Correcting my own math (was If only GEO we3e6 km in circumference)

--- In spacesettlers@yahoogroups.com, Al Globus wrote:
> --- In spacesettlers@yahoogroups.com, hitssquad wrote:
>> The paper also said: "just 600 solar power satellites, 1 km radius each, could supply a terawatt (one trillion watts) [Assuming 10% end to end efficiency] of energy continuously and extremely predictably."
Assuming a minimum (because the produced electric-power is supposed to be continuous) solar flux density of 1321 watts/sqm, the amount of solar power intercepted by such an SPS fleet would be 600 * .7854 * 1e6 * 1321 watts/sqm = 622.5 gigawatts. Multiplying that by your 10% efficiency figure gives us only 62.25 gigawatts (to the busbar?). Even increasing the assumed solar flux density to 1400 or 1500 watts/sqm wouldn't bring the total to anywhere near a terawatt.
> Given one million square meters and 1,000 watts/m2 thats a gigawatt.

Actually, I mistakenly used your radius figures as diameters. Therefore my numbers should all be converted by a factor of four. The number of square meters of a round collector area would be pi (3.14) million, and of a square collector area would be 4 million. Assuming 600 round SPS we get 2.49 terawatts (at 1321 w/sqm) at 100% efficiency, and a quarter terawatt at 10% efficiency. That's closer.

Assuming 600 square SPS of 1 km "radius" each (4 million square meters of collector area on each), and 1667 w/sqm, we get 4 terawatts at 100% efficiency, and 400 gigawatts at 10% efficiency. At 25% efficiency, we get a terawatt of electricity.

>> 10375 GW. To produce 15 TW would require 15000 GW / .10375 GW = 144,579 SPS units.

Since that's 1 km radius, and not diameter as I mistook it for, that should say "36,145 SPS units."

>> Next: "At a 10 km radius, fewer than 400 satellites are necessary."
the real answer is that 1,446 satellites would be necessary.

That should be 362 10 km radius satellites.

>> They wouldn't fit in GEO

That's still true.

>> Even without any comsats in the way, they would need GEO to be 20 km * 109 * 1,446 = 3,152,280 km in circumference.

That equation should read: 20 km * 109 * 362 = 789,160 km (still almost 3x the 264,869 km circumference of GEO).