Wednesday, October 27, 2010

Space RPGs: Flight Models

I've been thinking a lot about a space RPG lately. I never played Traveller, but I've reviewed it, and it is far too complicated. I know that Traveller spawned Elite, which in turn spawned Privateer (which was a childhood favorite game of mine), but it is just too much for me to want to run as far as rules go these days.

One problem that I've been putting some brain bytes towards is how to handle space combat. There are two approaches: realistic physics or arcade style. Video games had to deal with this too. Arcade style is popular because it is easier to grok, even if it is unrealistic. An example would be violating the law of conservation of momentum, capping maximum speeds in a vacuum at something significantly less than C (speed of light), and so on.

An RPG could go with the same sort of idea: each turn, a sub-light ship moves X squares and can make Y changes in direction. This effectively taps maximum speed at X squares. You could even justify it by saying that the sub-light technology has some sort of special property that perhaps cancels out inertia or momentum (converting velocity to heat or something).

However, this totally disregards some unique aspects of spaceflight. For example, if a ship continually accelerates at 1 MPH, its velocity will eventually get to be significantly greater than 1 MPH! One of the advantages of traveling in a vacuum is that you can get up to a great speed, especially if you have enough fuel/energy to generate thrust for 1/2 your trip. I think the solution is somewhere in between: use pseudo-newtonian rules that feel unique and space-shipish but are easy to implement.

I think the key is to focus on acceleration, not velocity. After all, if the relative velocity of the combatants is zero, you might as well be stationary.

The two things that help a lot as far as limiting factors go are:
  • Limited Acceleration due to Gs: The human body can take about 9 Gs before G-LOC occurs. Much equipment may not be able to handle that much. For example, a spindly vacuum-only ship may only be able to take 1/2 to 1 G. While that is not a limit on velocity, it does significantly limit acceleration. 1 G is about 10 m/s^2, or approx 22 MPH (so if you could accelerate from 0 to 65 MPH in one second you'd feel three gees). In another example, the Apollo trans-lunar velocity was something like 25K MPH, which is about 11,000 M/S. A 3G (30 m/s^2) burn would have to burn for something like 6 minutes to get you up to that speed.

    Note that a human body can take something like 45Gs without breaking under certain conditions. However, if you're talking about sustained, fighting capability -- 9 Gs is a good rule of thumb.
  • Limited Fuel: Unless you posit a never-ending energy source for your sci-fi world, then fuel will not be unlimited. Say your spaceship is 2000 tons, about the size of the space shuttle. Kinetic Energy = (1/2) mass * velocity ^2. A mass of 2000 tons is close to 2,000,000 kg, and the desired velocity for a 3-day moon shot is 11,000 m/s, so the energy wrapped up in that enterprise is 121,000,000,000,000 joules. By my rough reckoning that's about the amount of energy in a million gallons of gasoline, 7.5 million lbs of coal, -- assuming 100% perfect efficiency in the engine! If you could assume that you can crack uranium-235, it'd be much less (about 7.5 lbs), but the mass of the reactor would have to get added to your 2000 ton spaceship! With the exception of drives like Ion Drives or Solar Rocket Engines which are highly efficient as far as propellent usage goes (but provide very low thrust -- and thus are not tactically interesting for most PCs...), most of the other options use a ton of fuel and are propellant inefficient (TANSTAAFL). So, the bottom line is that if you limit fuel, then it will limit the "burns" that a ship can do, which limits maneuvering and acceleration.
Here's my rough estimate of how to figure out "useful" scales for tactical ship-to-ship combat. Let's assume that primary weapons are energy weapons, mass drivers/cannons, and missiles/rockets.
  • Energy: A light-second is 300,000 km. Particle weapons would travel much more slowly than C, but for lasers, 300,000 km is probably a reasonable maximum range. Anything longer than that and you'll start to have aiming problems. Note that this is a problem with sensors, too; a radar or lidar pulse needs to travel two ways (out and back), and the maximum unambigious range is likely going to be much less depending on waveforms and whatnot. There are also problems with sensor range due to the formula for a sphere; the returning energy pulse is reduced by a power of 4*PI*R^2 so you need VERY sensitive receivers to detect a returning pulse from extremely distant targets, even without atmospheric attenuation.

    I also imagine that you'd have trouble with dispersal reducing the power level of the beam as it spreads over distance. You'd need a very tight, focused beam and the power will attenuate over distance. The YAL-1, a megawatt class laser, has range of ~600 KM vs. thin skinned targets in an atmosphere. Here's a quick back of the envelope calculation:

    Power Density = Transmitted Power / 4 * Pi * R^2
    Power Density = 1 megawatt / 12.56 * 600 KM^2
    Power Density = 1 megawatt / 4,521,600 KM

    So, I think something on the order of ~1000 KM is reasonable for desired weapons effects with a megawatt-class laser weapon in a vacuum. If you assumed that a sci fi laser would be a giga-watt class system (1000 times more powerful than the YAL-1), then perhaps closer to 20,000 KM as a WAG, although I'm sure an engineer would tell me how far off I am.

    Power Density = Transmitted Power / 4 * Pi * R^2
    1 megawatt / 4,521,600 KM = 1000 megawatts / 12.56 * R^2
    12.56 megawatts / 4,521,600 KM = 1000 megawatts / R^2
    R^2 * 2.7777777777777777777777777777778e-6 = 1000 megawatts
    R^2 = 360000000
    R = 18973
    (Sorry I got lazy and dropped the units... this is a WAG anyways...)

