# Turning Lever and Turning Moment

Having understood the position of pivot point we now move to application of same to determine turning lever and turning moments.

As we know pivot point will act as center of rotation. Lever is distance from Pivot point from point of application of force, and Turning Moment will be product of lever and force applied.

Imagine a vessel of LOA 200 mtr which is being pulled with 20 T tug fwd and aft as shown.

1. While v/l is stationary, Turning Moment = Force X lever (Distance from Pivot point)

Turning moment due to fwd tug= 100 X 20=2000 TM (to port)

Turning moment due to Aft tug= 100 X 20=2000 TM (to stbd)

Hence both turning moments are cancelling each other and vl will not turn, it will only move sideways. Turning moment due to fwd tug= 50 X 20=1000 TM (to port)

Turning moment due to Aft tug= 150 X 20=3000 TM (to stbd)

Resultant turning moment = 3000-1000 = 2000 TM to Stbd

Hence when vessel is having headway, similar pulling force from both tugs will result in vessel turning to stbd due to difference in their Lever for force and resultant turning moments.

3. V/l falling back /sternway Turning moment due to fwd tug= 150 X 20=1000 TM (to port)

Turning moment due to Aft tug= 50 X 20=1000 TM (to stbd)

Resultant turning moment = 3000-1000 = 2000 TM (to Port)

Hence when vessel is having sternway, similar pulling force from both tugs will result in vessel turning to port due to difference in their Lever for force and resultant turning moments.

So with above starting concept, we will move further with application of same in various ship handling scenarios.