So much of this info is wrong. I'll do my best to redo it sometime soon. Read in the comments for more info.
I have been doing some research into how power generation works because I'm getting tired of the "try it and see" method of building power. I want to be able to calculate my power before I actually build the reactors. So there's what I've come up with
Power Charge(e/sec) = Σ(power objects)
Power objects for this explanation are any group of SD HCT xm3.4 Power blocks that are touching with at least one side. If a block is not touching the side of another they are not in the same power object. This counts for diagonals.
So the power generation of each individual power object is calculated based on the number of unique power blocks in each of the X, Y, and Z directions and the number of non-unique power blocks in each direction. Unique power blocks generate power in an increasing way based on the number of them that I will explain later. Non-unique power blocks give a flat 25 e/sec power generation per block.
So now what constitutes a unique power block and a non-unique power block? Let’s start with unique power blocks in one dimension (aka. a line). This dimension shall be X. Every block in the line fills a unique spot in the X dimension.
Now we will move to two dimensions. This second dimension shall be Y. In two dimensions there are several unique spots in both dimensions.
When determining uniqueness each block may only be used once. If a block is unique for both dimensions it is not counted twice. Therefor the block in the corner that is unique to both X and Y only counts for one.
Now for non-unique blocks in two dimensions. Any block that shares a location with another block in a two separate dimensions is non-unique. I will use U for unique blocks and N for non-unique blocks.
In this picture the N block shares a location in the X dimension with a U block and in the Y dimension with a U block so it is non-unique.
These same ideas apply to the third dimension as well. This dimension shall be Z. Z has its own set of unique blocks that are separate from X and Y.
Again Z does not get to count the block in the corner (the block that is currently hidden that was the first unique block in X). Also the rules for non-uniqueness apply in Z as well.
So now that we have determined what is unique and what is not lets go back to our calculations. As stated earlier I have found that:
Power = Σ(power objects) = Σ(Power generated by all unique blocks + Power generated by all non-unique blocks)
Power generated by non-unique blocks = (Number of non-unique blocks * 25 e/sec)
Where it becomes tricky is calculating the power of the unique blocks. The power generated by unique blocks is only based on how many there are as long as they are all unique. This means that placement does not matter as long as every block is still contiguous and unique.
Examples: (Note the blocks number and the e/sec generation)
(EDIT: I apologize for the pictures. I thought you would be able to see the e/sec and block count. Just go build these for yourself and see)
In each of those pictures the form the blocks are in takes up a larger area than the last but they still produce the same amount of energy. When I first began designing power generators I thought that the generation power was based on the amount of area that the blocks encompassed. This is not the case.
So after figuring out that the unique blocks could be placed in any configuration I began running some numbers.
I found out from this information that power generation for each power object increases in a logarithmic fashion. That means that each block will increase the total e/sec more than the last one did but also each new block will increase slightly slower than the last.
So in the end I came up with the power equation of:
Power = Σ(power objects) = Σ(Power generated by all unique blocks + Power generated by all non-unique blocks)= Σ((140.8+98.1*U+E)+(25*N))
EDIT: This equation is kinda made up and isn't really all that good. That's one of the reasons I posted this because I was hoping someone better at math could help me fix it. ThyLordRoot's equation lower is much better.
Where U= the number of unique blocks in each individual power object
N= the number of non-unique blocks in each individual power object
And E is the factor of growth represented by ΔΔPower. I wasn’t able to figure out this equation.
EDIT: So I was talking to Raok and we figured about the the dimensions of the bounding box that the blocks form (eg. 10x10x5) is a quick way to figure out the number of blocks used. How you do this is you take the three dimensions and you add them together (10+10+5=25) and then you subtract 2 (25-2=23) and that is how many blocks it took to make that structure.
Also ThyLordRoot figured out a really good equation for computing power that integrates U and N blocks in one equation and put it into use in a program that will compute the optumum power placement for a given area.
This is his equation: ((x+y+z )/ 3)^1.7029*114.8+25n+1 where n is the number of blocks used and x, y, and z are the longest of each of those dimensions in the shape
This is a link to his post: http://star-made.org/content/reactor-breeder-genetic-algorithm-reactor-design
Here's a link to all of my work: https://docs.google.com/spreadsheet/ccc?key=0At6aQJTDkXyMdERka0QxUk5FUlpfTy1xTTNMd3I2NFE#gid=0
It is late now and I feel like there are some things I forgot to explain and some things I explained badly. I will likely come back and edit this post later. Please feel free to ask questions! I'm tackling power storage next. Anyone have some numbers on that so I don't have to spend hours on it as well?
tl;dr: If you think power generation is based on the area the cube that the power blocks create you are WRONG! WRONG WRONG WRONG! Go read the post to know why.