rockets where the payload is multiple smaller missiles. 

Unguided or 'dumb' kinetics are a relatively poor option. Projectiles would have to be shot at hundreds of kilometers per second to catch warships before they accelerate out of the way. Coilguns are only able to launch projectiles up to a few dozen kilometers per second before the mass of capacitors and magnets exceeds any reasonable benefit. 

Overall, missiles and kinetics are much worse weapons than lasers... which is why they should not be used in the same way.


Missiles excel at extreme ranges, or when using stealth elements. At extreme range, a missile bus or coilgun can launch a packet of missiles, each containing enough deltaV to track and hit any target. A coilgun can easily handle the velocities involved, as we are only adding a 'crossing' velocity of a handful of kilometers per second to the missile. Tracking the target is done with the missile's on-board deltaV. A missile bus is a solution for even larger waves of missiles, or if the mass and energy required by the kinetic launcher becomes too great in comparison to a small-scale nuclear engine on-board the missile bus. 

A missile bus would resemble this.
Such a tactic ensures that all missiles reach the target, even if they do so slowly. Whether they suvive defensive fire depends on whether the missiles decide to spread out and 'go cold' after the missile bus is expended, or if they huddle behind a shield designed to survive the crossing. 

Stealth elements come into play at any range. Even at very short ranges, deploying a separate, cryogenically cooled impactor from your missile makes point defense much harder. Any time you can decouple a cold projectile from a 'hot' missile inserts an uncertainty in the target's missile prediction abilities. This is make exponentially more effective if your cold projectile has some form of ability to move itself, such as cold gas thruster. 

As mentioned earlier, all of these options and intracies make missiles the deciding factor in combat. Laser combat is easily predictable and leads to stalemates when the weaker side can avoid combat entirely. Missiles allow for surprise attacks, a range of tactical choices and more warship variety in design and approach to combat.

For chemical-fuel rockets, we will use an arbitrarily high amount of thrust. Liquid fuel engines today are already able to achieve dozens of kN of thrust per kg component mass. Solid rocket motors can achieve even higher thrust.

SSME

The main limitation is in the choice of propellant. Cryogenic propellants (liquid hydrogen, liquid oxygen) give the best exhaust velocities, but suffer from many complications, such as storing the liquids, fuelling before launch, insulating and pressurising the liquids on-board the missiles, powering turbopumps... it is likely that cryogenic fuels will be used in very long range missiles that reduce the loss of performance from tank and pump mass through sheer size, or in stealth missiles where liquid hydrogen boiloff is used to cool the projectile. This is the preferred missile type by Martians, who have easy access to orbital depots of liquid propellant, and have a shorter mission time, so do not worry much about boil-off. The liquid hydrogen reserve is extremely useful for tactics centered around stealth projectiles.

We use 4500m/s exhaust velocity, 5kN/kg thrust and 10% of the propellant mass becomes tank and pump mass. Overall propellant density is 300kg/m^3. We do not create a separate partition of liquid hydrogen for cooling the projectile. 
Rapid reaction ICBMs use hypergolic fuels.
Hypergolic propellants are better suited for missiles that need to be stored for long periods and fired on short notice. Due to their density, they allow for more compact missiles that require less armor to cover. These are perfect for missiles that are fired in full sight at the enemy, at closer ranges, or for defensive purposes, in a point defence or interception role. Their drawback, however, is an exhaust velocity a full 1000-2000m/s lower than cryogenic propellants. This is the preferred missile type by Terrans, who have to store their missile propellants for long periods of time. The density of the propellant also allows for armored missiles, which forgo stealth for the ability to withstand laser fire. This is important when Terran warships engage enemies on their own territory, therefore backed up by a web of sensors which would greatly reduce the effectiveness of stealth tactics.

We use 3300m/s exhaust velocity. 20kN/kg thrust and 1% of the propellant mass becomes tanks and valves. Overall propellant density is 1200kg/m^3. We need a separate reserve of cryogenic liquid to cool off stealth projectiles.

Solid propellants have the lowest exhaust velocity, but have distinct advantages. They can produce incredible thrusts, and more importantly, can survive being fired out of a coilgun. Electric Solid Propellants, ignited by electrical discharges and highly resistant to heat and damage, which is important if the missiles are fired upon. Exhaust velocity suffers, however. These will be used by coilgun-accelerated projectiles or as a final stage for very long range missiles. 

Electric Solid Propellant test
We use an exhaust velocity of 2700m/s. Thrust is very generous, limited only by what the delicate onboard sensors can handle. If the missile is externally guided, we do not attempt to set a limit. Propellant density is 1800kg/m^3 and does not need casing. 

The smallest nuclear thermal engine will mass 1500kg. It operates in a self-destructive supercritical mode, where the control rods are removed at launch. The reactor cannot shut down or moderate its power, but it will be lighter and smaller. Graphite walls prevent an immediate meltdown, but they are ablated away gradually. It is timed so that the engine's lifetime is long enough to complete the burn. We will assume 1GW/ton, and an exhaust velocity of 7000m/s. The only propellant allowed is liquid hydrogen, as it serves as expendable coolant for the reactor. 

Raytheon's triple Radar-IR-Laser sensor
Guidance is assumed to require no more than 1kg of electronics. On-board sensors mass for a missile are hard to guess, as there are no modern equivalents. We'll use a 500 gram figure for externally-guided missiles, rising to 1kg for a simple IR sensor. At 10kg, we can mount an an active (LIDAR) sensor and handle multiple trajectories. At 100kg, we can mount a cryogenic wide-angle, multi-spectrum sensor, and at 1000kg, we can have a full anti-stealth sensor suite.  

