ρ=Σ+Ψ
``` <!-- PrintGameHeader("Random Game Notes", "Wargames"); //--> ```

# Random Notes on an Unfinished Space Game

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.

### Balancing Ship Designs

See Ship Point System.

### Power Allocation

Power allocation is a good spot to give the players some options. The idea I was toying with was a system where it was difficult to change power allocation quickly, so the players could try to out-fox each other.
Now, look at the red triangular graph in the lower left. This is a standard "percentage of three elements" graph often found in metalurgy and chemistry. Every point corresponds to a different percentage of three elements. The circled point, for instance, is 25% A, 50% B, and
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.

### Movement

Vector movement is the king of space movement systems. The trouble is trying to find a way to make it easy enough to use by the players. My personal favorite is GDW's Triplanetary (also used in Steve Jackson Game's STAR FIST). But that involved drawing vectors on the map with grease pencil.
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. (e.g., if the good ship Sky Trash is at 3,6,10 and has a vector of -1, 0,+10, next turn it will be at 2,6,20)
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
So say Sky Trash is facing in direction #4. It accelerates for 6 units. Since #4 has two deltas in it (-x,+y) each delta gets 3 units. Its delta of -1,0,+10 becomes -4,+3,+10.
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.
Grapple Beams are different. While a Tractor beam is like an elastic band, Grapple beams are like iron rods. When your ship nails another with a Grapple beam, they first undergo a "completely inelastic collision" whereupon their vectors are identical. Then until the grapple is broken, the two ship accelerate and move as one.
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.
Example: Sky Trash, mass 5, vector energy 105,-21. Blorch Battleship, mass 15, vector energy -454, -164.
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.

### Damage Allocation

Task Force Game's STARFIRE has a simple damage allocation system. All ship systems are represented by letters. A string of letters represents the ship. As damage is done, systems are checked off from left to right. Naturally if a given system is checked off, it can no longer be used. Generally the systems on the extreme left are force fields and armor.
Nice system, but a bit one-dimensional.
So I attempted to make it two dimensional.
The idea is that one designs one's ship by placing ship systems into the white squares. Since we are playing on a rectangular grid, enemy weapons fire can come in from eight different directions. Each direction has a damage table. So if the above ship was under fire from the left, it would use the yellow table. Roll 2d6 to see which arrow to use ( two dice added in order to generate a bell curve with a bias to the center). Move in the direction of the arrow until an undamage ship system is encountered. Destroy that system, and reduce the strength of the weapon fire. Continue until one runs out of weapon strength or penetrates the ship.
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.
Another idea is to use different damage allocation for different weapons types. The allocation already described is the "pin beam". Rod beam is like pin beam, except it damages systems in a 2 wide swath. Cone Beam or Shaped Charge does it in a cone. Blast has one rolling on the table for every separate weapon strength point, this peels the surface of the ship. Fan Beam is like blast, but more systematic.

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.