Lasers, Mirrors and Star Pyramids

[MatterBeam]

Hi all! I thought you might enjoy this:
http://toughsf.blogspot.com/2018/05/lasers-mirrors-and-star-pyramids.html

Lasers, Mirrors and Star Pyramids

 

Lasers can hit targets at extreme ranges, at the fastest speed possible. They are ideal weapons for space warfare. 

However, everyone knows that lasers bounce off mirrors... does this make lasers useless?

The post is inspired by the discussion that arose from the conclusions stated by Kyle Hill (@sci_phile) in 'The Truth about Space Warfare' video for Because Science.

Many commenters asked me about how mirrors could be used to counter lasers. This is the response I promised. 

 

 

Common assumptions and common answers

 

 

An electrically pumped VECSEL, which promises high efficiency and powerful beams.

The usual understanding of laser weapons is that they produce a bright light that slices through armor. Mirrors can bounce away this beam, rendering it harmless.

 

A laser defeated by a mirror?

The realistic science fiction community, centered around the efforts of the Atomic Rockets website, did their research with regards to the effectiveness of mirrors against lasers, and found that no mirror could be 100% reflective. It would always absorb some of the laser's energy, which would result in it heating up, melting and therefore losing its reflective properties. Because laser weaponry produce several kilowatts to hundreds of megawatts of power, the transition from 'cold and reflecting' to 'molten and ineffective' would happen very quickly.

 

 

 

As a result, the common answer to 'what about mirrors?' is that they are ineffective.

 

ToughSF will revisit the concept, as it has done with other 'established' truths of science fiction.

 

How do lasers deal damage?

A laser guide star for a telescope's adaptive optics.

To first understand the effectiveness of a defense, we must first understand the type of damage it is trying to mitigate.

 

Lasers produce an intense spot of light on the surface of the target. As a directed energy weapon, its primary purpose is to heat up that surface until it deals damage. 

 

Continuous lasers produce a constant stream of energy. Pulsed lasers produce short bursts of much higher power, but much shorter duration, spaced by intervals as small as a microsecond.

 

Pulsed laser effects at different pulse lengths.

One measure of a laser's destructive capability is its intensity at the target, in watts per square meter (W/m^2).

 

Sunlight has an intensity of 1kW/m^2 on Earth's surface, lightbulb filaments produce an intensity of 1MW/m^2 at their surface and lightning strikes flash at an impressive 10GW/m^2 in some cases. 

 

When a laser strikes a surface, it raises the temperature of that surface's material. At a certain temperature, it melts and moves out of the way. Other materials vaporize, turning into a gas that expands rapidly. At very high intensities, such as those produced by a pulsed laser, the vaporization gases expand so quickly that they overcome the mechanical strength of the surrounding material and shear off chunks or drag along debris out into space.

The best armor materials are those that take the most energy to heat up (high heat capacity), the most energy to destroy (high melting or vaporization energy) and have the highest mechanical strength (tensile strength). In space, every kilogram is important, so we also want the armor to have good characteristics for its weight.

 

For these reasons, steel is a bad armor material while graphite is an excellent armor material.

Steel cutting.

Steel has a low heat capacity (0.5kJ/kg/K), a low melting energy (240kJ/kg at 1640K) and good strength (600MPa). 

Vaporizing graphite to produce carbon nanotubes require extreme temperatures.

Graphite has a great heat capacity (0.72J/kg/K), an extreme vaporization energy (59.5MJ/kg at 4000K) and poor strength (30MPa). 

 

Steel can only absorb 923kJ/kg before it is destroyed. Graphite absorbs up to 62MJ/kg, meaning each kilogram of graphite is worth 67kg of steel armor. 

 

What does this all mean in practice?

Laser heating up and vaporizing the surface of an asteroid.

Well, when no mirrors are being used, lasers can burn through significant depths of armor from long distances, and can keep scratching away at armor from even farther away. To find the penetration rate of a laser, we divide the laser intensity at the target by the armor's ability to absorb energy before being destroyed. 

 

Here's a worked example:

100kW MBDA laser.

Imagine a laser producing 10 MegaWatts of power. It has a wavelength of 450 nanometers, which is great at travelling through our atmosphere. The focusing mirror is 10 meters wide, about half as wide as the one the James Webb telescope uses. 

At 100 kilometers, this laser produces a beam 11mm wide with an intensity of 105.6GW/m^2 at the target. It can melt away 10.32 kg of steel per second, or vaporize 154 grams of graphite. This translates into a penetration rate of 13.5m/s and 0.7m/s respectively.

We'll assume a perfect weapon that produces diffraction-limited beams (as focused as possible).

At 1000km, the beam spreads to 110mm wide intensity drops to 1.05GW/m^2. The penetration rate falls to 7mm/s in graphite.

 

At 10,000km, the penetration rate falls to 0.07mm/s. At 20,000km, it is 0.017mm/s, and so on.

 

With each increase in distance, the penetration rate falls by the square of that increase. These numbers might not seem to be impressive at the distances usually discussed when talking about space travel (millimeters?!) but they do add up over time. If the distances are great, they take a long time to cross. During that time, a huge amount of armor can be removed. 

When talking lasers, we are handling distances long enough to make the Earth look small.

For example, a spaceship travelling from the Moon (400,000km away) in a straight line towards the Earth at a rapid rate (10km/s) while facing the 10MW laser described above would lose a full 3358 meters of graphite armor before it even reaches Low Earth orbits (200km)! It would be very impractical if all spaceships had to cover themselves in several kilometers of armor to survive crossing the relatively short Earth-Moon distance!

 

Hot Surfaces

 

At high temperatures, surfaces emit light and heat.

