Wednesday 2 March 2016

The Laser Problem II

If you strip down any combat system in any setting, you'll find a system of choices.
What choices do you have an a realistic scifi setting?

In generic fantasy, the author can choose to make a 'unit' don armor, ride a horse, use a sword, dagger, mace, spear or a combination thereof. If on horseback, they can charge or circle around. If on foot, they can form a battle line or attempt to rush into a weak flank.

In a WWII setting, an army can advance steadily behind a rolling artillery barrage, dig in behind machine-gun posts and trenches, or sweep forward on the backs of tanks and armored vehicles. The equipment can be mission-specific or salvaged from a defeated foe. 

Once the author has a set of tools and rules for their use in hand, they can develop tactics for their units. 'Meta-gaming' these tactics against each other gives rise to battlefield strategy, which, once you include factors outside the battlefield, results in overall strategy.

While it is entirely possible to conjure up a setting where conflict happens outside rather than on the battlefield, it is much more rewarding (and easier on the author) to devise a combat system that is exciting by itself. In a story, this usually means that the protagonist makes meaningful decisions that decide the outcome of a fight, in a game this means giving the player different ways to accomplish their objectives with the tools at hand, rewarding tactical thinking and player skill with proportionally better outcomes. In a combat system, the variety of choices available and their relative effectiveness make or break it.
Strategic, level-headed reasoning has determined that this is awesome.

Now, we come to realistic science fiction.

No terrain features, very early detection, near perfect information on everything the opponent is doing... in many ways, it resembles chess. Lasers are the weapon of choice, since of all weapon systems, they travel the fastest, concentrate the most energy at the target and do so at the greatest range. It is the ultimate evolution of archery, gunfire and missiles, where light itself is the projectile. It shapes the scifi battlefield in many ways that negate the variety of choices and the tactical thinking that makes combat a rewarding experience, and ultimately leads to the Laser Problem.
Not as exciting as you might think

Combat in space revolves around two central factors:

-relative acceleration
-engagement distance

Relative acceleration is how much you can change your velocity compared to your opponent's. Engagement distance is from how far away you can start to do appreciable damage against the enemy. 

If you have better relative acceleration, you can dictate at which distance combat takes place. If your engagement distance is shorter than the opponent's, you can use your acceleration to get closer. If your engagement distance is longer than the opponents', you'll use your superior acceleration to maintain the distance. 

Exciting space combat happens when relative acceleration is large compared to the engagement distance. Tactical maneuvering and risk-taking becomes important. Your position on the battlefield varies, giving the player or character a minimum of choice as to where to go. This might involve human decision making, giving you an excuse to place people on the battlefield.

Boring space combat is when relative acceleration is small compared to engagement distance. There is no maneuvering. In gaming terms, spacecrafts are min-maxed for the largest engagement range, at the cost of every single other factor. Tactics break down into a single choice: is my engagement distance longer than my opponents'? I win. Is it shorter? Then there is no fighting to be done. The job of shooting at a tiny speck of light is best left to computers - there is no reason to put humans in warships, and raising the stakes of battle becomes a difficult task.

The Problem 

If laser power is derived from engine power, then increases in engine power lead to greater accelerations and longer engagement distances in the same proportion.

To demonstrate, we'll first take a look at how laser effectiveness is calculated, then at some examples.

The laser spot size equation:
  •  Minimum spot diameter =  1.27 * Distance * Wavelength / Lens Diameter
Distance in this case is how far away your target is. The Wavelength is determined by your type of laser. A 'visible' laser has a wavelength between 700 and 400 nanometers. An Ultraviolet laser has wavelengths from 400 nanometers to 100 nanometers, and it is very useful because there is no atmosphere in space to absorb this wavelength. Lens diameter is how large your focusing element. There are several types, some are not even lens-like, but I've named it such for clarity.
A free electron laser, one type of laser expected to fight in space

The equation tells us that laser spot size becomes smaller with a shorter wavelength or a larger lens, but more importantly, it allows us to find the energy per area deposited on the target's surface at different distances:
  • Laser intensity = Power Output / ((Spot Diameter / 2)^2 * π))
Finally, the laser intensity tells us how quickly the laser goes through the target. To find out how much target material the laser can burn through per second, we need the material's molar volume and heat of vaporization.

