Here are my R calculation results. The first two columns are fractions (and multiples) of $c$.
Effect.Veloc.Astronaut Starship.veloc.stationary Joules.100000.kg.ship
0.01 0.01 4.50E+17
0.1 0.0995 4.50E+19
0.2 0.196 1.80E+20
0.5 0.447 1.10E+21
1 0.707 3.70E+21
2 0.894 1.10E+22
5 0.981 3.70E+22
10 0.995 8.10E+22
20 0.9988 1.70E+23
50 0.9998 4.40E+23
100 0.99995 8.90E+23
1000 0.9999995 9.00E+24
10000 0.999999995 9.00E+25
100000 0.99999999995 9.00E+26
As you can see, humankind's energy output for a year early 21st century would barely suffice to accelerate a 100 ton craft to 0.2 c.
5e20 Joules are about 1.5e13 watts. A mature type I Kardashev (so by the chart above humanity cca 2300) could get 1e17 watts, so output of 3e24 Joules. Even for a type I, relativistic interstellar travel is difficult.
A type II, about 900 years at 3% growth rates after Type I is reached, have 10e26 watts to play with, or 3e33 J, so launching a small ship at relativistic speeds would take no more than a few seconds' worth of the civilization's power output, similar to a Saturn V launch for 20th century mankind.
That does still leave a few major difficulties.
- Energy density of fuel.
- Deceleration.
- Shielding
(1) Can be alleviated somewhat by beaming power to the ship.
(2) Remains open, and I have no idea how to get enough reaction mass to decelerate on board. Perhaps a payload consisting of a miniaturized AI with self-replicating machinery (a few grams), or a Bussard Ramjet could work as well.
(3) A lot of ablation mass will be needed since each dust particle in the way will strike my ship like a shaped charge. Perhaps a powerful laser to clear the path?
As to where I'd go, I would probably go to the nearest Earth-like world, see what or who is there.
PS: I know it's generally bad form to give an answer to your own question, and all this might hinge on some miscalculation, but I got too excited about the effective FTL drive!