Control of the missile is done along two axis. During the initial burn, the rockets can vector their thrust. Afterwards, the missile relies on hypergolic thruster clusters, or if it relies on stealth, miniature versions of a cold gas rocket. At long ranges, the main laser weapons of the target warship only have to traverse by a few millidegrees to switch between missiles, so highly maneuverable missiles are pointless. At short ranges, laser turrets will be able to traverse at rates of over 100 degrees per second, so missiles will have to accelerate at hundreds of gravities to defeat them. Instead, missiles increase their survivability by scattering to maximal separation, which might be as long diagonally as their distance from the target, then converging from their furthest point. This maximizes the amount of time laser defenses will spend acquiring separate missiles and turning to track them. For this reason, thrusters do not mass much, as lateral acceleration requirements are minimal.

Stealth projectiles rely on three elements: a thermal insulator between the drive section and the payload, to minimize heat transfer, a cryogenic heat sink that boils off to remove the heat absorbed from sunlight, and a cold gas thruster that allows it to track its target. The insulator is lightest element, at only a few grams per m^2 covered. At 1AU, 1300W/m^2 is absorbed from sunlight, requiring an equivalent 3 grams per second per square meter of liquid hydrogen vaporized. The cold gas thruster is the heaviest element, since it is essentially a rocket engine with only 700m/s of exhaust velocity. If the unwitting target started accelerating at 1m/s after detecting a missile launch at 2000km, and the missile's main engine accelerated the stealth projectile to 5km/s, then the cold gas thruster must provide a minimum of 400m/s deltaV. This requires that 60% of the projectile be nothing but propellant. 

 
A fragmentation round.

Special warheads include sand rounds, Casaba Howitzer warheads and chemical lasers. 

Sand rounds carry several tons of cheap milligram sized grains that are spread out in a shotgun manner near the target. These grains will have no effect even on the lightest armor. However, they will scratch the windows that sensors look through, and will damage exposed laser optics. This can give a following wave of missiles an advantage against laser defenses, until the mirrors are repaired.
Casaba Howitzer warheads are expensive, multi-ton weapons made of a combination of rare fissile materials and advanced technology. They are the Terran's 'silver bullet', able to wipe out targets from thousands of kilometers away... but their effectiveness is limited by the fact that they cannot be sent in massed attacks like regular missiles, and therefore can be shot down by lasers unless they detonate from very far away.
Chemical lasers are the cheaper alternative to a Casaba Howitzer. Using a chemical reaction to pump an infrared laser allows for the creation of a multi-Megawatt beam with no cooling requirements. The beam quality is terrible, and it might only function for a few seconds, before its fuel runs out or it is shot down, but all is compensated for by the fact that it is deployed at very close range. A chemical laser at 100km is the equivalent to an advanced gigawatt laser at 1000km.

Launchers

Coilguns are the go-to kinetic launcher in this setting. Railguns are only able to reach velocities of a handful of kilometers per second before rail ablation becomes an unsurmountable issue. 

Also named 'Gauss Cannon'.
 Coilguns have no such limit, but their mass and power requirements have to be balanced between the initial kick they provide, and the deltaV the missile can produce on its own. 

Such launchers are limited by the acceleration they provide by meter of accelerator, and the total energy they can handle. Efficiency can reach 90% and above. The actual amount of energy the coilgun uses depends on the balance between ammunition stores (how much propellant is on the missiles) and the coilgun's energy (and the mass dedicated to the accelerator). A fair split for a 10km/s projectile using hypergolic fuels is 5km/s from the coilgun and 5km/s from the missile. The missile will be 77% propellant. If it masses 500kg, it would form a cone about 66cm wide and 300cm long. The energy required to accelerate it is 6.25GJ, and the coilgun requires 6.94GJ. This also means that the projectile needs a temperature resistant 'sabot' to absorb the waste heat and prevent it from reaching the projectile itself. This is quite important if the missile is tipped with a stealth projectile, or it we want the hypergolic propellants to not ignite inside the tanks. 
  Higher accelerations allow for shorter coilguns and less overall mass. They will also need to operate at high temperatures, as cryogenic superconducting magnets do not work well with gigajoules of energy. For these reasons, an asynchronous coilgun with potentially unlimited magnetic fields strength and operating temperature.

11.75 Tesla is what the largest modern MRI scanner achieves. 15 Tesla is therefore conceivable for a future weapons system. At that field strength, and using a 1m wide sabot, the coilgun will have to be at least 89m long, and produces a horrendous 28000g acceleration. The electronics will survive, and the bottom of the fuel tank must withstand a pressure of 300 MegaPascal. This requires very high strength steel, or that the fuel tank be built into the armor. 

Compared to a railgun, the coils are lightweight. A NASA study put it at 27kg/m for a 3 tesla magnetic field, so a conservative figure of 100kg/m is suitable for our purposes. The bracing support, however, must withstand stresses from both the momentum transfer and the radial component of the magnetic fields. Current experiments used thin shells of steel to hold the magnetic coils generating 25T fields, so the overall mass should not exceed 1 ton per meter length. 
A typical earth-bound Superconducting Magnetic Energy Storage
Power storage is another complex issue. The coilgun example mentioned above requires nearly 7GJ of stored energy, to be released at a rate of 390GW. Superconducting Magnetic Energy Storage is the solution - with future availability of high-strength materials, SMES can reach 50MJ/ton or above of energy capacity, and are able to deliver it very quickly and with few losses. A 140 ton SMES can deliver the energy required for a single shot.
      