Is the scenario described above actually realistic? Can lasers scrape away meters of armor if left unchecked?

Like many SF writers and thinkers so far, we ignored the fact that as the armor heats up, it radiates away energy like any hot surface does. Blackbody radiation is proportionate to the 4th power of temperature and can be measured in Watts of heat radiated per square meter (W/m^2).

Thermal radiators on all spacecraft are needed to radiate away waste heat.

This blackbody radiation is directly comparable to the laser intensity that reaches the armor.

If the blackbody radiation is equal to the laser intensity, then the armor is dissipating as much heat as it is absorbing. The temperature therefore cannot increase to the point where melting or vaporization happens!

 

Planets achieve thermal equilibrium with their star.

So, at what distance does the laser beam become weak enough that the armor's heat dissipation properties prevent any damage from occurring? Let's work this out for steel and graphite, using the same laser as before.

Steel melts at 1640K. The blackbody radiation rate at that temperature is 420.2kW/m^2. For the laser intensity to match this value, it needs its 10MW of power to be spread out over a 23.8m^2 surface area. This happens at a distance of... 50,000km. 

Graphite vaporizes at 4000K. It can dissipate up to 14.5MW/m^2, meaning it can withstand the laser beam from a distance of 8506km. 

What does this mean in practice?

Well, for steel, no damage occurs at distances further than 50,000km. For graphite, this distance is as little as 8506km. The armor only accumulates damage at distances shorter than that number of kilometers.

Furthermore, as the spaceship approaches the laser, you get to subtract the radiated energy from the laser energy to get the amount of heat absorbed and used to vaporize the armor. 

So, for example, if the spaceship closed in to 8000km, the laser intensity reaches 16.5MW/m^2. We subtract the heat radiated (14.5MW/m^2) and obtain a 'net' intensity of 2MW/m^2. This 'net' amount only vaporizes about 20 grams of graphite per second. 
 

The Mirrors

What if we used mirrors?

A mirror with 90% reflectivity at the wavelength the laser uses would reduce the heat absorbed by a factor 10. 

However, they are not good blackbody surfaces. A 90% reflective mirror would radiate 10 times less heat through blackbody radiation than a black surface such a graphite. Alone, if would not provide any benefit and it would just melt or burn up.

Low emissivity (reflective) surfaces don't lose a lot of heat through blackbody radiation.

Mirrors must be paired with active cooling.

Mechanisms such as those used to keep rocket nozzles cool or jet turbines functional can be applied to mirror armor to remove massive amounts of heat in a short amount of time. It involves moving a large amount of coolant at high pressure and velocity through the narrow channels of a heat exchanger to transfer heat from the component into the coolant. 

Again, we can describe the effectiveness of active cooling in terms directly comparable to laser intensity: W/m^2. 

If the laser intensity equals the active cooling rate, the mirror surface will not heat up.

Thermal receivers for concentrated solar power face many of the same challenges.

Let's continue the previous example and equip a spaceship with actively cooled mirrors that reflect 90% of the laser energy away. To use a real world example, we will use the numbers from the cooling system that absorbs intense, concentrated sunlight in solar thermal receivers. This example of a volumetric gas tube absorbs over 2MW/m^2. Another example from the solar energy industry is the High-Flux Solar Furnace that handles up to 11MW/m^2.  

 

Liquid salts coolants allow for higher heat fluxes to be absorbed.

We work out that the actively cooled mirror can survive a laser intensity of 11*10: 110MW/m^2. 

The laser would have to be firing from a distance of 3500km to overwhelm the set-up so that it can start damaging the mirror and then the armor underneath. 

3500km is of course, much shorter than the distances cited so far, and no damage takes place at longer distances.  

Active cooling systems that can handle even more impressive heat fluxes, and mirrors that reflect a greater percentage of the laser energy, will shorten the lasers' effective range even further. 
 

Sloped surfaces and Fresnel Reflection

 

 

There is more that can be done to reduce the combat distances imposed by powerful space lasers. 

Sloped surfaces are able to spread a laser beam's energy over a larger surface area. This decreases its intensity and the damage that it can do. We can work it out using cos(slope angle). 

At 45 degrees, the surface area is increased by 41% and the laser intensity decreases by 29%.

 

At 60 degrees, the surface area is increased by 100% and the laser intensity decreases by 50%.

 

At 80 degrees, the the surface area is increased by 476% and the laser intensity decreases by 83%.

 

If graphite armor is sloped at 80 degrees, it can withstand a laser of 5.76 times the intensity it could have without sloping. This reduces the 'no damage' distance from the laser by a factor 2.4.

 

This suggests that sharp cones are very effective at reducing laser effectiveness, and would be the optimal shape for armor on a spaceship. 

Space warship with conical frontal section, by Grokodaemon.

Polygonal shapes such as pyramids with triangular, square, hexagonal or other bases could be more effective than a rounded cone by creating a compound angle (vertical and horizontal sloping) against the laser.

The 75.04 degree vertical angle compounds with the 45 degree horizontal angle to create a 10.55 compound angle.

An even better arrangement would be a pyramid with a star-shaped base, or 'star pyramid'. 

Drawn in Geogebra.

The vertical angle can be compounded by a very sharp horizontal angle. For example, an octagram 'star' can form the base of a pyramid 10 meters wide and 57 meters long, and achieve an 80 degree vertical angle and a horizontal slope of 22.5 degrees. The compounded angle becomes just 3.81 degrees, allowing for a 15.05x decrease in laser intensity. 
 

Another benefit from extreme sloping is that Fresnel Reflection becomes significant. 

At low angles, even dark surfaces become shiny.

