FORMULAE FOR CALCULATING HEEL WHEN TURNING

Formula applicable to all ships as given in standard text books

V2 BG V2 ( KG D/2 )

Tan = ------------------ = -----------------------

g R GM(F) g R GM(F)

--- Heel due to turning ; V --- Ships speed (m/sec)

BG --- Vertical distance between COG and COB ; D --- Draft

R --- Radius of ships turning circle (m) ; g --- 9.81 m/sec

Formula applicable to passenger ships as given in IMO Res. A.749(18) 0.02 V2 ( KG D/2 ) W

H.M. = -------------------------------------

L

H.M. --- Heeling moment due to turning ; L --- Length of the ship at waterline

H.M. 0.02 V2 ( KG D/2 )

Tan = --------------- = --------------------------------

W GM(F) L GM(F)

Equating the above two formulae for Tan as applicable to passenger ships

V2 ( KG D/2 ) 0.02 V2 ( KG D/2 )

Tan = ----------------------- = --------------------------------

g R GM(F) L GM(F)

By eliminating the common factors in the above equation we get :

1 0.02

------------ = ------- ; Hence R = 5 L

9.81 R L

Even if we assume that the above formulae are applicable in open sea conditions, in calm weather and in deep waters, still the value of R will depend on whether the turn is to port or starboard, rate of turn of the ship and amount of helm angle used. Hence the value of R will be variable where as the value of L will be constant. Furthermore the ratio of R and L as derived above, is far too high when compared with manoeuvring data of any ship.

In view of the above calculation, how can both the formulae be acceptable for calculating heel due to turning?

Can someone clarify this please?