Practical assessment of manoeuvrability in adverse conditions

Ocean Engineering 203 (2020) 107113

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Practical assessment of manoeuvrability in adverse conditions Vladimir Shigunov DNVGL SE, Hamburg, Germany

A R T I C L E I N F O

A B S T R A C T

Keywords: Manoeuvrability in adverse conditions Criteria Standards Regulations

The introduction of EEDI raised the need for norming (standardising) of ship’s manoeuvrability under adverse conditions. Besides the necessary criteria, measures and standards, developed in several research projects and described elsewhere, also procedures and methods for the practical evaluation of the proposed criteria in design and regulatory approval are required, which are addressed in this paper. The idea is to develop a flexible assessment framework, ranging from advanced assessment procedures, necessary in cases with large un­ certainties and near the acceptance boundary, to simple procedures, which are sufficient for the majority of conventional vessels. The paper outlines the background of three levels of assessment procedures and describes in detail possible approaches towards level 2 and level 1 assessment procedures for propulsion and steering criteria. The proposed assessment procedures require definition of multiple input components: time-average wave-induced forces and moments, wind forces, calm-water reactions, rudder-induced forces and propeller characteristics. The paper discusses the availability of different methods (experimental, numerical or empirical) for these components and, besides, proposes and validates several simple empirical formulae developed spe­ cifically for the simplified assessment to further reduce its complexity.

1. Introduction The following terminology is used in the paper: the term criterion refers to a characteristic of the ship, such as ability to turn, keep course etc., by which ship’s abilities, relevant for the considered problem, are judged. A corresponding measure, e.g. turning diameter or overshoot angle, quantifies the ship’s performance with respect to the considered criterion. For manoeuvrability in adverse conditions, a convenient and popular measure is the marginal (maximum) severity of seaway (i.e. maximum wave height and corresponding wind speed) up to which the ship can fulfil the criterion. The term standard (sometimes called norm) refers to the acceptance limit of this measure to qualify the ship as ful­ filling the corresponding criterion (here, the standard is the specified significant wave height and the related wind force). Manoeuvrability of ships is presently specified by the rules of clas­ sification societies, ship owner requirements and non-mandatory but gaining increasing acceptance by administrations and classification so­ cieties IMO Standards for Ship Manoeuvrability, IMO (2002). The latter address turning, initial turning, yaw checking, course keeping and emergence stopping abilities, which are evaluated in simple standard manoeuvres in calm water. These Standards have been criticized for not addressing ship manoeuvring characteristics at limited speed, in restricted areas and in

adverse weather conditions, see e.g. Quadvlieg and van Coevorden (2008). The importance of the latter aspect increased after the intro­ duction of the Energy Efficiency Design Index (EEDI), which raised concerns, see e.g. IMO (2010), that some ship designers will achieve EEDI requirements by simple reducing the installed power, which may lead to insufficient manoeuvrability in heavy weather, see discussion in Shigunov (2018). To solve this problem, rational criteria, measures and standards are required which concern propulsion and steering abilities of ships in adverse conditions. These issues are summarised below and addressed in detail elsewhere, see IMO (2012a,b), Shigunov and Papanikolaou (2015) and Shigunov (2017,2018); the aim of this paper is to discuss assessment procedures that can be used for the evaluation of the pro­ posed criteria in practical design and approval. Work by IACS on minimum power requirements for manoeuvrability in adverse weather conditions led to the development of two criteria: a course-keeping criterion, which requires that the ship should be able to keep course in waves and wind from any direction, and a propulsion cri­ terion, which requires that the ship should be able to keep advance speed of at least 4.0 knots in waves and wind from any direction, IMO (2012a-c). For practical evaluation of these criteria, IACS proposed three assessment levels: the most accurate, comprehensive assessment (level 3), allows the best accuracy by solving three nonlinear motion equations to

E-mail address: [email protected]. https://doi.org/10.1016/j.oceaneng.2020.107113 Received 31 December 2017; Received in revised form 9 February 2020; Accepted 10 February 2020 Available online 25 March 2020 0029-8018/© 2020 Published by Elsevier Ltd.

