# Design and Calculation of Double Buoys Mooring System in Estuary of Yalu River

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2 2072 Sustainable Development of Urban Infrastructure F w =½ρgCV 2 (Acos 2 θ+bsin 2 θ) (1) In the Eq. 1,F w is the wind force (N) ;ρ is the density of the air (0.123 kg s 2 /m 4 ) ;V is the speed of the wind (m/s), C is the coefficient of the wind force, calculated by Eq. 2. C= cos(2θ)-0.35cos(4θ)-0.175cos(6θ) (2) In which, θ is the angle between the direction of the wind and the bow and stern line of the ship, or relative wind angle, it is 90 degrees if the wind abeam with the ship; A is the orthographic projection area of the ship (m 2 ); B is the lateral projection area of the ship above water (m 2 ). The values of A and B can be calculated in the following Eq. 3 and Eq. 4. loga= log( DW ) (3) logb= log( DW ) loga= log( DW ) (4) logb= log( DW ) In the f Eq. 3 and Eq.4, DW is the displacement of the ship (t). Generally, relative wind angle is not in the line of the direction of wind force. The direction of wind force can be calculated in following Eq. 5. With the Beaufort 8 wind blowing from different direction in the Table 1, we can get the value of the force and its direction as shown in table 1. ϕ = ( 1-θ 90) ( 1-θ 90) 3 (5) Relative wind angel { } The direction of the wind force when loaded Table 1. and its direction when ballast Relative wind angel The direction of the wind force when loaded when ballast From table 1, we know that when it is Beaufort 8 wind blowing the ship, wind force will be increase when relative wind angle increase, and when the wind abeam the ship, the wind force get its maximum values, they are: When loaded:f w =459.1 KN;When ballast:f w =958.6 KN. When the wind abeam the ship, the direction of the wind force will perpendicular to the bow and stern line of the ship, action point is nearly in the middle of the ship. Current force. According to the Load Code for Harbor Engineering (JTJ-215) [3], the current force can be calculated by the following Eq. 6. The maximum current speed of this sea area is 2.3 m/s which almost equal to 5 knots, and the direction of the current is 091. F f = CρV 2 S 2 (6) In which, F f is current force on the ship, C is a coefficient of the calculation of current force which can be calculated by Eq. 7, ρ is the density of the water (t/m 3 ), V is the speed of the current (m/s), S is the area of the ship under water (m 2 ), which can be calculated by Eq C = Re 0. +b (7) In which, b is the coefficient, equals to here. Re=V L/v,V is the speed of the current (m/s), L is the length of the ship when loaded (m), equals to 190 m here, is the coefficient, equals to 1.14 according to the temperature of water at 15. S = 1. 7LD+ C LB (8) b In which, D is the draft of the ship, B is the bread of the ship, C b is the block coefficient of ship, we use here. The following are results of calculation. When loaded:f C = KN;When ballast:f C =781.8 KN. The direction of current force is along the bow and stern line.

3 Applied Mechanics and Materials Vols Wave force. According to some other materials, most of time wave force is not considered when design mooring system. The reason is that the function of wave is periodically, and the anchor chain can absorb parts of force as their curve property. So we do not calculate wave force here [5]. Combination force. As noted in front, the direction or wind force when strongest is almost north and the direction of current is from west, so that wind and current are almost in vertical of each other. According to the principle of combination of forces shown in Fig. 1, the combination force of wind and current is: When loaded: = KN, direction is α=24.1 from bow and stern line of the ship, action point is almost int the middle of the ship. When ballast: = KN, the direction is α=50.8 from bow and stern line of the ship, action point is almost in the middle of the ship. Calculation of Tension on Mooring System and its Anchor Chains Make a stress analysis from the state of loaded and ballast as shown in Fig. 2. According to the balance of forces shown in Eq. 9, the tension on anchor chains of mooring system is shown in Eq. 10. T β 1 hlsin = FLsinα 2 t (9) T = sinα 2sinβ (10) F f Bow T β α α F w β T Stern Fig. 1Combination force Fig. 2 Mooring system Fig. 3 Deadman T h is the tension of mooring system in horizontal direction. Calculate the force respectively when the angle between mooring line and the bow and stern line of the ship, they are 10, 20, 22.5, 30, 40, 45, 50, 60, 70, 80, 90, results shown in the following Table 2. The angle between mooring lines and shipβ Table 2 The relationship between the horizontal tension on the buoy and the direction of mooring lines loaded T h (α=24.1 ) ballast (α=58.0 ) The angle between mooring lines and shipβ loaded T h (α=24.1 ) ballast (α=58.0 )

5 Applied Mechanics and Materials Vols According to Eq. 13, get the result of the length of mooring chain L=27.6 m, it is almost one shackle. With the standards of anchor chain, it is easy to get its weight =4.88 t, which is useful when choosing the size of buoys. buoy and anchor chain s diameter. According to the rules, mooring buoy should keep at least 1/3 to 1/2 freeboard when there is no load on them, and this is the basis to determine the size of the buoy. After calculation, the model of buoy is XF5.5-D. this kind of buoy is divided uniformly, which is easy to keep horizontal and has enough buoyancy when some parts are damaged. Another advantage of this kind of buoy is that it is symmetric, when one side is corroded, the other side can be turned back to be used again, so that service life can be prolonged [6]. According to the breaking load of mooring chain, it should be at least KN 3.0= KN. Looking up national standards of Electric welded Anchor (GB/T ), the diameter of the anchor chain should be 90 mm (breaking load 5840 KN)and texture of material is AM3 [7] to satisfy the requirement. Conclusion After calculation, the parameters of double mooring system of Yalu River are follows: (1) Buoy model is XF-D 5.5 with uniformly divided in side. (2) The diameter of mooring chain is 90mm with AM3 of texture of material. The length of mooring chain is 27.5 meters and 4.88 tons weight. (3) Deadman, made of iron and cement, 42 tons weight, pyramid in shape, with a hole in side by 3.0m*3.0m*0.2m and a ring outside made of 3 shackle, is 2 meters in length top side, 5 meters in length bottom side and 1.5 meters in height. (4) The hole to bury Deadman is 6.5 meters in depeth, when construction, it is necessary to dig the hole to 7.0 meters to have enough space and keep safety. Construction is strictly followed to the proposal of design and has a good effect at last, which means this design and calculation method are practible. Acknowledgements This work was financially supported by the fundamental research funds for the central universities (2012QN010). References [1] L. Zhengzhen, Y. Yanyi. Design and Construction of DWT Mooring Buoy System in Meizhou Bay Anchorage. Port and Waterway Engineering. 2000(6): [2] H. Chengli. Port Planning and Layout Beijing: People Transportation Press, p , (2007) [3] China Transportation Ministry. Load Code for Harbor Engineering. JTJ [4]. P.R. China. Design and Construction Standards of Slopping Wharf and Floating Wharf. JTJ [5] China Transportation Ministry. Code of Hydrology for Sea Harbour. JTJ213-98, (1998). [6] China Classification Society, Rules and Regulations for the Classification and Construction of Sea-going Steel Ships, (2006) [7] GB/T Electric Welded Anchor Chain, (2008). [8] M. Jianing. Shenzhen Shekou China Merchants Harbor Company DWT Operating Buoy Design. Port and Waterway Engineering, Vol. (10), p.53-54, (2002)

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