starship-design: Calculations involving self-powered spaceflight

[Timothy van der Linden <TLG.van.der.Linden@tip.nl>]

Hi Andrew,

>As a follow on from some work I recently did, I thought I would do a few
>calulations on what someone would need if they wanted to fly to a nearby
star.

A page on the web to check out would be the links "Calculations involving
self-powered relativistic spaceflight" at the following URL:
   <http://www1.tip.nl/~t596675/sd/sd.html>
I can't guarantee that you'll understand all of it, but the first link
includes a JavaScript calculator so that you may fiddle with some numbers.
(Be sure to check what the numbers mean before you start fiddling.)

>I visited the ftp server with the old postings to this list, and I
>downloaded the whole thing, but I haven't read it all yet (due to it being
>2000+ pages)

Wow, you are really serious if you want to go through that much trouble ;)

>But, on to the problem:

>The Velocity of the fuel would have to be greater than the speed of light
>at t = 1, so I have made a mistake somewhere... touble being that I do not
>know where :(

Well, it actually is logical that you'd need such a large velocity. Do you
really expect a 1000 ton ship (without fuel) to get any significant
acceleration by throwing out 10 kg with say 100 miles an hour?

You wrote it yourself:

>m * a = (Mf * Vf)/t

where m equals 1,000,000 + 26,784,000 = 17,784,000 kg (Ship including fuel)

17,784,000 * 10 = (10 * ?)/1

Quite clearly the ? should be 17,784,000 m/s

Another mistake you make in your calculations is that you assume that the
exhausted mass and the exhaust velocity are constant at any time.
It's quite simple to see that that can't be true: The ship continues to
become lighter while it exhausts fuel therefore it also becomes easier to
accelerate. So for a constant mass exhaust and a constant exhaust velocity
you'll accelerate with an increasingly larger rate.

Furthermore you assume the time to accelerate to 0.9c can be calculated
with a non-relativistic formula, well you can but the answer will be far
from reality. I can tell you that with a constant 10 m/s/s acceleration it
takes 511 days according to the crew and 717 days according to people on
Earth to see the ship reach 0.9c
The lesson here is that you should really use relativistic equations if you
do calculations above 0.5c
(BTW. You don't need to know the relativistic mass of the ship, but you do
need to know the relativistic mass of the exhaust fuel.)

There are some other things I think you should know, but it likely would be
easier for you to study a book about relativistics and a general physics
book that covers some pages about the rocket equation.

Sincerely Timothy