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evaluate separately propulsion and steering criteria. The simplified assessment (level 2) still considers the physics of the problem but uses a reduced number of assessment scenarios and reduced complexity of equations. The idea of the simplified steering ability assessment in IMO (2012a-c) was to replace the steering ability assessment in seaway from any direction by propulsion assessment in head seaway at a specifically defined forward speed, which replaces model tests or numerical simu­ lations in waves and wind from all directions with simpler tests or simulations in head waves only. To achieve this simplification, the required ship speed in the propulsion assessment, Vck, was defined in such a way that the fulfilment of propulsion requirement in head seaway at this speed automatically fulfils the course-keeping requirement in any seaway direction; the definition of Vck as a function of the rudder area and ship windage areas was derived empirically, using results of comprehensive assessment for several ships. A comparison of the marginal significant wave heights obtained directly from the evaluation of the steering ability criterion with the marginal significant wave heights obtained from the evaluation of the propulsion ability criterion at the maximum of two forward speeds, Vs ¼ max(4 knots,Vck) in Fig. 1 shows a good correlation, but also that the formula for Vck is in general not conservative. Level 1, the simplest assessment procedure in IMO (2012a-c), is an empirical formula defining the required installed power as a function of deadweight (minimum power line, MPL). The follow-up discussion at IMO led to a revision of level 1, removal of comprehensive assessment (due to the absence of methods for the components required in this assessment) and relaxing of standards (wave heights) in the simplified assessment and resulted in the 2013 Interim guidelines for determining minimum propulsion power to maintain the manoeuvrability of ship in adverse conditions, IMO (2013), updated in IMO (2014,2015). Thus, the presently acting guidelines include level 1 assessment (MPL) and simplified propulsion assessment, which imple­ ments both the propulsion ability and steering ability criteria (the latter indirectly through Vck speed). The project SHOPERA conducted a review of existing regulations, interviews of ship masters and detailed accident investigations in Shi­ gunov (2017), as well as accident statistics in Ventikos et al. (2015) to identify relevant scenarios, criteria and corresponding standards. This led to the identification of three scenarios (open sea, coastal areas and restricted areas at limited speed), each of which requires specific criteria, Shigunov and Papanikolaou (2015). For the open-sea scenario, the weather-vaning ability criterion was proposed: the ship should be able to keep heading in head to bow-quartering seaway up to 60� off-bow. A similar heading recovery criterion was pro­ posed in IMO (2016b), where it means the ability of the ship to turn from beam into head seaway. The formulation in IMO (2016b) is much more

difficult to evaluate in practice, since it requires model tests (or nu­ merical simulations) of transient manoeuvres in irregular waves and wind. Note also that weather-vaning in bow seaways is rather a pro­ pulsion than steering problem: inability to complete a turn in bow seaway is always related to insufficient propulsion ability, unlike steering in beam or stern-quartering seaways; IMO (2016b) confirms this since the results weakly depend on manoeuvring characteristics of the hull and rudder. For manoeuvring in coastal waters, the following two criteria were proposed in Shigunov and Papanikolaou (2015): steering ability (ship’s ability to perform any manoeuvre in seaway from any direction), and propulsion ability (ship’s ability to maintain a specified speed in seaway from any direction); the required speed in the propulsion criterion was increased compared to IMO (2013,2014,2015) from 4 knots to 6 knots, to consider possible strong currents in coastal areas. Because the ability to perform any manoeuvre is impossible to evaluate in practice, an equivalent but easier to evaluate steering ability criterion was formu­ lated as the ship should be able to overcome environmental forces to start or continue course change in seaway from any direction. The third scenario, manoeuvring at limited speed in restricted areas, concerning situations where the forward speed (and thus the applied engine power) must be reduced significantly below attainable due to navigational restrictions, e.g. during approaching to or entering ports, navigation in channels and rivers etc., led in Shigunov and Papanikolaou (2015) to the following criteria: course-keeping at a specified low speed in strong wind in shallow water, in shallow water near a bank and in shallow water during overtaking by a quicker ship. In Shigunov (2016,2018) it was shown that ships satisfying the propulsion and steering criteria in coastal waters satisfy the weather-vaning requirements in the open sea with a sufficiently high probability, thus the assessment for the open-sea scenario is unnec­ essary. Note also that in the third scenario the full available power cannot be applied, therefore, this scenario is not affected by the EEDI requirements and is not considered here. Therefore, SHOPERA proposed in IMO (2016a) the steering ability and propulsion ability criteria for coastal waters as a basis for the minimum requirements for manoeu­ vrability in adverse conditions, related to the installed power; see Shi­ gunov (2018) for a detailed discussion of scenarios, criteria and corresponding environmental conditions. In this paper, the aspects of the practical evaluation of the proposed criteria are addressed. For the practical evaluation of the proposed criteria, SHOPERA proposed level 1, 2 and 3 assessment procedures (each separately for the propulsion ability and steering ability criteria); besides, the project spent significant efforts to develop methods for the definition of the components required for the comprehensive and simplified assessments, see IMO (2016a) for overview and below for more details. In the proposal for revised guidelines concerning bulk carriers and tankers IMO (2017a,b), jointly prepared by SHOPERA and the JASNAOE-coordinated research project in Japan, MPL from IMO (2013, 2014,2015) are adopted as level 1, the propulsion ability criterion is evaluated using the simplified assessment procedure, and the steering ability criterion is dropped, thus the proposal in IMO (2017a) contains simplified assessment (level 2) for the propulsion criterion and MPL (level 1). 2. Comprehensive assessment Compliance with the Standards IMO (2002) is demonstrated in full-scale trials, which is impossible for the assessment of manoeu­ vrability in adverse weather conditions. Direct evaluation of the pro­ posed criteria in transient model experiments with self-propelled ship models in simulated irregular waves and wind, for all required combi­ nations of wave directions and periods, is unfeasible for several reasons: First, interpretation of transient manoeuvres in seaway as safe or unsafe is not always possible, especially in marginal cases (i.e. cases near the failure boundary, which are of interest in approval). Second, results of

