Beitrag Benedict

Development of ARROW software for decision support to avoid roll resonance and wave impact for ship operation in heavy seas

Prof. Dr.-Eng. Knud Benedict, Dr.-Eng. Michael Baldauf, Dipl.-Eng. Matthias Kirchhoff
Hochschule Wismar - University of Technology, Business and Design; Department of Maritime Studies

  1. Introduction and aim of this paper
  2. Summary of effects and formulas - description of the method
  3. ARROW - software program description
    1. Overview and parameter input
    2. Result display area and measures to avoid problems due to wave effects
  4. Examples for several situations analysed by ARROW
    1. Example from Guideline SeeBG 2004
    2. Example Analysis of an accident case for container ship
  5. References

1. Introduction and aim of this paper

Over the last years several vessels have experienced the dangerous effects of rolling resonance e.g. [1]. Moreover, there can be additional dangers by reduction of intact stability caused by riding on the wave crest on successive high wave attacks or dangers of surf-riding and broaching in following seas.

1. Synchronous rolling motionAll directions possibleNatural rolling period of a ship coincides with the encounter wave period.Heavy oscillations with high amplitude
2. Parametric rolling motionSpecifically for head and stern wave conditionsWave encounter period is approximately equal to half of the natural roll period of the shipHeavy oscillations with high amplitude
3. Reduction of stability riding on the wave crests of high wave groupsFollowing and quartering seasWave length larger than 0.8 x Lpp and significant wave height is larger than 0.04 x LppLarge roll angle and capsizing
4. Surf-riding and broaching-toFollowing and quartering seasThe critical wave speed is consider ed to be about 1.8 √ ~ 3.0 √ Lpp with respect to ships' lengthCourse deviation and capsizing

Table 1: Overview on dangerous phenomena in high sea state, occurrence and effects

The IMO 1995 has published guidelines to the master for avoiding dangerous situations [2][3]. In 2003 a draft of a new German guideline for stability on board ships was published [6] and some of its aspects were given to the IMO where a review of the IMO guideline is currently taking place [4].
Summarizing these methods, the current methods are lacking a simplified, user friendly approach for the calculation of the effects, necessary for education and training, for use on board. Therefore an overall approach for presentation of all effects in one diagram related to the actual ship and wave conditions was developed to support the ship's crew in order to give effective guidance for the operation of ships: Simplified calculation methods were given to even manually calculate a polar diagram presentation (e.g. on RADAR Plotting Sheets), presented first time in a meeting of German Seafaring Lecturers in 1998 and fully described in [7].
This paper introduces briefly this method to effectively find out and display the potentially dangerous situations. The software program ARROW will be described as a tool to estimate and display the potential dangerous conditions of rolling resonances or high wave impacts on ships due to complex wave encounter situations.

2. Summary of effects and formulas - description of the method

The method presented here briefly allows for calculating and plotting a polar diagram for ship operation in a very simplified way as indicated in Figure 1 and with formulas given in Table 2. In comparison to [3] and [6] where the information is given in a dimensionless format related to one standard wave direction and on numerous diagrams the information is given here now related to the current values of ships speed, wave period and direction.
Using a Radar Plotting sheet (with speed values at the axis instead of distances) the only task is to draw a line in the direction of the wave propagation and to calculate the encounter speed values V (indicated by small circles and numbered according to the numbers of the formulas in Table 2) on courses with direct head sea (V positive) or following sea (V negative).The Table 2 summarizes the effects and formulas for calculating the circles with the respective numbers of the formula in the table.

Figure 1: Resulting Polar diagram with dangerous course and speed vectors calculated with the respective formulas from Table 2 indicated by coloured circles. (Example-Ship: Lpp=113m, B = 17.6m; rolling coefficient Cr = 0.74; i.e. Tr=Tr(10°)= 10s; Sea from 23° with Tw= 8 s in Wind sea (k=1.04)

PhenomenaDirection/Sector/AreaEquations to Calculate the speed values as basis for the Diagram Elements
1. Synchronous rolling motionStripe segments over diagram; All directions possible1. for TE=Tr/0.8:

2. for TE=Tr/1.1:

2. Parametric rolling motionSegment for direct head and stern wave conditions ±30°3. for TE=Tr/1.8:

4. for TE=Tr/2.1:

