The numbers I have seen have been for a vegan diet, also. Animals take at least 10x the space unless you can feed them only waste materials.
The numbers you've seen are for a highly diversified vegan diet. A primarily potato based vegan diet would suffice at 300 square meters. Getting a more diversified diet would take 700 square meters, and getting the kind of diversified diet Europeans and Americans are accustomed to (vegan or otherwise), which yes would include animals, would indeed take far more.
Your numbers work for Earth's current population, it was in reference to 100x the population.
I already addressed that concern though; please re-read my post more carefully.
I was talking about farming over the entire planet.
Which wouldn't be necessary.
(And neglecting the fact that in high latitudes you aren't going to be able to farm by sunlight, period.)
So what? We're talking vertical farming... there's absolutely no sane reason to rely on natural sunlight for vertical farming whatsoever... especially given I just told you were can achieve at least 3 times the yield with LED lighting. So why even bring up sunlight at high latitudes at all?
It made the energy calculations simpler. How the vertical farming is arranged doesn't change the energy needed and thus is immaterial.
Nonsense; concentrating things into a single building allows you to save considerably on required energy when compared to spreading it out over multiple buildings. This again, ignoring the fact that modern LED based farming is already far more energy efficient than you originally gave it credit for.
Fail. You keep shipping organics to Earth in the form of food.
Do you imagine that it would somehow be a 1:1 ratio? One wonders how we ever manage to more volume of food than the base we started with. I trust you understand organic material *grows*, right?
The best powerplants aren't even 1/3 efficient.
Sorry, what? Water turbines are 90% energy efficient. Cogeneration plants manage 80%. Combined cycle Gas turbine plants manage up to 60%. Coal plants manage up to 40% (Still more than one third). Wind turbines manage up to 45%.
This is inherent in the existing technologies and probably can't be improved upon.
Except... they already have been. As I just pointed out. If you seriously think our most efficient power plants are only reach 33% energy efficiency, you're seriously out of touch.
(All current power generation systems are variations on a steam engine and there are theoretical limits on steam engines.)
Nonsense. The photovoltaic effect; for one; is not a bloody variation on the steam engine.
In fact, nuke (and there's nothing other than nuke in our current tech that could power it) is more like 1/4 efficient--they run them cooler than coal plants for safety reasons.
So first you grossly underestimate the energy efficiency of many of our modern power plants... next, you DRAMATICALLY overestimate the energy efficiency of nuclear power plants. In actual reality, nuclear power plants have an energy efficiency of LESS than ONE percent; that one percent is the amount of nuclear energy that gets converted into heated water; as for the efficiency of electricity generated over THAT 1%, I've seen figures ranging from the low thirties to as high as 91%.
A quick check of LED efficiencies is no better--for most colors it's around 25%. The best is 40% for red. I assumed 100% efficiency in figuring the heat load of the lights, reality appears to be no more than 10% and probably less than that. Thus heat numbers as high as I came up with.
Plantlab's growth process only involves blue and red leds. Other colors are eliminated. I don't know how recent the figures you've found are: Today's LEDS are at least 3 times as efficient as the most efficient ones from just 2005. Modern LED's can achieve a 100 lumens per watt.