Armour Calculation

[Feeble (OP)]

Can anyone tell me how armour is calculated? I found previous posts that basically said that armour is calculated using the formulas for converting from the volume of a sphere to the area of a sphere, divide by 4, then divide again by the strength of the armour tech, then round to the first decimal place, but that calculation is very inaccurate at larger ship sizes.   If I start to include the armour rating, the calculation is even more inaccurate (where i calculate each successive layer by taking the weight added by the previous layer, adding it to the weight of the ship, and performing the same calculation as above, only once i reach the point of dividing by armour strength i also multiply by the armour layer) this is accurate to some degree, but at larger ship sizes and higher armour ratings, the calculation underestimates the amount of armour needed by a lot (>5% error).   Can someone (ideally Steve) please detail how armour is calculated?

[mtm84]

I think its in the necronomicon some where.

(but seriously, I know how it works in theory but I've never had my numbers match up with Auroras.)

[SevenOfCarina]

I've heard that the armour width is calculated as  [(3*(Total Ship Size in HS)/(4*pi))^(2/3)]*pi rounded down to the nearest integer. The armour volume required is then (Armour Width x Armour Depth)/(Armour Strength per HS)

As I understand, Aurora iterates the armour calculation only a fixed number of times, so for very large ships you could end up needing appreciably less armour volume than you should. Also, 'ships' under 30 tons have zero armour width due to the aforementioned rounding.

[amram]

I do not know how to take a tonnage, add armor, and learn how much that adds on. 

I do know how to take a final tonnage with armor, and find out how much of that was added by the armor.

For a 10,000 ton ship, 4 layers of armor, Compressed Carbon Armor which has a strength of 15

Code: [Select]

ROUND(ROUND(Layers*ROUNDUP(0.356317748049092*(ship_tons)^(2/3),1)/4,1)/armor_strength,1)*50
 ROUND(ROUND(4*ROUNDUP(0.356317748049092*(10000)^(2/3),1)/4,1)/15,1)*50
 ROUND(ROUND(4*ROUNDUP(0.356317748049092*464.1588834,1)/4,1)/15,1)*50
 ROUND(ROUND(4*ROUNDUP(165.38805,1)/4,1)/15,1)*50
 ROUND(ROUND(4*165.4/4,1)/15,1)*50
 ROUND(ROUND(165.4,1)/15,1)*50
 ROUND(165.4/15,1)*50
 ROUND(11.02667,1)*50
 11*50
 550

https://prnt.sc/s271z5

That's exactly what we get too.  11.0x is 11 HS of armor, 550 tons.

So the warship before armor is 9450 tons, 10,000 with.

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armor strengths:

1 conventional steel
2 conventtional composite
3 convent adv composite
4 duranium
6 HD duranium
8 composite
10 ceramic composite
12 laminate composite
15 compressed carbon
18 biphase carbide
21 crystalline composite
25 superdense
30 bonded superdense
36 coherent superdense
45 collapsium


Same method applied to a 384,000 ton ship with 11 layers of armor, also compressed carbon:

Code: [Select]

ROUND(ROUND(Layers*ROUNDUP(0.356317748049092*(ship_tons)^(2/3),1)/4,1)/armor_strength,1)*50
 ROUND(ROUND(11*ROUNDUP(0.356317748049092*(384000)^(2/3),1)/4,1)/15,1)*50
 ROUND(ROUND(11*ROUNDUP(0.356317748049092*5283.084,1)/4,1)/15,1)*50
 ROUND(ROUND(11*ROUNDUP(1882.4565,1)/4,1)/15,1)*50
 ROUND(ROUND(11*1882.5/4,1)/15,1)*50
 ROUND(ROUND(20707.5/4,1)/15,1)*50
 ROUND(ROUND(5176.875,1)/15,1)*50
 ROUND(5176.9/15,1)*50
 ROUND(345.12667,1)*50
 345.1*50
 17,255 tons

And that's what we find: https://prnt.sc/s27n55

345.1 HS is 17,255 tons.

[Feeble (OP)]

I've heard that the armour width is calculated as  [(3*(Total Ship Size in HS)/(4*pi))^(2/3)]*pi rounded down to the nearest integer.  The armour volume required is then (Armour Width x Armour Depth)/(Armour Strength per HS)

As I understand, Aurora iterates the armour calculation only a fixed number of times, so for very large ships you could end up needing appreciably less armour volume than you should.  Also, 'ships' under 30 tons have zero armour width due to the aforementioned rounding.

