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Re: starship-design: FTL drive designs

kyle writes:
 > Steve VanDevender wrote:
 > > 
 > > kyle writes:
 > >  > Another idea, perhaps the most promising aside from my earlier
 > >  > design, is forgetting FTL completely.
 > > 
 > > Oh, phew, I was hoping you'd get to that eventually :-)
 > Ah, but if you go on to read the rest of my idea, warping space to make
 > travel at sublight speed to destinations possible within minutes
 > ship-time AND earth-time, you'd see that travel to the stars as viewed
 > by earth time could be just a few minutes. (or hours, or days, or
 > however fast you wanted to go (up to c)).
 > And belive me: I can give you a very close estimate as to the size,
 > internal workings, mass, basic theory, etc. of this. 
 > Oh by the way, equations. I have equations to back up my claims. Want
 > them?

Sure, as my understanding is that in order to "warp space" in the way
you want, quite exorbitant amounts of energy would be required, not to
mention that people would notice for hundreds of light-years around
since this "warp" would produce spectacular distortions of space and
probably quite impressive gravity waves.

I have equations to back up my claim, too:

t = 2 * c/a * acosh((a*d/(2*c^2)) + 1)

t = ship time
d = trip distance
a = acceleration
c = speed of light

This equation describes the ship time needed to travel a distance 'd'
(as measured by Earth observers) assuming a trip profile of constant
acceleration 'a' (as measured by the ship) to d/2, then turnaround and
constant deceleration 'a' until the destination is reached.

If you increase 'a' then you decrease 't'.  In relativity there is no
theoretical upper bound on 'a', so 't' can be made arbitrarily small.
Of course, your ship or passengers may not survive high values of 'a'.

A specific example: You want to travel from one side of the galaxy to
the other, about 100,000 lyr, at a comfortable ship acceleration of 1 g.
Plug those values in for 'd' and 'a' and you get a total trip time of
22.37 years, as experienced by the passengers on the ship.  Of course,
it does take a little over 100,000 years of time as measured by the
inhabitants of their home planet, so if the passengers visit briefly and
then return they way they came, they're 44.8 years older and their home
planet is 200,000 years older.

In essence, you don't need fancy hypothetical "space warps" to get to
distant stars in human lifetimes, because going fast enough makes space
appear to contract in the direction of motion.