Tuesday, 1 March 2016

The Laser Problem

One of the most important decisions to be made during worldbuilding is choosing the pace of the events to unfold. This is usually the frequency of major events, modified by the focal point of the narration (an individual, a group, a government or a civilization as a whole). 

In science fiction, the frequency of 'major events' generally has an upper limit, that is how long it takes for the characters to travel to another location. 
In a space opera or fantasy setting, the travel speed is arbitrarily defined. You can do the same... but if you want to create tough scifi, you'll have to follow the numbers.

Many of you should be familiar with Hohmann transfer orbits.
An 8.6 month journey to Mars
These are minimum energy trajectories to raise your orbit from a lower to a higher altitude, or to travel from one planet to another. If your setting relies on chemical energy, such as Liquid Hydrogen and Liquid Oxygen, you will have to use these trajectories, since anything more energetic is outside of your reach.

The principal advantage of creating a setting that has to follow Hohmann transfers is realism. Low energy, chemical-fuelled rockets are very real, and you'll have huge amounts of actual data with which to anchor your setting as believeable to the audience.

However, Hohmann trajectories are slow.

A Mars transfer takes nearly 9 months at best. Getting to Jupiter can take more than 6 years. If settlements on opposite ends of the Solar System enter into conflict, it'll be entirely over the phone. If war breaks out, it'll be done and settled before any spacecraft is halfway through the transfer.
Don't do anything until I get there!
For this reason, science fiction authors are tempted to make their rockets more powerful. Higher energy output means higher exhaust velocity, which means a greater dV budget:
  • DeltaV = Exhaust Velocity * Natural Logarithm of the Ratio between Empty and Fuelled mass
In a setting with a military focus, travel times, and therefore the energy output of rocket engines, is even more important. They determine how fast spacecraft will approach each other, how much of their mass is devoted to propellant instead of weapons, how large and fragile their radiators are...
  • Rocket Engine Power Output = (Exhaust Velocity * Thrust) / 2
The Rocket Engine Power Output equation also tells us that dropping the exhaust velocity, for example, during a combat situation, increases our thrust proportionally. This means the travel times we choose have the side effect of determining how fast spacecraft accelerate.

One of the juiciest prizes for a scifi author is Brachistochrone transfers.

Unlike Hohmann transfer orbits, they ignore most of the effects of gravity, and allow a writer to simplify spaceflight into a series of straight lines. Your spacecraft accelerates away from the origin, coasts, then reverses acceleration near the end, coming to a stop at the destination.

This both greatly speeds up travel between planets, and greatly eases the author's work when it comes to calculating trips and deltaV budgets. 

There is one catch, however, and it is the need for provide significant acceleration and high deltaV. This can be as low as a few m/s2, or a whole G. As authors don't want their spacecraft to be baloons of propellant with a payload pimple on top, they'll vastly increase their exhaust velocity and rocket engine power output. These are called 'torchships'.
Massive nozzle, little room for propellant... yup, a torchship
Examples:

Low-end torchship:
Dry mass 100 tons.
Mission: Earth to Mars.
Rocket Engine Output 5 GigaWatts.
Exhaust Velocity 30km/s
Mass ratio: 5
Full mass: 500 tons.
DeltaV budget: 50km/s
Thrust = Engine Power * 2/Exhaust Velocity = 333kN
Initial Acceleration = F/m = 0.66m/s2

High-end torchship:
Dry mass 100 tons
Mission: Earth to Mars


Rocket Engine Output 100 GigaWatts.
Exhaust Velocity 200km/s
Mass ratio: 2.72 
Full mass: 272 tons.
DeltaV budget: 200km/s
Thrust = Engine Power * 2/Exhaust Velocity = 1000kN
Initial Acceleration = F/m = 3.6m/s2 

The low-end torchship is impressive by today's standards. 5 GW output implies some sort of efficient fusion energy, if it can be packaged alongside a useful payload within 100 tons. The acceleration of 0.66m/s2 is about7% of Earth's gravity, and will be barely perceptible. The rocket will take about 7 hours to burn half of it's deltaV. By then, it be travelling at 25km/s. 