We first have to find the refractive index of the armor material with regards to the wavelength the laser is using. A database such as this one is excellent for this purpose.

We find that graphite has an refractive index n = 1.5179 in 450nm light. 

 

That index, along with the slope angle, can be used to calculate how much of the laser's energy is reflected away. At 45 degrees, it is an insignificant 5.45%. An extreme compounded slope such as the one produced by the star pyramid as described above would allow for 68.9% of the laser energy to bounce off harmlessly. 

 

A graphite octagram star pyramid with 80 degrees of vertical slope and 67.5 degrees of horizontal slope would survive the 10MW laser at a distance of 2010km. 

Dielectric mirrors, when sloped, lose effectiveness against lasers of certain polarizations. Omnidirectional mirrors are needed. 

If we used an extremely sloped pyramid (80 degrees) in addition to a star-base with a very large number of sides (18 sides for 80 degrees), omnidirectional dielectric mirrors (99% reflectivity) and active cooling (11MW/m^2), we could expect to increase the damaging intensity threshold to 33.16*100*11: 36.5GW/m^2. 

The effective range of the 10MW laser falls to a mere 1700km.
 

Further damage reduction techniques and conclusion

 

 

With a bit of imagination, we can come up with even more ways to reduce laser damage.

 

By rotating the armor, we would force the laser beam to wander over fresh, unheated surface area. The maximum effectiveness of spinning is to divide the circumference of the armor by the width of the laser beam.

 

For example, a 4 meter wide cylinder would have a circumference of 12.56 meters. At 2000km, the laser example we have used so far would produce a beam 0.195 meters wide. Spinning the armor would therefore spread the laser by a maximum of 12.56/0.195: 64.4 times. 

 

The effectiveness of armor rotation increases as distances become shorter. The laser beam becomes narrower, so we divide the circumference by a smaller number to get a bigger reduction in intensity. At 1000km, the beam thins to 0.0976m, increasing the spread to a factor 128.7.

Or, instead of just spinning in circles, armor can be split into segmented bands (like tank tracks) that move diagonally up a spaceship's hull. This would spread the laser both along the circumference of the spaceship and along the band's length. 
 

Another option would be to stop thinking of armor as solid blocks of material. A forest of metal wires could intercept a laser and absorb its energy, but it would have a much better surface area to mass ratio - like a hot surface of graphite, it could passively radiate away a lot of energy.

 

If we using several of these techniques together, we can reasonably conclude that lasers will always be powerful, long-ranged weapons, but they actually have an effective range that can be reduced to a few hundreds kilometers, instead of the tens of thousands of kilometers assumed so far.

 

Why bother with all this?

Well, at shorter distances, other weapons can come into play. Railguns would be able to hit targets before they can dodge out of the way, and missiles don't have to grow to obscene sizes so that they may pack enough propellant to drive themselves up to immense speeds. 

Particle beam weapons, generally shunned for their short effective range when compared to lasers, can bypass reflective surfaces and deal damage directly. You'd even want different types of laser, to shoot at wavelengths that mirrors struggle to handle, or in pulses intense enough to overwhelm active cooling. 

 

More weapons means more options in combat, and sci-fi writers have more tools to shake up their action scenes and make them more interesting.

 

Maneuvering can become important again too. At extreme distances, a spaceship accelerating as hard as it can will only shift its position in its enemy's sky by a few degrees, and it cannot close or open the distance meaningfully before the battle is over.

 

At shorter ranges, flanking maneuvers become possible. Tactics such as rushing the target or accelerating away are suddenly more effective. The importance of pre-positioning before a battle become less important than the maneuvers taken during a battle. 

"Very, very far away..."

In other words, shorter ranges allow for more dynamic battles where tactical decisions matter and human actors would have a role to play.

 

Without all this, space warfare would solely be determined by which side brought the most spaceships with the biggest lasers into the fight. Fleets would know whether to engage or not deterministically, and even if they do lock themselves into battle, it will be a drawn-out sequence of spaceships' armor being burned away over the course of days to weeks. That's boring.

Edited May 22, 2018 by MatterBeam

[wumpus]

4 hours ago, MatterBeam said:

"At 10,000km, the penetration rate falls to 0.07mm/s. At 20,000km, it is 0.017mm/s, and so on."

 

Of course, laser weapon will take an unbelievable amount of power to fire, and it is unlikely to manage 50% efficiency from fusion reactor heat to laser output.  This means that you need some massive heat sinks desperately dumping all your heat.  You might manage to do some internal tricks to limit huge arrays of cooling fins from being unfurled, but you will quickly have to make a decision to cut the fusion power plant or unfurl the heat sinks.  The moment you unfurl the heat sinks you are going to have difficulties building an array that can't be quickly counter attacked by anybody attacking from a different direction to the original attacker (or whichever direction the ship tries to hide their heat sinks from).

Lasers and optics are only a small part of this (and all they show you is that they don't work well).  *Powering* those laser is key, and dealing with the waste heat is even more important: you don't want to give your enemy a larger target (although you may have to, there are only so many ways to emit heat in a vacuum).

The key here is multiple directions of attack.  The Navy that does the space equivalent of "crossing the T" will win, while the massed fleet will be firing into safe targets.  It is by no means certain that this can be planned in advance. 

I included that tiny quote as the real problem with spacewarship design.  If maneuver is important, you need the mass of your heat sinks as thin (and thus as mass-efficient) as possible.  But you don't want to have them vulnerable to someone keeping a laser on them for any significant length of time (seconds? milliseconds?  who knows).  From at least one direction those arrays will be vulnerable, and if they are cooling a magic power plant [presumably fusion, but could be anything up to and including antimatter] they will have enormous amounts of area.

