I actually made the exact same mistake the first time I tried running through it in my head, too.WarDaft wrote:Then there are 125 seconds of darkness to deal with. Thus 42 KW * 125 s = 5.25 MJ to buffer the panel's overnight power. But that's a ratio of 20:21 panels:accumulators, not ~21:25, and something is wrong, and it has to be something in this paragraph.
While dusk / dawn do last 83.33 seconds, the amount of time it takes for your solar panels to transition to/from accumulators is actually much shorter, because it takes your solar panels 83.33 seconds to transition to their max capacity, not to your current consumption. They hit your consumption level much more quickly.
Another way to word what Koub says is basically this: You'll switch between solar panels and accumulators as your solar panel output crosses the threshold of the power you actually need. Also the amount of power your solar panels can produce is of course proportional to the number of solar panels you have, but the day <-> night transition takes the same amount of time, it's constant. Therefore, the more solar panels you have, the earlier in the dawn the accumulators will switch off (because more panels = less light required to power your factory, so the panels get there more quickly), and the later in the dusk they'll switch on (same deal, the panels will take you longer into dusk).
If you're better at thinking about it purely geometrically, your (incorrect) thinking is that you have two overlapping trapezoids of the same height (one for accumulator capacity, one for solar panel capacity) that cross at exactly halfway through dawn or dusk. But in reality, the more solar panels you have, the steeper the sides get, and they don't "rotate" around the center point of dawn/dusk, they stay fixed to the start of dawn and the end of dusk.
Yet one more way of thinking about it, if you're better with conceptual extremes: Imagine you have infinite solar panels, so the most infinitely small amount of light will generate enough power for your factory. In this case your accumulators will switch off as soon as dawn starts, and switch back on as soon as dusk ends. So you can see in this extreme case you actually have 41.67 seconds of accumulator time (night) and 375 seconds of pure solar panel time (dawn, day, and dusk). This directly contradicts your notion that it's always a 50/50 split at dusk and dawn, and therefore your hypothesis must be false, by contradiction. The more solar panels you have, the more your effective power generation times approach this limit, and so you have to account for this when doing the math. The OP's geometric proof is one good way to break it down.
hmmm
