Applied Mechanics and Materials Online: 2012-12-13 ISSN: 1662-7482, Vols. 253-255, pp 2071-2075 doi:10.4028/www.scientific.net/amm.253-255.2071 2013 Trans Tech Publications, Switzerland Design and Calculation of Double Buoys Mooring System in Estuary of Yalu River Guoyou Shi a, Jiaxuan Yang b and Weifeng Li c Navigation College, Dalian Maritime University, Liaoning China 116026 a shiguoyoudmu@163.com, b ytyjx@163.com, c weilfengli@163.com Keywords: Estuary of Yalu River; Double buoys mooring system; ; Current force; Wave force; Chain; Deadman Abstract. In order to design a double buoys mooring system in the estuary of Yalu River for loading work of 40,000 tons of bulk cargo ship, the article mainly based on the practicality of the meteorological condition of this sea area and the data of the vessel as well as the national criterion, do some calculations of wind force, current force, wave force as well as the total force on the ship, with the calculation result to make a designation of double mooring buoy system, decide the size of the mooring buoy, the size and length of the chain, the size and the depth of the Deadman. The construction according to the designation has a good effect; the method of calculation and the designation are proved useful. Introduction Use ships to transport some sands from Dandong to Taiwan, but some high draft ships cannot proceed into territorial water to load sands because of the depth of water. It is necessary to use 2000 tons barges to transfer sands from inland port to the estuary of Yalu River and then load them onto the high draft bulk ships. The project builds two mooring buoys in the estuary of Yalu River to moor ships by two mooring buoys bow and stern. The estuary of Yalu River is located in the junction of Dandong and North Korea. It is reciprocating flow here and the maximum and minimum speed of flow are 2.30 m/s and 1.9 m/s. with the time 4h50min and 8h10min, and the direction is 091. According to the 10 years statistics of Big Deer Islands, lower than 0.6 meters waves occupy 93% and the highest wave happens in the West water Estuary with the height of 1.1 meters. It is very obvious monsoon here, the days with stronger than Beaufort wind 6 are just 39.7, and the strongest wind is weaker than Beaufort 8 comes from north. Over this area, the depth of water on chart is 14 meters. The mooring bulk ship, 40000 DWT, is 190 meters long and 30.5 meters bread, 11.2 meters draft when loaded and 5.0 meters when ballast.all manuscripts must be in English, also the table and figure texts, otherwise we cannot publish your paper. The Design Procedure of Double Buoy Mooring System Stage I: Calculate the outside forces on the system, include wind force, current force, wave force and the combination of them; Stage II: Calculate the force on anchor chains of mooring buoy system; Stage III: Design and Calculation of the holding capacity of the Deadman; Stage IV: Selection of the mooring buoys and its chains; Stage V: Examination of the safety of mooring system [1]. Calculation of the forces on ships The outside forces on the ship include wind force, current force and wave force.. On the calculation of the wind force, there are two different formulas in the books of Load Code for Harbor Engineering and Port Planning and Layout, but the calculation result of later one is bigger than the first, so here, in order to keep safe, we choose to use the later formula by the following named formula (1). According to the climate here, the strongest wind was Beaufort 8, the scale of the speed is 17.5 20.5 m/s, use 20.5 m/s when calculation in order safety. All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of Trans Tech Publications, www.ttp.net. (#69783574, Pennsylvania State University, University Park, USA-16/09/16,07:28:38)
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=1.325-0.05cos(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= 0.427+ 0.480 log( DW ) (3) logb= 0.648+ 0.550 log( DW ) loga= 0.377+ 0.553log( DW ) (4) logb= 0.733+ 0.601log( 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 = 90 1-0.15 ( 1-θ 90) - 0.8 ( 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 0 4.5 82.3 159.0 50 69.8 425.8 877.7 10 13.2 108.8 211.9 60 77.5 426.1. 882.0 20 35.9 186.1 368.8 70 83.4 426.9 888.9 30 49.0 293.8 592.3 80 87.6 446.8 932.3 40 60.3 386.0 788.4 90 90 459.1 958.6 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. 8. 134 C = 0.046 Re 0. +b (7) In which, b is the coefficient, equals to 0.015 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 0.825 here. The following are results of calculation. When loaded:f C =1026.6 KN;When ballast:f C =781.8 KN. The direction of current force is along the bow and stern line.
