## Wednesday, July 21, 2010

### Realistic (and gamable) Space Travel

The biggest thing that I learned from Orbiter Space Simulator was how to accurately represent space travel realistically in a RPG.

The two key terms you need to know it delta-vee and time.

Delta-vee
This represent a change in velocity. For example to get into orbit you need to have enough fuel and thrust to go from zero to 7.8 km/sec. Sure if you doing it for real you have to have the right ascent trajectory so that when you hit the 7.8 km/sec mark everything is right to have a stable orbit. But for gaming all you care about is whether the character makes his piloting roll (or navigation depending on the system) and whether there is enough Delta-Vee to make that change in velocity.

All space maneuvers have a cost in delta-vee. So if you rate your fuel in delta-vee (instead of liters or kg) then you know how many of these maneuvers you can make. So if you on the moon of Alpha Leonis and want to goto Alpha Leonis. It may take a DV of 2.7 km/s to get into lunar orbit. Another 1.5 km/s to a trans-lunar trajectory to get to Alpha Leonis, and then a 3.5 km/s maneuver to achieve stable orbit around Alpha Leonis. So if you have fuel with a total of 7.7 km/s Delta-Vee in it then you have enough to make it the trip.

Time
Many Sci-fi systems have antigrav or some other superscience means of propulsion. In this case the limiting factor is time not fuel. In that you can only change your delta-vee by so much in X time. Normally this isn't a factor but if you are trying to catch someone that trying to escape that in a different orbital plane then it becomes critical.* Or if you coming in hot and trying to make a stable orbit in 2 minutes you may finding that you wished that you bought that 6G maneuver drive back on Efate.

*Changing the plane of your orbiter (the degree it is tilted to the planet's equator) requires 10 times the amount of delta-vee then simply raising and lower your orbit's altitude. This is why when there are mission to other planets or the ISS there is a window for the launch time. Mission Control is waiting for the orbital plane of the target to cross the launch site. Generally there is a couple of minute leeway on both sides. But the further you are off the more fuel (or time) it will take.

The Hex Master said...

I think you might enjoy this site on orbital mechanics. It has the math for working out the delta-v cost of various orbital transfers.

And, all of this varies from world to world based upon gravitational pull (including competing tides in a multi-lunar planet), atmospheric density, and ceiling to space. :)

Rob Conley said...

Which is why delta Vee is a good number to use as you can compute it for any world.

Eric Wilde said...

Shouldn't "Time" really be "Acceleration"?

Rob, it would have to be re-calculated for each environment, given the specifics I cited, as well as others.

Delta Vee is a universal term, but not a universal value, and as such, energy requirements ('fuel'/'output'/'reaction') would still have to be determined for each stop, thus it is possible to have enough D-V to escape Luna, but not to escape Earth.

http://en.wikipedia.org/wiki/Delta-v

Rob Conley said...

To clarify, space maneuvers have a requirement in Delta Vee to execute.

Spacecraft and Rockets are capable only effecting so much change in Delta Vee.

The Spacecraft and Rocket values remain constant regardless of where they are located.

However the planet will have to be recalculated based on the path. I still digging for the formulas I used which is why I being a bit vague.

This diagram from Wikipedia is an excellent illustration of what I am talking about.

http://en.wikipedia.org/wiki/File:Deltavs.svg

This goes more into what is called a Delta-Vee budget.
http://en.wikipedia.org/wiki/Delta-v_budget

You need to use the Rocket Equation as simple thrust over time is not accurate (your fuel is decreasing and thus your thrust increases). However from long experience the basic formula is complicated to use as a gaming tool.

I have created some formulas that start with Fuel mass, thrust rating, Rocket mass, and tells you what your delta-vee is.

The basic issues is that gaming system don't give you the ISP of the rocket. That can be computed.

This is a good summary of what Specific Impulse represents.

http://en.wikipedia.org/wiki/Specific_impulse

The formulas for orbital maneuvers can be found here.

http://en.wikipedia.org/wiki/Orbital_mechanics

Rob,

Great resources, for Rockets.

The 'Time' or Accelleration values for reactionless drives, though (really my point) are not going to deal with D-V in the same way at all, and that using D-V as a gaming metric still says nothing about fuel capacity (power), or rate of consumption per Round (without becoming a mini-game, like Orbiter), and doesn't make calculations for travelling from one extraterrestrial body to a series of others, each with their own variables.

Fuel or Power, and Power Cost are very game-able, still allowing for intra-atmospheric shenanigans or dogfights, whereas D-V requirements are the computer's job of calculating, as variable accrue.

I suppose it comes down to a general semantics issue, as I understand and appreciate that sort of physics-inclusion (as in GDW's Mayday), but not to the detriment of the gameplay, especially when the term is sort of misleading in a multi-extraterrestrial context where it would have to be calculated afresh each time (as I originally posted) a new body's gravitational well was entered or traversed.

If one did a FASA Starfleet Combat Simulator (or whatever it was called)-sort of thing, with a physical resource display and allocation chits, etc., then I think calculating D-V (and Fuel/Power Consumption over Current Capacity ;) ), that it would be a great mini-game.

I think, though, that a lot of ships would crash, and a lot of 3d6's x 6 would be rolled before the Players became comfortable enough with the rules of flight to be able to visit other locations with any sort of frequency.

Rob Conley said...

Yes you are correct about D-V for Reactionless Drives, the only thing that matters for Reactionless Drive is time. Does your drive produce enough thrust to do the manuever in the time you want. For example the recent series of probes using Ion Drive tend to use long spiral paths to escape earth orbit because of the small amount of thrust they produce. '

Delta-Vee is a proprotional value when it comes to fuel. If you have half your Delta-vee remaining you have roughly half your fuel left as a rough rule of thumb. And the purpose of this isn't to make a space combat game but rather to answer the question of do I have enough fuel to do X. With X being one of a number of space manuevuers.

As for the travel, real orbital mechanics is not gamable. All you need is an idea of how long it takes and if desired a rough idea when the windows are. Just get a rough idea of how far apart they are and then just wing it from there. The important point and is that you can't take off at any old time and expect to have the fuel to reach where you are going.

Even reactionless craft have to work about this. As while they won't run out of fuel if they don't leave at the right time they will spend a lot of time trying to get the other planet. Something I tried in Orbiter. Even 6G thruster have windows (much more frequent than 1G or 2G)

The issues is that everything is in orbit under the influence of the central star. So you can't just point or even lead and expect to get there. What will happen is that you will need to spiral into your destination which takes time. Of course if you can go fast enough then it doesn't matter. But anything over a day travel you run into problems.

Yu don't need to be exact just get some ballpark numbers about the periodic appearance of windows and wing it from there. FOr example if a transfer orbit opens up every 84 days between two planets for a 1G drive. You can say that a 6G can leave +/- 24 days while a 1G drive has to leave within a day. So this means for a 6G drive that they only have to wait 28 days from the last day of the first window to the first day of the 2nd window.

The way the formulas work you can get a good sense of what the ballpark is. I guess I will need a future post with actual numbers to show how it is.