Stability. criterion. Yihuai Hu. at present no. ever, there is. conservationn. ship correctly is one technology. Cleary et al., 1996).

Transcription

1 csnak, 15 Int. J. J Nav. Archit. Ocean Eng. (15) 7:1~9 pissn: 9 678, eissn: Stability criterion and itss calculation orr sail-assisted ship Yihuai Hu 1, Juanjuan Tang, Shuye Xue and Shewen Liu 3 1 Proessor, erchant arine college, Shanghai aritime University, Shanghai, P. R. China Postgraduate student, erchant arine college, Shanghai aritime University, U Shanghai, P. R. China 4 anager, China Oshore Technology Center, ABS Greater China Division, Shanghai, P. R. China ABSTRACT: Stability criterion and its calculation are the crucial issue in thee application o sail-assisted ship. How- ever, there is at present no speciic criterion and computational methods or thee stability o sail-assisted ship. Based on the stability reuirements or seagoing ships, the stability criterion o the sail-assisted ships s is suggested in this paper. Furthermore, how to calculate the parameters and determine some speciic coeicients or the ship stability calculation, as well as how to redraw stability curve are also discussed in this paper. Finally, to give ann illustration, the proposed method is applied on a sail assisted-ship model with comments and recommendations or improvement. KEY WORDS: Sail-assisted ship; Ship stability calculation; Ship stability criterion. INTRODUCTION Propelled by main diesel engine primarily and assisted by sails as auxiliary is a major m application method to make the use o the wind energy on modern ships. To make the use o wind energy on modern ships primarily p propelled by main diesel engines, one o the major application methods is to t use sails as auxiliary power source. Under the reuirement o energy conservationn and emission reduction, sail-assisted technology has been rapidly developed (eng et e al., 9). Due to the action o wind, the sail assisted ship has some dierent characteristics compared to the conventional powered ship in n terms o stability. eans o correctly checking the stability o the sail-assistespeciic rules or stability criterion o the sail assisted ship. any researchers have proposed speci- ications or checking the stability o their own sail-assisted ships according to their study situation (Tsai and Haciski, 1986; Cleary et al., 1996). Some institutions in China primarily use the passenger ship criterion romm the Stabilityy Criterion or Seagoing Ships to check the stability o the sail assisted ship and simply correct the roll angle in order to relect the eect o sail area (Register o Shipping o the People's Republic o China, 198). Because the orm, structure and material o the sails used on modern ships are dierent, it is diicult to obtain comprehensivee comparison speciication through limited experiments. Energy saving eiciency cannot be achieved when the wind is too weak, while the ship s s turning-over risk will increase when the wind is too strong, so the sails should be used withinn certain wind speed range. Because B the action o wind and wave to the ship will be magniied ater sail installation, the moving eect o sail area is supposed to be included in the calculation o heeling moment when considering the stability o the sail-assisted ship (Yang, 1996; 1988). ship correctly is one o the major problems in the application o sail-assisted technology. Currently there are no With better aerodynamic perormancee arc sails are easily manuactured and manipulated, andd are widely used in modern Corresponding author: Yihuai Hu, yhhu@shmtu. edu.cn This is an Open-Access article distributed under u the termss o the Creative Commons Attribution Non-Commercial License ( which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

