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PostPosted: Sat Aug 30, 2014 10:18 pm 
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I'v done these calculations a few times before in various places, but apparently I've never presented them here - so here's a pretty straightforward way to calculate travel time assuming standard "constant acceleration-turnover-constant deceleration".

The 'official' scientific way to calculate this is using t = SQRT(2s/a) (where t = time to midpoint in seconds, s = midpoint distance in metres, and a = ship's (constant) acceleration in m/s²)... but that's somewhat too complicated for use in a game since we generally don't use those units in RPGs . However, we can simplify this a lot by redefining our distances to be in AU, travel time in days and acceleration in Gs. If we do that, then the equation we end up with is this:

Quote:
TOTAL Travel time in days = 2.835 * SQRT(S/a)
where S is TOTAL distance in AU and a is the ship's acceleration in earth gravities.

So, a ship travelling a total of 10 AU and accelerating at 2g to the midpoint and then turning over and decelerating at 2g to its destination would take just over 6 days to get there. This is very easy to enter into a calculator or even do it roughly in your head, so it won't disrupt a game to figure it out.

However, even this could be a bit too fiddly for some tastes - but there's an easier way to get the same result:

Quote:
TOTAL Travel time in days = 4 * SQRT(s/a)
where s is the MIDPOINT distance in AU and a is the ship's acceleration in earth gravities.

Note that unlike the previous version of the equation this uses the MIDPOINT distance (the halfway point between the origin and destination), but it still gives you the TOTAL travel time in days. I think most people should be able to figure an approximate answer in their head using this simple equation.

Try it: How long does it take for a ship to travel 60 AU if it's using the standard accelerate-turnaround-decelerate method with an acceleration of 4G?

Just doing it in my head using the second equation (remembering to use the MIDPOINT distance of 30AU), I figure about 10 or 11 days. The actual answer is 10.98 days. It's not hard to do if you have any numerical literacy at all (it took me about 10 seconds to do that in my head).

Now try this one: How long does it take for a ship to travel 2 AU if it's using the standard accelerate-turnaround-decelerate method with an acceleration of 1G? (this one is REALLY easy, I'll let you figure it out).

Another thing to realise is that in-system travel time tables have limited use - they'll only give you travel times for a specific time where the planets are at a certain distance from eachother, but as time passes the planets will move relative to eachother in their orbits. e.g. at closest approach the distance between Earth and Mars is about 0.6 AU, but if Mars is on the other side of the sun then it's more like 3 AU (given that you'd have to go around the sun). But still, the simple calculations I have provided here will let you figure out on the fly how long it takes to get from A to B if you know how far apart they are.

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PostPosted: Sun Aug 31, 2014 3:53 pm 
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Hmm, since that's effectively 4 * SQRT(S/(2 * a)), how about instead SQRT(8 * S / a). A bit larger number, but then you don't have to divide the distance by 2.

Frank


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PostPosted: Mon Sep 01, 2014 1:20 pm 
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What does SQRT stand for?

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PostPosted: Mon Sep 01, 2014 2:40 pm 
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Jame Rowe wrote:
What does SQRT stand for?

Square root (Excel uses that abbreviation IIRC.)

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PostPosted: Tue Sep 02, 2014 1:03 pm 
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I have used 3*sqrt(s/a) for a LONG time. Rounding up to 3 makes it really easy and I figure the extra time is taken up in orbit/deorbit burns around the planets prior to firing off the main engines.

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