Note: I've designed electronic equipment for the US [wet] Navy.  You'd be surprised how much MIL-STD810 (harsh environment testing requirements) comes up simply due to power consumed and having to be cooled.  And that is on a Navy that can take arbitrary amounts of cool liquids from the ocean and pump it through heat exchangers.  Don't ask how much it is on the mind of a [real] star wars design engineer who designs for use in vacuum.

[MatterBeam]

1 hour ago, wumpus said:

Of course, laser weapon will take an unbelievable amount of power to fire, and it is unlikely to manage 50% efficiency from fusion reactor heat to laser output.  This means that you need some massive heat sinks desperately dumping all your heat.  You might manage to do some internal tricks to limit huge arrays of cooling fins from being unfurled, but you will quickly have to make a decision to cut the fusion power plant or unfurl the heat sinks.  The moment you unfurl the heat sinks you are going to have difficulties building an array that can't be quickly counter attacked by anybody attacking from a different direction to the original attacker (or whichever direction the ship tries to hide their heat sinks from).

Lasers and optics are only a small part of this (and all they show you is that they don't work well).  *Powering* those laser is key, and dealing with the waste heat is even more important: you don't want to give your enemy a larger target (although you may have to, there are only so many ways to emit heat in a vacuum).

The key here is multiple directions of attack.  The Navy that does the space equivalent of "crossing the T" will win, while the massed fleet will be firing into safe targets.  It is by no means certain that this can be planned in advance. 

I included that tiny quote as the real problem with spacewarship design.  If maneuver is important, you need the mass of your heat sinks as thin (and thus as mass-efficient) as possible.  But you don't want to have them vulnerable to someone keeping a laser on them for any significant length of time (seconds? milliseconds?  who knows).  From at least one direction those arrays will be vulnerable, and if they are cooling a magic power plant [presumably fusion, but could be anything up to and including antimatter] they will have enormous amounts of area.

Note: I've designed electronic equipment for the US [wet] Navy.  You'd be surprised how much MIL-STD810 (harsh environment testing requirements) comes up simply due to power consumed and having to be cooled.  And that is on a Navy that can take arbitrary amounts of cool liquids from the ocean and pump it through heat exchangers.  Don't ask how much it is on the mind of a [real] star wars design engineer who designs for use in vacuum.

Well... unbelievable depends on who you are talking to.

The example I used throughout the blog post is that of a 10MW laser. It is one hundred times more powerful than lasers being used right now, at this instant, in commercial applications such as metal cutting or at sea, in naval trails. It is only 10 times more powerful than lasers being developed for the end of this decade.

How you power it is a bit beside the point. Laser efficiency is increasing, with 60 to 80% efficiency diodes existing laboratories (meaning that the 10MW laser produces between 2.5 and 6.7MW of heat). We have multiple real world applications where that rate of heating is handled.

You can hide radiators in the shadow of your armor, or use radiators that cannot be damaged, such as liquid droplet or Curie point radiators.

Even at the distances shortened by reflective surfaces and active cooling, flanking will remain slow and predictable. At 1000km, a spaceship burning through all of its propellant to accelerate at 1g will only change its angle relative to your armor by about one degree per minute. You can easily rotate the spaceship to match their movements, or if you are facing multiple spaceships, you can try to increase the distance and reduce their angle.

Powering the lasers is a very important part of warship design and it will heavily affect space warfare, but it will be a burden to both sides of a conflict, so it won't be a balancing factor. Also, we must limit the variables in play to be able to objectively discuss certain concept or solutions.

[cubinator]

This was a good read. Interesting to see all the different solutions presented to the various issues.

[p1t1o]

What I'd really like to see is a treatment of what would the distances really be like in a "realistic" space battle/war.

Lasers may be great at 10,000km but what if the average distances are 100,000km+? Then lasers are useless, or you have to multiply power (and related issues) by some significant amount.

Or what if the analysis turns out that distances rapidly close to <1000km? Then other weapons may have advantages over lasers.

I'd like to see how lasers stack up against various other types of weapon (kinetic [small & large], nuclear, particle, radiation etc) up against an analysis of how distances would vary in a space battle with near-future tech level.

I used to think lasers were the weapon of the future too, when I was small, but it hasnt quite turned out that way. Their effects can be awesome, but they have a lot of drawbacks.

[Scotius]

2 hours ago, p1t1o said:

I used to think lasers were the weapon of the future too, when I was small, but it hasnt quite turned out that way. Their effects can be awesome, but they have a lot of drawbacks.

Same here. I used to think a laser cannon would be weapon of choice in space battles. I mean - virtually instant hit, perfect tracking etc. And then i realised that hitting something is not the same as destroying\disabling your target. And heating problems on your own ship. And brutal energy losses with distance. Ugh. Kinetic weapons (railguns, coilguns etc.) looks more favourable now. Or directed nuclear weapons like Casaba Howitzers.

Edited May 23, 2018 by Scotius
A mistake. Thanks p1t1o for correcting my blunder :)

[p1t1o]

11 minutes ago, Scotius said:

Same here. I used to think a laser cannon would be weapon of choice in space battles. I mean - virtually instant hit, perfect tracking etc. And then i realised that hitting something is not the same as destroying\disabling your target. And heating probles on your own ship. And brutal energy losses with distance. Ugh. Kinetic weapons (railguns, coilguns etc.) looks more favourable now. Or directed nuclear weapons like Masada Howitzers.