2 Int. J. Nav. Archit. Ocean Eng. (15) 7:1~9 sail-assisted ships. Based on the present rules o Stabilityy Reuirements or Seagoing Ships and reerring to past experience, e this paper discusses the stability criterion and calculation c o the sail-assisted ships. STABILITY REQUIREENT ON SAIL-ASSISTED SHIP The rules o Stability Reuirements or Seagoing Ships are the technical regulations enacted to guarantee the saety when the ship is heeled by ocean wind and/or other external orces. The ship should have the ability to return back to the upright. Static stability and dynamical stability should be checked, besides, both initial stability at small angles and overall stability at any heeling angle should be taken into account in the ship stability calculation. Shipp inclining velocity could be neglected and static stability o the ship is measured in righting r moment or static stability calculation. On the contrary, in thee calculation o dynamical stability, external orce moment and inclining velocity o the ship should be taken into account, ship's ability to withstand the external orce is measured in terms o work done by righting moment, which is numerically eual to the areaa enclosed by static stability curve against heeling angle. Taking into account the damping eect o the sail,, it is necessary to make correction in the calculation o rolling angle. What s more, i the sail is all unolded on voyage, the loads applied on the sail are large and the heeling moment on the ship by wind and wave will be magniied. It is obvious that the calculation o weather criterion K depends s on total moment o the ship, heeling moment by wind and waves, and rolling angle o the ship. In addition to alll reuirements o stability calculation men- tioned above, it is noteworthy that the weight distributio on o the ship will change ater sail installation, which will impact the calculation o parameters and the shape o static stabilityy curves. The recommendatory stability criterionn on sail-assisted ships includes: 1) weather criteria K : K 1 ) metacentric height G : G. 3 CALCULAT TION OF STA ABILITY PARAETERSS Calculation o minimum overturning moment inimumm overturning moment is the maximum heeling moment the ship could undertake, which also represents the limits or the ship to withstand heeling moment in the most t dangerous situations. I thee heeling moment reaches or exceeds this criterion, the ship will overturn. Fig. 1 Static stability curve. The calculation o minimum overturning moment is related to rolling angle, angle o looding and the area enclosed by static stability curve as shown in Fig. 1, where 1 represents the ship ss maximum rolling angle in the beam sea as:

3 Int. J. Nav. Archit. Ocean Eng. (15) 7:1~ CCCC Zg d (1) here C1, C, C 3 are coeicients related with the basic particulars o ship and navigating zone, which could be determined by the related inormation (see Shen et al. (1) and reerences therein). C 4 is inluence coeicient o anti-rolling eect generated by sails, which is deined as: C4.6 S LB 1.6S LB 1. () The value o in Fig.1 is usually chosen as the minimum rom the angle o looding, 5 or (the second intersection point o l and static stability curve). The enclosed area o a and b could be seen as the work done by heeling moment and righting moment respectively. Under the action o wind and rolling motion, stability under each standard load conditions o the ship should meet the reuirement that area b is eual to or greater than area a. Here, a concept o stability modulus is proposed as the ratio o the absolute value o b to a, the minimum overturning moment l is then the value o GZ when stability modulus is 1. For static stability curve GZ is symmetric to the originand when Sb Sa d l d l d d d d l 1 d d 1 l 1 d l 1 Then l d m 1 1 ( ) (3) The overturning moment could be described as: l ( kg m) (4) The calculation o wind heeling moment The wind heeling moment that acts on the ship is called under rough sea conditions. structure (Luo et al., 1986). b has two parts including the moment acts on the sails s, which represents the wind dynamic moment that acts on ship and the moment acts on the ship s b (5)

4 4 Int. J. Nav. Archit. Ocean Eng. (15) 7:1~9 Fig. oments acting on sail and ship. According to the calculation o transverse wind heeling moment: 1 (6) b CHb sin U AZ1 kg m Hence, the ship is not only propelled by the lit orces rom sails, but also in the risk o being overturned by drag orce. When wind blows towards the ship at apparent wind speed V in the direction o, the aerodynamic orces on the sails induce lit orce L, drag orce D and the moment on the mast, as shown in the Fig.. The angle between V and chord line o sail is called attack angle. The moment on the sail is mainly made by lateral orce and lever o wind pressure as: s Y Z 1 1 CLU Scos CDU SsinZ 1 CH U SZ kg m (7) where: : constant o air density ; U : wind speed at the center o wind; S : the whole canvas here; A : the lateral projected area o the ship. Z1 ZA d : lever o wind pressure, where Z A is the height between wind center on the ship and base line. Z ZS d : lever o heeling, where Z S is the height between the center o sail area and base line, d is mean drat o current loading condition. CH CL cos CDsin : coeicient o lateral orce, where C L is lit coeicient o sail and C D is drag coeicient o sail, obtained rom the wind tunnel test. It should be noted that the coeicients are rom the wind tunnel test where only the sail is exposed in the wind without navigation direction being taken into account, so the angle is the angle between wind and sail, while in C H is the angle between wind and navigation direction.

