open All Channels
seplocked Ships and Modules
blankseplocked The Big Ninetails Thread of Useful Formulae™
 
This thread is older than 90 days and has been locked due to inactivity.


 
Author Topic

Ninetails o'Cat
League of Super Evil
Posted - 2010.04.27 16:42:00 - [1]
 

Edited by: Ninetails o''Cat on 29/04/2010 14:03:18
NOTE: I have worked out none of these formulae! All credit should go to whoever discovered them in the first place, not me!

It has come to my attention that the good people of Ships'n'Modules have lost the wisdom that has been so carefully acquired by those who went before them. So, to rectify this, I have made a big list of any strange and useful formulae for anyone who needs them.

1. Motion Mechanics

Acceleration time

a = Agility
m = Mass
x = Percentage change of speed you want (E.g. if you want to get to 75% of your speed from 0%, you use 0.75 for x). Essentially, x = ABS(v-(wanted speed %age))

Quote:
-ln(1-x)*m*a/1000000 = t


Note: The Speed required to enter warp is 75% your maximum, so when x = 0.75, you are working out align time.


Speed after time

v = Velocity
Vmax = Maximum velocity
x = Time spent accelerating
a = Agility
m = Mass

Quote:
v = Vmax * (1 - e^(-x * 10^6 / (a * m))


Orbit Radius given speed

r = Range from source
a = Agility
m = Mass
v = Velocity
Vmax = Maximum Velocity

Quote:
r = a*m*v^2 / (SQRT ( Vmax^2 - v^2 ) x 10^6))


Orbit Speed given radius

r = Range from source
a = Agility
m = Mass
v = Velocity
Vmax = Maximum Velocity

Quote:
v = ((1+vmax^2)/(((a^2*m^2)/((10^12)*(r^2)))))^(1/4)


WARNING: This gets steadily more imprecise as the v gets larger or m*a gets smaller!


Displacement given time

v = Velocity
Vmax = Maximum velocity
x = Time spent travelling
a = Agility
m = Mass

Quote:
d = Vmax*(x+(m*a/10^6)*(e^(((10^6)*-x)/(m*a)) - 1))


2. Combat Formulae

Turret Tracking

h = Hit Chance
x = Transversal Velocity
r = Range to target
T = Tracking of your turret(s)
sig = Signiture of the target
tsig = Signiture Resolution of your turret(s)
o = Optimal of your turret(s)
f = Falloff of your turret(s)

Quote:
h = 0.5^((((((x)/(r*t))*(sig/tsig))^2)+((MAX(0; r-o))/f)^2)


There is also a 1% chance of high quality hits, which always hit, and deal 3x damage.

Turret Damage Formula

h = hit chance
tbd = Turret Base Damage = damage mod/ROF (for each turret)
aDPS = Average DPS

Quote:
When h > .01
aDPS = TBD * (h-.01)(h+.99/2)+.03

When h < .01
aDPS = TBD * 3h


Missile Damage Formula

D = Damage
BD = Base Damage
sig = Target's signiture radius
Er = Explosion radius
Ev = Explosion Velocity
v = Target's velocity
drf = Damage reduction factor

Quote:
D = BD*MIN(MIN(sig/Er,1),(Ev/Er*sig/v)^(log(drf)/log(5.5)))


TRUE Missile Range

r = Range
v = Velocity of missile
f = Flight time of missile
m = Mass of missile
a = Agility of missile

Quote:
r = v*(f-(10^6/(m*a)))


ECM Single Jammer Formula

Ch = Chance to Jam
J = Jammer Strength
S = Target's Sensor Strength

Quote:
Ch = MIN(100*(J/S); 100)


ECM Multiple Jammer Formula

Ch = Chance to Jam
J = Jammer Strength
S = Target's Sensor Strength
x = Number of Jammers on Target

Quote:
Ch= (1-(1-J/S)^x)*100


Locking Speed Formula

t = Time taken to lock target
res = Scan Resolution
sig = Target's Signiture Radius

Quote:
t = (40000/(res))/(asinh(sig)^2)


3. Fitting Formulas

Stacking Penalty

S = Stacking penalty for given module
x = number of modules already affecting that attribute

Quote:
S = 0.5^[((x-1) / 2.22292081) ^2]


Note: the modules with the greatest effect are calculated first, so they have the lowest stacking penalty.



