How long does it take to travel 36 light years with tolerable acceleration and deceleration?

At constant 1 g acceleration half-way through, then constant 1 g deceleration the remaining half, it takes 7 years in rocket time, 38 years in Earth time:

http://www.cthreepo.com/lab/math1.shtml

Scroll down to Long Relativistic Journeys and enter your data.

To the Andromeda Galaxy (2.5 mil ly) it's 29 years in rocket time! :)

Since you're doing the thought experiment anyway, there are at least two important engineering considerations that limit this more severely than what accelerations humans can stand (which is trivially solvable with robots anyway):

(1) The energy needs would be huge. What percentage of the total mass would have to be fuel in order to supply enough energy to accelerate and decelerate the payload 36 ly at any acceleration worth doing? I haven't done the calculations, but the engineering case is daunting: (fuel+rocket+payload) all need to be accelerated, fuel may be decreasing as you go, and maybe rocket is if you have a staged spacecraft. Is it even possible, given strength limits of any known materials, to have a few-human-and-life-support sized payload, a big enough rocket to house that and the fuel, and make the equations work out? That very well may be the limiting factor to interstellar flight, regardless of the technology.

(2) If you go fast enough, even a dust-sized micrometeorite would cause fatal damage. I think I've read somewhere that 10% light speed makes hitting a dust grain like a nuclear bomb. So there may be a "speed limit" much lower than light, above which would simply be too dangerous to travel.

Inspired by David Zaslavsky's words that "this site is not really about what existing technology allows or doesn't allow":-), I'd like to discuss a possibility that is downright outrageous from the point of view of technology, but seems feasible from the point of view of physics. What maximum constant acceleration can a human survive? According to another answer, it's 4g. Maybe so. Maybe somewhat more. Maybe somewhat less. That does not matter much. However, it is my understanding that there is one exception: if acceleration is caused by gravity, the latter acts in the same way on all parts of the human body. Thus, it does not cause relative displacements and does not kill. Moreover, according to the equivalence principle, free fall is felt like inertial movement (as far as I know, an accelerometer in free fall registers zero acceleration). Therefore, theoretically, we could boost a huge celestial body (say, the Sun) and let a human freely fall on it. I guess the free fall acceleration near the surface of the Sun is about 28g, so if we boost the Sun with such acceleration, the human will freely fall on it as long as the Sun is boosted (if he/she is moving in the same direction as the Sun) without being killed by the acceleration (he/she will need protection from Sun's radiation, but will be protected from meteorites by the Sun). Thus, the flight duration can be decreased dramatically. Raising funds for such a journey is no easy task though:-)