What mathematical formula do architectural engineers use in calculating the bollard pull of a tug boat?

Engineers use almost all mathematical formulas that exist, since engineering covers the entire range of science.

Normally we use a simple formula

if tug has amain engines and standard 4:1 gear box : we use formula of 1/ 10

if you bhp is 900 , you get Normal 9 bollard pull

how ever if you have Kort nozzles & K type propeller you can multiply by 1.3 henf 9 x 1.3 = 11.7 approx 12

you have to do Bolard pul test wiht Steel wire rope as it has no Give and use a standard length of 120 meters

sea condition has ot be "CALM " or Still normally one hour after high tide

angle of rope has to not over 2 - 5 degrees over 120 meter

never do Bollard pull test with Nylon ropes or length below 120 meters

the test is then invalid

you can get very high bollard pul if you increase Reduction gear by say

16 : 1 and use large Pitch and Diameter propllers wiht slow speed engines max 100 rpm - 120 rpm call me if you need advice