(Its "Casaba" ) Im sceptical about those too, if you dig a bit you can find information on some nuclear tests designed to investigate the principles (accelerating projectiles with nukes) and whilst there were some results that resembled the popular picture of the weapon (ultra-high velocity shrapnel, long range), it was judged to be ineffective at long distances (the angular spread is quite tight, just not tight enough to make probability-of-kill a useful value) and there have been some order-of-magnitude errors between the published results (what little has been published) and what has made it into popular knowledge. 

Its very difficult to beat a fast moving mass for moving energy from one place to another without dissipation proportional to distance.

(I wish I had the documents to back all that up to hand, all I can really say for now is that Im sceptical)

 

[sh1pman]

So it looks like the best weapon for space combat is a conventional missile with proximity-activated shrapnel charge. 

Lasers might be useful for missile defense though.

Edited May 23, 2018 by sh1pman

[YNM]

Good article.

 

Lasers are that odd niche. Unless we find lenses better than Fresnel lenses.

[wumpus]

16 hours ago, MatterBeam said:

Even at the distances shortened by reflective surfaces and active cooling, flanking will remain slow and predictable. At 1000km, a spaceship burning through all of its propellant to accelerate at 1g will only change its angle relative to your armor by about one degree per minute. You can easily rotate the spaceship to match their movements, or if you are facing multiple spaceships, you can try to increase the distance and reduce their angle.

Flanking once battle begins should be effectively impossible (for the means stated).  The real question should be if you can hide a ship/drone/mine with sufficient power to fire an effective laser (if only blow away heat sinks) at laser range distances.  Like many battles, the whole thing would be won or lost before the first shot is fired (granted, that was your thesis as well, but I suspect position is at least as critical as numbers).

Don't forget the power supply when determining the total efficiency: if you are using a fusion (or other heat-based engine) Carnot will not be friendly to high temperature heat sinks and your efficiency will plummet (modern power plants are near ideal at ~62% efficiency, but they typically have available water for heatsinks.  Even with these high efficiency your overall "nukes to laser" efficiency would be less than 50% with 80% efficient lasers and 60% efficient fusion generators.  You aren't getting 60% fusion generators with "liquid droplet or currie point" radiators.  It is entirely possible that futuristic navies may have to forsake anti-matter power plants and limit themselves to fuel cells, and campaigns will make stopping at tenders for oxygen and hydrogen as critical  as "coaling" was before the nuclear age.

All this means that any means to add heat to the heatsink will effectively neutralize the ship.  Also, those radiators have to be *big*.  They might be obscured in one or two directions (requiring the ship to be flanked multiple times before your batteries bare on a target), but it is an amazingly vulnerable spot.  And while flanking may be effectively impossible with the warships themselves, missiles may be able to "flank"  (with ablative gas streams in front of them or ablative covering) in attempts to get the missiles to flanking areas to send some sort of heat (their own lasers?  incendiaries?  Thermally hot nuclear waste?  Solar reflectors?).

You mentioned "armor" and "hiding behind".  I'd be very surprised if such a warship couldn't be designed sufficiently long and this and with ablative armor at the fore that could withstand long distance laser fire until the crew died of old age.  Combat would be similar to submarine warfare where the sub would point toward (or away from) surface ships to effectively become invisible.  Only when flanked and the side exposed is a sub likely to be heard by SONAR.  It isn't so much that flanking attacks are effective, just that head on attacks are pointless (making any "barely effective" attack far preferred).  Considering that "built along a single spine" is how humans currently build large spacecraft (see the ISS, which I'd expect any transmartian habitat to resemble), this shouldn't be unexpected.

Granted, the way drones are heading I'm not sure I should assume a difference between "warship" and "missile".  I suspect that in modern naval warfare (I basically built hardened IT for the Navy, not anything that went "bang".  This is mostly speculating from old Tom Clancy leaks) "underwater drone", "torpedo", and "mine" are only different in how they are deployed, they are likely converging on very similar designs.

[MatterBeam]

15 hours ago, cubinator said:

This was a good read. Interesting to see all the different solutions presented to the various issues.

Thanks!

7 hours ago, p1t1o said:

What I'd really like to see is a treatment of what would the distances really be like in a "realistic" space battle/war.

Lasers may be great at 10,000km but what if the average distances are 100,000km+? Then lasers are useless, or you have to multiply power (and related issues) by some significant amount.

Or what if the analysis turns out that distances rapidly close to <1000km? Then other weapons may have advantages over lasers.

I'd like to see how lasers stack up against various other types of weapon (kinetic [small & large], nuclear, particle, radiation etc) up against an analysis of how distances would vary in a space battle with near-future tech level.

I used to think lasers were the weapon of the future too, when I was small, but it hasnt quite turned out that way. Their effects can be awesome, but they have a lot of drawbacks.

I think the average distance will be determined by the longest effective range of the different weapons systems available. If you stay out of that distance, you're essentially not being shot at.
So far, lasers have always been that 'longest effective range' weapon. With the use of appropriate mirrors, active cooling, rotation and sloping, their range might instead be reduced to the point where other weapons are more effective.

Particle beams, for example, do not care about reflectivity. Guided projectiles can cross the shortened distances much more easily. Missiles don't need as much propellant, and so on. 

A full analysis will be limited by its assumptions: will we have fusion? Will we be fighting around Mars? Will there be a planet-full of lasers aimed into space? We can't exactly say no or yes to any of these questions.

2 hours ago, YNM said:

Good article.

Lasers are that odd niche. Unless we find lenses better than Fresnel lenses.

Most laser weapons rely on high-reflectivity mirrors. Large mirrors focus the laser better.