Fig. 1. Marginal significant wave height from steering ability requirement (y axis) and propulsion ability requirement at forward speed Vs, IMO (2013), (x axis) for bulk carriers (empty symbols) and tankers (filled symbols) of various sizes. 2

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such tests strongly depend on the time history of steering, which causes too large variability and uncertainty of test results, i.e. such tests cannot be reliably verified. Third, reliable statistical predictions in irregular seaway require repetition of tests in multiple long realisations of each seaway, which is too expensive. Fourth, very few facilities exist world­ wide able to perform such tests, which makes such tests impractical for routine design and approval. Finally, verification of such tests by regu­ lators is impossible unless the test program is repeated, which makes this approach impractical. Alternative to such model tests, direct numerical simulations of transient manoeuvres in irregular seaway, is not mature enough pres­ ently for routine use in design and regulatory approval, see Shigunov et al. (2018). A practical assessment approach in Shigunov (2017), referred to as the comprehensive assessment, is based on separate evaluation of different contributions (forces due to waves, wind, propeller, rudder etc.) from simple model tests, numerical calculations or empirical formulae and a combination of these contributions in a simple mathematical model. The details of this procedure and a discussion of the assumptions used can be found in Shigunov (2017); here, details related to its practical use are discussed. The solution method is based on neglecting oscillatory forces and moments due to waves, since the time scale of such oscillations is shorter than the time scale of manoeuvres, and thus considering only average in time forces, moments and other variables (propeller thrust, torque and rotation speed, required and available power, drift angle and rudder angle). Note that oscillatory motions in waves may influence time-average characteristics, e.g. oscillatory pitch and heave can lead to propeller ventilation and thus influence time-average characteristics of the engine and propeller (which is, however, not relevant in the envi­ ronmental conditions concerned here); see Shigunov (2017) for a detailed discussion. Neglecting oscillatory forces and moments due to waves reduces the evaluation of manoeuvrability criteria to a solution of coupled motion equations in the horizontal plane under the action of time-average waveinduced (index d) forces and moments, wind forces and moments (w), calm-water reactions (s), rudder forces (R) and propeller thrust (T). Projecting forces on the x- and y-axes and moments on the z-axis of the ship-fixed coordinate system, Fig. 2, leads to a system of motion equa­ tions, which converges to a steady state described by the following system (note that a converged solution can be achieved in various ways, including time-domain simulations): Xs þ Xw þ Xd þ XR þ Tð1

tÞ ¼ 0

(1)

Ys þ Yw þ Yd þ YR ¼ 0

(2)

Ns þ Nw þ Nd

(3)

