Scenario Idea: The Orbital Shuffle

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Scenario Idea: The Orbital Shuffle

Postby grafvonbarnez » Mon Jun 09, 2014 9:24 am

Here's a short, very basic scenario for Intercept Orbit I've been kicking around for a little bit.

First, a little background on spacecraft. You can ignore this if you're only concerned with the rules (it's very long, I enjoy writing about spaceship physics too much :D), but it does give a good justification for the scenario.

Spoiler: show
All spacecraft, except for those using solar sails, move in space through the use of reaction engines. A reaction engine uses energy from fuel or solar power to accelerate mass ("reaction mass" or "re-mass") in the opposite direction of the ship's thrust. This causes, due to Newton's third law, the ship to accelerate forward with the same force used to expel the mass backwards (the "equal and opposite reaction" that gives them their name). In current day rockets, the fuel and reaction mass are usually the same thing, a chemical propellant. This doesn't have to be the case, with things like nuclear thermal rockets or ion drives.

Since space has no friction, ships don't really have a "top speed", and "how fast can you go?" is a lot less interesting a question than "how much can you change your velocity?" Because of this, the best way to quantify the performance of a ship is through two quantities: thrust and delta-v. Thrust is a measure of how much force your engine can put out, and thus how fast it can actually accelerate. Given the way the :IO movement rules work, it's a reasonable assumption that ships in this universe have relatively high thrust in proportion to their mass. The differences in movement between capital ships, frigates, and frames seem to indicate that the thrust output of engines is sort of linearly proportional across ship sizes. Big cruisers can change their movement vector on average a lot less quickly than frigates, and frigates are downright clumsy compared to frames.

That still leaves delta-v though. Delta-v, from the delta symbol meaning "change in" in physics and math, and v for velocity, is exactly what it sounds like, how much a spaceship is able to alter its velocity vector with its engines, fuel, and available propellant. If a ship can accelerate 1km/s, then turn around at it's destination and decelerate back to its original speed by using all of its re-mass, that ship has 2000 m/s of delta-v. Delta-v is based on a combination of factors including mass ratio (how much of the ship is dedicated to storing re-mass compared to the rest of it), and the specific impulse of the engines used. Specific impulse is essentially propellant efficiency, how much force you can exert on the ship for every kilogram of reaction mass spat out of the engine. It's based on the exhaust velocity of the engine, how fast your re-mass is going when it's expelled. Like thrust, we'll assume it's pretty standard and fixed across ships and factions. Delta-v, specific impulse, and mass ratio are related through the Tsiolkovsy Rocket Equation: delta-v = specific impulse * g * ln(total ship mass with propellant / ship mass without propellant), where g is 9.81 m/s^2 and ln() is the natural logarithm function. What the rocket equation basically comes down to is that, given a fixed specific impulse, the mass ratio of a ship increases exponentially with the required delta-v.

Now, what does this mean for the game? Most warships will have a large delta-v and thus a high mass ratio. This doesn't really matter for them: they're warships, meant to fight in space in a variety of quickly-changing situations. That 90% of the ship's mass is re-mass makes no difference, if they can carry weapons, armor, frames, and personnel, and use them in a battle, that's good enough. Like any purely military asset, warships are economic liabilities. They cost you a lot of money for no direct economic gain, so their economics are mostly tangential. If a faction needs to fight, and needs warships to fight, they'll pay for them or lose.

HVAs, on the other hand, typically don't have that luxury. If they are hauling cargo, be it peaches or people, they can't afford a high mass ratio. Imagine a 747 flying cargo from Boston to LA, but the entire passenger compartment is a fuel tank and the only cargo they can actually carry needs to fit in a one foot box between the pilots. If they're only flying from Boston to Detroit, you can fill the passenger compartment with people instead of fuel. (Well, a better way to think about it is that both warships and HVAs can get from Boston to LA with decent payloads, but warships are sacrificing payload to be able to fly Boston to LA by way of Ottawa, Miami, and Albuquerque without refueling. HVAs can only fly the direct course.)

