ON THE CORRELATION BETWEEN THE OVERSHOOT ANGLES IN ZIGZAG TESTS AND THE NAVIGATIONAL DIFFICULTY
Key-Pyo Rhee (Seoul National University, Rep. of Korea)
Sun Young Kim (KRISO, Rep. of Korea)
Young Jae Sung (Seoul National University, Rep. of Korea)
Nam Sun Son (KRISO, Rep. of Korea)
Abstract: Correlation between the overshoot angles of zigzag tests and the difficulty of navigation are investigated through auto-tracking simulation. Sea-trial data and detailed information of the forty recently built tanker ships were collected for this study. For the evaluation of navigational difficulty, rudder index and swept-path index from auto-tracking simulation were adopted. Comparing the calculated indices with the overshoot angles measured from manoeuvring sea trials, we can relate the overshoot angles with the navigational difficulty and review the IMO standards for yaw-checking and course-keeping ability.
Recognizing that the manoeuvrability of a ship is an important factor for the safety of navigation, International Maritime Organization (IMO) adopted the Interim Standards for Ship manoeuvrability (A.751 (18)). IMO also recommended Governments to collect data obtained by the application of the standards, and report them to the Organization . Based on the collected data, active discussions on the revision of the interim standards had been made  〜, and the Standards for Ship Manoeuvrability (resolution MSC.137 (76)) was finally decided at the seventy six meeting of IMO Maritime Safety Committee . One of the main issues in the discussions is how much overshoot angles in zigzag tests should be allowed concerning the safety of navigation. Korea and Japan actively proposed their suggestions on this issue , and our study was executed as a part of constituting Korean proposal on the revision of yaw-checking and course-keeping ability. We tried to approach the problem by answering the following questions;
1. What are the characteristics of normally operating ships?
2. How can we evaluate the navigational safety of the ships?
3. Is there any relationship between the evaluated difficulty and overshoot angles?
4. How much overshoot angles should be allowed?
From now on, our paper will proceed by answering these four questions and make some conclusions at the final section.
2. CHARACTERISTICS OF NORMALLY OPERATING SHIPS
2.1 Normally Operating Ships
In connection with the revision of IMO A.751 (18), Korea collected the detailed information on the manoeuvring sea-trial data of the seventy-five ships . They were recently built in the Korean shipyards, have been successfully delivered, and being normally operated without any trouble report on the manoeuvrability. Among this data, we selected the forty tankers (crude oil tanker, product oil carrier, and chemical tanker) whose hull forms are similar and sea-trials were executed at design draft. Table 1 shows the information of the selected ships. These ships can be categorized into four groups by their length L, as we can see from Fig. 1. We can also see that, for the smaller ships (group 1 and 2), the scatter in the length or size is the larger, however, the scatter of the large ships (group 3 and 4) are relatively small. Fig 2 shows the L/U values as ship length base. Because of the small differences in the sea-trial speed, L/U is almost proportional to L except a ship in group 3. This exception is due to the relatively low speed of the ship; averaged trial speed of group 3 is 14.9 knots, but this ship's speed is only 10.8 knots.
2.2 Manoeuvrability Indices at Design Stage
Although there are many ways to predict the manoeuvrability of a ship, numerical simulation and calculation of simple indices using the empirical formula is the most practical choice at design stage. Using the colleted information and empirical formula , we can calculate the following indices .
Table 1 Distribution of the principal dimensions of collected ships
||Crude Oil Tanker
||Product Oil Carrier
|Numbers of ships
||152.00 〜 322.00
||163.00 〜 235.00
||26.80 〜 58.30
||25.50 〜 42.40
|Draft at sea-trial [m]
||6.88 〜 22.42
||9.10 〜 14.80
|CB at sea-trial [
||0.797 〜 0.848
||0.793 〜 0.840
|Trim at sea-trial [m]
||-0.11 〜 0.80
||0.00 〜 0.26
|Propeller diameter [m]
||4.50 〜 9.70
||5.60 〜 7.70
|Propeller pitch ratio [ ]
||0.66 〜 0.81
||0.68 〜 0.77
|Rudder height [m]
||5.90 〜 15.70
||7.40 〜 11.40
|Rudder area [m2]
||26.91 〜 152.84
||31.00 〜 77.90
|Sea-trial speed [knots]
||10.80 〜 16.00
||13.00 〜 16.60
Fig. 1 Four groups of the collected ships by length.
Fig. 2 Distribution of L/U of the collected ships.
σ1 : Straight-line stability index
K : Rudder gain of K-T equation
T : Time constant of K-T equation
PKT : Turning ability index (〜K / 2T)
Fig. 3 shows the calculated indices for various bases.
Fig.3 Calculated indices using empirical formula.
(a) L/T vs. σ1
(b) Cwa vs. KT
(c) AR/LTvs. PKT
Correlation coefficients between the simple indices and hull form parameters
Table 2 summarizes the correlation coefficients between the indices and hull form parameters. σ1 is closely correlated with L/T and the real part of σ1 is positive, all the ship does not have straight-line stability. KT is known to be approximately proportional to the overshoot angles, and it is closely related to the aft-hull water-plane area coefficient, Cwa. Norrbin's PKT approximately shows the course change angle per rudder angle at one ship length travel after rudder execution and it was closely related to rudder area ratio.