1 hour ago, wumpus said:

Flanking once battle begins should be effectively impossible (for the means stated).  The real question should be if you can hide a ship/drone/mine with sufficient power to fire an effective laser (if only blow away heat sinks) at laser range distances.  Like many battles, the whole thing would be won or lost before the first shot is fired (granted, that was your thesis as well, but I suspect position is at least as critical as numbers).

Don't forget the power supply when determining the total efficiency: if you are using a fusion (or other heat-based engine) Carnot will not be friendly to high temperature heat sinks and your efficiency will plummet (modern power plants are near ideal at ~62% efficiency, but they typically have available water for heatsinks.  Even with these high efficiency your overall "nukes to laser" efficiency would be less than 50% with 80% efficient lasers and 60% efficient fusion generators.  You aren't getting 60% fusion generators with "liquid droplet or currie point" radiators.  It is entirely possible that futuristic navies may have to forsake anti-matter power plants and limit themselves to fuel cells, and campaigns will make stopping at tenders for oxygen and hydrogen as critical  as "coaling" was before the nuclear age.

All this means that any means to add heat to the heatsink will effectively neutralize the ship.  Also, those radiators have to be *big*.  They might be obscured in one or two directions (requiring the ship to be flanked multiple times before your batteries bare on a target), but it is an amazingly vulnerable spot.  And while flanking may be effectively impossible with the warships themselves, missiles may be able to "flank"  (with ablative gas streams in front of them or ablative covering) in attempts to get the missiles to flanking areas to send some sort of heat (their own lasers?  incendiaries?  Thermally hot nuclear waste?  Solar reflectors?).

You mentioned "armor" and "hiding behind".  I'd be very surprised if such a warship couldn't be designed sufficiently long and this and with ablative armor at the fore that could withstand long distance laser fire until the crew died of old age.  Combat would be similar to submarine warfare where the sub would point toward (or away from) surface ships to effectively become invisible.  Only when flanked and the side exposed is a sub likely to be heard by SONAR.  It isn't so much that flanking attacks are effective, just that head on attacks are pointless (making any "barely effective" attack far preferred).  Considering that "built along a single spine" is how humans currently build large spacecraft (see the ISS, which I'd expect any transmartian habitat to resemble), this shouldn't be unexpected.

Granted, the way drones are heading I'm not sure I should assume a difference between "warship" and "missile".  I suspect that in modern naval warfare (I basically built hardened IT for the Navy, not anything that went "bang".  This is mostly speculating from old Tom Clancy leaks) "underwater drone", "torpedo", and "mine" are only different in how they are deployed, they are likely converging on very similar designs.

Flanking would be difficult, yes, but not impossible. If you start the battle with two spaceships 1000km apart, and 1000km from a single enemy ship, then the enemy ship will be forced to point towards at least one enemy and lose their sloping against the other.

Efficiency is a very important measure of power and output in space... but it is not the *most* important statistic. Power density (watts per kilogram) is the most important number. I call system power density the total output of a system that adds up the mass of everything you need to use or produce that output, from reactor and heat exchangers to voltage transformers and radiators. 

If I have a 85% efficient system that has a 100W/kg system power density, and a 10% efficient system with 1000W/kg power density, I will select the lower efficiency but better power density option. This is because a 1000 ton module on a spaceship would produce a 1GW laser beam, but only 100MW with the 'more efficient' system. 

Instead of missiles, you can send mirrors. The mirrors can drift past my armor and then you can shoot off a beam that bounces into my spaceship's backside. 

Detecting spaceships at 1000km distances won't be hard. They will show up as very bright spots against the dark background of space in almost all wavelengths (from UV to radio). It becomes impossible to hide after a few laser beam shots have heated things up too. 

[YNM]

6 minutes ago, MatterBeam said:

Most laser weapons rely on high-reflectivity mirrors.

Many resonance lasers rely on partial mirrors.

[MatterBeam]

5 minutes ago, YNM said:

Many resonance lasers rely on partial mirrors.

There is a difference between the internal optics for generating the beam, and the focusing optics that stretch it out over thousands of kilometers.

Internal optics:

Focusing optics:

[wumpus]

49 minutes ago, MatterBeam said:

If I have a 85% efficient system that has a 100W/kg system power density, and a 10% efficient system with 1000W/kg power density, I will select the lower efficiency but better power density option. This is because a 1000 ton module on a spaceship would produce a 1GW laser beam, but only 100MW with the 'more efficient' system.

The theoretical limits are pretty easy to calculate.  The maximum possible efficiency of your power generator is limited by the Carnot cycle limit (and this actually limits real power plants, and even some research car engines are approaching it).

Efficiency<1-(Tc/Th) where Th is the heat of your steam (or whatever) going into a turbine (presumably a combined cycle).  Assuming using Tungsten-Halfnium-unobtanium alloys throughout, this could be somewhere between 3000-4000K.

Tc= the temperature of your heatsink (in Kelvin).  Note that for ISS, this is less than 200K (you could presumably generate power for the ISS at 93% efficiency).

Blackbody radation increases at the fourth power of temperature.   So if you want to produce massive increases of power, you could presumably have the same size radiators and replace the ammonia with molten iron of something and have an efficiency of 10% and have the radiators at 3600K and the steam at 4000K (ok, this assumes your generators and lasers are 100% efficient, but still).  This gives you a 324 fold increase in the amount of power you can produce with the same sized radiators.  I optimized this a little more and came to the conclusion that Th/Tc should equal 3/2 and that for a Th of 4000 you would get 500 times the power over ISS using the same sized radiators (with an efficiency around 33%, but radiating a bit more than a third as much).  The ISS radiators are about 1/10th the size of the solar panels, and not visible from any view directly facing the solar panels (what most pictures show), I'll use this for a "heat sink area unit" for theoretical spacecraft.

