Tachyon Mathematics by Ptolemy - 8 Jan 2007
- Source: Thread at HWF
This is from earlier calculations I did to provide concise information on how tachyon detectors work. The common misconception is that tachyon detectors make SS cloaking useless - this is not so. The most important use of tachyons is to be able to incoming fleet MORE than one year of travel at warp 9 or 10 in space to a planet. They are also helpfull in finding those pesky cloaked minesweepers, scouts and other annoying lesser ships.
Stars uses the following formula to calculate cloaking reduction from TD's:
95% ^ (SQRT(#_of detectors)). Increasing the number of detectors past 17 has no effect due to the cap on TD efficiency reduction. To make this simple, if you have 9 TD's (the square root of 9 is 3), reduction in cloaking is calculated as:
0.95 x 0.95 x 0.95 = 0.857375 reduction in cloaking (rounded to 86% cloaking effectiveness). If the cloaked ship was 98% cloaked, its cloaking now is 98% x 86% = 84.28% (84% cloaked). With a 100ly scanner, you will be able to see the ship 16 ly away (instead of only 2 ly away). A 500 ly scanner will see the ship 80 ly away instead of 10 ly away.
So, lets take a look at the next easy example; 16 TD's (square root is 4) 0.95 x 0.95 x 0.95 x 0.95 = 0.81450625 which rounds to 0.82 (82% cloak effectiveness). Cloaking on a 98% cloaked ship is now 0.98 x 0.82 = 0.8036. The 98% cloaked ship is now only 80% cloaked.
The next major value would be 25 TD's. However, (anybody want to take a guess as to what 0.95 ^5 is?) No... Don't worry, I'll tell you: its 0.7737809375. That means a 98% cloaked ship now has 77% cloak efficiency. 98% x 77% = 0.7546 (76% rounded). With 25 TD's, a 98% cloaked ship SHOULD now only be 76% cloaked. However, just as Stars! caps cloaking to a maximum of 98%, it also caps TD cloaking reduction to 81% effectiveness of cloaks. Therefore, 17 TD's is the absolute usable maximum.
And, 98% x 81% = 0.7938, so, 79% cloaked. What Tachyons can do is reduce SS extra cloaking down closer to the innate 75% cloaking that SS ships have.
Additional information - Is on the above linked thread: Tachyon Detectors do not have to be on the same ships as the Scanners.