Could We Build a Dyson Sphere?
popularmechanics.com
popularmechanics.com
http://www.dennisantinori.com/Resources/Ringworld/
Edit: a reference
>>> Peter Weston passed the word from a British college professor: the tensile strength of the Ringworld floor needs to be on the order of the force that holds an atomic nucleus together. From such stuff you could make a garbage bag that would hold a thermonuclear explosion. http://www.larryniven.net/stories/macrostructures.shtml
A sufficiently thin continuous sphere can be held up entirely by radiation pressure, but still presents engineering challenges with damping oscillations; a continuous structure is likely to tear itself apart just because it's practically impossible to keep everything absolutely perfectly balanced on such a large scale. Which is why, per the article, the Dyson Swarm, a sphere made of lots of independently flying satellites, is much more plausible.
Incidentally, there are ways to eliminate the tensile load on a ringworld; you "just" have to stack enough suborbital mass outside of it (coupled by maglev rails or some such set up) so that the compression balances it out.
Tension is much stronger than compression, especially at larger scales.
But then you don't have the "nice" way of keeping the atmosphere in.
If you still need more power after that, then you consider the ring to be the equator of a sphere, and start building out the rest of the sphere, one ring of latitude at a time. Maybe build it as a basic grid or something initially, and add the solar collectors as needed. The stress would probably start to get higher and higher as you built up and down, since the pieces wouldn't be in orbit anymore, and so would rely on the structure to keep them in position and connected.
The problems in getting started are probably more along the lines of needing the kind of robot technology to gather the materials and build something like the initial satellite without much supervision, being able to gather the energy, and being able to do something useful with it.
"400 septillion watts per second"
... And the context is talking about solar output, not a rate of change.
Sigh.
Imagine a Dyson sphere surface, every square meter of which would have more than enough potential energy available for virtually any purpose. Imagine something crude like a steam-driven power plant. A facility at the sphere surface would heat water to steam below the surface, then drive a piston or turbine, then recondense the steam to water above the surface by radiating the waste energy into space.
Or one could use a thermocouple, not very efficient, but very reliable. There's a thermocouple power supply on the moon right now, it's been there for about 45 years and it's still going strong. The Curiosity Mars rover has a thermocouple power supply also. These devices exploit a temperature difference to generate electricity. Again, not very efficient, but reliable -- no moving parts.
> Are there obvious answers I'm not thinking about for energy transmission when you don't have a physical grid of wires to move it through?
Well, there's no reason not to have wires if that's desired. Just generate electricity in one of many ways as above, then transmit it to where it's more useful. An alternative would be to live on a moon orbiting the sphere, and radiate the power up to the moon in the form of microwaves or laser beams.