Fortunately, we have the Laser Weapons Calculator to help us.
Pulsed lasers can increase penetration rate significantly

With all these tools together, we can work out a few examples of how effective lasers deriving their energies from rocket engines are, and how they affect combat.

Low-end torchship:

Rocket Engine output 5 GigaWatts.
Inefficient electric power conversion rate 10%
Inefficient laser power output 30%

Laser Power 150MW
Laser Wavelength: Ultraviolet (100nm)
Laser lens diameter: 20m
Spot sizes: 6.1mm @1000km, 6.1cm @10,000km, 61cm @100,000km

Target material: Aluminium (10 cm^3/mol, 300 kJ/mol)
Penetration rate: 228 m/s @1000km, 0.228 m/s @10,000km, 0.228 mm/s @100,000km

Target material: Diamond (5.3 cm^3/mol, 356kJ/mol)
Penetration rate: 100.5 m/s @1000km, 0.1 m/s @10,000km, 0.1 mm/s @100,000km

To summarize the numbers, the low-end torchship is a laser monster. It will obliterate anything within ten thousand km. It will tear through meters of armor at a ten thousand km. It can dig through nearly a meter of armor an hour at a hundred thousand km. An opponent can only reasonably expect to survive at a distance of half a million kilometers (where the laser burns through 10 cm of aluminium in 10.4 hours). Replacing aluminium with fancy carbon-based armor only halves the effectiveness of the laser. 

From the previous post, we found that this ship can accelerate at a gentle 0.66 m/s^2, rising to 3.3 m/s^2 when its propellant tanks are empty. Lets say combat takes place with an average accelerate in between those figures, at 1.5 m/s^2. 

If the target has a similar spaceship to ours, it may try to close the distance or escape. 

Acceleration: 1.5 m/s^2 average
Distance travelled after 1 minute: 2700 m
Distance travelled after 1 hour: 9720 km
Distance travelled after 10.4 hours: 1,000,000 km

If you remember some of the values from last post, you'll notice that it takes 9.3 hours to burn through the craft's entire supply of propellant, so it won't even reach the 1 million km safety distance.

The conclusion is that the low-end torchship cannot escape its own laser, much less so if the attacker chases after you and reduces relative acceleration.

But, you might ask, what if the spaceship was the High-end torchship? It would accelerate five times faster!

Let's run the numbers:

High-end torchship:

Rocket Engine output 100 GigaWatts.
Efficient electric power conversion rate 30%
Efficient laser power output 60%

Laser Power 18 GW
Laser Wavelength: Ultraviolet (100nm)
Laser lens diameter: 20m
Spot sizes: 6.1mm @1000km, 6.1cm @10,000km, 61cm @100,000km

Target material: Aluminium (10 cm^3/mol, 300 kJ/mol)
Penetration rate: 27.4 km/s @1000km, 27.4 m/s @10,000km, 27.4 mm/s @100,000km

Target material: Diamond (5.3 cm^3/mol, 356kJ/mol)
Penetration rate: 12 km/s @1000km, 12 m/s @10,000km, 12 mm/s @100,000km

If the low-end is a monster, the high-end is a nightmare. It is ridiculously effective up to lunar distances, and the target has to be at 2.5 million km to escape this laser's death stare. The same technology improvements that allow for more powerful propulsion also mean the lasers get better... although we would get similar results using the same laser technology, as the base power the machinery is converting (100 GW!) into laser beams gets increased by so much.

Acceleration: 6.8 m/s^2 average
Distance travelled after 1 minute: 12.2km
Distance travelled after 1 hour: 44,064 km
Distance travelled after 7.5 hours: 2,500,000 km

Even with much improved acceleration over the low-end torchship, we see that it cannot escape its own beam in a reasonable amount of time. A battle between high-end torchships that starts at one lunar distance, with both sides immediately running away from each other (so 13.6 m/s^2 combined acceleration) until they reach 2.5 million km separation, would still result with 847 cm of armor shaved off each ship.