Armor

We now move on to armor....
Although the proper worldbuilding process should have us design the two in tandem. Weapons are designed to reliably defeat armor, while armor is designed to reliably withstand the very same weapons. 
General armor scheme for the Yamato
Laser armor

Defending against lasers is heavily dependent on the engagement distance. At very short ranges (100km or so), putting up armor against lasers is pointless, as they will be able to carve your spaceship in half in a matter of seconds. At extreme ranges (100000km+), they might not be able to heat up the surface enough to melt it....

A Megawatt laser with an effective range of 300km against thin-skinned missile boosters.
Laser armor would also have to deal with an incredible variety of situations. In a high speed enounter between an attacking fleet and an intercepting force, relative velocities can be in excess of 150km/s. At those velocities, the difference between extreme and short ranges can be as short as 10 minutes. On the other hand, we have situations where two warships of equivalent acceleration capabilities attempt to chase each other, and do not close the gap. The armor would have to withstand laser fire for minutes to hours on end. 

Worse, the attacks can come from any direction. The closer the combatants, the faster an attacker can position themselves at an angle and fire diagonally at your armor. 

Finally, the armor has to be very effective per unit of mass, not volume. 

Despite all these constraints, there are constants we can rely on. Lasers damage the armor through a very rapid transfer of energy. The transfer is so rapid that we cannot rely on the material, either through passive conduction or active cooling, to spread the energy received to other areas. The most effective way to deal with a laser strike is therefore to focus on the material's vaporization energy first, and yield strength (hot material expands and wants to break away) second. 

Diamond-Like Carbon. Can be made transparent or into lenses.
One material stands out from the rest in all domains: diamond-like carbon.

It combines the excellent 355kJ/mol heat of vaporization, a very high Young's Modulus of 40 Gigapascals, and a low molar mass of 12g/mol. This leads to a very high heat and damage resistance per kilogram. 

Here's a small table of values demonstrating its effectiveness against a 250MW/400nm/4m laser at various ranges:

10000km: No damage.
4000km: 0.3mm/sec
1000km: 20mm/sec
200km: 2.6m/sec

We can see that the same armor which impervious to damage at longer ranges, becomes paper as it approaches a target firing at it. The penetration rate increases linearly with laser power, but increases by cube with the mirror radius and laser wavelength. This means that a laser of the same power will penetrate eight times faster with a mirror twice the size, or a beam of half the wavelength.

Warships might be reduced to a series of these floating in space thousands of kilometers apart.
The laser wavelength is strongly tied to the technological limits of the setting, as military lasers will operate at the shortest wavelength that is practicable, not the shortest possible. This is because there are serious design consequences in attempting to generate and focus, say, and x-ray laser beam. From a worldbuilding perspective, it is easy to justify why military lasers use 400nm beams, instead of the eight times more effective 200nm beams. It is much harder to justify why the mirrors aren't 'just bigger'.

A 20m mirror proposal for illuminating the Earth's surface.

Laser warships will therefore try to stay outside of the opponent's effective range, especially if they detect that the opponent has a larger mirror. The 'effective range', however, if further complicated by heat management. As mentioned above, M^2 values increase sharply with the laser's temperature. A laser that can just spent several minutes at full output shooting down incoming missiles will have an M^2 value up to a hundred times larger, and penetrate a thousand times less, than a cold and fresh laser that has just arrived at the scene of battle. For this reason, as the battle goes on and combatants use up all of their flash coolant charges, lasers run hotter and hotter, and you can get closer to your target without being damaged in return.

Here is another small table detailing the penetration rates, at the same ranges, but with multiple M^2 values.

10000km: No damage. (M^2): (1.1) No damage. (3) No damage. (100) None.
4000km: 0.3mm/sec (M^2): (1.1) 0.24mm/sec (3) No damage. (100) None.
1000km: 20mm/sec (M^2): (1.1) 16.5mm/sec (3) 2.22mm/sec (100) None.
200km: 2.6m/sec (M^2): (1.1) 2148mm/sec (3) 288mm/sec (100) 0.26mm/s


We quickly see that a hot laser rapidly becomes ineffective. At very high temperatures and M^2 values, it becomes unable to stop even a thinly armored missile at close ranges. 


A one ton mirror will have a diameter of about 5.6m. A 1000 ton mirror will have a diameter of about 178m and should be the largest possible combat mirror available to a military. Against the largest mirrors, warships have to use some way of spreading the damage inflicted by a laser. This is necessary as the closer the warship is to its target, the shorter the distance the missiles have to travel, and therefore the more survive the defensive fire and/or the lower the number of missiles are required to overwhelm such defenses.

As stated in our list of objectives, we want warships to withstand 'significant damage'. This can be translated into a lifetime expectancy, or in other words, how long the average warship will survive against an average laser at a distance where the average missile swarm becomes effective against that laser. It sounds simple, but it is hard to balance. 


The best way to solve the problem is to turn a variable into a constant, and solve the rest. In our case, the laser is expected to produce a 400nm beam with 250MW of power, and we will solve for a range of 1000km. 

At a distance of 1000km, a 10km/s projectile takes 100s to reach its target. Over that period of time, our laser removes 1650mm of armor from the warship, and about 198 meters of armor from a missile. A sensible solution is to distribute this amount over several missiles, but the numbers required quickly favor lasers in fleet engagements. 