YR lR ¼ 0

water plane; x-, y- and z-axes point towards bow, starboard and down­ ward, respectively (positive rotations and moments with respect to zaxis are clockwise when seen from above). The ship speed is vs, its heading deviates from the course by the drift angle β (positive clockwise when seen from above). The main wave and wind directions are described by angles βe and βw, respectively; rudder angle δ is positive to port. The lever lR in the yaw moment due to rudder YR lR in eq. (3) in general differs from Lpp/2 because of pressure redistribution on the ship stern due to rudder influence. Note that eq. (1) uses longitudinal projections (i.e. projections on the x-axis of the ship-bound coordinate system) of the forces on the ship hull, since they are required to define the thrust. These projections are frequently called resistance (or added resistance), erroneously or for brevity, although resistance is the time-average force in the opposite direction to the time-average ship speed, which is equal (in the absolute value) to the longitudinal force only in cases with zero mean lateral drift. A converged solution described by the system (1)–(3) contains the required propeller thrust T, drift angle of the ship β and the rudder angle δ. From the required propeller thrust, the propeller advance ratio J and the rotation speed nP of the propeller are found using thrust identity, see section 5.6. The assessment is based on the comparison of the required delivered power PD with the available delivered power Pav D , both of which are defined at the actual rotation speed of the propeller, using open-water propeller characteristics for the former, see section 5.6, and engine characteristics for the latter, see Fig. 4 and the corresponding description in the text. It is convenient to plot the converged solutions in polar coordinates ship speed (radial coordinate) – mean seaway direction (circumferential coordinate) for a given sea state (i.e. significant wave height hs and mean zero-upcrossing wave period Tz), see examples in Fig. 3. Line A, along which PD =Pav D ¼ 1, shows the maximum attainable speed (for the given propulsion system and given sea state) vs. the mean seaway direction. It has a smaller radius in bow seaways than in following and sternquartering seaways, because added resistance in bow seaways is significantly greater than in following and stern-quartering, and reduces in radius with increasing seaway severity and, for a given sea state, with reduced installed power. The line of the maximum available steering effort C limits the area within which the required steering effort exceeds the available one, e.g. along this line the required rudder angle achieves possible maximum. This line shows the minimum speed at which steering is possible (for a given steering system and given sea state) vs. mean seaway direction; it is usually located between following and beam seaway directions and increases in radius with increasing wave height or reducing wave period and, for a given sea state, with reducing rudder area or increasing lateral windage area. For illustration, lines A and C are shown for examples discussed below (solid lines) and for 1 m lower and 1 m greater significant wave height (dashed and dash-dot lines, respectively); arrows indicate increasing wave height for each group of three lines. Finally, along line B, the ship speed is equal to the required advance speed in the propulsion criterion (here 6.0 knots). To satisfy the propulsion ability criterion, the maximum of the ratio PD =Pav D along the line B (vs ¼ 6 knots) should not exceed 1.0 (in other words, lines A and B should not cross). To satisfy the steering ability criterion, the maximum of the ratio PD =Pav D along the line C (i.e. line of maximum available steering effort) should not exceed 1.0 (i.e. line A should not cross line C). Thus, the area between lines A and C corre­ sponds to combinations of ship speed and wave directions for which steering is possible, whereas crossing of these lines means that steering is impossible for some wave directions. The left plot shows an example of a seaway in which the vessel fulfils both criteria (line A does not cross lines B and C); in the middle plot, the installed power is marginally sufficient to fulfil the propulsion ability criterion (it provides the maximum advance speed of 6.0 knots in head

The coordinate system has an origin O in the main section at the

Fig. 2. Coordinate system and definitions. 3

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Ocean Engineering 203 (2020) 107113

Fig. 3. Examples of results of comprehensive assessment in polar coordinates ship speed – seaway direction (radial and circumferential coordinates, respectively): lines A, B and C correspond to maximum available power, 6.0 knots ship speed and maximum available steering effort, respectively.