5 Int. J. Nav. Archit. Ocean Eng. (15) 7:1~9 5 The calculation o metacentric height etacentric height G is an important index o the initial stability o the ship when the ship heeling angle is smaller than Its value determines the value o the rightingg moment ater heeling at a small s angle. G is determined as (Sheng and Liu, 3).. G KBB KG (8) Fig. 3 etacentric height o ship. Vertical height o buoyant center KBB and initial metacentric radius B are related with the ship drat, which could be accurately determined by molded lines and osets table, and is little related to thee installation o sail. But vertical height o gravity center KG should be recalculated because the gravity center o ship will be changed ater installing sail assisted device (Zhao, 1997). The value o KG is deined as: KG PKG i i (9) where P is weight o load and i KG is the t height o its center. i Static stability curve (Shen et al., 1) As a sail assisted ship, its static stability curve needs to be re-measured, because the gravity center and ship drat will be inluenced by installed sails. Since the lever o static stability could be calculated indirectly i romm lever o orm stability, the stability cross-curve should be given priority beore static stability curve. Stability cross-curve has relationship between displacement volume and lever o orm stability as shown in Fig. 4. Fig. 4 Principle o cross-curve o stability.

6 6 Int. J. Nav. Archit. Ocean Eng. (15) 7:1~9 A concept o assumed center is proposed to assume that the location o the gravity center will not change with the dierent ship loads, and will be ixed at the point S. According to the geometric relationships in the Fig. 4, with heeling at an angle o, the distance rom the action line o buoyancy to point S is the lever o orm stability as: ls OEROSQ l OO'cos d KS sin (1) where: OO ' : the distance rom pivot point to the center line o transverse proile, which is generally 15% % o ship width; KS : the height rom the assumed center S to the baseline; d : the drat when the ship is upright. The distance rom action line o buoyancy to reerence axis NN is marked as l l V (11) where is the volume static moment o V i axis NN is taken as reerence. According to the theorem o resultant moment, it could be expressed as V OE v OA v OB V OF (1) 1 where: V : the displacement volume under current heeling waterline; V : the displacement volume under current heeling waterline when the ship is upright; v 1 : the wedge volume in the water, v : the wedge volume out o the water when the ship is heeled by an external inclining orce. V will be as: V V v 1 v (13) where OA, OB and OF represent the distance rom the center o v 1, v and V to axis NN respectively. OF could be calculated by OF d KBsin OO ' cos (14) And 1 v1oavob a b d dx 3 L 3 3 cos L (15) where: L : the length o the ship; a : the hal breadth o side into the water; b : hal breadth o side out o the water. When dierent position o S is selected, the dierent orm o stability cross-curve will be obtained. I the point S is set on the base point K, the method is called base point approach to draw cross-curve o stability. I the point S is set on the gravity center o the ship, the method will be called gravity center method. The latter is used more oten because the result is accurate

7 Int. J. Nav. Archit. Ocean Eng. (15) 7:1~9 7 enough to two or three decimal accuracy. Ater getting the data o l, S the values o GZ could be easily calculated as: GZ l GG sin l Z Z S A S g ga sin (16) Then the be obtained. curves indicating the relationships betweenn heeling angles and rightingg arm at dierent loading conditions could Fig. 5 odel o sail-assisted ship. CALCULAT TION EXAPLE Based on the calculation method proposed above, a model o sail assisted ship was made, and its stability is i checked. As shown in Fig..5, the ship model is euipped with our sails, the two bigger ones placedd ore and at, and the rest in the middle. The particulars o the model, sail and wind conditionn are listed in the Table 1, Table and Tablee 3 respectively. Table 1 Particulars o the ship model. L (m) B (m) D (m) d (m) KG (m) KB (m) B (m) Table Particulars o the sail. Width o bigger sail B S1 1 (m) Width o smaller sail BS S (m) Height o both sail HS (m)( Area o bigger sail S 1 (mm ) Area o smaller sail S (m( ) ) Total area o sail S T (m Height between sail projected area and baseline ZS (m) Wind heeling lever o sail Z (m)