Here is a graph of the armor penetration over time, as the missile wave approaches the laser. It is important to note that while penetration rates quickly go up, the missiles become less vulnerable over time. They drain their combustible fuel, and turn into inert cones of carbon. This creates a boundary within which damaged missiles will still hit their target.  


Y-axis is in millimeters, X-axis is in seconds
For the first 60 seconds, over half of the crossing, a perfect laser goes through 4.2m of armor. In the remaining 30 seconds, it goes through an additional 86 meters. The orange curve is an non-perfect laser, where the M^2 value goes up by 1 per second, starting at 1.1 and ending at 91. The armor penetration drops to only 10 meters

100km, or 10 seconds before impact, is chosen as the range at which it becomes more effective to use multiple turrets with small mirrors than a single large mirror. This 'point defense' is too heavily affected by finite tracking rates and  acquisition times to conform to a simple penetration rate vs armor analysis. 

The number of missiles required depends on how each faction in this setting approaches the problem.

The first larger missile wave forces the targets to heat up their lasers, and the second smaller wave attacks them when their lasers become unfocused. For each enemy warship, two such strikes are required, although the use of flash coolant can push this number to three or four strikes. The battle becomes a balance between reserving missiles for another wave and forcing the targets to heat up, between staying at close range to reduce the number of missiles required and send out more waves or staying at longer range and saving your armor, and between dedicating your lasers to shooting down missiles or attacking the opponent directly and forcing them off. 

Such an analysis is too great for one person. Instead, we will work backwards from the intended results. Our 'significant damage' objective can be fulfilled with 20 minutes of sustained fire resistance. Against a single laser with perfect cooling and 16.5mm/sec penetration rate, this would require a whopping 19.8 meters armor thickness.

To reduce the armor requirement, we will rely on rotation and sloping.
Rotation will reduce the penetration rate by a factor (Rotation velocity/spot size). At 1000km, the standard laser has a spot size 24.4cm in diameter. A 6m diameter warship with an armor belt rotating once per second can have a reducing factor of 77. Against a larger laser equipped with a 10m mirror and producing a spot size of 9.76cm, the reducing factor is an even higher 193. This means that against rotating armor, more focused lasers fare worse than less focused lasers.
Effective armor thickness at various angles.

Sloping depends on the angle the laser is firing at. If the target is returning fire from straight ahead, extreme angles can increase the effective armor depth by a factor 5 or more. If the warship's nose is a 30 degree cone, its effective depth is twice that of its nominal depth. At 15 degrees, it is 3.86 times the depth. 

If we consider the average fleet to be composed of three laser-equipped warships, one coilgun equipped warship for stealth rounds, and an 'arsenal' warship dropping waves of missiles, then we can expect up to three standard lasers firing at our warship. We obtain the following numbers:

16.5mm x 3: 49.5mm/sec penetration
49.5 x 1200: 59400mm total penetration over 20 minutes
59400/77: 771mm/sec after rotating the 6m diameter armor belt once per sec
771/3.86: 199mm after angling the armor at 15 degrees. 

200mm of armor masses about 460kg per square meter. 

We will need thicker armor or suffer lower survivability if we face more powerful beams, more numerous beams or a flanking attack.

If we manage to use contra-rotating nestled shells (a larger outer shell rotating in one direction, a smaller inner shell rotating in the opposite direction), we can double the rotation reduction factor. If we wobble the nose cone back and forth, we can force the beam spot to travel vertically as well as horizontally, reducing penetration rate by another factor 3-4. 

Advanced armor techniques can reduce the armor required to only 25mm.       


Martians will use 'simple' armor techniques, but more violently. For example, the armor shell will rotate at higher velocities, the warship will rotate itself in the opposite direction, and random micro-bursts from the rocket engines will force the laser beam to travel up and down the armor. 

Terrans will use the advanced armor techniques to save mass. Multiple contra-rotating shells and a wobble program, compensated for by electromagnetic bearings and high velocity flywheels to compensate for the mass shifts. 


Kinetic armor
 
In some ways, defending against kinetic strikes is vastly more complicated than laser damage. However, designing defenses for it is a simpler matter.

Exoatmospheric Kill Vehicle, Capability Enhancement II, by Raytheon
Kinetic strikes at space velocities deliver nearly all of the projectile's kinetic energy to the target armor. At 10km/s, as described in Electric Cannons, you must treat the impactor and the target as fluids. Penetration is equal to the length of the penetrator times the root of the ratio in densities.

A 5kg missile with 500m/s of deltaV, using hypergolic propellants that double as maneuvering reserves, released at 10km/s by a missile bus, will be armored with a needle-like cone of carbon armor. It will have an average density of about 2100kg/m^3 (2300kg/m^3 carbon, 1200kg/m^3 propellant). It can be shaped into a cone 15cm wide and 40 cm long, and will be empty by the time it impacts.

Using our hydrodynamic approximation, we know that it will penetrate up to 40cm of carbon armor. This is too much armor to be practical. A 10kg penetrator, for example, will go through about 60cm, and a single 500kg stealth missile can launch ten of them. A regular, direct-attack all-chemical missile bus of 10 tons will carry a hundred of them. 

Rotating such a heavy armor shell, then excavating a chunk out of it and imparting between 50 and 100 kiloNewton.meters of momentum per impact, will lead to its complete failure. If anyone has witnessed an unbalanced load in a washing machine, then they have seen the result.

Sloping will be useful, but missiles have enough deltaV at combat ranges to run loops around their targets and hit the sides straight-on. Instead, sloping will be optimized for laser combat.  

