Posted by: amram
« on: April 19, 2020, 06:09:26 PM »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:
Code: [Select]
mine = 0.356317748
magic = 0.356317748049092