At this velocity, it will reach Mars in 26 days at the closest approach. It will then take 3 hours to brake to Mars orbit.

A total trip time of about 27 days is a major step up from the 8.6 months expected from a Hohmann transfer.

If the low-end torchship is an ocean cruise, the High-end torchship is a jetliner. 3.6m/s2, rising as the spacecraft expends propellant, is about a third of Earth's gravity, and it will reach 1G acceleration at the end of the trip. The high-end torchship will burn half it's deltaV in 5.4 hours, then coast at 100km/s. 

This shortens the trip to 6.5 days... less than a week. 

Trying to get shorter and shorter travel times increases your power requirements exponentially, but it is not the focus of this post.     

What's the Catch?

I'm sure you've heard of the Kzinti Lesson. An incredibly powerful rocket engine is an incredibly powerful weapon, either because of it's exhaust, or indirectly, because it can turn the entire rocket into an unstoppable projectile.
The laser problem is an expanded, more general and more serious application of that lesson.

Specifically, the problem arises when your engine design allows you to extract electrical energy from the exhaust, and that electrical energy is fed into weapons systems.

For example, a nuclear-electric rocket will have a nuclear reactor producing thermal energy, which is then converted into electric energy for use by the ion engines. A fission fragment rocket works by directing and ejecting uranium ions. Those ions can be fractionally slowed down by magnetic fields to convert their kinetic energy into electric energy. The more powerful the engine, and the more advanced the technology, the easier it is to extract electric energy from the engine.

We can boil down the issue to percentages.

For direct-to-electric engines, such as those that run on a nuclear reactor, the extraction rate is 100%, meaning that all of the engine's energy can be diverted for use by weapons. For thermal engines, the fraction will depend on the technology used, but 1% extraction is a given minimum, rising to 50% for engines where the exhaust is composed of ions that are easily affected by magnetic fields. 

100%, 50%, 1%... what is the significance of these numbers?

We need one more percentage to complete the picture. It is the efficiency of your weapon system, in this case, lasers. On Earth, commercially produced lasers range from 5% to 30% efficiency. The most advanced versions (solid-state or free-electron) have efficiencies ranging from 60% to nearly 80%. 

Now we multiply those percentages.

Depending on the technologies you chose, you'll get a moderate (20%) to very low (0.1%) figure.

This is the percentage of rocket engine power that will be converted into laser power. 
In the next post, we'll explore the ramifications of being able to place even a sliver of a rocket engine's power in a laser, and how it affects combat, engagement ranges and how 'fun' your setting is.

10 comments:

  1. Feel free to ask any questions.

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  2. What equations did you use to find the earth to mars trip time?

    I have been creating a world building project for a while now and one of the hardest things was figuring out how to build torch ship without fusion. I tried a variety of electric drives that used Mercury as a "port" with the 7x sunlight and cheap, one use disposable, solar cells I could get a rough estimate of a "torch" ion engine (which uses the current 30KW a Newton).

    It wasn't very good and when I revisited the problem I started looking at beamed power. The main idea I came up with is simply a pusher plate of basically carbon ablative using a pulsed laser gives a "pseudo-torch" which after a burn of a few hours has enough delta V to sling you anywhere in the inner solar system in a few months.

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    1. I'll be discussing beamed power in detail in a few days.

      For the Mars trip time, I used the distance = at^2/2 equation, with a being acceleration and t being time.

      Give yourself a distance, and you can work out the acceleration required to reach it in a certain time. Alternatively, how long it takes to cross the distance given a certain acceleration.

      You just have to take into account that you'll burn up half your dV long before you're crossed half the distance before a flip over and de-acceleration burn, so most of the journey will be drifting with burns on both ends.

      There are many, many options between the fantastic power of fusion and the very low accelerations and power densities of electric drives. Most of them are nuclear-thermal.

