Hyperspace Reach Increment Formulas & How the Devs Try to Mislead Us!

[xisec]

First of all, I would like to advice you that my english is not the best, so my apologies for that :)

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SUMMARY:

 

1) The formula to calculate the increment of the hyperspace range for each group of hyperspace cores of the same material is:

 

or, which is it the same:

with:

Naonite K= 1,45597631      http://prntscr.com/hp8plk

Trinium K= 1,666669836    http://prntscr.com/hp8psz

Xanion K= 1,907852049    http://prntscr.com/hp8q24

Avorion K = 2,499968584  http://prntscr.com/hp8q6x

 

legend for this and other formulas:

I = increment of hyperspace range

V= total volume.

K= some numeric constant.

round['x']() = a function that rounds the number at 'x' zeros: if 5 or more, rounds up, if not, rounds down.

M= a number correlated with a material: it is 6 for Avorion, 5 for Ogonite, 4 for Xanion, 3 for Trinium, 2 for Naonite, 1 for Titatnium and 0 for Iron.

 

2) this advices for formula seeker players:

1- Danger, THIS DEVS ARE EVIL and can introduce some random changes to formulas just to mislead us  ;D

2- Try to find some kind of introduction of the famous constants into the formulas in order to fix/tune them.

3- Use functions like round() and truncate(), because devs usually use them.

 

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BODY

 

I have started to try to investigate some formulas and mechanics for this game. I started with Integrity Field Generators and the Crew Quarters formula, and yesterday I started with the Hyperspace cores.

First of all, I wanted to find out the formula for calculate the increment of hyperspace range provided by the hyperspace cores.

 

After a lot of time watching and calculating numbers in a spreadsheet, I figured out that the formula to calculate the range for a particular volume of a particular material of hyperspace core was:

 

I started to calculate the K for each material: naonite, trinium, xanion and avorion. The successful values were:

Naonite K = 1.4560      http://prntscr.com/hp808d

Trinium K = 1,66666    http://prntscr.com/hp81lv

Xanion K = 1,90785    http://prntscr.com/hp82dq

Avorion K = 2,5            http://prntscr.com/hp82dq

 

Comparing this numbers, I realized that there was a progression:

 

and, if ogonite hyperspace cores would exist, the progression would be clrearer:

 

And then I asked myshelf, why that 14,47% extre for each material?

I figured out that 1/7 (seven, because there are 7 material) was 0,1428571429, so I though that I had found the logic of the number.

I could calculate, then, all the Ks from the Avorion K, that was exactly 2.5, and create an unique formula:

 

This formula also gives us a new calculable K for each material (except for Avorion, that it is the same):

Naonite K = 1,458333333

Trinium K = 1,66936875

Xanion K = 1,910943102

 

Have you seen that they are a bit different? yes, they are.

And the worst of all: the numbers fails sometimes  :(

But why? it is a really nice and rounded formula!

Here are the errors:

Naonite: http://prntscr.com/hp8fep

Trinium: http://prntscr.com/hp8fl0

Avorion: http://prntscr.com/hp8fsp

 

Then I thought... Are this devs evil enough to add some random numbers to formulas just to mislead the players? Is this possible?

 

And I started to play with the numbers to find somekind of patron trying to fix this...

And I found this encouraging thing:

(this are the results of dividing the "experimental Ks" by the "calculated Ks"):

 

Do you see that? 1.62, 1.62... It is Phi? Phi divided by 1000?

Then I figured out this new formula:

 

And yes! the numbers were very accurated...

This are the results with the new calculated Ks:

Naonite K= 1,456007726    http://prntscr.com/hp8kfc

Trinium K= 1,666701252    http://prntscr.com/hp8kmh

Xanion K= 1,907883465    http://prntscr.com/hp8kyc

 

But have you seen that right? It still failed at highest numbers... :(

I started to play with numbers and Ks again, and I saw this:

 

I said: why not? lets try with pi.