Three methods will be used to defeat kinetics and save mass:

Armor belts on the US battleship Iowa.
-Armor belt. 
We use 'armor belts' because protecting the entire ship from a kinetic strike is pointless. It would mass a huge amount to do so, and most of the ship's volume is propellant. With water as propellant, it does not need to be pressurized, only insulated and heated to remain liquid. If a propellant tank is pierced, some water will be vaporized, a lot of it will be expelled out of the hole... but then it freezes once exposed to space and plugs up the propellant tank. Furthermore, leaking propellant doesn't stop the warship from fighting. We only protect the vital parts of the warship, which are the crew and computers, and the nuclear engine, in 'all or nothing' scheme.  


Whipple shields after hypervelocity impact. Effectiveness is directly tied to plate separation.
-Whipple shields
The best defence against kinetics is a Whipple Shield. The kinetic energy of a projectile is used against it: a thin plate is placed at a distance from the main hull. When the projectile strikes this plate, part of the nose is vaporized by the impact, and the rest of the body shatters. Complete disruption of the aforementioned 5kg projectile would only require a whipple shield of a few millimeters thickness, even made of plastic. This works perfectly for micrometeorites, but is less effective against projectiles designed to defeat whipple shielding. Such projectiles will eject a small projectile ahead of themselves. This 'tandem' projectile will strike the whipple shield and clear a path for the main penetrator. Three, four or more tandem projectiles can be sent ahead, going through multiple shields, at a very small cost to the projectile. Of course, the Whipple shields themselves can be burnt away by lasers. 

Reactive armor bricks on the T-72 Main Battle Tank.

-Reactive armor
Chemical explosives used in modern reactive armor function at velocities three to five times slower than space projectiles will impact at. Whipple shields may be able to break up a projectile and vaporize the nose, but they will be have to be excessively massive to stop a relatively compact clump of metal shards from striking the main armor. Instead, we will use Explosively Formed Projectiles. A brick of explosives is topped by a thin plate of metal and a sensor. The sensor can detect projectiles at short ranges, and within microseconds, will work out whether it can intercept the projectile. The explosives are detonated. The metal plate is flung outwards at velocities of about 1.5 to 2.5km/s. At terminal ranges, it will take a handful of seconds between detection and impact. The EFP's task is helped by the fact that missiles reach the terminal stage with tanks empty and very reduced maneuvering deltaV. 

Due to the velocities involved, only a small plate of metal is required, and the entire assembly can mass less than a kilogram. Even if they have to face an unusually large projectile that does not get destroyed by the impact, they will act is a Whipple shield with an extreme separation distance, meaning debris will spread out much more than within a hull-mounted shield with a separation of a meter or less.   
An Explosively-Formed Projectile.
Reactive armor is more effective than a static Whipple Shield, and can be mounted on racks that are unshuttered once a kinetic strike is detected to protect the bricks from laser attack. However, they become expensive, as thousands are required to cover all angles of attack. They too can be used in armor belt configurations. It is more likely that Terran warships will have a lot of reactive armor that can be 'reloaded', while Martian ships will feature less reactive armor, with the smallest ships relying on conventional multi-layer Whipple Shields. 

With these conditions, we set 60m as the effective armor required to survive a three-laser attack for 20 minutes. This figure will be reduced through rotating shells and sloping to a sub-200mm figure. Kinetic armor will be divided into belts of about 0.4 to 1 meter thickness, of only a few meters length. Large-diameter ships will use steel belts. If it is deemed worthwhile, reactive armor bricks will line important areas of the ship instead of, or in addition to, conventional armor. Whipple shields will be relegated to inexpensive or small ships that do not expect to come under laser fire.
  In the next instalment, we will discuss point defense, mass ratios and put together a baseline spaceship from which we can develop full designs.

23 comments:

  1. Hello, I just had a few questions that I was thinking of when I was reading this post and would like to ask them. I apologize before hand if these questions are either out of place or currently impossible to answer.

    1. How would particle beams fit in the scheme in which you depict? I've heard that what particle beams lack in range make up in damage potential, and I thought they would have some role in space combat. Do particle beams actually out perform lasers in terms of damage? If they are useful, what kind of range could be expected of these weapons? If particle beams are used in space warfare, what kind of beams would be used (plasma, neutron, hadron, etc.)?

    2. Are photon molecules able to be used as space weapons? I keep hearing that they can be theoretically used to make lightsaber blades, but I'm not sure if that is one hundred percent publicity or if there is some truth to that; I tried to find the information on my own, but few sources were forth coming about its properties. Would a photon molecule weapon be like a hybrid between a laser and particle beam (practical for a turret with a reduced range compensated by little to no dwell time)? Would a photon molecule weapon be used as a charged (orbit to ground attack) or neutral (ship to ship) particle beam?

    I apologize for the mouthful of questions and thank you for your time.

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    1. Always willing to help!

      Particle beams have these main advantages:
      -Greater efficiency compared to lasers
      -Do not rely on massive mirrors to be focused
      -Spread their energy deep into the target material
      -Produce secondary radiation upon impact
      However, they suffer from:
      -Much lower focusing ability
      -Charged particle beams can be deflected, neutral beams less so

      When I say 'lower focusing ability', I mean that a particle beam is the equivalent to a microwave to mid-infrared laser at best. I mentioned in this post that the penetration rate increases by cubes with wavelength. A regular blue laser will therefore deal more than 10000 times the damage of a particle beam at the same range. This is a good enough reason for particle beams to be disregarded for use as your main weapon.