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    2. Your calculations will likely have a considerable error, especially for lesser velocities. First, remember that most trajectories will be curved, which means that the actual distance travelled will be much larger than orbit to orbit distances, or even point to point distances. Second, you need to take into account "gravity drag". Even though you don't feel it, the Earth has a significant gravitational pull well beyond lunar orbit. You need to factor in the vector components from gravity into your delta-v figures. Third, it is not enough to cover the distance... you also need to match the velocity of your destination.

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  3. I looked at that equation and it does provide a rough estimate of the delta V needed. I used (distance/time)*2 for total delta V, which is the same equation just rearranged slightly.
    I have reservations in using the nuclear thermal rockets in any writing since I have a hard time seeing nuclear anything being widely distributed. The liquid and gas cores to me look like almost impossible rocket technologies due to their use of the bleeding edge limits of materials. It's a pet peeve of mine, I have seen the abuse machines have to endure, and how long maintenance of complex machines actually takes.

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    1. Keep in mind that less than 100 years ago, solid core nuclear reactors were similar "bleeding edge" constructions. Rockets capale of going to the moon were unimaginable constructs requiring "bleeding edge" materials and construction methods. In the case of the latter, it took less than a decade to turn the previously "almost impossible" into reality.

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  4. Regarding the rocket power equation: I would point out that the thrust itself is determined by exhaust velocity multiplied by mass flow. Effectively, this means that reducing the exhaust velocity means increasing the mass flow geometrically. However, I would also point out that this is not automatic. If you just cut your exhaust velocity, the real result is that ou decrease your rocket power. It is rather important to keep in mind that the increase in thrust, or mass flow, is dependent upon maintaining the same rocket power. If you cut one, you HAVE to compensate by adding to the other. Again, it is not automatic.

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    1. Agreed! However, for this scenario, I was doing a power-limited comparison since the main issue raised was that of the laser power output.

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  5. Just to throw some extra thoughts into the "low end" torchship you mention, that 30km/s 333kN motor you mention could probably be done at the upper end of nuclear thermal systems. A NERVA style solid cored rocket couldn't do it but a gas core (open or closed cycle) might well be up there at those performance levels, and if one alone can't give that much thrust you can always have a few if you don't mind the mass of multiple motors. It should however be noted that with the 50km/s of delta V you still can't totally ignore orbital mechanics on your way to mars, you'll have to probably spiral around a bit when leaving earth and reaching mars, I'm not sure the acceleration would be enough to manage the transfer from a hyperbola to/from a circular orbit at either planet in one burn. You'll still have travel times wildly differing depending on the orbital positions of Earth and Mars at launch and for some positions you'll have to wait some months at the first planet before beginning the transfer. Earth's orbital velocity around the sun is about 30km/s, so your delta-v, even accounting for tricks in planetary gravity wells of oberth like forms, is broadly comparable with this rather than vastly greater. The high end torchsip will be a lot more immune to the intricacies of orbital paths and will follow a much more straight line like course. If you ever fancy seeing what sort of trajectories you'll really end up taking check out NASA's open sourced GMAT software, it's a bit buggy and tricky to use but when you learn how you can plug in the sort of performance your vessels have and plan out any spaceflight in your sci fi writings to well within +/-1% accuracy.

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    1. Hello!
      Please find a name, there is no registration required.

      You are correct that the low-end torchship's performance cannot ignore orbital mechanics like a true torchship.

      The designation is mostly related to the excellent Project Rho's Atomic Rocket's website's designation of Terawatt rocket outputs are being strong indicators of 'torchship' levels of performance.

      30km/s exhaust velocity and 333kN thrust translates into about 0.1% of a true torchship, hence the 'low-end'.

      A 1000 ton spaceship equipped with this level of output would need to dedicate 811 tons to propellant to produce 50km/s delta with 30km/s exhaust velocity. Its initial acceleration would be 0.033 g, and its dry acceleration would be 0.18g. If KSP is any indicator, this level of performance requires the interplanetary burns to be divided into two or three segments, but it is far from the solar-electric milligee spirals!

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