Ninetails o'Cat
League of Super Evil
Posted - 2010.04.27 16:45:00 - [2]
 

Edited by: Ninetails o''Cat on 29/04/2010 13:34:02
Edited by: Ninetails o''Cat on 29/04/2010 13:25:45
3. Fitting, Continued

Capacitor Recharge Rate given Percentage

CRR = Capacitor Recharge Rate
CC = Maximum Capacitor Capacity
CR = Capacitor Recharge Rate
C = Current Capacitor

Quote:
CRR = (4.8/(CC/CR))*SQRT((1-C/CC)^2-(1-C/CC)^4)


Warp range

R = Range
CC = Capacitor Capacity
wcn = Warp Cap Need
M = Mass

R = CC / (wcn * M)

4. Agent and Skill related.

Agent Required Standing

rs = Required Standing
l = Level
q = Quality

Quote:
rs = 2* [l - 1] + [0.05 * q]


Skill Point Training speed

P = Primary Attribute
S = Secondary Attribute
Sk/m = Skillpoints per minute

Quote:
Sk/m = P + (0.5*S)

Kuar Z'thain
Amok.
Goonswarm Federation
Posted - 2010.04.27 17:25:00 - [3]
 

Edited by: Kuar Z''thain on 27/04/2010 17:27:02
Impressive, but how did you end up breaking the tables?

edit: this brokes:
*[*code]Note: the modules with the greatest effect are calculated first, so they have the lowest stacking penalty.[/code]

Poldarn Joaq
Caldari Provisions
Posted - 2010.04.27 17:42:00 - [4]
 

Nice :D

Seriously Bored
Minmatar
Posted - 2010.04.27 17:44:00 - [5]
 

Awesome compilation Cat. I have most of these going in my EVE calculation cheat (spread)sheet...but I could use to update it with some of these. Smile

stoicfaux
Gallente
Posted - 2010.04.27 17:55:00 - [6]
 

Edited by: stoicfaux on 27/04/2010 17:59:12
You can also glean useful formulae from
* Eve Dev wiki: http://wiki.eve-id.net/Main_Page
* Evelopedia: Ex: Acceleration formulas

You can also experiment on the test server, Sisi. Check the stickies in the test forum: Test Server Forum

PS- here's the link to the missile formula thread: missile formula thread


Joshmanus
Gallente
Toy Makers
Posted - 2010.04.27 17:56:00 - [7]
 

Amazing, now if someone would be kind enough to use these formulae in an excel spreadsheet or create a php form to use that would be teh cheery, sprinkles & silver balls on the cake.

Ninetails o'Cat
League of Super Evil
Posted - 2010.04.27 18:09:00 - [8]
 

Originally by: Seriously Bored
Awesome compilation Cat. I have most of these going in my EVE calculation cheat (spread)sheet...but I could use to update it with some of these. Smile


Thank you! But I'm not Cat...

Please visit your user settings to re-enable images.

I'm the one on the right. Very Happy


stoicfaux
Gallente
Posted - 2010.04.27 18:16:00 - [9]
 

Originally by: Ninetails o'Cat

Thank you! But I'm not Cat...

...

I'm the one on the right. Very Happy




Also, the goatee gives it away.


M'ktakh
Posted - 2010.04.27 22:10:00 - [10]
 

Glue-worthy thread.

Yakumo Smith
Gallente
Body Count Inc.
Pandemic Legion
Posted - 2010.04.27 22:41:00 - [11]
 

Flashbacks to my old School days maths classes.

Marko Riva
Posted - 2010.04.27 22:59:00 - [12]
 

Not a fan of formulas other than figuring out how things actually affect stuff. But a question actually, is there a warp range formula for how far a ship can warp at full cap?

dtyk
Posted - 2010.04.27 23:55:00 - [13]
 

Standing required to use an agent =
2* [agent level -1] + [0.05 * quality]

Skill training rate =
Primary attrib. + [0.5x Secondary attrib.] SP per minute

De'Veldrin
Minmatar
Norse'Storm Battle Group
Intrepid Crossing
Posted - 2010.04.28 03:24:00 - [14]
 

Originally by: Ninetails o'Cat
Originally by: Seriously Bored
Awesome compilation Cat. I have most of these going in my EVE calculation cheat (spread)sheet...but I could use to update it with some of these. Smile


Thank you! But I'm not Cat...

Please visit your user settings to re-enable images.

I'm the one on the right. Very Happy




You evil impostor!! You will never defeat the real CAT!

Also, she's cuter then you are are.

So there.

God I'm tired. I should go to bed

Toshiro GreyHawk
Posted - 2010.04.28 04:20:00 - [15]
 

Thanks.

Rutger Centemus
Phantom Squad
Atlas.
Posted - 2010.04.28 09:21:00 - [16]
 

Very nice work, hat's off.

Unfortunately, this however
Quote:

Orbit Speed given radius

r = Range from source
a = Agility
m = Mass
v = Velocity
Vmax = Maximum Velocity

Quote:
v = SQRT((10^6*r^2*SQRT(Vmax^2-v^2))/am)


doesn't do much for calculating, as the value to be calculated [v] is used in its own equation. I'ld have a crack at it myself, but I'm late for work as is Smile.

Baron Agamemnon
Caldari
The Einherji
Supernova Federation
Posted - 2010.04.28 10:46:00 - [17]
 

Interesting thread.