3. Reduction of stability riding on the wave crest of wave groupsSegment for direct Following and quartering seas ±45°5.


4. Surf-riding and broaching-toSegment for direct following and quatering seas ±45°7.

(marginale Zone)


Table 2. Summary of effects and formulas for calculation of basic polar diagram values

The results will be used to draw specific shapes of areas with potential danger in a Polar Diagram taking the speed values (in the circles) as a basis for drawing lines orthogonal to the sea direction as margins for the diagram elements:
A synchronous resonance area will be drawn as a red stripe over the whole angle area of the polar diagram, orthogonal to the sea direction It represents conditions in the range 0.8 = Tr/TE = 1.1 where still up to about 50% higher amplitudes occur.
The parametric excitation will be drawn in the same way but only for a red sector segment of ±30° around the direction of stern sea or against the sea respectively.
Additionally the areas for surf-riding (green) and encounter of wave groups (blue) in zones of ±45° around stern sea directions will be drawn.
By means of the polar diagram an assessment of situation or estimation of countermeasures can easily be done to find out suitable values of the ships' speed and course or measures to change stability and likewise the ships roll time period T to avoid resonance.
In more complex situations with more than one wave systems and significant differences of rolling periods Tr for small and large roll amplitudes it is more convenient for the ships officer in charge to use the following computer program ARROW.

3. ARROW - software program description

3.1. Overview and parameter input

The ARROW program (Figure 2) is a software tool to estimate and display the potential dangerous conditions and countermeasures to Avoid Rolling Resonances Or Wave impacts on ships due to complex wave encounter situations [8]. Only a small amount of data is needed to be entered into the areas of the Ship Parameter Input (top left side) and Wave Parameter Input (lower left side) to provide the results in the Result Display Area (right hand side):

Figure 2: ARROW program - overview on main user interface elements

Ships course and speed can be entered in the respective data fields. The heading direction of the ships contour and speed vector in the Result Display is immediately displayed according to changes in the data fields.
Natural Roll periods of the ship can be either calculated (a) by using stability data or alternatively (b) by entering observed roll periods directly:
(a) Using Stability Data Input the data can be entered into the respective input fields of Stability Data Window (left).
(b) Using alternatively the direct input of natural roll period from observations - for this purpose a checkbox is available to change between "calculated" and "observed" roll periods.


Figure 3: Stability Data Window - Graph of up righting lever versus roll angle Phi and GM tangent (left) and Graph of Inertia coefficient Cr and respective Cr value due to draft input (right)

For Wave Parameter Input the ARROW program accepts the input of two different wave systems. Only a few wave input parameters, taken either from observations on the ship or from weather reports and forecasts, have to be entered in the respective fields.
If two wave systems are activated, the transmission direction and wave height of the interference wave is calculated. The interference height is displayed numerically; the transmission direction of the interference wave is drawn as a magenta arrow outside of the polar diagram in the ARROW - Results Display Area (see Figure 4). If the interference wave is of no interest the display of this data can be disabled using the Field 'Hide Interference Data' in the Menu 'Display Options'.
Interference waves have to be additionally taken into account for planning counter measures to reduce the critical ship's motion caused by the sea.

Figure 4: ARROW - two wave systems and interference wave vector

3.2. Result display area and measures to avoid problems due to wave effects

The polar diagram provides the critical course and speed ranges resulting in resonance areas by stripes and sectors and other aspects of high wave impact according to IMO guidelines. All types of resonance and wave impacts are drawn with different colours and shapes to distinguish between them. Even for large amplitude rolling periods the potential resonance conditions can be shown in brown colour next to the red areas for small rolling amplitudes displayed in parallel. Beneath the polar diagram a legend is drawn to clarify the relation of the different colours and shapes with respect to the different types of resonance and wave impacts. If the point of the ships' arrow (ships speed vector) is within one (or even more) of the dangerous areas the ships conditions are potentially unsafe. In this case the ships speed and course have to be changed to bring the arrow top out of those areas. Alternatively the ships rolling period could be varied by changing the stability parameters (GM or GZ_values) in order to avoid resonances. All of these countermeasures can be checked by trial variations using the ARROW program modules which will be supported by examples given in the very comfortable HELP system of ARROW Program.
The ARROW tool can be effectively used to check for countermeasures, e.g. by using a change of ships stability and therefore natural rolling period Tr to avoid resonance on a voyage segment with given course and speed. An example will be given on how the conditions for direct synchronous resonance in Figure 5 can be avoided by changing the ships natural rolling period. One can clearly see that the ship at course 149 and speed 18 kn is in the middle of the red stripe i.e. in direct synchronous resonance: The encounter period is 16 s that means the same value as the ships natural period Tr(10°) = 16 s. In case the ship has to maintain her course and speed there could be an option to change the ships' natural period in order to avoid resonance (if this is possible from the ships' stability and loading/tank capabilities).