Technically, you'll be cornered from 2,500,000 km away

Why exactly is this bad?

It leads to boring combat. With the examples above, we've had a taste of how proportional the relative acceleration and engagement distances can be, when laser power is derived from engine power. 

Lasers push combat ranges to such extremes, that they make spacecraft with any level of acceleration seem immobile over the course of the engagement. Historically, we've had combat between two seemingly immobile opponents.... it's called siege warfare, conducted between fixed walls and catapults planted in the ground. However, unlike the messy, lethal affairs of medieval past, spacecraft cannot sneak closer to the walls, not without being detected and zapped on the spot. 

On a personal level, lasers remove the human element from combat. Machines will forever be better at comparing engagement distances, then making the decision to go on or retreat. Their only task afterwards is to click on the tiny dot on the screen. 

With their range, lasers also remove other weapon systems from the battlefield. Kinetic rounds would take years to cross the same distances lasers do in seconds. Missiles are a very nuanced system, but it is difficult to make missiles more effective than lasers without structuring the entire setting around that objective.

I understand that the analysis so far is very simplified: 

I haven't taken into account waste heat management, multiple unit engagements, combined arms tactics, laser accuracy, laser re-focusing and mirror drones... but when trying to design a combat system which can place two players against each other, they will have identical equipment and characteristics. We can therefore eliminate these factors. The Laser Problem then appears, since it reduces the final point of comparison to maximal engagement range of player A versus maximal engagement range of player B.

In the next and final post dedicated to the laser problem, we'll discuss solutions to the Laser Problem. Hard scifi authors do not have to write out conflict from the battlefield, and game designers will have exciting space combat if they tweak their settings in the right ways. 


  1. Interesting, but what if there is stealth tech, and one cannot see the opponent until a certain distance. this means that combat would be concentrated around valuable areas, (stations and planets) and long range laser-fire would not be nearly as effective.

  2. I will discuss solutions to the Laser Problem in the third post, but even if stealth tech reduces the long-range effectiveness of lasersm they would do nothing against the fact that they become ravenous beams of instant death at short range.

    Also, combat would likely take place BEFORE the attackers have started de-accelerating into an orbit around the objective. This would give the defenders the upper hand, by creating two 'win' conditions: destroy the opponents, or stop them from de-accelerating into orbit.

    In the first case, there's no-one left to worry about. In the second case, they'll be flung out into outer space and you won't have to worry about them again for months or years.

    The point is, stations and planets will be defended from millions of km away.

    1. Another point to address is your description of "ravenous beams of instant death". Even accepting that the laser will penatrate any defense at relatively close ranges, this does not necessarily constitue "instant death". There is a misconception that if a laser penetrates a target, the target dies. In much the same way that a human can often sustain several hits from a 9 mmm gun, without being slowed down very much (especially if under the influence of strong drugs), the same feature that allows a laser to drill through armour plate will reduce the likelihood of the beam actually resulting in a good kill. This is usually refered to as "lack of stopping power". 9 mm guns are often very powerful, and specially tipped bullets allow them to penetrate most wearable armour... but they often just pass straight through the body, often without doing any significant damange to tissue. You bleed, but unless you hit a vital organ you don't stop an attacker, and one can live for several hours before the actual bleeding becomes life threatening. Same for a laser. If you have a vessel that is properly laid out, it will take dozens (and perhaps even hundreds) of penetrations before the vessel loses its ability to fight.

  3. @Hal Effect
    In space, there simply *is* no stealth.

    The only way to make lasers miss (assuming their tracking is accurate enough) is to be so far away from the emitter that lightspeed lag allows you to be elsewhere - preferably where the enemy did not predict you would be.

    1. A common misconception. It will be discussed soon, but you just have to achieve stealth in different ways.

      Also, lasers in space are not extremely accurate at long range because they are physical constructs that have to be immobilized without solid ground to push against. In fact, they'll use many of the vibration-reducing technologies employed by submarines today.