Goumindong
SniggWaffe
Posted - 2010.04.28 12:45:00 - [18]
 

Originally by: Ninetails o'Cat

Transversal velocity

v = velocity
r = range

Quote:v*r



Where velocity is the orbit velocity at that range or alternatively how much you are moving parallel to the target.


This is not right Maybe you're thinking of angular which is Transversal Velocity/Range

Transversal is just the velocity of the target tangential to you (I.E. remove the portion of the vector coming towards or away from you and what you're left with is transversal)

Quote:
h = hit chance
tbd = Turret Base Damage = damage mod/ROF (for each turret)
aDPS = Average DPS

Quote:aDPS = tbd*((h^2+h+0.0499)/2)


This is incorrect. I should know. K1zg got the data, and I derived it.

When h > .01
aDPS = TBD * (h-.01)(h+.99/2)+.03 (if you were to expand this where h = real h -.01 then you get (h^2+h)/2)+.03. or (h^2+.98h-.0099)/2+.03) [Clearly subtracting the 1% before hand is much easier)


When h M< .01
aDPS = TBD * 3h

So if your hit chance is 1% your final DPS is 3% of your TBD. If your hit chance is 50% your final DPS is 39.505% of your TBD

.49 x (1.49/2) + .03 = .39505

Originally by: Me from another forum, explaining how it works
O.K. for a simple "how it works"

Hit quality is a number between .5 and 1.49 or its 3.

This is determined on the same roll as the "to hit" roll for tracking

The game basically uses a "roll under" mechanic to determine whether or not you hit. You get a "hit chance" based on transversal tracking, and falloff and then compare that to a randomly generated number. If the number is lower than the hit chance, you hit. If the number is higher than the hit chance you miss.

So if you have a 100% hit chance you will hit for all numbers rolled and if you have a 0% hit chance you will hit for no numbers rolled[because they will all be higher than 0]

This random number also determines whether or not you wreck, or how well the hit quality is.

Such there is a hit distribution. Anything under 1% of the total % will deal 3% damage. Anything over will deal more damage the HIGHER the roll is.

Low roll <--------------------------------------------------------> high roll
3,.5,.60,.65,.70,.75,.80,.85,.90,.95,1.05,1.1,1.15,1.25, 1.35, 1.4, 1.49

So if you have a 11% chance to hit, your hit distribtion will look like this

Low roll
3,.5,.60

1/11 of all hits will be wrecking,
1/11 of all hits will be 51% dmg
1/11 of all hits will be 52% dmg
1/11 of all hits will be 53% dmg
1/11 of all hits will be 54% dmg
1/11 of all hits will be 55% dmg
1/11 of all hits will be 56% dmg
1/11 of all hits will be 57% dmg
1/11 of all hits will be 58% dmg
1/11 of all hits will be 59% dmg
1/11 of all hits will be 60% dmg

Now if you had a .5% chance to hit, you would still only hit .5% of the time. But all those shots would be wrecking hits, because only the wrecking distribution would be under the hit chance.

Another way figure it easy would be

Take your hit chance and then add .49. That is the highest amount of damage you will do in a non-wrecking hit. If you take that add .5 and then divide by 2, you will get your average dps for all of your shots except the wrecking shots.

Vessper
Indicium Technologies
Hephaestus Forge Alliance
Posted - 2010.04.28 13:54:00 - [19]
 

Originally by: Marko Riva
Not a fan of formulas other than figuring out how things actually affect stuff. But a question actually, is there a warp range formula for how far a ship can warp at full cap?

Range = CapacitorCapacity / (WarpCapNeed * Mass)

Range is in AU.

Ran Khanon
Amarr
Swords Horses and Heavy Metal
Posted - 2010.04.28 14:00:00 - [20]
 

*Enters thread, spots nasty maths, is impressed and leaps the hell out*

Ninetails o'Cat
League of Super Evil
Posted - 2010.04.29 13:21:00 - [21]
 

Originally by: Goumindong
lots of good stuff!


Thank you, I'll roll it into the V2. Razz

Originally by: dtyk
Standing required to use an agent =
2* [agent level -1] + [0.05 * quality]

Skill training rate =
Primary attrib. + [0.5x Secondary attrib.] SP per minute


Thank you, I'll put it into the second post.

Originally by: Vessper
Originally by: Marko Riva
Not a fan of formulas other than figuring out how things actually affect stuff. But a question actually, is there a warp range formula for how far a ship can warp at full cap?

Range = CapacitorCapacity / (WarpCapNeed * Mass)

Range is in AU.


That could be useful, I'll put it up with the other ones.

On another note, I found the actual formula for velocity at a given orbit range. Very Happy


 

This thread is older than 90 days and has been locked due to inactivity.


 


The new forums are live

Please adjust your bookmarks to https://forums.eveonline.com

These forums are archived and read-only