Figure 5: ARROW detected conditions for direct synchronous resonance

In Figure 6 it was found by trial and error methods how to change the roll period so as to be with the ships speed vectors tip (set on course 149° and speed 18 kn) outside or at least at the edge of the resonance stripe. There are two options to reach this goal:

  • either by a new roll period of Tr(10°) = 12.5 s (related to an GM=4.3m)
  • or by a new roll period of Tr(10°) = 17.8 s (related to an GM=2.12m) respectively.
  • The user on board will know best which condition he can achieve with his ship.


Figure 6: Two options to avoid resonance, either by an roll period of Tr(10°) = 12.5 s (left) or by Tr(10°) = 17.8s (right)

For those ships having natural periods which are changing very much with the rolling amplitudes the areas of critical conditions will become larger: the larger the difference between the two parameters for natural rolling periods Tr(10°) and Tr(40°), the wider the areas of resonances will be.
This can be demonstrated by an example for two different sets of natural rolling periods in Figure 7.


Figure 7: Example for two different sets of natural rolling periods

Within the very comfortable HELP system of ARROW Program even video sequences give more insight into the functionality of the ARROW program Figure 8.
One video demonstrates the changes of results in the stripes for synchronous resonance and the sectors for parametric resonance when the natural rolling period Tr of the ship changes. Here the period changes in a range of 10s to 50s in steps of 0.2s.


Figure 8: ARROW demonstration videos presenting results due to changes in ships rolling period (left: pictures from start T(10°)= 10s and right: end situation at T(10°)= 50s)

Another video demonstrates the changes in the results of synchronous and parametric resonance as well as the changes in the encounter with high wave groups. This time the wave period changes from 15s to 5s in steps of 0.1s whereas the ships rolling period remains constant Tr(10°)=10s.


Figure 9: ARROW demonstration videos presenting results due to changes in wave period (pictures: left from start at Tw = 15s and right Tw = 5s at the end situation)

The blue line at the broader end of the area for encounter with high wave groups represents the speed value of the waves. If the ship runs faster than this wave speed another chances for resonance are given when the ship is overtaking the waves: this is indicated by the respective stripes and segments for resonance beyond that speed.

3.3. ARROW-versions for use in training in institutes and on board

There are two version of the ARROW software in existence. One is for Education and lecturing of Wave Effects at Seafaring Training Institutions. For this reason several different vessels and encounter situations can be prepared and loaded for demonstrations according to the specific training needs. An encounter situation consist of ship information on speed, course and own rolling period and of wave information (direction, period, height) of two wave systems. Figure 10 show the procedure of loading an encounter situation from a list of several different situations e.g. the samples from the guideline [6].


Figure 10: Procedure to selection of different stored encounter situations for education

After selecting a situation the data will be loaded and displayed; additionally a previously stored comment will be shown explaining the encounter situation.
The submenu "Max Speed Range" allows the selection of a maximum speed range for the ARROW - Result Display Area to adjust the scaling to the different speed of several ship types. The user can choose from values between 5 and 50 kn.
The version of ARROW for on-board use is specifically designed and database adjusted to quickly calculate and display all wave effects for that one specific vessel.

4. Examples for several situations analysed by ARROW

4.1. Example from Guideline SeeBG 2004 [6]

In order to demonstrate the advantages using the ARROW software and to show the coincidence with the Guidelines of the SeeBG the examples used in that guideline will be taken to compare the results and the different modes of display.

