Need Math Help! Options

[Garrowolf]

Okay I am still working on that STLPunk game but I need some help with some math. Basically I am trying to figure out the acceleration rates and durations I want. I need a calculation where I can start just with it's acceleration rate and the distance I want it to travel before it looses it's maneuverability and goes ballistic. This way I can set the preferred range for their use.

Basically I need this:
Input: Acceleration and Distance
Output: Time

Any help would be appreciated.

[Austere Emancipa...]

You mean you would like a formula for determining the time it takes to travel a set distance starting from a speed of zero with a known constant acceleration?
Distance = x
Initial velocity = v0
Time = t
Acceleration = a
x = v0t + ½at^2
Since v0 = 0
x = ½at^2 <=> t = (2x/a)^½
In other words, multiply distance by two, divide by acceleration, take the square root of that, and you've got the time elapsed.

For example:
Acceleration = 1km/s^2, Distance = 500km
Time = (2*500km/(1km/s^2))^½ = (1000s^2)^½ ~= 31.6s

[Garrowolf]

THANK YOU!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
I have been driving myself crazy trying to find that formula!
Thank you again!

[Lindt]

Yay for Physics 1?

[odinson]

Wasn't that grade 8 science.

[Kagetenshi]

That only works for calculating time measured by an observer in the initial frame of reference. You're going to need to account for relativity if you want the time on board the accelerating object.

~J

[Austere Emancipa...]

The error will be less than 1% unless you get up to ~40,000km/s. At under 1,000km/s, which is apparently the kind of speed expected of his space ships for moving short distances (based on this), time dilatation will be of E-6 or lower order which is really not worth getting excited about.

[Kagetenshi]

Ah, didn't realize he was talking about velocities that small. I recommend still accounting for it, because it makes the math more interesting.

~J

[Austere Emancipa...]

I don't see why ((1-v^2/c^2)^½)*((2x/a)^½) is that much more interesting than just plain (2x/a)^½. Although I suppose making use of that several times during every turn of combat in a space opera is a good excuse to remember every digit of c^2.

[Garrowolf]

Yes it's a low speed setting. I am wanting the setting to grow and so I am starting small. I want travel around the system to take weeks at this point. The fastest ship out there goes 400 kps based on a system like LDS from Independence War (but alot slower). When they are not using their Inertial Displacement Drives they accelerate at between .1kps^2 for transports and 1kps^2 for fighters.

I am currently trying to figure out the acceleration I want on these.

So far I have:

Space Dart Class Minimissiles -4AP (x5) Fired in clusters Range 500km
Javelin Class Ship to Ship Missiles -8AP (x 15) Range 2,000km
Ballista Class Ship to Ship Missiles -10AP (x25) Range 8,000km

The acceleration rates shouldn't be over 10 kps^2 but I'm not sure how fast they should be. No missile will have an IDD, though Torpedoes do. Basically I'm trying to figure out how much warning the PCs or an enemy should have from a missile launch.

Any recommendations?

[Kagetenshi]

Unless I'm tired enough to have made an error, you realize that that means that a transport just needs to accelerate for 4000 seconds in the original frame of reference (just under an hour and seven minutes) to exceed the velocity provided by the IDD, right?

~J

[Garrowolf]

Yes people can still do that. However the ability to manuever at least a little to dodge incoming small asteroids is alot more difficult. Also the gravitic sensors that they use to find objects have a limit to the ranges based on trying to make sure that the ships have about a minute's warning of an object in the way.

Also for the purposes of space opera the ships are not flying gas cans. They use up about as much fuel at lower speeds as they do at IDD speeds because the ID Drives distort how inertia is working on the ship.

Basically a ship can go some place fast enough for story but stop when they discover something, then go again afterwards.

Now missiles can accelerate up to the use of their fuel which the range I have listed. They can hit targets that are much farther then that if they are programmed to. They just loose their manuverability at that point and go ballistic.

[Garrowolf]

Actually I think I figured it out.

Space Dart Class Minimissiles -4AP (x5) Range 500km 10 kps^2 10 sec
Javelin Class Ship to Ship Missiles -8AP (x 15) Range 2,000km 8 kps^2 20 sec
Ballista Class Ship to Ship Missiles -10AP (x25) Range 8,000km 8 kps^2 40 sec

The rounds for space combat are 10 seconds so this should work well.

Thanks for the feedback guys!