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I have been using the Auto-Flicker mod, and it works great!  First thing in the morning, my pawns get out of bed and turn on all the sun lamps.

A single Generator/Battery pair can keep a Sunlamp on for about 85% normal growing time.  Perfect efficiency would be to have more generators and switch them off when the sun lamps go off, but that's a bit more micro than I'm up for.

Encouraging my pawns to plant trees in high-density patterns is a challenge.  Max density is 30 trees per lamp, but this requires a lot of micro to sustain.  Left to their own devices, you'll get 25-26 trees per lamp, but with a little trimming of the growth-zone, you can get them to plant 27-28 trees on a regular basis.

I found a minor exploit where you can plant trees in a crop field and grow both (but no crop replant).  If I plant a long-growing crop like Corn, then by the time its ready to harvest, the trees should be past the 40% threshold and yield useful wood from chopping.  Set the field to "Plant: Corn", then after it is sown, switch them to "Plant: Cecropia Trees".  ~35 tiles of crop are dug up and ~26 trees will be planted.  After the trees reach 40% or the Corn is nearing maturity (whichever comes later), switch to "Plant: Corn" again.  The trees will be chopped down, and the corn will be automatically re-sown as it is harvested.  Once sown, switch back to trees.  This will let you get double-use out of your fields, and is a simple way to manage the harvests, but it will slow down your tree planting cycle a bit.  Also it's kind of an exploit.

In any case, Chopping the trees at 40% will greatly boost your yields.  You get half the wood right then and there, and trees (like all crops) start with 5% growth.  0.5x wood in 0.35x time is better than 1x wood in 0.95x time.  Then again, more frequent chopping and replanting will also add time back into the cycle, so it might not be quite as powerful.  But I'm sure you can expect at least a 20% increase in yield by chopping at 40%-growth.  And given the slim margins we are working with, that will have a significant impact on the viability of the project (as foolish as said project is).

This was my experience too.  A colony has more power draws than just the sun lamp, and its margin of return is so slim that the whole thing is basically just an expensive way of slowly burning your wood.  If you need wood in a treeless environment, you should harness the power of wind and sun more directly.

But the point of it isn't to be useful, it's to create an Over-Unity Device to violate the conservation of energy!

I don't see what the problem is.  They're both gay, so doesn't it cancel out?

Calculation readjustments:

Poplar trees rest for 10 hours per day regardless of anything, so really the optimum growing period should be 15*24/14 = around 25.71 days.

So in theory this should work, but only with max efficiency and hoping that nothing goes wrong.

Ah yes, that does complicate things.  Growth time is "total growth time", not "number of days it takes".

Also keep in mind that yield is affected by the difficulty level. I just did a quick test and a Popular tree on Extreme yields 27 Wood, whereas at the opposite end on Peaceful it yields 39 Wood. Cutting and planting trees also takes a lot of time, so you'd likely need a lot of Pawn power to cut and plant 25 trees quick enough for it to be negligible factor. Otherwise that time would need to be accounted for in the calculations.

Overall I think it's an interesting idea, but one that fails quite badly due to opportunity cost (amongst other things). As if you are powering sun lamps to plant fields of trees just to generate power, then you are not using sun lamps to plant fields of something else, and using power generated for free* (*Wind/Solar are not strictly free, but using it here for simplicity). Pawns also have to use their time to service this system (refuelling, cutting , planting, hailing), which is time they can't use doing something else.
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So regardless of the viability or not on paper, the hassle to the player of regularly flicking switches isn't something that can be ignored).

I was testing this out on Peaceful, no wonder I was getting anomalously high values for wood yields!  As a further twist though, it seems as though you can get Half of the max wood yield after a tree becomes harvestable at just 40% growth!

Yes, manually ordering flick-switching to save power is a huge pain in the butt.  I wonder if there's a mod which generates orders for switch-flicking on and off at particular times.  A sort of compromise that doesn't feel quite as cheaty as using the Time of Day switch.

It would work, but if you're resigned to dedicating that much real estate to power, why not simply use a wind turbine with solars in the blank spots?  Less micro, more power.

Yeah, this fails horrible when compared to literally any other method to generate power, but It's an interesting demonstration that we CAN in fact violate conservation of energy!  With no external inputs, it is theoretically possible to generate NET POWER from roofed soil!

A question I have been pondering, but have not yet fully figured out the answer to, is whether it is possible to create a "Perpetual Energy Farm": A Sun Lamp powered by Fueled Generator whose wood comes from the trees being grown by said Lamp.

As we know, neither conservation of energy nor conservation of mass is an inherent property of game simulations (I'm looking at you, Dwarven Water Reactor), so there is no reason to reject this outright.  It simply comes down to the math.

-How much Power does a Sun Lamp need? (assuming it turns off during the plant rest period)
If paired with a battery, can a single Fueled Generator power a Sun Lamp all day and recharge at night?  Or does that waste too much fuel, and you should try to equalize your Lamps and Generators?
-How much wood does a Fueled Generator consume?
(20 per day, I believe)
-How long does it take for a Tree to grow?
(Wiki says Poplars are 15 days)
-How much wood per tree?
I think 40 when mature
-How dense can trees be planted around a Sun Lamp?
Looks like 25 on average, 30 max (using careful layout)

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By my calculations, 5 Sun Lamps can be constantly powered by 8 Fueled Generators at a cost of 160 wood/day.  These lamps will provide growing area for ~125 trees.  If each tree gives 40 wood at maturity, then we are looking at a total harvest of 5,000 wood.  Dividing the yield by the daily wood consumption gives us 31.25 days/tree.  If we can Plant/Grow/Chop a tree in ~30 days, then the self-fueling tree farm starts to look like a viable possibility.

Am I missing any variables, information, or have I made any math errors here?