      If you want some numbers: a particle beam will be useful or ranges up to 1000km, and they do outperform lasers up to this distance. Neutral beams must be used (a positive ion beam is neutralized by a co-axial electron beam of 1860 times less energy).

      Photon molecules are hypothetical, but even if they behave the way we expect them to, they can only do so in extreme conditions or in carefully controlled near-zero temperature experiments. They have no use as a weapon or a substance. They might be useful as an extremely fragile way to store energy, but for now, all applications are in quantum computing and data storage...

      What has been mentioned as a mechanic behind lightsabers is magnetically-confined plasma. However, it has so much problems trying to fit with the various ways lightsabers are depicted in the movies that you have to admit that lightsabers are too magical to be explained scientifically.

      Feel free to ask for clarifications, or more questions.

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  2. Why use liquid hydrogen as a coolant when water (and vaporization of water) requires less tank mass, less complicated plumbing, and is easily 30x as efficient per unit mass of coolant used?

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    1. Liquid hydrogen holds many advantages over water, as a coolant.

      It has 9.8kJ/kg/K heat capacity compared to water's 4kJ/kg/K. It can operate over a wider range of temperatures without starting as a solid or decomposing into voracious free oxygen. You can start at 2K temperature instead of liquid water's 273K, giving you a larger heat sink. As a flash coolant, it can reduce operating temperatures back to the cryogenic levels the laser starts off with (with consequent M^2s of 1.x) instead of merely reducing it to relatively hot temperatures.

      Water will, of course, hold advantages in terms of volume and complexity. You have a boatload of it in your propellant tanks. However, there is no reason why a warship on a month long trip between planets won't use that time to extract hydrogen from its water tanks, cool it into LH2, boil off the hydrogen in combat, then burn the hot hydrogen back into water after combat. Mass saving and larger temperature range all in one.

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    2. This is not entirely accurate, and it overlooks at least one important consideration.
      First, LH solidifies at 14°K (under standard pressure), which sets the actual start point. LH at 2°K IS possible, but this is typically classified as a superfluid, and is VERY difficult to achieve. It is more difficult to maintain in a liquid state. Liquid Helium, which does not have a (known) solid state under standard pressure, would be much more useful for very cold heat exchange.
      Second, although the hc of LH is superior to that of liquid H2O, per degree, the functional temperature range is MUCH lower. You get about 5°K of heat absorbtion using LH, but 100°K using H2O. This means that LH will absorb a total of 50kJ, while liquid H2O will absorb 400kJ. Likewise, although it would still be possible to use both even in solid form (for instance, as a slush mixed with liquid helium, or as cryostatic plates), hydrogen again has a much smaller temperature range. Thus, the actual heat absorbed by "superior performance" hydrogen (I believe that even the latent heat of fusion is higher, but I could be mistaken) would be much less than that of H2O. The REAL benefit of H2O comes with the latent heat of evapouration, which is much greater than Hydrogen. Once in vapour form, IIRC, hydrogen will slowly begin to catch up with H2O in overall performance, but it is much more difficult to contain expanding hydrogen gas. Thus, you really can't use it as a heat sink at this point. Instead, hydrogen would be much better used as a cold vapour reaction mass.

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    3. Yes, sorry, my mistake. Hydrogen starts is likely to be kept at about 20K, not 2K. The difference is only about 262kJ/kg.

      The major advantage of LIQUID hydrogen is that the phase change into gaseous state absorbs several hundred kJ of energy per kilo. The heat of vaporization is about 10x the amount of energy absorbed by water going from 0 to 100C.

      Another issue is that water is just too hot. At 273 to 373K, it shines brightly in infrared compared to hydrogen.

      > The REAL benefit of H2O comes with the latent heat of evapouration, which is much greater than Hydrogen

      Exactly my point!

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  3. Does Particle field armor have any relevancy in this setting or is it too technologically advanced for this scenario? I know it will provide no protection against lasers, but is it effective against guided missiles and dumb rounds (solid slug, fragmentation round, etc.)?

    Even if they are not useful during combat, wouldn't ships mount them anyway, or at least a different form of them for protection against cosmic radiation or weaponized radiation? Wouldn't this play a part in the duration of battle (a captain with a ship with a shield operating at say "10-12%" due to battle damage would have to retreat and seek shelter to protect the crew from being irradiated)?

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    1. If by Particle field armor, you mean magnetic fields used to deflect particle beams... then, no, they have no place here. The sheer radiation depth provided by the solid armor of 200-1000mm thickness means that magnetic shielding against natural cosmic rays is not needed.

      Kinetics are unaffected by magnetic fields. They can be, but it requires velocities of 100km/s, not 10km/s. At 100km/s, just striking gas is enough to blow up the projectiles into balls of plasma. This plasma can then be deflected by magnetic fields.

      The average crew count is 3 people per ship, by the way.

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    2. Hey hey, but there can be shields with magnetic fields making plasma bubble, or with particles instead of plasma, but I don't know how would they perform. I think Atomic Rockets says the plasma could protect against microwaves, but I'm not sure. If plasma would be hot, dense, and bubble would be big enough, it could help with kinetics I think.

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    3. Kinetics at 10km/s are not affected by plasma shields held together by magnetic fields. They'd have to hit it at much greater velocities.