8 8 Int. J. Nav. Archit. Ocean Eng. (15) 7:1~9 Table 3 Particulars o the wind. Density o air ρ (kg s /m 4 ).15 Coeicient o lateral wind pressure on ship C Hb 1.5 Lateral projected area o ship A (m ).99 Height between lateral projected area o ship and baseline Z A (m).35 Wind heeling lever o ship Z 1 (m).17 According to E. (9), the height o ship gravity center ater sail intallation is 1.5 m ater sail installation, thus, the curve o static stability at light loading is redrawn. As indicated in Fig. 6 it shows that ater installing the sails were installed, the static stability curve becomes lat, which means heeling moment becomes larger, and the stability condition becomes worse. Based on the revised static stability curve, at light loading is calculated as 4 N m. Tests were carried out at dierent angles between sail and ship, and dierent angles between wind and ship. Here in the Table 4, SSx WS y means that the tested angle between ship and sail is x degree, and the tested angle between wind and ship is y degree. Fig. 6 Comparison o static stability curve beore and ater installing sail. Table 4 Record o the parameters o stability. item condition C L C D C H K W U (m/s) s b SS -WS SS -WS SS -WS SS 3 -WS SS 3 -WS SS 3 -WS SS 6 -WS SS 6 -WS SS 6 -WS SS -3 -WS SS -3 -WS SS -3 -WS SS -6 -WS SS -6 -WS SS -6 -WS

9 Int. J. Nav. Archit. Ocean Eng. (15) 7:1~9 9 Through the data in Table 4, the ollowing results are obtained: 1) According to the E. (8) in Section.3, the vertical height o gravity center G is.59 m, which is higher than its limitation o.3 m. ) The heeling angle o the ship model under natural condition is 4. degrees, the minimum overturning moment is 4 N m, which is obviously higher than thewind heeling moment as shown in the Table 4. CONCLUSION Ater combining dierent stability reuirements o ships, a stability assessment method is put orward ocusing on the weather criteria. Considering the characteristics o arc sail, this paper not only corrects the calculation o ship rolling angle o ater sail installation, but also accurately calculates the heeling moments o the sail and ship assisted by the results o windtunnel tests. What s more, calculation improvement o the gravity center, weight distribution and static stability curve are made in order to accurately calculate the minimum capsizing moment o the sail assisted ships. Compared with other types o ship, the stability calculation o sail-assisted ship is uite complicated and diicult. There is no experimental method o measuring the ship stability by now. Further research in this ield needs be carried out. A laboratory euipped with model tank and wind tunnel should be established, where ship overturning moment and heeling moment could be easily measured as the indicator o ship stability. The uture research work should be ocused on conducting reasonable experiments to veriy the sail-assisted ship s reliability with the theoretical stability method. ACKNOWLEDGEENT This research work is supported by STCS within the project o Research on Sail Application on Sea-going Ships, Project Number: REFERENCES Cleary, C., Daidola, J.C. and Reyling, C.J., Sailing ship intact stability criteria. Journal o arine Technology, 33(3), pp Luo, H.L., Li, G.L. and Tan, Z.S., Stability check o airoil sail. Journal o South China University o Technology, 14(), pp.36-4(in Chinese). eng, W.., Zhao J.H. and Huang, L.Z., 9. Application prospect o sail-assisted energy-saving ships. Journal o Ship & Boat, 4, pp.1-3(in Chinese). Register o Shipping o the People's Republic o China, 198. Stability Criterion or Seagoing Ships. Beijing: Renmin Jiaotong Press. Shen, H., Du, J.L. and Xu, B.Z., 1. Calculation o Stability and Strength. Dalian: Dalian aritime University Press. Sheng, Z.B. and Liu, Y.Z., 3. Principles o naval architecture. Shanghai: Shanghai Jiao Tong University Press. Tsai, N.T. and Haciski, E.C., Stability o large sailing vessel: a case study. Journal o arine Technology, 3(1), pp Yang, B.L., Study on stability o sail assisted ships. Journal o Wuhan Shipbuilding, 3, pp.-7. Yang, H., Study on stability o sail assisted inland river ship. Journal o HuNan Communication Science and Technology, 4, pp Zhao, H.L., The height o gravity center o ships. Journal o arine Technology, 3, pp.1-3.