Because of all this, HVAs are limited in the courses they can make, and most of them will follow longer, lower delta-v trajectories. The boring, coasting through space parts of these are actually pretty safe. Space is very big, and you won't actually manage to intercept something halfway along its trajectory unless you blow a whole lot of delta-v and get lucky with your launch window. The closer things get to planets, though, the more vulnerable they are, so most space battles will tend to take place near things. This is good and cool and cool and good; the closer you are to a place you've got a good reason to be, the more likely there are to be ships you can fight with, so we get our sweet 3+ player space battles.

Now, usually, if you're doing something in space you've got a good reason to do it; you won't just fiddle around in the void, you'll have a destination. This destination is almost certainly going to be in an orbit around something. It could also be on the surface of something, but you're probably not landing with the same ship that you used to move through space. Much better to have orbital spaceports transferring cargo to the surface with optimized shuttles, and if you're on a better developed planet, bringing cargo back to orbit with something like a space elevator, mass driver, or other non-rocket launch system.

Once your spaceship gets to the planet or other body it was headed to, if you did your math right, you'll be in a capture orbit. This is a parabolic orbit that enters on one side of the body, swings around it, then flies back out into space. You probably don't want that, so at the lowest point in your trajectory (closest to the body) you'll fire your engines to bring you into an elliptical orbit, where you'll go around the planet for as long as you want with no danger of shooting off into space. Unfortunately, unless you did all of your math and every maneuver incredibly precisely, you're probably not already next to whatever station you were headed to. This is fine though, if you ended up in the same orbit as your target, but not very close to them, you'd have just wasted fuel.

Orbits are defined by six quantities, three of which we care about: apoapsis distance, periapsis distance, and true anomaly. (The other three are: argument of periapsis, longitude of the ascending node, and inclination, but those are very involved and you'll basically just want to match your own with your target's. Also, in real orbital mechanics apoapsis and periapsis distances are usually replaced by length of semi-major axis and eccentricity, but the two pairs of quantities are freely convertible). Apoapsis and periapsis distances are simple, they're how far and how close you are to the body at your furthest or closest orbital points, respectively. True anomaly essentially means where you are in your orbit at any given time. The important thing to realize is that for us to rendezvous and dock with a station or another ship, all of these quantities have to be the same when we're near them. If we've got the same apses as them, but different anomaly, we'll be over South America while they're over India. The other thing is that two objects in the same orbit have the same average speed. If our anomaly isn't the same as theirs when we enter the same orbit, it never will be. Fortunately, physics gives us an easy tool to get where they are and stay there, the fact that closer orbits are faster than further ones. This means that the rate-of-change of the true anomaly of a closer orbit will be larger than for a further orbit. It's why the ISS, in a 420km orbit, goes around the Earth once every 90 minutes, and the moon, in a 384,000km orbit, goes around once a month.

From here, the solution is easy. If we're in a higher orbit than our target, we'll be going around slower than them, so we can calculate when we need to use our engine to change our periapsis distance to equal theirs, such both of us will reach periapsis at the same time. Once we're next to them, we just burn our engine one last time to match our apoapsis to theirs, and we're done. There are a few hairy bits here though. The first is that it will take exactly as much delta-v to travel between a capture orbit and the orbit of a station as it will to accelerate from that orbit to an escape velocity. This can be a problem if you're aiming for a lower orbit, it takes a little over 2000 m/s of delta-v to move between an Earth capture orbit and a geosynchronous orbit.

The other problem is that the most efficient time to change your periapsis or apoapsis is at the respective opposite. This is because your orbital velocity is tangential to your orbital path, and your apses are dependent on your orbital velocity. Thrusting tangentially to your orbit will raise or lower the point on the opposite side of it. Therefore, the most efficient way you can change your periapsis altitude is by thrusting directly tangential to your orbit at your apoapsis. At any other point you need to thrust in a different direction to change your periapsis, so some of your delta-v isn't being used to change your orbital speed, and that's delta-v that didn't have to be wasted. Remember, you still need fuel in the tanks to match orbits at periapsis.