And new formula:

 

After this, the numbers were accurated in all cases:

Naonite K= 1,45597631      http://prntscr.com/hp8plk

Trinium K= 1,666669836    http://prntscr.com/hp8psz

Xanion K= 1,907852049    http://prntscr.com/hp8q24

Avorion K = 2,499968584  http://prntscr.com/hp8q6x

 

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I have thought that, maybe, the way I have found to solve this formula could help other players to find/solve other ones.

I will also add this formulas to the wiki, as well as I have made with the IFG and CQ.

 

See you guys :)

 

[ZK456]

Just dropped by to thank you for taking the time to find out the formula  :) That must have taken some time. Up until now, I used an approximation that worked well enough (like 1% error margin), but it's good to have the exact stuff.

 

Do you know if there is also an exact formula for hyperspace cooldown vs mass, and how the game convert torque produced by thrusters and gyros to radial speed?

 

The hyperspace cooldown/mass ratio is not linear, and I don't see how to use the usual formulas involving torque and moment of inertia because it gives you the angular acceleration and the game displays the angular speed...

[xisec]

I am with the hyperspace cooldown now, but it seems a hard nut to crack  ::)

Anyway, if I would find something, I would put it into the wiki.

 

About angular movements, I have no idea, and I have not planned to investigate them soon xD.

 

This community have to move on! there are very few deciphered mechanics  ;D

[ZK456]

What would be left to do apart from HS cooldown? Cargo bays & fighters, thrust/braking thrust calculations have been done, and all the other stuff is linear. Maybe max velocity?

[xisec]

Well, although linear, the rest of formulas have to be calculated. Energy consumptions and crew requeriments, for example, could be important.

 

And I think that the ideal would be to put all of them of the wiki.

I have not seen the formula for thrusters for example  :-[

[ZK456]

Oh I see. I have to complete a few things, but I did the crew requirements and everything for trinium components.

 

About thrusters/engines/dampeners, the basic idea is that thanks to Newton, F=M * a. So, a = F/M.

 

But, F is linearly proportional to the volume of engines/thrusters/dampeners, and that volume can be expressed in terms of mass like M_engines = p * V.

 

In the end, a = M_engines / M * C, with:

• M_engines = mass of the engines
  
• M = total mass of the craft
  
• C is a constant that depends on the material you use for thrusters/engines/etc, to take p (the volumetric density) in account.
  

 

Let's take trinium engines. If you make a ship that is only an engine (so M_engines/M = 1), its thrust will be 1904.8 m/s².

 

1904.8 m/s² is what I call the base acceleration value (e.g. the constant C), for the trinium engines.

 

That value changes with material, because a_engine= F_engine/M_engine but M_engine changes with the material used (p is different) whileF_engines stays the same across all materials.

 

Now, if you make a ship in which M_engines = 0.5 * M (so engines represent 50% of the craft's total mass), the acceleration will be 0.5 * 1904.8 = 952.4 m/s². If it's 10%, then the acceleration will be 0.1 * 1904.8 = 190.48 m/s² and so on.

 

You could say that for each % of trinium engine against the craft's total mass, it gains 19.048 m/s² of thrust.

 

Works the same way for dampeners and thrusters, only that the base value is different.

 

Finally, roughly speaking in terms of force (for a 1x1x1 block):

• F_engine ~ 20 MN
  
• F_dir.thruster ~ 12.5 MN
  
• F_{omni.thruster} ~ 4.9 MN for the three axis XYZ, if it's a cube
  
• F_dampener ~ 54.4 MN
  

[Shrooblord]

Haha, this is great. Thank you for taking all that time to decipher this. I love seeing complex formulae and algorithms behind hidden systems. Keep on experimenting,

.

[Kamo]

It'd be cool to calculate the Hyperspace Energy formula next, that one's nasty for spaceship builders :).

It seemed linear at first, but it isn't.

8kt is 1,53 GW, but 16kt is 2,52 GW (987,71 MW more), 24kt 3,94 GW (806,63 MW more), and 32kt 4,03 GW (701,61 MW more), so I suspect a root/decimal 0-to-1 power function at play.

It seems to be the sole function of mass and, at zero mass, starts as zero.