Is "Armour Depth" the same as Armour Rating?

[mtm84]

Amram: any idea where the magic number came from?  I’ve seen this in various ship design spreadsheets.

Feeble: it is my understanding that armor depth is armor rating, which is the number of armor box layers.

[Feeble (OP)]

Amram: any idea where the magic number came from?  I’ve seen this in various ship design spreadsheets. 

Feeble: it is my understanding that armor depth is armor rating, which is the number of armor box layers. 

Okay, thanks.   Also, I would like to know where that number came from too.   It isn't (4*PI/3)^(-2/3) (though it is close to it) which would make sense as this constant comes from the equation to convert from the volume of a sphere to its surface area (at least partially, i don't know what happened to the 4*PI, which would have made the constant 4*PI*(4*PI/3)^(-2/3).   This is obviously too large)

In my mind, the calculations should look a lot like the calculations for an onion, where each successive armor layer has to account for the volume added by the previous layer.

[mtm84]

I am guessing that someone made a lot of ships at certain tonnages, with 1 to n armor layers at x armor tech, and graphed them in excel to come up with an exponent in a function.  But I digress.  In theory the way the armor is set up you should be able to calculate the next layer of armor by using the current ship tons.  But I’ve never been able to match my numbers with the games numbers.  Armor represents the volume of a spherical shell need to cover a sphere of X hull size volume. The higher your armor tech the thinner that shell is, which means the less hull size worth of armor you need. Armor width represents the surface area of the ship “sphere” you need to armor.

[Feeble (OP)]

The best formula I have found/made so far is:

=ROUNDUP(
       ROUNDUP(
           4/4*3. 14*((CEILING("Ship init HS" + "HS of previous armour layer",1)
       /(4*3/3))^(1/3))^2
       ,0)
  *("Armour Layer number"/"Armour Strength Rating")
  ,1)

This formula initially overestimates (<30% error at 1 Armour Rating) the armour needed at low armour ratings, then underestimates at higher armour ratings (<4% error at 40 armour rating), then goes back to over estimating the armour needed at (3. 23% error at 100 Armour Rating)

Note: Test bed was a ship with 1 bridge and 1 50 ton fuel storage and 60 months deployment time

[Feeble (OP)]

I am guessing that someone made a lot of ships at certain tonnages, with 1 to n armor layers at x armor tech, and graphed them in excel to come up with an exponent in a function.

I figured it was some kind of curve fitting.

But I digress.   In theory the way the armor is set up you should be able to calculate the next layer of armor by using the current ship tons.   But I’ve never been able to match my numbers with the games numbers.   Armor represents the volume of a spherical shell need to cover a sphere of X hull size volume.  The higher your armor tech the thinner that shell is, which means the less hull size worth of armor you need.  Armor width represents the surface area of the ship “sphere” you need to armor.

This has been my understand as well.

[amram]

Amram: any idea where the magic number came from?  I’ve seen this in various ship design spreadsheets.

Nope, I spent a couple days rooting around the net, mostly reddit and old forum postings here trying to figure out how to calculate armor.  I couldn't get it either until I came across the formula I use now and working from the final tonnage works for my purposes.

Did a little digging, found where I probably picked it up from:
https://docs.google.com/spreadsheets/d/1TKzgbroNAKD8qMSny0a_78n93RHWfSMCKWRcEaC3tNo/edit#gid=0

He credits Sombody1212 with the formula.

It's not a perfect match, but very close for area.  Using a 10,000 ton ship:
165.3880481 = 4*PI()*(((HS=200)/(4*PI()/3))^(1/3))^2
165.3787038 = 0.356297616552724*(tons=10000)^(2/3)

A quick look at my prior post, I also hit 165.38805, so yes, this is probably where I got it from.


Had some time, worked through it, that is the source of the magic number.

Code: [Select]

truncating to 4 digits, but working with 9
4 * PI() * ((HS / (4*PI()/3))^(1/3))^2
4 * PI() * (HS / (4*PI()/3))^(2/3)
4 * PI() * HS^(2/3) / (4*PI()/3)^(2/3)
4 * PI() / (4*PI()/3)^(2/3) * HS^(2/3)
12.5663 / 4.1887^(2/3) * (tons/50)^(2/3)
12.5663 / 2.5985 * tons^(2/3) / 50^(2/3)
4.8359 * tons^(2/3) / 13.5720
4.8359 / 13.57208808 * tons^(2/3)
0.356317748 * tons^(2/3)

comparing:

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mine  = 0.356317748
magic = 0.356317748049092