Topic: The Travel Mod: math shortcut for missile flight times

[NicholasHMCaldwell]

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

[Thos]

Fantastic! I am all for shortcuts that eliminate as much math as possible. Math and I never really got along well...

[lazarus]

Hm.  Almost makes me want to write a flight-time calculator program.  Takes input in the form expected (basically, velocity and accel vectors on this turn) and makes a projection.  Then, updates turn by turn with new accel and velocity vectors ...

(that's the easy part of a 3d space combat program - the hard part is the displaying stuff in 3d and so on, but just outputting some various numbers, especially if it doesn't need to give projections and just needs to run the numbers that you give it)

Laz

[Rasyr-Mjolnir]

I can most likely do up a small table that figures distance in millions of kilometers (i.e. 1 - 10), and speed (g) on the other axis to give a table for quick look up so the GM doesn't have to do the figuring on the fly (I like the simplified math as well... hehe)

[chk]

I like it. As you said, for practical purposes missile accel isn't terribly significant to travel time, and simpler rules are always good .

[Marc R]

Considering there are people who get 6-7 figure saleries for making minor improvements in these kinds of calculations, simplification sounds good. . .getting something like this right to the second (or the mile) doesn't matter really unless you're actually launching missiles and actually need to hit the target based on your calculations. Since it doesn't really matter, game wise if the missile arrived in the start or end of the round (or turn) the approximation seems to just give the "Right enough" answer. . .(I'm trying to think of any benefit you'd get from using the longer formula, other than smug self satisfaction.)