turbocharged marine diesel engine is shown in Fig. 4. The horizontal axis corresponds to the rotation speed as percentage of rotation speed at the maximum continuous rating (MCR), and the vertical axis shows shaft power as percentage of MCR (note logarithmic scales used for both axes). Line 1 corresponds to the maximum rotation speed (shown at 105% of the nominal rotation speed, MAN, 2014); the minimum rotation speed limit, or idle limit, corresponding to 25%–30% of the nominal rotation speed, is not shown. Curve 2, light propeller curve, corresponds to resis­ tance and propulsion characteristics of clean hull and propeller in calm water; shaft power along this line is defined by hull resistance, open-water propeller characteristics and hull-propeller interaction co­ efficients. Curve 3, heavy propeller curve, is assumed in design as a pro­ peller curve for fouled hull and propeller in heavy weather; it is obtained by shifting the light propeller curve to the left by the so-called light propeller margin (LPM), and upwards by a sea margin (SM), up to point M; point M corresponds to MCR and is the layout point for the engine. The maximum continuous output of a diesel engine is bounded by the power limit, line 4, at maximum rotation speeds (maximum power continuously provided by the engine is constant and equal to MCR), the maximum torque limit, line 5, defining the shafting system bearing strength and corresponding to the full mean effective pressure (mep) in cylinders, at moderately reduced rotation speeds (torque is constant and thus the maximum engine output is proportional to rotation speed nP), and the surge limit, line 6, relevant at low rotation speeds and imposed by the availability of air from the turbocharger. Line 8 is the engine overload limit (typically about 10% of MCR at point M): whereas the area between lines 2, 4, 5 and 6 is available for continuous operation in adverse conditions or during manoeuvres without time limitation, the area be­ tween lines 4, 5, 6 and 8 is available for overload running for limited time periods (1 h per 12 h according to MAN, 2014); this area should not be used for manoeuvring in adverse conditions. Increased resistance in adverse conditions or during manoeuvres shifts line 2 upwards (e.g. up to line 9), thus the maximum engine output is defined by the intersection point A of line 9 with one of the engine limit curves 4, 5 or 6. The above concerns low-speed two-stroke diesel engines working directly on a fixed-pitch propeller. For vessels equipped with a controllable-pitch propeller, it was assumed that the propeller operates at a constant (nominal) rotation speed and the pitch of propeller blades is adjusted to the required forward speed and thrust. More application examples and validation of the comprehensive assessment in comparison with model tests can be found in Shigunov

Fig. 4. Diesel engine diagram.

seaway, where solid line A touches line B); in the right plot, the installed power is marginally sufficient to fulfil the steering ability criterion (in nearly beam seaway, solid line A touches solid line C). One of critical aspects for the assessment of manoeuvrability in adverse conditions is modelling of the main engine and propulsion system under high load. Frequently, constant rotation speed, constant torque or other assumptions are used which lead to wrong results. Here, to evaluate the manoeuvrability criteria, the required delivered power PD is compared with the available delivered power Pav D at the actual propulsion point in adverse conditions; the former is defined by the assessment procedure from resistance and propulsion characteristics, whereas the latter depends on the characteristics of the main engine and should be provided, as a function of the rotation speed, by the engine manufacturer. Note that the available brake power vs. rotation speed is provided by the engine manufacturer for the actual, as built, engine for EEDI verification, thus the proposed assessment does not require any new measurements (in the examples in this paper, data from MAN (2014) were used when manufacturer data were not available). The available delivered power on the propeller was calculated as av Pav PPTO ; PD is the delivered power to the propeller, PB is the D ¼ ηs ηg PB brake power of the engine, ηs is the shaft efficiency, ηg is the gear effi­ ciency, and PPTO is the power take-off. For illustration, the engine diagram of a two-stroke low-speed 4

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Ocean Engineering 203 (2020) 107113

(2018); the aim of this paper is to develop a simpler assessment pro­ cedure and validate it in comparison with the comprehensive assessment. 3. Simplified assessment 3.1. Simplified propulsion ability assessment The idea of the simplified assessment is to provide a simple pro­ cedure for routine use by reducing the number of assessment cases, the number of terms in motion equations and the amount of the required input, while keeping all relevant physics and addressing the same criteria as those evaluated by the comprehensive assessment. For the propulsion ability criterion, the starting point is the system of equations (1)–(3), which is solved for all relevant forward speeds and all possible seaway directions. Noting that bow seaways are most critical for the required power at a given speed (Fig. 3, middle plot), it is enough to consider only seaways from 0 to about 60� off-bow. Further, in the sit­ uations corresponding to the maximum required power at 6 knots advance speed, the drift angle achieves up to about 15� in the cases considered so far, which may lead to a change in the longitudinal calmwater force up to about 25% (both increase and decrease). However, the corresponding change in the required installed power due to lateral drift is up to about �3.5%, which is small compared to other contributions. Therefore, lateral drift is neglected, which significantly simplifies the problem: equations (2) and (3) can be omitted, thus only eq. (1) needs to be considered, and only in bow seaways: Xs þ Xw þ Xd þ XR þ Tð1

tH Þ ¼ 0

Fig. 6. Marginal significant wave height from simplified (y-axis) vs. compre­ hensive (x-axis) propulsion ability assessment for bulk carriers (BC), tankers (TA), container ships (CV) and general cargo vessels (GC).

