Since this keeps coming up, I've pulled this post I made from a tangent in another thread into a new one so people can refer to it more easily:
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As an example of how this doesn't have to be hard, the actual "rocket science" formula to calculate travel time for standard constant acceleration-turnover-constant deceleration is t = SQRT(2s/a) (where t = time to midpoint in seconds, s = midpoint distance in metres, and a = ship's acceleration in m/s²)... that's too complicated for use in a game, but it doesn't need to be that way at all. We can simplify this a lot because we're not going to have our units in metres or seconds or m/s² - we're going to have them in AU and days and Gs.
If you change the time units to days, the distance units to AU, the acceleration to Gs (1G = 10 m/s²), and then figure it out to get the TOTAL travel time in days, then what you end up with is this:
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. If you have a calculator to hand it takes less than 10 seconds to use it to figure that out, and the game is in no way disrupted.
But, you may argue that even that is fiddly. So here's another way to get the same result:
You could do that in your head for many cases. That's it - it's that simple.
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).
Besides which, travel time tables are largely useless anyway. They'll give you travel times assuming that the planets never move in their orbits, but of course that never happens - sometimes planets are on the other side of their orbits relative to another one. 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.
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As an example of how this doesn't have to be hard, the actual "rocket science" formula to calculate travel time for standard constant acceleration-turnover-constant deceleration is t = SQRT(2s/a) (where t = time to midpoint in seconds, s = midpoint distance in metres, and a = ship's acceleration in m/s²)... that's too complicated for use in a game, but it doesn't need to be that way at all. We can simplify this a lot because we're not going to have our units in metres or seconds or m/s² - we're going to have them in AU and days and Gs.
If you change the time units to days, the distance units to AU, the acceleration to Gs (1G = 10 m/s²), and then figure it out to get the TOTAL travel time in days, then what you end up with is this:
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. If you have a calculator to hand it takes less than 10 seconds to use it to figure that out, and the game is in no way disrupted.
But, you may argue that even that is fiddly. So here's another way to get the same result:
where s is the MIDPOINT distance in AU and a is the ship's acceleration in earth gravities.
You could do that in your head for many cases. That's it - it's that simple.
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).
Besides which, travel time tables are largely useless anyway. They'll give you travel times assuming that the planets never move in their orbits, but of course that never happens - sometimes planets are on the other side of their orbits relative to another one. 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.
