ρ=Σ+Ψ

```
```

The game was conceived to be a starship combat game, with a tactical emphasis. Players would control only a few ships in great detail, rather than a fleet in sparse detail.

25% C, which totals to 100%.

I suppose you see where this is leading. The light bulb went on when I realized that there are three elements in the Attack power, Defense Power, and Movement Power equation.

For game purposes, I made the graph so each point totals to 150% instead of 100%. I just pulled this figure out of the air, feel free to experiment with other values.

I then chose a limited number of points to become the allowable power allocation options. They are the circles in the upper graph. The ship starts a game at the center (333) at 50% Attack, 50% Defense, and 50% Move.

The real fun comes with the paths. I drew a series of arrows from node to node. They show nodes one can move to from one's current node. Note that some of the arrows are one way, for instance one can move from node 422 to node 440, but not vice versa.

The theory behind the arrows was that the further one moves out of balance to favor one system over the others, the harder it is to get back into balance. Also note that one can move from node 044 to node 700, inverting the allocation.

Each ship can change its node by one arrow per turn. If you mis-read what your opponent is trying to do, you can paint yourself into a corner.

Other networks of paths are possible, see what you can come up with.

Failing that, I used a simple system where on the ship record sheet one records the ship's current vector as the delta X, delta Y (and delta Z if doing three dimensions). These are the values added (algebraically) to the ship's current x,y,z co-ordinates in order to calculate the new location. (

This is using a rectangular grid for the map. If you wish to adapt this to a hex grid, be my guest.

An assumption was made that a ship can only thrust in the direction it is currently facing (which has nothing to do with which direction it is travelling in). So the ship would used the facing chart to see which deltas got the benefits of any acceleration this turn.

x-y chart

x-y-z chart

Ships may only change facing by following the arrows. So a ship that could change its facing by 2 square a turn, if it started in #4, it could move to #14, but could not move to #15.

Tractor beams, once they have sucessfully latched onto an enemy ship, can change the deltas of the enemy ship. The limits are:

- [1] Whatever changes are made to the enemy ship's deltas have to be made to your ship's deltas in the opposite direction. This is due to Newton's third law. For example, Sky Trash pegs a Blortch Battleship and changes it's current vector from +2,-10 to +1,-15. Poor Sky Trash's vector changes from -4,+3 to -3,+8. Its just too bad that this puts Sky Trash into a decaying orbit around an antimatter neutron star.
- [2] There is a limit on how many vector points a given tractor beam array can transmit.

Again their is a limit to how much a given grapple array can transmit, so the grapple can be broken during the inelastic collision if the limit is exceeded. And afterwards a grappled ship can frantically accelerate in an effort to break the grapple.

To do an inelastic collision simplistically, merely add the two ship's deltas together and use the results. If Sky Trash grappled the Blortch, both would get the vector -2, -7.

This highlights a limitation. The above tractor and
grapple rules work fine, as long as the two ships have the same mass. Differing
masses can be accommodated, but things get much messier.

The basic idea is to keep track of a ship's vector
*energy
x,y,z*. You divide these by the ship mass to get the actual deltas used
to move the ship.

So if Sky Trash had a mass of 5, it could have vector
energy of -20, +15, and a vector of -4,+3. Say the Blorch Battleship has
a mass of 15, vector energy of +20,-150, and a vector of +2,-10. Sky Trash
tractors it, and gives the Blorch a -5,-75. Now the Blorch has a vector
energy of +15, -225, and a vector of -1, -15. Unfortunately Sky Trash receives
a +5, +75, resulting in a vector energy of -15, +90, and a vector of -3,+18.
This actually might be a good way to make a fast getaway.

Things really get ugly with grapple beams.

- [1] Add the vector energies together
- [2] Add the ship masses together
- [3] Determine each ship's vector share. Do this by dividing the ship's mass by the total mass.
- [4] Divvy up the vector energies between the ships by vector share.

Total vector energy = -349, -185

Total mass = 20

Sky Trash vector share = 5 / 20 = 0.25

Blorch vector share = 15 / 20 = 0.75

Sky Trash new vector energy:

x = -349 * 0.25 = -88

y = -185 * 0.25 = -47

Blorch new vector energy:

x = -349 * 0.75 = -262

y = -185 * 0.75 = -139

As a check the ships should now have the same vectors:

Sky Trash

vector x = -88 / 5 = -18

vector y = -47 / 5 = -9

Blorch

vector x = -262 / 15 = -18

vector y = -139 / 15 = -9

The crew of the Sky Trash fly bone-crushingly into the nose of the ship as it comes to a screeching halt and starts going backwards.

If either ship accelerates, the acceleration units are divided between
the two grappled ships by vector share.

Nice system, but a bit one-dimensional.

So I attempted to make it two dimensional.

An idea is to count remaining weapons strength that penetrates the ship as causing general structural damage. Once this is gone, the ship falls part.

Here is a small cutter's damage chart.

Here is a damage allocation chart based on hexes.

Here are some prototype symbols for ship systems.