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Now: 16 October 2019 19:51

Gravity Trampoline Table, Seeking a formula/equation

Post  Post #1 
Reputation 7
Group humans Alliance Experience 40 3 8 Points 1 308 344 Messages 27
Warnings
The catalogue has the following table showing limits on distance and fleet points for Gravity Trampolines...

Amount Distance Fleet points
1          10000    10625
2          18661    21250
3          26879    31875
4          34822    42500
5          42567    53125
6          50158    63750
7          57622    74375
8          64980    85000
9          72247    95625
10        79433    106250
11        86547    116875


Suppose I would like to send a fleet (of, say, 25000 points) a distance greater than the last row in the table (say, 100000).
Do the grav tramp rules forbid me from sending a fleet farther than that shown for 11 grav tramps (final row in the table)??
Is there a formula/equation that can show me the number of grav tramps needed for combinations of fleet size and distance (besides those shown by the catalogue)?
14 September 2019 07:47
14 September 2019 07:47
Post  Post #2 
Reputation 6
Group xerj Alliance Experience 22 12 36 Points 1 043 887 Messages 636
Warnings
Hello whbloom,

unfortunately the game doesn't provide formulas for this case.

When you want to see different distances/fleet points in the information table you can simply have more trampolines on your planet. When you have 10 Trampolines on your planet the first row of the table will change to either 8 or 9 trampolines and you can see up to 20 trampolines then in the information table.

Further the fleet points are very easy to calculate. You simply multiply the amount of tramps with the base amount of fleet points of one tramp. So if you want to know how much fleet points you can send with 20 trampolines you do: 10625 * 20 = 212 500 maximum fleet points with 20 trampolines on each side of the jump.

The much more difficult part is the distance because the game doesn't provide formulas. Therefor you need to find out the formula first. An very easy way is to use www.wolframalpha.com for this.
You visit the website and type into the "search bar": fit [(1, 10000), (2, 18661), (3, 26879), (4, 34822), (5, 42567), (6, 50158)].
This will give you an approximate formula through the given points. http://prntscr.com/p62h5j

You can use this formulas to APPROXIMATELY find out the necessary amount of trampolines for jumps later on. But let me warn you: This will NOT give you a 100% exact result. The resulting equation and graph will not match 100%. The further you try to extrapolate the less correct your result will be.
Example: When calculating the sendable distance for 10 trampolines while having a formula that were given only 6 points your result will be: http://prntscr.com/p62iet
-> (I am german so my . and , are swapped.)
You see that the result is pretty much off by 2000. This is because the extrapolation distance is too large. You need to add more points in order to get a more exact result.
It seems wolframalpha limits the input to 7 points. So this method is pretty limited but it's still better than calculating anything from hand or trying to derive an exact formula.

When doing the same with the first 7 pairs as input you get this result: http://prntscr.com/p62l74
This one is only 1000 off the real result for 10 trampolines. So it's more accurate than the example with 6 points.

You also have the ability to scratch the first points out of the equation and add more points that come later. Here I calculated it for 10 tramps again: http://prntscr.com/p62mhr
You see that this result is only 9 off the real result for 10 tramps!

It's possible to play around with this even further but the best accuracy can be achieved if you use the 7 points right before the one you're trying to calculate.


And let me warn you again: This is a mathematical approximate aproach. No exact result can be achieved like this. You need the exact formulas the game uses too to work it out exactly.


If you want a certain combination of fleet points and distance you can simply set it up like above for both and work out the points for each graph where it exceeds your required amount. You then choose the larger result. Example: The graph for the distance tells you you need 15 tramps and the fleet points says you need only 12 tramps. Choose 15 and you're good to do both - jump over distance and with enough fleet units.


This is really annoying over time and I recommend to not try this at all. The best you can do is to use the information table. If you want the infos for more than 11 tramps you need to have more trampolines present on your planet. If you have 10 trampolines present the information chart will start at 8 or 9 trampolines and range up to 20.
You could do this once and screenshot the results and save them - then you can look it up any time without the need for having tramps on your planet again.



I want to add that I would enjoy a real calculator for distance/fleet points for trampoline jumps too.



Disclaimer: I do not have a degree in mathematics. There may be more efficient solutions to this but they're probably longer (like spline interpolation: https://en.wikipedia.org/wiki/Spline_interpolation or to have n equations for n data points ( http://prntscr.com/p62snv )). This methods probably need more work from the user than the method of using the last 7 points and getting a formula from wolframalpha. The least amount of work would be to screenshot the gravity trampoline information and save them. When you get more tramps do different combinations until you screened the whole range from 0 to your max amount of trampolines.
14 September 2019 18:10
14 September 2019 18:10
Post  Post #3 
Reputation 7
Group humans Alliance Experience 40 3 8 Points 1 308 344 Messages 27
Warnings
Thank you, Tii, for a very informative and practical answer!

It happens that every time I've consulted the gravity trampoline catalogue page, I happened to have my grav tramps in expedition for the moment. Hence I had no idea that the table self-expands according to the number of grav tramps actually on-planet. Hah! The admins ought to add a comment to that effect at the top of the table. I'm surely not the only one that mistakenly thought that the table is static.

Great tip on the wolframalpha site, too! Even though, as you said, simply viewing the grav tramp table with all of one's grav tramps on-planet is the most efficient way to find limits for distance and flleet points, that website is bound to be useful for other things.
15 September 2019 05:02
15 September 2019 05:02

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