Space And Gaming

I mentioned before that space is a bit large.  The brain tends to skid off the distances and not comprehend.

The next problem in space is all the math.  There's no escaping it unless you're going to handwave a lot of it away.  Do enough hand waving and people stop recognizing it as a space world.

To get the answers you need for the players you don't really even need complex math, just some algebra.  Much of the work on the calculus end has been done for us and gelled down into some nice simple equations.

Some things that remain complicated are the amount of acceleration as fuel and/or reaction mass is consumed, delta v and specific impulse.  Since most moderately realistic space worlds are going to have ships which are mostly fuel, and have very small amounts of thrust; those numbers all matter and you need to know how to calculate them.  Again, it's been gelled down for you.

Traveller gets around some of this by having its maneuver drive (apparently) move a volume at given acceleration rather than apply a thrust.  Inertialess drives are common enough in fiction.

Albedo (Erma Felna) doesn't shy away from it at all.  The ships are at least 60% tankage and the drive is a fusion thruster.  Albedo is the hardest science fiction setting I've ever run.  And the most difficult.

Somewhere in here I should point out that gaming is made of math.  Even diceless games have probability based systems to do conflict resolution.  Rock-Paper-Scissors is still probability and statistics.

A great site for seeing the reality of space is Atomic Rocket.  He's good with the hand holding.

Learn the math.  Everything important involves math at some point and refusing to learn it is accepting a secondary role in the universe.  Even if it's as simple as, "did I get enough change?"

You don't need precision down to a thousand decimal places for a space game.  But your answers need to be plausible.  1g (ONE GEE!) of acceleration gets you from Earth to Jupiter in how long?  The players will want that answer because there's always something they want to do that requires some time being run off.  Is it enough time to learn or upgrade a skill?

The answer is in the old Traveller books and some editions of GURPS Space.  Time (T) = 2 x Square Root of Distance (D) / Acceleration (A).  In spreadsheet notation: T=2*((D/A)^(1/2)); note that this assumes a turn over and deceleration to the destination.

How long does it take to get to Jupiter at 1g?  It depends.  Let's ignore orbital mechanics because with 1g on tap we don't have to deal with Hohmann transfer orbits.  Jupiter is between 5.46 and 4.95 AU from the sun at any given moment with a semi-major axis of 5.20 AU.  Earth is between 1.02 and 0.98 AU with a semi-major axis of 1.00.  That puts Jupiter between 6.48 and 3.93 AU from Earth.

That formula is looking for inputs in seconds, meters and meters/second.

1 AU is 149,597,870,000m
1g is 9.81m/ss

With my handy spreadsheet I get....  628703.24 seconds for the 6.48 AU.  Divide by 60 for minutes, then 60 for hours then 24 for days... we get 7.28 days when Jupiter is as far from earth as possible (at opposition).  There's a pesky Sun in the way of the trip...  When Earth and Jupiter are closest it takes a mere 5.67 days.  A Traveller maneuver drive is good for 28 days at this acceleration.  Note: that assumes constant acceleration for the whole trip.  One can get the same travel time with higher accelerations at each end with coasting in between burns too.

I mention 1g being impressive because it is.  It's also entirely unnecessary to have such high accelerations to just get to Jove.  Even a tenth of a g gets you there fairly fast, 17.92 days.

Where you need high acceleration is to get out of deep gravity wells, like Earth.

Take the moon launch.  The Saturn V was pulling just over a g at engine start and 4g just as it ran out of fuel, 150 seconds later.  This acceleration was mostly up and away from the planet to get out of the thick atmosphere which was applying deceleration in the form of drag on the vehicle.  The second stage peaks just under 2g and the third doesn't even pull 0.75g.  6,200,000 lb. lifts off, less than 250,000 lb. gets into orbit.  And not just fuel is abandoned; the first and second stages are discarded.

The above graph was derived from the Flight Evaluation Report for AS-510 and displays how the acceleration of the vehicle changed throughout the boost, from about 1g on leaving the launch pad to weightlessness 11½ minutes later. The key events in the graph are:

1. Launch with ignition of the S-IC. Note how the acceleration rapidly rises with increasing engine efficiency and reduced propellant load.
2. Cut-off of the centre engine of the S-IC.
3. Outboard engine cut-off of the S-IC at a peak of 4g.
4. S-II stage ignition. Note the reduced angle of the graph for although the mass of the first stage has been discarded, the thrust of the S-II stage is nearly one tenth of the final S-IC thrust.
5. Cut-off of the centre engine of the S-II.
6. Change in mixture ratio caused by the operation of the PU valve. The richer mixture reduces the thrust slightly.
7. Outboard engine cut-off of the S-II at a peak of approximately 1.8g.
8. S-IVB stage ignition. Note again the reduced angle of the graph caused by the thrust being cut by a fifth.
9. With the cut-off of the S-IVB's first burn, the vehicle is in orbit with zero acceleration. 

The 4g reached during boost is not the highest that will experienced during the mission. Entry through the Earth's atmosphere decelerates the Command Module by about 6½g.

That's the Apollo 8 acceleration curves from here.

Isn't space FUN?

This sort of thing is why Star Trek has a transporter.  It's why Albedo has smaller shuttles to make the trip and why Traveller has the insanity drive.

And it's ALL math.

There's more too.  I'll probably talk about getting to orbit in a plausible and playable way.