Solution Naval Numerical 31

Numerical 31: A ship of 9.900 tonnes displacement has KM 7.3m, and KG 6.4m. She has yet to load two 50 tonne lifts her own gear and the first lift is to be placed on deck on the inshore side (KG = 9m and centre of gravity = 6m, out from centre line). When the derrick plumbs the quay, its head is 15m above the keel and 12m out from centre line. Calculate the maximum list during the operation.

Solution: the maximum list will occur first when the lift is in place on the deck and the secondly when the weight is suspended over the quay.

Moment about the keel

weight	KG	Moment
9900	6.4	63360
50	9.0	450
50	15.0	750
10000		64560

$Final\, KG =\frac{Final\,Moment}{Final\, Displacement}$ 

$Final\, KG\,(KG_1) =\frac{64560}{10000}$ =6.456m 

w	d	List Moment stbd
50	12	600
50	6	300
		900

listing Moment =900 t-m

Listing Moment is also = W x $G_1G_2$

 W x $G_1G_2$ = 900 t-m

$G_1G_2$ = $\frac{900}{10000}$ =0.09m

Now $GG_1 = KG_1 - KG$

= 6.456 -6.400 = 0.056m

GM = KM -KG = 7.3 - 6.4 = 0.9m

In Triangle $G_1G_2M$

$G_1M = GM - GG_1$ = 0.9 - 0.056 = 0.844m

Tanθ = $\frac{G_1G_2}{G_1M}$

= $\frac{0.09}{0.844}$ = 0.1066

$θ = 6^o6'\, (Max\, List)$