      One option, however, is to maintain solid plates of metal at a distance from your hull, using magnetic fields to pin them in place. They would disrupt the projectile, and use the space between the plate and the hull as a Whipple shield. However, in this specific setting, large magnets sucking power to hold a metal plate against the combat accelerations the warship can produce came out to be a heavier and more expensive alternative to cheap 'reactive EFP plates' that do not consume any power, can withstand any acceleration and can intercept projectiles up to a kilometer away, if not more.

      Plasma can reflect radiations. They can even reflect lasers. However, shorter wavelengths require hotter plasmas. Re-entry plasma at 6000K can reflect radio. Trying to do the same with optical wavelengths requires extreme temperatures. Reflecting ultraviolet requires something like 25000K+. You'd have to hold this extremely hot plasma around your hull, which would cook you, you'd have to keep putting energy in to compensate for the plasma energy being radiated away, and you'd still need massive magnets to hold it in place at useful densities (higher density plasma at higher temperatures requires stronger magnetic fields. See: magnetic confinement fusion).

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  4. Some thoughts:

    Small person crews, being carried on a main bus before battle along with other craft... sounds like a space 'bomber'. Would small escorts be space 'fighters'> >> << >>

    Sorry, couldn't resist.

    I'm also thinking of The Millenium Falcon in ROTJ in terms of crew dynamic. Or Firefly.

    Regarding armour, I presume the turrets that can't rotate would be hidden behind a spinning armour section, popping out at will, or thickly armoured themselves? Same for sensors.

    Finally, I've notices an increasing number of military space craft designs (especially those by William Black) have wrap around radiators rather than panels. I've had a thought on this. I'm not a numbers man, so it might be impractical, but have a look at this if it helps.


    Heat radiators- Layered over pyramidal prisms extending out of the main hull. A nacelle essentially joined to the hull. Between each layer is a propellant tank, small equipment that can be crammed in the space between, and armour. Being essentially a wrap around radiator, the panels will not be easily shot off. If the prism on each side is solidly constructed, it too will withstand fire. Shutters could come down over the panels (or the panels withdraw, shutter-like in to the main hull like a conventional radiator panel) in the event of concentrated enemy fire.
    Furthermore, the radiators would be protected by each other- their thickness obscuring sides from the enemy if the craft manoeuvred properly. If done well, only one side of two radiators might be exposed to incoming fire… leaving the other six untouched. With lasers and close-proximity nuclear warheads capable of flaying the surface of a spacecraft of its surface material, possessing such a radiator design would be preferable to that of a drum radiator, with 50% of its surface constantly exposed to enemy fire. The website ‘Children of a Dead Earth’ has a good illustration of concentrated laser fire on a spacecraft hull, of which I’m sure you are aware.

    While these prism protrusions might increase the profile (and the mass) of the spacecraft, the profile of the radiators panels would be reduced due to the base of each panel being further away from the tip of the prism. Such a design could allow a craft to expose its radiators in times of thermal build-up, and to buy its heat-sinks more time, or simply increase the rate of laser firing.
    This may not work entirely, but I believe that in light of the advantages it could deliver, it should be an option for some types of spacecraft.

    (it also gives you another aesthetic difference from civilian spacecraft).

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    1. Have we finally found the solution to Space Fighters?!

      If you need to mount turrets on rotating armor, just use a non-rotating section, or if they are of the bolt-on type, a counter-rotating external band that keeps them stable relative to the target.

      Pyramidal prisms increase surface area, but would radiate into each other.

      Wrap-around radiators are an excellent solution if the temperatures they operate at can handle your heat load, as they are restricted in surface area available. They can only radiate from one side, too.

      If you need more surface area, you can cover the whole hull, along with plumbing and interference nightmares... or just stick panels out the side.

      I will try to work out a setting where the very armor plates surrounding the spaceships are run through with coolant. I'm assuming in-armor radiators would make for a low temperature, low emissivity but extremely durable cooling system.

      In comparison, wrap-around radiators are no more or less vulnerable than wing radiators. Maybe less-so, as wing radiators can be angled into the direction of fire, reducing their cross-section.

      CoaD is a bit of a schizo-tech setting in my opinion. Megawatt nuclear reactors in space! Railguns! But lasers are pumped by flashlights with a maximum 6% efficiency. I understand the objective, which is to drastically reduce combat ranges and create a more engaging experience, but I do believe players can learn to appreciate actual combat ranges, just like Kerbal Space Program created fans of Real Solar System 11-minute launches to earth orbit despite the developer's original intent of creating a fun and easy 2-minute to space option.

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    2. "Pyramidal prisms increase surface area, but would radiate into each other.

      Wrap-around radiators are an excellent solution if the temperatures they operate at can handle your heat load, as they are restricted in surface area available. They can only radiate from one side, too. "

      Indeed, with that in mind (CoaD seems to think radiators radiating each other is a minor problem, I'm not so sure on that), I'd limit the prisms to either two or three. Thus the only impossible to solve problem remaining is the inability to angle the radiators. (I plead guilty of being attached to them due to the aesthetic appeal of 'glowing nacelles')

      For more conventional solutions though, I have wondered for many years about the value of ballenite- overlapping armour with non-overlapping holes over a radiators. A low-emissions kinetic craft might protect its panels/ drum with shutters of the stuff, confident that its heat sinks will have more time to store heat due to the holes in the armour letting some of the heat through. Mr Chung seemed to think it had potential, though practicability if obviously not garunteed without serious numbers work.