Applied Mechanics and Materials Vols. 253-255 2073 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: =1124.6 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: =1237.0 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 ) 10 1322.2 2760.2 50 299.7 625.7 20 671.3 1401.4 60 265.1 553.4 22.5 600.0 1254.5 70 244.3 510.0 30 459.2 958.6 80 233.1 486.6 40 357.2 745.7 90 229.5 479.1 45 324.7 677.8
2074 Sustainable Development of Urban Infrastructure From Table 2 we can get: (1) as β is the same value, when the ship is loaded, the buoy is bigger than when ballast, (2) the buoy will be decrease when β decreases. So, we choose the value of loaded situation when we design and β =22.5 is preferred. That is because: (1) the design standards will be too high and need too much investment if β too small, (2) 22.5 is a quarter of 90 and is easier to see and control than 10 or 20. Calculation of the anchor chains is according to the following formula (11), which is in appendix B Calculations of anchors and anchor chains of one of the standard of China transportation Ministry Design and Construction Standards of Slopping Wharf and Floating Wharf. F = Th+ wh (11) In which, F is the chain at Hawse pipe, T h is the division tension of anchor chain on horizontal direction, w is the weight of unit length of anchor chain (KN/m), H is the distance from Hawse pipe to the water(m). Put T h =1254.5 KN into the Eq. 11, we get the anchor chain is 1296.2 KN, and the vertical tension is 326.1 KN. Design of Deadman In the calculation of this paper, the safety coefficient of Deadman is 2.0 in order to safety [1], the breaking force in vertical when buried into earth should be at least 326.1 KN 2=652.2 KN. Design of Deadman. The Deadman is made of cramp iron and cement, with a pyramid shape, the length of upper is 2 meters and bottom 5 meters, height is 1.5 meters, and the weight is 42 tons. There is a square hole in the bottom of the Deadman with the dimension of 3.0m*3.0m*0.2m, which not only can reduce the weight, but also can increase the breaking force of Deadman. The ring is made of 3 stoped-chains with the diameter the same size as anchor chain. The dimension of the hole to bury Deadman is 6.5 meters in depth. In the construction, it is necessary to dig the hole to 7 meters in depth in order to have enough space to put into and keep safety. The shape of Dead man is shown in Fig. 3. Breaking force Examination of Deadman. The magnitude of the breaking force affects safety of mooring system greatly. If the division tension on mooring chain in vertical direction is bigger than the Deadman s breaking force, the Deadman will be pulled out. Breaking force can be calculated by Eq. 12 [1]. H 2 2 G = ( a + b + ab)r (12) 3 Here, G is the breaking force of Deadman, H is the depth the Deadman will be buried, H = 6.5-1.5 = 5 m, a is the length of Deadman s bottom side, b can be calculated by b=a +2H tg18 =8.25m, r is the density of sand, 9KN/m 3 here. After calculation, G = 2014.7 KN > 652.2 KN, satisfy with the requirement of design. Buoy s and Anchor Chain s Parameters Most of times, anchor chain s safety coefficient is set to 2.5 to 3, we use 3 here in order to keep safety [1]. The designed mooring chains breaking force can be calculated as follows. 1296.2 KN 3.0=3888.6 KN. The length of mooring chains. The length of mooring chains can be calculated by Eq. 13 [1]. ( H + H + H + H ) f L= 1 2 3 4 (13) Here, L is the length of anchor chain (m), H 1 is the depth of anchorage, 14 meters, H 2 is the height of the tide, 3.5 meters, H 3 is the distance from the top of Deadman to water surface, 5.0 meters here. H 4 is the freeboard of buoy, 1.5 meters, f is a coefficient, 1.15.
Applied Mechanics and Materials Vols. 253-255 2075 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 177.4 27.5=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 1296.2 KN 3.0=3888.6 KN. Looking up national standards of Electric welded Anchor (GB/T549-2008), 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 100000 DWT Mooring Buoy System in Meizhou Bay Anchorage. Port and Waterway Engineering. 2000(6):18-22. [2] H. Chengli. Port Planning and Layout Beijing: People Transportation Press, p. 40-52, (2007) [3] China Transportation Ministry. Load Code for Harbor Engineering. JTJ215-98. [4]. P.R. China. Design and Construction Standards of Slopping Wharf and Floating Wharf. JTJ294-98 [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/T549-2008 Electric Welded Anchor Chain, (2008). [8] M. Jianing. Shenzhen Shekou China Merchants Harbor Company 125000 DWT Operating Buoy Design. Port and Waterway Engineering, Vol. (10), p.53-54, (2002)