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Final KG Plus Twenty Reasons for a Rise in G

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Final KG Plus Twenty Reasons for a Rise in G Chapter 13 Final KG plus twenty reasons for a rise in G When a ship is completed by the builders, certain written stability informa- tion must be handed over to the shipowner with the ship. Details of the information required are contained in the 1998 load line rules, parts of which are reproduced in Chapter 55. The information includes details of the ship’s Lightweight, the Lightweight VCG and LCG, and also the posi- tions of the centres of gravity of cargo and bunker spaces. This gives an ini- tial condition from which the displacement and KG for any condition of loading may be calculated. The final KG is found by taking the moments of the weights loaded or discharged, about the keel. For convenience, when taking the moments, consider the ship to be on her beam ends. In Figure 13.1(a), KG represents the original height of the centre of grav- ity above the keel, and W represents the original displacement. The original moment about the keel is therefore W ϫ KG. Now load a weight w1 with its centre of gravity at g1 and discharge w2 from g2. This will produce moments about the keel of w1 ϫ Kg1 and w2 ϫ Kg2 in directions indicated in the figure. The final moment about the keel will be equal to the original moment plus the moment of the weight added minus the moment of the weight discharged. But the final moment must also be equal to the final displacement multiplied by the final KG as shown in Figure 13.1(b); i.e. Final momentϭϫ Final KG Final displacement or Final moment Final KG ϭ Final displacement Final KG plus twenty reasons for a rise in G 119 w2 g1 G g2 G1 K K w1 W W ϩ (w1 Ϫ w2) (a) (b) Fig. 13.1 Example 1 A ship of 6000 tonnes displacement has KG ϭ 6 m and KM ϭ 7.33 m. The fol- lowing cargo is loaded: 1000 tonnes KG 2.5 m 500 tonnes KG 3.5 m 750 ttonnes KG 9.0 m The following is then discharged: 450 tonnes of cargo KG 0.6 m and 800 tonnes of cargo KG 3.0 m Find the final GM. Weight KG Moment about the keel ϩ6000 6.0 ϩ36 000 ϩ1000 2.5 ϩ2500 ϩ500 3.5 ϩ1750 ϩ750 9.0 ϩ6750 ϩ8250 ϩ47 000 Ϫ450 0.6 Ϫ270 Ϫ800 3.0 Ϫ2400 ϩ7000 ϩ44 330 120 Ship Stability for Masters and Mates M Final moment Final KG ϭ 1.00 m Final displacement G 44 3330 ϭ ϭ 6.33 m 7000 7.33 m GMϭϪ KM KG 6.33 m KMϭ 7.33 m, as given Fiinal KGϭ 6.33 m, as calculated K Ans. Final GM ϭ 1.00 m Note. KM was assumed to be similar value at 6000 tonnes and 7000 tonnes displacement. This is feasible. As can be seen on Figure 6.2, it is possible to have the same KM at two different drafts. Example 2 A ship of 5000 tonnes displacement has KG 4.5 m and KM 5.3 m. The follow- ing cargo is loaded: 2000 tonnes KG 3.7 m and 1000 tonnes KG 7.5 m Find how much deck cargo (KG 9 m) may now be loaded if the ship is to sail with a minimum GM of 0.3 m. Let ‘x’ tonnes of deck cargo be loaded, so that the vessel sails with GM ϭ 0.3 m. Final KMϭ 5.3 m M Final GMϭ 0.3 m 0.3 m G Final KGϭ 5.0 m Final moment Fiinal KG ϭϭ5.0 m 5.3 m Final displacement 5.0 m 37 400ϩ 9x ⌺ І 5 ϭ ϭ v 8000 ϩ x ⌺1 40 000 ϩϭ5x 37 400 ϩ 9x K 26600ϭ 4x xϭ 650 tonnes Ans. Maximum to load ϭ 650 tonnes Weight KG Moment about the keel 5000 4.5 22 500 2000 3.7 7400 1000 7.5 7500 x 9.0 9x (8000 ϩ x) ϭ⌺1 (37 400 ϩ 9x) ϭ⌺v Final KG plus twenty reasons for a rise in G 121 Twenty reasons for a rise in G When the vertical centre of gravity G rises, there will normally be a loss in the ship’s stability. G may even rise above the transverse metacentre M to make the ship unstable. The master and mate onboard ship must be aware of changes in a ship that would cause such a rise in G. The following list gives reasons for such a rise: 1. Free-surface effects in partially filled tanks. 2. Collapse of a longitudinal division/bulkhead in a partially filled tank of liquid. 