Pivot Point New 641oo

By Dhakshina Perera A Practical Method to find the location of the pivot point In order to determine the location of the pivot point relative to the ship following attempt were made.

GPS Assume if two GPS were fitted at the Bow(A) and stern(B), [see Fig (1)], then a turning motion is introduce to the ship.

FIG(1) After t=t

time v/l shifted it’s position to a new location due to turning motion see fig (2)

FIG (2)

After t=t time GPS at point “A” shifted to “ A’ “ , Course over the ground(COG) and speed over the ground(SOG) of point “A” can be given by vector AA’ , assuming that t=t time is small. Accordingly COG,SOG of point “B” can be given by vector BB’ , and as per the drift angle definition “ is the drift angle at point “ A” ( = Difference between the ship’s head and the COG of “A”), accordingly “ “ is the drift angle at “B” . Definition of pivot point As per definition of pivot point (position at which drift angle becomes zero) at point “P” drift angle becomes zero, “P” represents the pivot point.

FIG (3) VB = Speed over ground (SOG)of point “A” VS = SOG of point “ B “ VBT = Transverse component of VB VBL = Longitudinal component of VB VST = Transverse component of VS VSL = Longitudinal component of VS

Consider SOG of “ A” as VB, transverse and longitudinal components as VBT , VBL and SOG of point “B” as VS and components as VST, VSL [See fig (3)]

Vessel acting as a rigid body Since vessel is a rigid body VSL = VBL ,if these two are unequal , then there should be a relative motion between Point “A” and point “B” along the longitudinal direction creating a compression or tension, which does not exist on a rigid body.

Fig(4) Now consider point “X”[See fig(4)], the components SOG of “X” are VXT, VXL , since the vessel is a rigid body VXL = VBL = VSL = VPL But at pivot point(P) , transverse component does not exist due to drift angle is zero, as explained earlier. Hence all the points along the AB line or the longitudinal axis , will have equal longitudinal components, but transverse component will change as the SOG of points “A” and “B” changes, thus the pivot point changes it’s location along the AB line. By this,It can be determine that location of the pivot point is a function of the transverse components ONLY. Determining the Pivot Point location relative to the stern point “B”

Fig(5) Considering PAX and PBY triangles [See Fig (5)]

=

=

But BY = VSL x tan( AX = VBL x tan( And VSL = VBL = =k

=

=

= k ; (k as a variable )

PA = k x PB But PA + PB = Length Overall (LOA)

PB = LOA – PA PB = LOA – (k x PB) PB=

So Location of the pivot point relative to the stern point”B” can be given as

where

k=

, is the difference between Gyro heading and the respective GPS courses over the ground: the drift angles of point “A” and “B”.

“k” can be “+” or “-“ ve, as per the directional convention used

Thus pivot point can exist outside the ship, and can be determine by the sign of “k”