In the guideline some sheets are given as examples: to avoid calculations in polar diagrams it is practical to plot each possible roll period of the ship in full seconds on a separate sheet. Such sheets are illustrated as an example for the roll periods of 15 and 20 seconds in Figure 11. The heading scale in the polar diagrams is related to the direction of the seaway. Ship's speeds are plotted as vectors which have their origin in the centre of the diagram and the direction of which is related to the direction of the seaway. The length of the vector corresponds to the speed in kn. All speeds which can lead to resonance are plotted as vectors the tips of which lie on straight lines running transversely to the direction of the waves.
A ship of about 120 m in length is chosen as an example to compose the diagrams. The red (continuous) lines apply to the period ratio 1 (TE equal to Tr=TR). For wave periods of 8 seconds and more these lines run transversely over the entire diagram, because they apply both to parametric excitation in longitudinal seas and to the excitation in transverse or quartering seas. For shorter wave periods, the range of ±30° from longitudinal seas can be omitted, because the energy transmitted by the wave slope is too small for such encounter angles and, additionally, the wave length is not yet adequate for parametric excitation.
The orange (dotted) lines apply to the period ratio 0.5 when TE is equal to 0.5*TR. These lines are plotted only for encounter angles in the range ±30° from longitudinal seas. In this case too, only wave periods of 8 seconds and more have been considered on account of the wave length necessary for parametric excitation.
The resonance diagrams must be prepared individually for each ship, based on the ship's length and speed range. Sheets should be prepared for Tr=TR in steps of whole seconds, at least for values that correspond to 0.5*B to 2*B (B = ship's breadth in m). Each sheet must be identified with the valid roll period.


Figure 11: Polar Diagram from Guideline SeeBG 2004 for two roll periods Tr=TR =15 (left) and 20s (right) of a ship with speed arrows for the examples No. 2 and 3

The following text is given in the guideline to describe Example No. 2:
"The ship has a roll period TR of 15 seconds and, with a speed of 15.0 kn, follows a true course of 25°. The waves come from the direction 165° true with a wave period TW = 8 seconds.
For using the diagram, the course relative to the direction of the waves has to be calculated which is (360° + 25°) - 165° = 220°. The speed vector in the diagram (Fig. 2.8) is plotted towards 220° with a length corresponding to 15.0 kn. The tip of the vector lies more or less on the red (continuous) line for an 8 second wave period. However, it can be seen that the lines for 6, 7 and 9 seconds also lie in the vicinity. Therefore again and again severe resonance-like roll motions will occur.
An alteration of course is planned to improve the situation. A course change of 15° to starboard does move the tip of the vector away from the lines around the 8 seconds wave period, but can still generate a resonance-like roll with the wave components of 11 to 12 seconds wave period contained in the wave spectrum.
A course change of 15° to port leads into a range in which there are no further components in the entire wave spectrum which could lead to an encounter period of 15 seconds. It is known that the ship's motions in a seaway can be reduced very effectively in this way if, for example, brief inspections on deck or in the hold need to be performed. Therefore, the course change to port side is preferable if there are no navigational reasons against it.
However, with this course change to port side, the waves now come more from aft. This is no problem in the given example, because the breadth of the ship is 20 m and so the roll period of 15 seconds yields a GM of approximately 1.14 m. This means adequate stability".

In Figure 12 the same situation is shown from the ARROW program: it is of great advantage that all of the data are related to the actual course like on a navigational display. As additional information is given that there is a potential of high wave group encounter even if it is marginal only. In parallel it is to be seen from the brown colored area that for large roll angles there is a danger of resonance if the ship is turning to port; therefore a course change to starboard seems to be more efficient eventually.