      Just imagine the mass of a 10m diameter dielectric mirror, and how much momentum it generates trying to change target, How would you suppress that quickly without making the beam wobble? How do you react to the mirror heating up slowly and changing shape? How do you deal with random impacts of micro- and macro-projectiles on your ship and on the mirror itself?

      It's never a perfect world.

    2. It is useful to think of a laser as an inverse telescope. Since light takes the same route coming as going, if you trace the light rays from a spaceship, say, that you are observing with a telescope to your light collecting sensor in the scope, then if you replace the sensor with a beam emitter, the beam will follow that same path back.

      This is useful because we have a number of examples of very large telescopes that are limited only by the diffraction of light. That is, the pointing error of the beam axis is much less than the diffraction limited resolution of the scope. Reversing this, the same scope shooting a laser would have a pointing error less than the diffraction limited spot size at the target. This means that for practical purposes, inaccuracy of the beam can be neglected. The main limit is that beyond a certain range, the beam spot size is too large to do much damage (while at the same time the resolving power of your optics isn't good enough to figure out what are the best parts to shoot at, for the same reason).

      Of course, this is all for visible light lasers and longer wavelengths. For x-ray telescopes, you still get a pointing accuracy better than the resolution, but we don't know how to get diffraction-limited resolution from an x-ray telescope yet and if we did, the instantaneous resolution might be less than the pointing error (which would of course reduce the resolution for a scope, because the image would be jittering all over the sensor plane). So it might be possible that a super-duper x-ray laser might not have perfect aim (or maybe it would - engineers are very clever).

    3. That's a bit of a downer...

      Let me appeal from another direction: what factors could plausibly reduce the acuracy of a laser weapon in vacuum?

    4. A rocketpunk scenario of 1950's tech IN SPACE with vacuum tube electronics and gunners plotting firing solutions with slide rules?

  4. What if we include some charge up/cooldown time in a femtosecond laser blast.Lasers requires lot of power and also generate a lot of heat so adding capacators and heat sinks are a welcome choice . Then the combact might revolve between bating your enemy to use his countermesures and landing a mulmultiple hits while wour enemy was not ready. This could make the combact intresting. So what could be the countermeasures if your sensors can detect the buldup and relese of energy. Also what type of heat sinks and readiators can take such loads

    1. The problem with that 'charge up time' is that pulsed lasers usually have pulses of a handful joules, which take milliseconds to charge up. They work by sending thousands of those pulses per second, in a stream.

      A femtosecond laser firing pulses of 1 Joule each would have a peak power of 1 TeraWatt. If it is being given 1 MW of energy, then it would fire 1 million pulses per second, with 0.999999 microseconds in between the pulses.

      Unlike in Star Trek, there is no way to detect a 'build up of energy' inside an enemy ship. But, there are thermal constraints on the lasers. Perhaps you could have a battle where overloading your lasers gives you a short term advantage, but forces you to stop shooting after a while to let the laser cool off? And if you continue overloading for too long, the laser is damaged and eventually melts?

  5. I don't really agree with the "Lasers push combat ranges to such extremes, that they make spacecraft with any level of acceleration seem immobile over the course of the engagement." , the further away the opponent is in a laser fight the more likely it is that it's maneuvering will have a material effect on it getting hit. The probability of a laser hitting can be taken down to ,
    Number of shots to hit a given size = Pi x 0.25 x a^2 x 16d^4 x c^-4, where laser diameter is greater then the area to be hit d^4 reduces to d^2.
    Where a is acceleration of the targeted craft, and d is engagement distance. Depending on exactly how far away lasers can reach, and how crafts cross sectional area scales with weapon ranges, the decisions made can dramatically effect outcomes.

  6. I think I understand how most you get most of the numbers, but...

    How do you get the electric power conversion rate and laser efficiency? Is that mostly up to the author, who decides based on the technology at hand, or are there equations for them?

    1. Oh, those are certainly just example figures to help the demonstration.