Re: [nbos] [AS] Travel TimesDoug Jessee Sat Aug 29th, 2009Thanks for all your help!

I appreciate it.

-Doug Jessee

On Sat, Aug 29, 2009 at 2:56 AM, Ben Trafford <ben-at-prodigal.ca> wrote:

>

> I'm going to give a more convoluted answer than others, because I've

> found breaking it down helps me to finesse my gaming system.

>

> 1 g = 9.80665 m/s squared. Meaning, every second, the vessel would

> accelerate by 9.80665 meters * .75. With the effects of cosmic dust and

> light and whatnot, you can safely round a bit in whatever direction

> serves your story. However, at this speed, it'll never reach its top

> speed -- it'll get where it needs to go long before that.

>

> In this case, 61 Cygni is 11.4 light years away, or

> 107,852,327,387,421,120 meters.

>

> Now, what your travel time is missing is a top-end to the speed.

> Let's

> assume, for the sake of argument, that your vessel's top end flight

> is .25c (c being the speed of light), to avoid relativistic effects. The

> speed of light is 299,792,458 m/s, so your top speed (in this example)

> would be 74,948,114.5 m/s.

>

> You have to figure out two things -- how long it'll take your vessel

> to

> reach its top speed; how far it will have travelled by that point; and

> then how long it'll take to travel the rest of the way at its top speed.

>

> To figure out how long it will take to reach its top speed, we do

> this:

>

> (v_f^2 - v_i^2) / (2*a) = x

>

> where v_f equals "final velocity" and v_i equals "initial velocity"

> and

> a equals "acceleration" and x is the "distance travelled."

>

> In our case, it looks like this:

>

> (74,948,114.5 ^2) - (0 ^2) / (2 * (9.80665 * .75)) =

> 5,617,219,867,105,110.25 meters to reach maximum velocity

>

> Since all these figures are in meters and seconds, we know that the

> ship will travel 5,617,219,867,105,110.25 meters before it reaches top

> speed.

>

> Next question is how long will it take to reach it. For that, we do

> this:

>

> (v_f - v_i) / a = t

>

> Where t is the "time to travel" in seconds, since we're thinking in

> meters per second. It looks like this:

>

> (74,948,114.5 - 0) / (9.80665 * .75) = 10,190,107.66503682 seconds to

> reach maximum velocity

>

> Let's assume they take the same distance and time to decelerate,

> which

> is always a safe bet. So, we double the distance and time required to

> accelerate, and we have acceleration and deceleration covered. Now,

> let's figure out the bits in the middle, when we're cruising along at a

> happy .25c.

>

> 107,852,327,387,421,120 - (5,617,219,867,105,110.25 * 2) =

> 96,617,887,653,210,899.5

>

> And how long will that take them to cover?

>

> 96,617,887,653,210,899.5 / 74,948,114.5 = 1,289,130,331

>

> Let's round things to the nearest zero, and take this to the finish

> line.

>

> The time to reach maximum velocity: 10,190,107 seconds

> The time to decelerate: 10,190,107 seconds

> The time to go the rest of the trip: 1,289,130,331 seconds.

> Total trip time is thus: (10,190,107 * 2) + 1,289,130,331 =

> 1,309,510,545 seconds or 42 years, 6 months, 11 days, 22 hours, 8

> minutes and 45 seconds.

>

> Phew. I tend to enter all this stuff into a spreadsheet and just

> plug

> in the numbers, but you get the idea. I've put the spreadsheet I use up

> here as a zip file containing Excel and ODS formats:

>

> http://www.prodigal.ca/SublightCalcs.zip

>

> Feel free to use and re-distribute them. The stuff in red is

> calculated

> -- the stuff in black is what you can tweak to get different outputs.

>

> --->Ben

>

> On Fri, 2009-08-28 at 21:38 -0400, Doug Jessee wrote:

> > Hello,

> >

> > I am trying to figure out some travel times at slower than light.

> >

> > Anyone know of any easy way to compute these times?

> >

> > For example, a sleeper ship that is going from earth to 61 Cygni.

> > Assuming acceleration of 3/4 Gs, I was just trying to figure out how

> > long it would take to travel.

> >

> > -Doug Jessee

> > _______________________________________________

> > Nbossoftware mailing list

> >

> >

>

> _______________________________________________

> Nbossoftware mailing list

>

>

>

_______________________________________________

Nbossoftware mailing list