REALITY CHECK: This assumes theoretically ideal turbines crafted out of unobtanium (to withstand 4000C), impossibly perfect lasers, and equally impossibly perfect generators (it doesn't spare any heating back from the lasers, and I doubt that such an equation will fit on the envelope used for the above).  And you still have to deal with radiators only a couple orders of magnitude smaller (per Watt) better than a space station lifted into orbit in the 20th century.  So for an *absolutely perfect* system (optimzed to reduce the heatsink), you get ~60MW per ISS-sized-heatsink.  These are fundamental physical limitations and the only ways around them are open cooling cycles, matter that remains solid at 4000K, or perpetual motion machine.  No amount of other tech will change this.  There's a reason I want to fire on the heat sinks.

Note this limitation is unlikely to be an issue outside of deliberate attack.  It places no bounds on the radiators aside from shear size.  You could presumably use gold leaf for the majority of you heatsink (not gold, you need something that won't melt at 2600K).  It is only when you need something that can endure deliberate attack does the issue of raw surface area become an issue.  Note that I suspect that with tech in barely doable (in parts, not all at once) 21st century tech we could bump this up to 30MW per ISS heatsink, but after that the asymptote gets *steep*.  I'm guessing that any "missile based" laser will fire only briefly and use some sort of open cooling scheme.  Open loop cooling works great if you need high-Isp "flanking speed', but also has the same tyranny as the rocket equation (bring *lots* of mass).  Liquid hydrogen gives you great Isp, but little cooling.  I suspect things like tungsten, halfnium, and depleted uranium (or just spent fuel rods) would be good for open loop cooling.

 

[MatterBeam]

19 hours ago, wumpus said:

The theoretical limits are pretty easy to calculate.  The maximum possible efficiency of your power generator is limited by the Carnot cycle limit (and this actually limits real power plants, and even some research car engines are approaching it).

Efficiency<1-(Tc/Th) where Th is the heat of your steam (or whatever) going into a turbine (presumably a combined cycle).  Assuming using Tungsten-Halfnium-unobtanium alloys throughout, this could be somewhere between 3000-4000K.

Tc= the temperature of your heatsink (in Kelvin).  Note that for ISS, this is less than 200K (you could presumably generate power for the ISS at 93% efficiency).

Blackbody radation increases at the fourth power of temperature.   So if you want to produce massive increases of power, you could presumably have the same size radiators and replace the ammonia with molten iron of something and have an efficiency of 10% and have the radiators at 3600K and the steam at 4000K (ok, this assumes your generators and lasers are 100% efficient, but still).  This gives you a 324 fold increase in the amount of power you can produce with the same sized radiators.  I optimized this a little more and came to the conclusion that Th/Tc should equal 3/2 and that for a Th of 4000 you would get 500 times the power over ISS using the same sized radiators (with an efficiency around 33%, but radiating a bit more than a third as much).  The ISS radiators are about 1/10th the size of the solar panels, and not visible from any view directly facing the solar panels (what most pictures show), I'll use this for a "heat sink area unit" for theoretical spacecraft.

REALITY CHECK: This assumes theoretically ideal turbines crafted out of unobtanium (to withstand 4000C), impossibly perfect lasers, and equally impossibly perfect generators (it doesn't spare any heating back from the lasers, and I doubt that such an equation will fit on the envelope used for the above).  And you still have to deal with radiators only a couple orders of magnitude smaller (per Watt) better than a space station lifted into orbit in the 20th century.  So for an *absolutely perfect* system (optimzed to reduce the heatsink), you get ~60MW per ISS-sized-heatsink.  These are fundamental physical limitations and the only ways around them are open cooling cycles, matter that remains solid at 4000K, or perpetual motion machine.  No amount of other tech will change this.  There's a reason I want to fire on the heat sinks.

Note this limitation is unlikely to be an issue outside of deliberate attack.  It places no bounds on the radiators aside from shear size.  You could presumably use gold leaf for the majority of you heatsink (not gold, you need something that won't melt at 2600K).  It is only when you need something that can endure deliberate attack does the issue of raw surface area become an issue.  Note that I suspect that with tech in barely doable (in parts, not all at once) 21st century tech we could bump this up to 30MW per ISS heatsink, but after that the asymptote gets *steep*.  I'm guessing that any "missile based" laser will fire only briefly and use some sort of open cooling scheme.  Open loop cooling works great if you need high-Isp "flanking speed', but also has the same tyranny as the rocket equation (bring *lots* of mass).  Liquid hydrogen gives you great Isp, but little cooling.  I suspect things like tungsten, halfnium, and depleted uranium (or just spent fuel rods) would be good for open loop cooling.

Again, efficiency does not tell you much about how much power you can extract from a certain mass of equipment.

There is no single figure or measure you can optimize for to get the best power density. Radiators are heavy, yes, but at certain temperatures, they become lightweight in comparison to other systems, such as a homopolar generator or a lasing module. 

Open cycle works great, until you run out of coolant. There is a mathematical relationship that tells you whether open or closed cycle cooling is the better option.

The mass of coolant you need for open-cycle cooling is the waste heat production rate, times the duration of use, divided by the coolant's heat absorption capability. So, 100MW of waste heat, divided by water's ability to absorb 2.7MJ/kg after boiling, requires 133 tons of coolant per hour

If a closed cycle heat rejection system can only handle 1000 Watts of waste heat per kilogram of mass, then 100MW needs 100 tons of equipment.

We can then see that if you plan to run your heat-producing equipment for longer than 45 minutes, then the closed-cycle cooling option is better.

Liquid hydrogen is the best open-cycle coolant there is. 