Putting this all together, what have we got? Say you've got your convoy of warships and HVAs on an intercept trajectory with a spaceport or transit gate. They've already closed their capture orbit, so there's no danger of careening back off into space, but you need to rendezvous with your target on this orbit. Why? It could be any number of reasons. Maybe it's a spaceport and you need to deliver the supplies you're carrying quickly. Maybe it's a transit gate currently in sync with your destination, and you need to get there before it becomes unaligned. Maybe your crews will mutiny if you miss last call at the space-bar again! :D Regardless, you've gotta get to your rendezvous... and so do the other players' ships. Now, since we're all on different orbits, but heading to the same place at the same time, our orbits will eventually converge. What happens when the orbits of convoys from different factions converge? A space battle!

So all of our ships are now fighting it out in orbit, with Doomsday (rendezvous with the station) rapidly approaching. Space battles tend to involve a lot of Trying-Not-to-Get-Shot, which means a lot of evasive engine burns that are going to throw our orbits out of whack. All of our warships will be fine, they've got the spare delta-v to make inefficient course changes close to periapsis. Our poor HVAs though, hauling all of that precious cargo that needs to make it to the station? They've gotta get back to their trajectory before it's too late, or they're going to miss.

So, without further ado, on to the actual scenario!

Scenario: The Orbital Shuffle:

Convoys of warships escorting HVAs are all on converging rendezvous orbits with a target over the surface of a planet. They're carrying much-needed supplies for their factions, and not resupplying their ground forces fast could spell disaster!

When each player comes to the table, after they've determined final army composition but before they've placed any ships, mark out a thin line across the entire length or diameter of the table. The line can be drawn by common consent of all players, but give the defender final say in case of disagreement. The defender then places his first HVA somewhere on the line. All other setup proceeds as normal.

Play proceeds as normal for a game of Intercept Orbit, but calculation of final scores at Doomsday changes.

The line marked out on the table during setup is the vector of the orbit required to rendezvous with the target station. If an HVA misses this rendezvous, they don't have the fuel required to correct in time, and have to wait for their next opportunity to get to the station.

For final scoring only, do not count HVAs that are not within point defense range of the marked line. HVAs, as normal, score points for the current owner, or no one if they've missed their target.

Well, that's it! A lot of talk for so simple a change perhaps, but give it a try if you're so inclined. I've seen a lot of HVAs start to disappear to the edges of the board when more of the catapults that are in play get blown off. Now there's some incentive to keep them a little more in the mix. Thoughts? Comments or concerns?
Last edited by grafvonbarnez on Mon Jun 09, 2014 12:59 pm, edited 2 times in total.
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Re: Scenario Idea: The Orbital Shuffle

Postby Luke_BMM » Mon Jun 09, 2014 11:16 am

First, a little background on spacecraft...

I've played enough Kerbal Space Program to see where this is going... and it makes me quite happy.

As far as the objective, at first blush it sounds great. You've set up a good reason to force action to happen. That's a big win right there.

I would, however, be very mildly concerned about the choke point (choke vector?) slightly reducing the value of support range and increasing the value of point and assault range. If the objective of the game is to cluster ships together, long range seems like a bad pick - or at least the first system to go. Any thoughts or concerns in that regard?
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Re: Scenario Idea: The Orbital Shuffle

Postby grafvonbarnez » Mon Jun 09, 2014 1:16 pm

Luke_BMM wrote:
First, a little background on spacecraft...

I've played enough Kerbal Space Program to see where this is going... and it makes me quite happy.

Haha, yup. And thanks! KSP has helped me really understand more about how spacecraft intuitively work than every physics or astronomy class I've ever taken put together.

Luke_BMM wrote:As far as the objective, at first blush it sounds great. You've set up a good reason to force action to happen. That's a big win right there.

I would, however, be very mildly concerned about the choke point (choke vector?) slightly reducing the value of support range and increasing the value of point and assault range. If the objective of the game is to cluster ships together, long range seems like a bad pick - or at least the first system to go. Any thoughts or concerns in that regard?

That is a good point, but I think (or am hoping) the pluses and minuses for support weapons smooth each other out. Sure, everyone's in a scrum at the middle of the board, but your TAs don't have to worry about where they end up at the end of the game. If you've got a vulnerable all-in support ship like 2W2Rs2YG or 2W2Rs+d82Y you might be able to slink it off to the edges and snipe while everyone's preoccupied defending their HVAs and going at it in the middle. And if someone does board it, they've pulled their frames out of the most vulnerable and contentious area of the board.
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