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## Conference Proceedings Vol. I, II, III

 事業名 海事シミュレーションと船舶操縦に関する国際会議の開催 日本船舶海洋工学会
3.2.2. Rudder Inflow Angle

Contrary to rudder inflow velocity, rudder inflow angles are highly dependent on the type of vessel and rudder holding time.

The simulated rudder inflow angles of 158K COT are shown in Fig.5. We used a rudder holding time as a parameter.

Fig. 5 Rudder Holding Time & Rudder Inflow Angle Variation

With increase of rudder holding time, rudder inflow angle becomes large. The predicted torque with the simulated angle are shown in Table 3.

Table 3 Effect of Rudder Holding Time on Rudder Inflow Angle & Torque
 Rudder Holding Time (sec.) Rudder Inflow Angle (deg.) Calculated Torque (Ton-m) 5 3.6 256 10 4.9 291 15 6.0 330 20 6.7 357

We present the relation between rudder inflow angle and rudder holding time as 2nd polynomial and coefficient of polynomial according to the type of ship are shown in Table 4. The rudder inflow angle of container ship is less than the COT or Bulk carriers and this shows the influence of maneuverability to steering gear torque.

 Table 4 Coefficient of 2nd polynomial for Rudder Inflow Angle as a function of Rudder Holding Time
 a b C VLCC -0.0022 0.2726 1.2120 Cont. Vessel -0.0070 0.2815 -1.7419 COT/BC (< 90K) -0.0070 0.3106 1.9605 COT/BC (> 90K) -0.0051 0.3247 1.9858 LNGC -0.0097 0.4742 3.2900 RORO -0.0093 0.3852 0.4779

3.2.3. Investigation of the Results

Fig. 6 shows the comparison of predicted torque.

Fig. 6 shows the comparison of predicted torque.

'DWSTD' is predicted torque using the Jossel-Beufoy and safety factor and 'STavrCF' is measured torque at sea trial.

'Mo' is torque that is predicted from newly developed program based on Molland's method. In this prediction, rudder holding time is assumed to be 10 seconds.

In case of bulk carriers that hull number starts with H1 and LNGC/LNPC with H2, the new prediction method overestimates the torque. Contrary to this, the new prediction method predicts the torque more accurately than the method which uses safety factor in case of container ship that hull number starts with H4 and tanker with H5.

It seems that this difference between ship types is derived from the loading condition at sea trial.

Except for tanker, all the loading condition of other type of ships was ballast at sea trial. For correction to full load, we only considered draft and did not consider the change of maneuverability according to load condition.

Generally, the directional stability gets to be improved at ballast or stern trim. So at ballast, rudder inflow angle becomes smaller than at full load condition.

As rudder inflow angles of bulk carrier and LNG carrier are bigger than those of container, the change of steering gear torque according to the load condition is expected to be bigger at these types of ship.

The predicted torque is compared with that of the sea trials of AFRAMAX tanker series in Table 5.

Table 5 Comparison of Predicted Torque of AFRAMAX Tanker
 Method Torque(Ton-m) J-B(w/o Safety Factor) 103.0 J-B(w/ Safety Factor) 156.3 Molland(w/o Maneuver) 88.8 Molland(w/ Maneuver) Holding Time 15 sec. 205.2 Sea Trial(Minimum) 177.2 Sea Trial(Maximum) 236.3

Though the torque was measured at series ships, the measured torque varies from 177 Ton-M to 236 Ton-M. We could reproduce this variation by changing the rudder holding time at prediction and show in Table 6.

Table 6 Predicted Torque of AFRAMAX Tanker according to Rudder Holding Time
 Rudder Holding Time (sec.) Torque (Ton-m) 5 152 10 180 15 205 20 225

4. CONCLUSION
In the research, we converted steering gear torque from the measured oil pressure of steering gear cylinder and compared this with the standard prediction method using Jossel-Beaufoy method and safety factor.

The safety factor that has been used has some margin compared with the converted steering gear torque of sea trial.

But this comparison is inadequate, because the information about the environmental and ship conditions at sea trial has not recorded in detail.

We developed the new steering gear torque prediction method considering the rudder inflow and this program has the graphic interfaces of windows for the comfort of designers.

The difference of measured torque of same series ships can be partly explained by the difference of rudder holding time and we showed that the difference of maneuverability according to type of vessel can influence the steering gear torque.

However, for more practical application, further systematic measurements of the cylinder pressure during sea trials and continuous studies on this subject are requested in the future work.

REFERENCE
[1] A.F.Molland,"The Free-stream Characteristics of Ship-Skeg Rudders", Ph.D.Thesis, University of Southampton, 1981

[2] Glauert H.,"The Elements of Aerofoil and Airscrew Theory", Cambridge, 1948

[3] Abbott and von Doenhoff, "Theory of Wing Sections", Dover, 1959

[4] SNAME,"Principles of Naval Architecture", Vol.3, 1989

[5] J.Brix et al,"Manoeuvring Technical Manual", Seehafen Verlag, 1993

[6] J.N.Newman,"Marine Hydrodynamics", MIT, 1986

[7] D.I.Son, K.P.Rhee, Development of empirical formular for prediction of steering gear torque of tanker , the journal of SNAK(Korean), vol 37, may,2000

AUTHORS' BIOGRAPHY
S.W.Lee, research engineer at DSME. He graduated (M.sc.) from Seoul National University in 1997 and has since then been employed at DSME. He has mainly been involved in the area of he ship maneuvering and the submarine development.

Y.S.Hwang, senior research engineer at DSME. He graduated (M.sc.) from Seoul National University in 1996 and has since then been employed at DSME. He has mainly been involved in the area of the ship resistance and propulsion, propeller cavitation analysis.

M.C. Ryu, senior research engineer at DSME. He graduated (M.sc.) from Seoul National University in 1992 and has since then been employed at DSME. He has been mainly involved in the area of the ship resistance and propulsion, propeller cavitation analysis, and AUV development.

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