Figure 12: ARROW presentation of results according to example No. 2 from Guideline SeeBG 2004

The following text is given in the guideline to describe another Example No. 3:
"The ship has a roll period TR of 20 seconds. The corresponding resonance sheet Figure 11 right indicates that all the wave periods that can lead to periods of encounter of 20 seconds give a narrow band of critical speed vectors for running in following seas or quartering seas.
If the tip of the speed vector is in this band, particularly strong resonance phenomena must be expected, because not only the significant wave period but also the neighbouring periods in the wave spectrum lead to periods of encounter of 20 seconds.
The ship then also sails at the group speed of the significant wave, which can mean that it remains in a group of particularly high waves for a long time.
If the ship now runs in exactly following seas at a speed of 17 kn, for example, no resonance phenomena are to be expected. However, if, on account of increasing wave heights, the speed is reduced to 14 kn, for example, strong parametric excitation will occur. Moderate motions may only be expected after a further reduction below 11 kn.
The right measure in this situation has to be chosen depending on the wave period actually encountered. With wave periods of more than 8 seconds, maintaining the speed at 17 kn may lead to surfing. These periods also belong to longer waves, in which the average effective stability may be reduced, which in turn lead to longer periods of roll.
Therefore, the resonance sheets for longer roll periods should also be considered. This will show that reducing the speed to below 11 kn is absolutely preferable to maintaining a high speed".

In Figure 13 the same situation No 3 is shown by the ARROW program result display: also here for this example it is of great advantage that all of the data are given together on one display. It is clearly to be seen that a speed below 17 kn lead to synchronous resonance (and not to parametric as mentioned above); parametric resonance will occur for a speed of less than 7 kn.

Figure 13: ARROW presentation of results according to example No. 3 from Guideline SeeBG 2004

4.2. Example Analysis of an accident case for container ship

Over the last years several vessels have experienced the dangerous effects of rolling resonance. One result of these harmful encounters is shown in Figure 14 below, left hand side. According to an article in SNAME [1]] these damages were caused by a heavy storm on 26th of October 1998. The so called C11 vessels are the second generation of Post-Panmax containerships which have overall dimensions of LBP 262 m, B 40 m, D 24.45 m with a maximum summer draft of 14 m. At the time of the events the vessel's mean draft was 12.34 m, making the freeboard slightly more than 12 m. In the pre casualty condition, the vessel's GM was approximately 2 m giving a natural roll period of 25.7 sec.


Figure 14: Representative Container Damages

The ship was in the north Pacific, steering into severe short-crested seas from forward of the beam to head seas that, according to her officers and crew, had experienced heavy roll angles up to 35 deg to 40 deg rolls coupled with large pitch angles.
The wind speed at the vessel's positions ranged up to 29.5 m/s (57 kt) at the time of the most severe motions. Significant wave heights steadily increased to 13.4 m and a wave period of 15.4 s at the time of the most severe motions was measured.
The master had tried to keep the vessel's head into the waves and that the relative direction of waves during the period of most severe motions varied between about 45 deg off the starboard bow to dead ahead and even off the port bow.
The analysis for these ship and wave conditions shows that the ship was in the area of parametric rolling conditions as to be seen in Figure 15 indicated by the ships speed vector which is within the red segment for these course sectors.

Figure 15: Container vessel in parametric resonance condition: C11-PANMAX ship: LBP 262 m, B 40 m, D 24.45 m, mean draft was 12.34 m (Example from ARROW - Program)

5. References

[1]France & William a.o. 2001. An Investigation of Head-Sea Parametric Rolling and its Influence on Container Lashing Systems. SNAME, Annual Meeting 2001.
[2]IMO 1993. Code on Intact stability for all types of ships, Resolution. A.749 (18) Nov 1993
[3]IMO 1995. Guidance to the master for avoiding dangerous situations in following and quartering seas, MSC circular 707, adopted on 19. October 1995.
[4]IMO 2005. Paper: REVISION OF THE CODE ON INTACT STABILITY, Proposed revision of MSC/Circ.707: SLF 48/4/8, 10 June 2005 (Submitted by Germany)
[5]Ammersdorffer, R. 1998. Parametric exited Rolling Motion in bow and head seas (in German: Parametrisch erregte Rollbewegungen in längslaufendem Seegang). Schiff & Hafen Heft 10-12, 1998.
[6]BMVBS / See-BG 2004 German Ministry of Transport: Guidance for Monitoring Ship's Stability. Verkehrsblatt-Document Nr. B 8011; Release 2004
[7]Benedict, K., Baldauf, M, Kirchhoff, M. 2004. Estimating Potential Danger of Roll Resonance for Ship Operation. Schiffahrtskolleg 2004, Proceedings Vol. 5, p. 67-93, Rostock 2004