For those who don't want to use the quadratic formula but where the distances are shorter than those on Tim's table, I've produced a SysOp's Tip. This and some version of Tim's tables completes the "Travel Mod".
SysOp?s Tip: Simplifying the Mathematics
Few SysOps will want to be solving the quadratic formula to calculate the length of time it takes a salvo of missiles to arrive in the middle of a starship dogfight. By making two assumptions, we can use the much simpler equation T(ime) = D(istance) / S(peed) for distances of up to ten million kilometers. The first assumption is that the starship is traveling towards the target when the missile(s) are launched, and hence the missiles start with the initial velocity of the starship. The second assumption is that the starship is moving at some reasonable speed (i.e. a fraction of lightspeed.) If these two assumptions hold, then the extra acceleration of a missile (even if it is capable of 1200g) will not significantly reduce the time taken to reach the target in game terms of rounds (or turns).
Specifically, the time calculations for a missile launched at 1200g from a starship already traveling at 0.07c will differ by less than a second over a range of one million kilometers. In both cases, the answer will be approximately 47 seconds or 24 rounds or 1 turn. Performing the same calculations for a range of ten million kilometers (same acceleration, same starting velocity), the difference is less than 1 minute as the answer is just over 7 minutes using the accurate formula and just under 8 minutes using the approximation, which means the missiles would arrive in 8 turns in ?turn-based?combat (see Combat chapter).
For distances of up to one million kilometers, the SysOp should use the T = D/S formula and convert the result into rounds or turns as appropriate. For distances of between one and ten million kilometers, playing out the game time in rounds will take far too long and slow the game play to a crawl, so convert the results into turns and play the combat using that measure of time. For missiles launched at distances greater than ten million kilometers, the targets will need to detect them first and by the time that happens the missiles should be within the ten million kilometer range or closer and the shortcuts above can be employed again.
Best wishes,
Nicholas