Vessel Stopped
If the tugs apply the same bollard pull of say 15 tonnes each, it is to a position 80m fore and aft of the pivot point. Thus two equal turning levers and moments of 80m x 15t (1200tm) are created resulting in even lateral motion and no rate of turn.
Making Headway
With the ship making steady headway, however, the pivot point has shifted to a position 40m from the bow. The forward tug is now working on a very poor turning lever of 40m x 15t(600tm), whilst the after tug is working on an extremely good turning lever of 120m x 15 t (1800tm).
This results in a swing of the bow to starboard.
Making Sternway
The efficiency of the tugs will change totally when the ship by contrast makes sternway. Now the pivot point has moved aft to a position 40m from the stern. The forward tug is working on an excellent turning lever of 120m x 15t(1800tm) whilst the after tug has lost its efficiency to a reduced turning lever of 40m x 15t(600tm).
This now results in a swing of the bow to port.