      Running coolant through armour... I keep thinking that opens up other possibilities. A plumbing nightmare certainly, but could other materials be pumped through too? Sealing foam or molten metal (this last one beyond the plausible mid future I'll admit) to seal breaches, microbots (not nano) to work repairs on the surface. Having thought about your nano-bots page, I've been thinking that slowly healing a 'skin wound' with microbots being pumped around a spacecraft with sensors inside that register damage makes it more and more like a facsimile of a living creature, especially if it had an ai. The fact that major repairs would require outside help only reinforces the image of a self-reliant but not invulnerable 'synthetic yet living' spacecraft.

      And yes, you finally have a potential space fighter solution. :)

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    3. Could you give me more details on your overlapping armor radiators idea?

      Sealing foam is unlikely to be pumped through armor, because what is it keeping sealed? Self-healing propellant tanks? Depressurized compartments? How will it know when to solidify?

      Microbots repairing the spaceship is definitely a futuristic technology. Microbots replacing sensors or unplugging a damaged circuit-board, yes, microbots being used to weld tiny particles of metal into place when slapping a repair kit on the hole would do, no.

      They would also run directly against the 'humans are needed in space warfare' trope by removing the 'humans do repairs' excuse :(

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    4. Microbots would fill in micro-fractures that humans would find fiddly to fill in themselves (Preventing them from becoming bigger when strained under acceleration). Humans WOULD supervise them to make sure they were filling in the right holes- no point having these robots if you fail to spot those with bit-rot and corrupted programming. If successful, this would allow valuable macro-plates and other repair resources to be devoted to larger gashes. They'd also repair sensors, fuel lines, etc. These microbots wouldn't be that small, maybe between the size of a finger or a hand. Humans would plate over the larger holes in the traditional way.

      Regarding foam, I just thought that having two agents congregate at a hole, mix and then seal to cover a hull breach and stop air leaving was a reasonably low-tech idea. I heard it discussed somewhere.

      The overlapping armour would consist of multiple sheets like whipple armour. These would have small holes cut into it, but in a way that the holes wouldn't overlap, you can't shoot straight through (and the edges could bleed kinetic energy off an incoming projectile). The radiators are encased in this when under fire, and exposed when not. Essentially the holes would allow some heat through into the vacuum, though the armour would be heated up significantly. It's just an attempt to allow some minimal radiating of heat even when being fired at.

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  5. Hey, do you know the rec.arts.sf.science Google discussion group? I have an interesting conversation there, titled "waterskiing spacecraft manevuering", but we talk mostly about interstellar waterskiing warship there, mostly about idea with modular ship, the engine part ("tug") and a warship attached to it on cables... What do you think? Check out this group if you have time :)

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  6. "The solution is a heat pump. It would extract the waste heat at 500K and push it through a cooling system at 1500K. Doing so requires energy, but leads to an 81-fold reduction in radiator area. By moving the heat in 200K steps, we will require 1.25W input for each 1W moved."

    There are several errors here. First, for each 1W of 500K heat that goes into your heat pump, 3W of 1500K heat will come out (2nd law of thermodynamics). This assumes a perfectly efficient pump.

    Second, for each 1W of heat that goes into the pump, you'll need 2W of work (electrical power probably). Chaining smaller pumps won't change that. Generating these 2W, in turn, will create an additional 6W of waste heat (assuming a 2000K reactor).

    So for each 1W of waste heat that comes out of your laser you'll need to dissipate 9W in your radiators. Since radiators three times as hot are 81 times more performant, you've got a 9-fold reduction in radiator area.

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    1. "Chaining smaller pumps won't change that."

      I have tried finding answers to this, to no avail. What I do know is that moving heat in small 100K steps requires much less energy than doing it all at once, with a single pump.

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    2. I think you've forgotten to account for the increase in heat at each step. Say you're moving 1W of heat from 500K to 1500K in 500K steps.

      The power requirement for moving heat (assuming perfect efficiency) is : heat input * temperature difference / input temperature.

      If you suppose you'll only have to move 1W of heat at each step, then you find a power requirement of 1W * 500K/500K + 1W * 500K/1000K = 1.5W. Taking more, smaller steps decreases this even more.

      However, after the first step you'll actually have to move 2W of heat (again, 2nd law : entropy in equals entropy out (at best), and entropy is heat over temperature).

      So your power requirement is 1W * 500K/500K + 2W * 500K/1000K = 2W, the same as with one step. More steps won't change that.

      It's simply conservation of energy, by the way: if you put 1W of heat in and get 3W of heat out (and the 2nd law dictates you do) then you have to put 2W on the table.

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    3. Thanks for the explanation. This will mean I have to rework some things...

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  7. A note about "miniaturising" nuclear reactors for missiles: for interplanetary missiles, you really don't need any miniaturisation, as even gas-core reactor designs will easily fit into a 3m diameter shell. That said, smaller designs (1.5 or 2m shell) are equally possible, but would require a modest reduction of Isp and overall thrust (pressure containment limitations will limit the amount of fuel that can be burnt, as well as the amount of propellant), but this would still be superior to chemical performance.
    The REAL downside, however, is the cost of each missile. OTOH, if you are using a solid core reactor, this solid mass of fuel rods can be used as the injection mass that brings a nuclear warhead core to supercritical mass. Injected gaseous core material, depleted of coolant, should also work, but I don't know how this would affect the dynamics for initiating a cascading (uncontrolled) chain reaction.

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    1. I've been looking into solutions for greatly increasing the pressure limitations on gas-core nuclear rockets. I might make a post on it!

      Also, I've been playing Children of a Dead Earth, and the tiny nuclear rockets you can make on there are giving me a new perspective on missile performance...

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