14500 million toe per year is 19 terawatts, roughly world marketed energy consumption; 1000 watts per m² (nominal solar constant below the atmosphere) times 1.28 × 10¹⁴ m² (area of a circle with radius 6371km) is 128000 terawatts. 19 is 0.015% of 128000, not 2%. so why do your calculations differ? let's see
possibly by '510mm sqkm' you mean 510 million square kilometers, as opposed to, say, 510 millimeter square kilometers (which would work out to 510'000 m³). 510 million square kilometers is a good value for the surface area of earth (4πr² ≈ 510066 km²) and 340 watts per square meter is a reasonable estimate for 24-hour mean insolation, disregarding clouds. but 340 watts per square meter times 510 million square kilometers gives 173000 terawatts, higher than my estimate. in terawatt hours per year, that's 1.52 billion terawatt hours per year, which is definitely a lot more than 50 times 26936 terawatt hours
i think maybe your error there is that you were trying to convert from square kilometers to square meters by multiplying by 1000. but actually a square kilometer contains a million square meters, not a thousand. so you ended up calculating about 2% instead of about 0.002%, which is what your inputs give if calculated correctly
using the units(1) program from unix is a good way to avoid errors like this; in this case you can do the calculation as follows:
You have: 26936 TWh / (340W/m^2 * 4 pi earthradius^2 * 1 year)
You want: %
* 0.0017718851
/ 564.37068
however, you also made a smaller error in the opposite direction. the 26936 terawatt hours per year figure is only a small fraction of the total energy supply; as the paper you linked explains:
> Considering electrical energy, while 6,131 TWh of energy was produced in 1973, 26,936 TWh of electrical energy was produced in 2019 (IEA, 2021c).
that's only about 3 terawatts, not 19, because it excludes virtually the entire transport sector, coal consumption by steel mills, climate-control heat and process heat provided directly by fossil fuels, inefficiencies in the electrical generation process, etc. using the correct figure of 19 terawatts, we derive that world marketed energy consumption is currently 0.01% of global terrestrial insolation, including light that hits clouds and oceans but not including light absorbed or reflected by the atmosphere
growing energy consumption by this factor of 6700 at 1.66% per year would take 535 years, but in fact now that pv has dropped the cost of energy so dramatically, i expect energy production growth to speed up. also presumably there will be power-production satellites in solar orbit within decades, permitting progress past kardashev type 1
hope this helps!