 

[wumpus]

You'll note none of the limits are on power extraction, although I did use some very real limits on efficiency of said extraction.  What I *can* point out is how much surface area you need to extract a given amount of power an maintain thermal equilibrium.  If you extract more power for a given surface area, your temperature will continually increase.  If you assume a sufficiently long space battle, at some point the spacecraft will melt.

59 minutes ago, MatterBeam said:

The mass of coolant you need for open-cycle cooling is the waste heat production rate, times the duration of use, divided by the coolant's heat absorption capability. So, 100MW of waste heat, divided by water's ability to absorb 2.7MJ/kg after boiling, requires 133 tons of coolant per hour

This works fine if you are on the surface of a planet and can simply take "the water" from a river and return same.  This is also how you compute for open loop.  In vacuum, the only way you are going to cool "the coolant" is by black body radiation and the only thing that matters are temperature, surface area, and albedo.  Albedo is going to be black (ideal), temperature is a critical factor in power extraction efficiency, and you can then solve for the ideal temperature for the smallest amount of surface area, and then finally compute how much surface area you need for the same power.  Mass never shows up in the equation, at least until you have to physically construct the radiator of given surface size and uniformish temperature.

I wouldn't be surprised if only open loop cooling mattered in space combat.  It is ghastly inefficient, but if one side can cool itself while heating you beyond what any feasible radiator can handle, it will win regardless of how inefficient its use of liquid hydrogen is (it can also maneuver at >1000Isp  with a hydrogen open loop).  But I was somewhat astonished that no amount of E. E. doc Smith space opera technology could beat the radiators on the ISS by more than about an order of magnitude (in size, not mass) [also I assumed they can dissipate max power at 200K.  The temperature is too high, but they really need to dissipate max power*(inefficiency of the solar panels), so the final figures are probably close enough].  If you win the "first round using open loop cooling", there won't be a "second round using radiators".

The point is to never ignore cooling.  You can scale up power generation easily enough: kilopower shows how to build a fission reactor in space.  Scaling the power generator up could be as simple [for those with exactly the right clearance and need to know] as copying submarine reactors.  Cooling such a beast that always submerged in water with same constantly available is another story, and any technological improvement is pretty much limited to increasing surface area/mass.  I also don't think anybody has ever worried about the [power] efficiency of a nuclear reactor (obviously excepting the few designed to be in space), so that is a pretty new thing, but if you can get near Carnot efficiency out of coal and natural gas, doing same for nuclear doesn't seem to far a stretch.  You can handwave anti-matter all you want, but it will still have the same thermal efficiency of any other heat engine, and still need to be cooled with the same black body radiation that the ISS uses (but presumably you can handwave in unobtanium leaf radiators).

I find it odd that you can accept limitations on a lens (although I don't *think* they're fundamental), but not realize the fundamental limitations of heat engines and cooling requirements in vacuum.

[MatterBeam]

@wumpus

Not really, no.

10kW/kg is achievable with current turbines that operate on a 1600 to 600K temperature difference. 7kW/kg is demonstrated by electric generators. Cooling systems of dozens of kW/kg are achievable with liquid droplets, and a multiple kW/kg with solid fins. 

Here is an example of a 16% efficient 100kW (thermal) to 14-16kW (electric) Brayton generator running off the low-power heat of a nuclear rocket's core: https://www.sciencedirect.com/science/article/pii/S1738573315001540

It only need 50m^2 of radiators and fits inside a 390kg package. 

[wumpus]

1 hour ago, MatterBeam said:

@wumpus

Not really, no.

10kW/kg is achievable with current turbines that operate on a 1600 to 600K temperature difference. 7kW/kg is demonstrated by electric generators. Cooling systems of dozens of kW/kg are achievable with liquid droplets, and a multiple kW/kg with solid fins. 

Here is an example of a 16% efficient 100kW (thermal) to 14-16kW (electric) Brayton generator running off the low-power heat of a nuclear rocket's core: https://www.sciencedirect.com/science/article/pii/S1738573315001540

It only need 50m^2 of radiators and fits inside a 390kg package. 

First, the engine is designed primarily for open cycle mode.  When the hydrogen runs out, your power drops considerably.

My claim: You can't exceed 60MW per ISS heat sink radiator size

ISS power (max) 90kW @ 382 m**2 radiators or .090MW per ISS heat sink radiator size
your link: 16kW @ 50mm*2 radiator size or .122MW per ISS heat sink radiator size

What don't I get?  I certainly get that space is in vacuum, and heatsinks are a hard limit.  I don't see a 35% improvement of a paper design over an existing (in space) design from 30 years back as a huge shock. It certainly doesn't hit my outlandish temperatures (used to generate the outlandish power limits), but then it doesn't hit any outlandish power outputs either.  My point was that the laws of physics would have limits on even "Star Trek" level technology, and this paper hardly seems to hit that.

Edited May 31, 2018 by wumpus
silly crtl enter got me again.

[hms_warrior]

you don't "get" that heatsinks are massivly dependent on the temperature they run on ;-) basicly, a Heatsink running at 2000°C has a much higher black body radiation than one running at 100°C.

Now all those reactors are running pretty hot. Say Your Reactor gets a working fluid to 2000°C, wich turns to 1000°C after extracting the energy, that means your radiator can radiate at 1000°C.

Now You want to cool the Laser you fire. The parts of the laser can't be hotter than say...100°C? So your working Fluid will be max 100°C and your Radiator needs to cool it at this tempaerature too.

 

TDLR: Cooling the Reactor is easy. Cooling all the components that use all that energy is not. (the second part is where Lasers realy suck compared to say...missles;-) )