Just eyeballing the chart in the link -
I guessed about 2.75 years to halfway earth time; maybe about 1.5 years ship time.
It’s somewhere between 1 year and 2 years ( 0.56 lightyears and 2.90 ly) ship time.
So double that for the trip out. Repeat for return.
The next fun trick is to pick a fuel (deuterium fusion, hydrogen fusion, pure matter conversion?) and guess what proportion of the vessel has to be fuel to make the trip.
The link I gave does all that for pure matter conversion.
Back of the envelope calculation: If it takes you 300 million years to travel 4.5 light years, your average speed is about 10 miles per hour. I don’t know much physics, but I’m pretty sure you don’t have to accelerate at 1 g for very long to get going that fast.
1g acceleration up to C for half the distance, then 1g deceleration for the rest of the distance.
e.g., 1g for a distance to 2+1g,then 3+1g, 4+1g, ect…
I don’t know the speed ratio of 1g in a vacuum. :dubious:
( I read someplace, more or less 100k years a while back, at that rate, but I don’t do calculus)
Terr, thanks for that link. It explains what I was wanting to know.
I’ve always enjoyed the coincidence that one g times one year is very close to the speed of light (accurate to about 3 percent as shown above), thus without doing any math, it is obvious that the time to go to Alpha Centauri is only a bit larger than 4.4 years as viewed from Earth.
I’ve always felt that meant that humans (or at least Earthlings) were destined to travel to the stars. 
But it should be noted that while 1g = 1.03 lyr/yr^2, accelerating at 1g for one year only gets you to 0.77c because of SR effects. But it is handy for calculations
I’ve also used the rather tortureous 1g = 22mph/s for estimating air time (weightlessness) on roller coasters and other thrill rides based upon their velocities. For example, a ride like Superman at SFMM shoots you straight up at 100 mph where you coast to a stop and fall backwards. In theory that could get you eight seconds of air time, four seconds falling up and four seconds falling down. In practice it’s about seven seconds.
Here’s a cite I picked up from another thread on star-travel several weeks ago.
As I recall from reading it (several weeks ago), this is not particularly technical or heavy on the math, and it doesn’t work through the detailed arithmetic, but it does give a fairly clear but non-technical discussion of how relativistic interstellar travel works. It focuses on the question: If Stella travels to a distant star and back at near-light speeds, and she and earthbound Terence keep an eye on each other during the trip, which of them will see the other’s clock slowed down relative to his/her own, and why?
Didn’t you ask if anyone remembered their calculus? Calc <> The integral of Physics, dt.