3. Icing up of superstructures. 4. Loading cargo in upper reaches of the vessel. 5. Water entering the ship through badly maintained hatches on upper deck and flooding the tween decks. 6. Hatches or bow doors inadvertently left open on the main deck. 7. Water landing on the deck from the sea in heavy weather conditions. 8. Raising of a weight from a deck using a mast and derrick. 9. Raising a weight low down in the ship to a higher position within the ship. 10. Timber deck cargo becoming saturated due to bad weather conditions. 11. Vessel making first contact with keel blocks in a dry dock at the stern. 12. A ship’s first contact with a raised shelf or submerged wreck. 13. The raising of the sails on a yacht. 14. A bilging situation, causing free-surface effects. 15. A collapse of grain-boards or fish-boards. 16. A blockage of freeing ports or scuppers on the upper deck. 17. Passengers crowding on superstructure decks at time of departure or arrival. 18. Adding weight at a point above the ship’s initial overall VCG. 19. Discharging a weight at a point below the ship’s initial overall VCG. 20. Retrofits in accommodation decks and navigation spaces. Exercise 13 1 A ship has a displacement of 1800 tonnes and KG ϭ 3 m. She loads 3400 tonnes of cargo (KG ϭ 2.5 m) and 400 tonnes of bunkers (KG ϭ 5.0 m). Find the final KG. 2 A ship has a light displacement of 2000 tonnes and light KG ϭ 3.7 m. She then loads 2500 tonnes of cargo (KG ϭ 2.5 m) and 300 tonnes of bunkers (KG ϭ 3 m). Find the new KG. 3 A ship sails with displacement 3420 tonnes and KG ϭ 3.75 m. During the voyage bunkers were consumed as follows: 66 tonnes (KG ϭ 0.45 m) and 64 tonnes (KG ϭ 2 m). Find the KG at the end of the voyage. 4 A ship has displacement 2000 tonnes and KG ϭ 4 m. She loads 1500 tonnes of cargo (KG ϭ 6 m), 3500 tonnes of cargo (KG ϭ 5 m) and 1520 tonnes of bunkers (KG ϭ 1 m). She then discharges 2000 tonnes of cargo (KG ϭ 2.5 m) 122 Ship Stability for Masters and Mates and consumes 900 tonnes of oil fuel (KG ϭ 0.5 m) during the voyage. Find the final KG on arrival at the port of destination. 5 A ship has a light displacement of 2000 tonnes (KG ϭ 3.6 m). She loads 2500 tonnes of cargo (KG ϭ 5 m) and 300 tonnes of bunkers (KG ϭ 3 m). The GM is then found to be 0.15 m. Find the GM with the bunkers empty. 6 A ship has a displacement of 3200 tonnes (KG ϭ 3 m and KM ϭ 5.5 m). She then loads 5200 tonnes of cargo (KG ϭ 5.2 m). Find how much deck cargo having a KG ϭ 10 m may now be loaded if the ship is to complete loading with a positive GM of 0.3 m. 7 A ship of 5500 tonnes displacement has KG 5 m, and she proceeds to load the following cargo: 1000 tonnes KG 6 m 700 tonnes KG 4 m 300 tonnees KG 5 m She then discharges 200 tonnes of ballast KG 0.5 m. Find how much deck cargo (KG ϭ 10 m) can be loaded so that the ship may sail with a positive GM of 0.3 metres. The load KM is 6.3 m. 8 A ship of 3500 tonnes light displacement and light KG 6.4 m has to load 9600 tonnes of cargo. The KG of the lower hold is 4.5 m, and that of the tween deck is 9 m. The load KM is 6.2 m and, when loading is completed, the righting moment at 6 degrees of heel is required to be 425 tonnes m. Calculate the amount of cargo to be loaded into the lower hold and tween deck, respectively. (Righting moment ϭ W ϫ GM ϫ sin heel.) 9 A ship arrives in port with displacement 6000 tonnes and KG 6 m. She then discharges and loads the following quantities: Discharge 1250 tonnes of cargo KG 4.5 metres 6675 tonnes of cargo KG 3.5 metres 420 tonnesof o cargo KG 9.0 metres Load 980 tonnes of carrgo KG 4.25 metres 550 tonnes of cargo KG 6.00metres 700 tonnes of bunkers KG 1.0 metre 70 ttonnes of FW KG 12.0 metres During the stay in port 30 tonnes of oil (KG 1 m) are consumed. If the final KM is 6.8 m, find the GM on departure.
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