    Likewise, if you went DOWN to a kilowatt laser, then range would shrink to something like 50 KM vs. a thin skinned target.

  • Projectiles: Range is effectively infinite due to Newton's First Law. However, against a maneuvering target, there might be problems with anything at longer ranges. If you assume a mid-case 6G manuevering target, then in one second that target can change velocity by 60 meters/second^2. A bullet usually goes at a velocity on the order of 1500 meters/second; artillery shells are much slower (hundreds of m/s) but we're in the ballpark. If you want to be able to hit a 10 meter sized "kill zone" on a maneuvering target, then your projectile needs to arrive in 1/6 of a second or you need to really be able to guess where it will be. That makes the effective range about 250 meters! That makes sense, though; ~750 feet is the heart of the envelope for a fighter aircraft trying to gun another fighter, which has similar acceleration and size issues; atmospherics don't even really come into it.

    If you're going after a 100 meter vital zone on a 3G target, then your bullet has 3.3 seconds, so max effective range would be ~4000 meters.

  • Missiles: Like mass drivers/projectiles, range is effectively unlimited. In fact, it is greater because a missile (A) accelerates after launch and (B) can correct its course with terminal guidance. The only issue is how long it takes to get to the target, and if it has sufficient maneuvering ability to catch a maneuvering target.
So, really, tactical space combat scales can be smaller than you might think. Hexes as small as 250 meters might make sense! Remember, velocity doesn't matter; the only thing that matters is DELTA V (the difference in velocity between combatants). If you went with a 500 meter hex then you'd get the following:
  • Guns vs. Maneuvering Point Targets: 1 hex range
  • Guns vs. Non-Maneuvering Area Target: 8 hex range
  • Megawatt Class Laser vs. Thin Skin Target: 2000 hex range (effectively infinite)
  • Megawatt Class Laser vs. Medium Skin Target: 1000 hex range (still effectively infinite)
  • Kilowatt Class Laser vs. Thin Skin Target: 100 hex range (still effectively infinite)
  • Kilowatt Class Laser vs. Medium Skin Target: 50 hex range
    Note that if you posit armored targets, or better yet, some sort of energy shields, then you could shrink the ranges significantly, especially for a kilowatt class laser. The YAL-1 takes up an entire 747. I understand that sci-tech will make major strides in a sci-fi setting, but if you're talking about a laser that can sit inside a turret like you see in Star Wars, that's a LOT of miniaturization. So saying that small turret-based weapons are kilowatt class is reasonable. A megawatt class laser might be something like a mining cutting laser or a destroyer (not fighter) class weapon.
  • 1G acceleration over a one minute period of time: ~1 hex delta vee (and this relationship holds fairly steady, so 9Gs = 9 hexes of delta vee)

The last bullet there is actually a good argument for using a 600 meter hex for tactical spaceship combat. It would basically create a 1G acceleration = 1 hex movement direct relationship, which is pretty sweet; it wouldn't really affect the maximum weapons ranges much, except that the guns vs. maneuvering targets is getting a bit optimistic. I can also think of some cool things you could do with a D6 and 600 meter hexes. The 500 meter hex is easier to extrapolate to greater ranges, however, and you could assume there are some inefficiencies in the burn or something that keeps acceleration from being perfect.

Alternatively, you could go with some multiple (2-3G) for the hex, which would lead you to 1200 or 1800 meter hexes. You could just round to 1KM, 1.5KM, or 2KM. That basically reduces movement rates for very rapidly accelerating objects such as guided missiles, but it also reduces movement rates for the typical player-controlled ship. If you think that a 3-5G rated ship is "typical" with 9-10Gs being a peak manned combat vehicle, then using 1800 meter hexes means that the typical ship only moves 1-2 hexes, which may not be very satisfying.

Remember, the key is acceleration capability in a fight, not velocity. Assuming that the combatants are intentionally getting into a fight, then one of them has matched velocity with the other. The aggressor in that case should basically be able to enter the fight with whatever starting relative velocity they want. For example, if they enter the fight with an advantage of +3600 KM/HR, then they'll have a velocity delta of 60,000 m/s, or 100 hexes. So, they'll blow through the engagement and only get one pass, which may be what they want. They'll have to do a long ~10 plus minute burn after blowing through to come around for another run which burns a lot of fuel.

It is much more fuel efficient to basically match velocities and enter the fight with manageable Delta Vee. That way you're not burning a bunch of mass to get up to high speed then burning yet more to rapidly decelerate. So letting the aggressor pick their starting relative Delta Vee advantage makes a lot of sense. In a more reasonable and tactical scenario, the aggressor could enter the engagement with a delta vee of +260 KM/HR, which gives them 10 hexes of movement. They could then make a pass on the victim, do a 9G braking burn, and be drifting along one hex faster than the target for round two of the fight -- a manageable place to be! It is a little more complicated than that because they could apply angular delta vee but still, you could come up with rules of thumb to keep it simple and manageable.

I'm going to stop now before I embarrass myself further. It has been a long time since I took physics. But I think that with some careful thought you can create a pseudo-Newtonian feel to the system fairly easily.


kipf said...

Thanks thats a neat post.

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