Required towing power? , Towing resistance calculation

""A vessel of any kind is to be moved by tug/tugs from one point to another ""

HOW MUCH TOWING FORCE ( BOLLARD PULL ) IS REQUIRED ???

Simplified towing pull formula ( ref : OPL vol 4, page 382 )

'Using 1 tug'
a) TF ( bollard Pull ) = √ 1.5 x Displacement

eg : barged displ = 5000 t
therefore : TF = √ 1.5 x 5000 = 86.6 mt

'Using 2 tugs'
b) TF ( bollard pull ) = { √ (1.5 x Displacement) } + 50

'Using 3 tugs'
c) TF ( bollard pull ) = { √ (1.5 x Displacement) } + 75

***note : Bare in mind that above formula are base on standard environment conditions as below. ( ref : OPL vol 4, page 379 )


Standard limiting conditions
Decided towing power ( bollard pull ) is to have sufficient towing power available to hold a tow hove-too at zero speed in the following set of environmental conditions ;

Wind speed = 20 m/s from ahead ( 40 knts)
Wave = 5 meters in height from ahead
Current = 0.5 m/s from ahead ( 1 knts )


*** Considering of the towing route planing and towing force, pls see detail on TOPL vol 4, page 379~ 382.