directions to check that the ship is able to start or continue course change in seaway from any direction. For the steering ability assessment, both steering and propulsion systems are involved as integral parts: e.g. ships with powerful propul­ sion may have a smaller rudder, and ships with weaker propulsion may compensate this with larger or more effective steering devices. In the comprehensive assessment of steering ability, which takes into account both the available steering effort and the available power, it is convenient to find the conditions (ship speed and wave direction) which maximize the ratio PD =Pav D along the line C of the maximum available steering effort, called for brevity critical conditions for steering. To satisfy the steering ability criterion, the maximum of the ratio PD =Pav D along line C should not exceed 1 (in other words, line A should not touch line C): the area between lines A and C corresponds to combinations of ship speed and wave directions for which steering is possible, whereas crossing of these lines means that steering is impossible in some wave directions. Compare what happens with the satisfaction of the propulsion ability and steering ability criteria when the installed power is systematically reduced whereas other parameters are kept the same: line A will reduce in radius, and the minimum required installed power to satisfy the propulsion ability criterion will correspond to the situation when line A touches line B, whereas the minimum required installed power to satisfy the steering ability criterion will correspond to the situation when line A touches line C (similarly, wave height can be systematically increased while keeping the other parameters the same – in this case, the result will be the marginal wave heights for the propulsion ability and steering ability requirements for a given installed power). Since the ship has to satisfy both the propulsion ability and steering ability requirements, such situations, when due to reducing line A in radius it first touches line B (in bow seaways) while not touching yet line C, like in Fig. 3 middle, are not relevant in this section since the mini­ mum required power for such cases will be defined by the propulsion ability criterion (the simplified assessment procedure for which was developed in the previous section) and therefore, it does not matter what happens if the installed power is further reduced. For the development of the simplified steering ability assessment, only such cases are relevant when line A touches line C while not crossing yet line B, like in Fig. 3 right. Experience of sea farers, as well as results of the comprehensive assessment for many ships in many environmental conditions in this work, indicates that the stern-quartering seaways are always most crit­ ical for the steering ability requirement: with the increasing wave height, the area limited by line C (where the required steering effort exceeds the available one) always occurs first at low forward speeds in stern-quartering seaways, see Fig. 3 left and middle, frequently already in moderate environmental conditions. In wave directions from about 40

(4)

Here, the sum of the time-average longitudinal force due to waves Xd, wind force Xw and rudder force XR is taken as the maximum force over mean wave directions from 0 to 60� off-bow. Figs. 5 and 6 compare the results of the proposed simplified pro­ pulsion ability assessment with the results of the comprehensive assessment of propulsion ability for 4 bulk carriers, 3 tankers and 4 container ships at hs from 0.0 to 9.5 m. The results indicate that the simplified assessment procedure is sufficiently accurate, becoming slightly conservative when PD =Pav D > 1 (however, such cases are not relevant anyway). 3.2. Simplified steering ability assessment For the simplified steering ability assessment, the starting point is system (1)–(3), solved for all relevant forward speeds and all seaway

Fig. 5. Ratio PD =Pav D from simplified (y-axis) and comprehensive (x-axis) pro­ pulsion ability assessment for bulk carriers (■,▴,▾,●), tankers (▸,◄,◆) and container ships (□,△,▽,○) in waves of hs from 0.0 to 9.5 m. 5

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to about 60 degree off-stern, line C has the biggest radius, which means that fulfilment of the steering ability criterion in these wave directions requires the highest speed (but not the highest required power since added resistance in these wave directions is relatively low). However, as long as the area limited by line C is localised in stern-quartering waves like in Fig. 3 left and middle, reduction of line A in radius (due to reducing installed power or increasing wave height) will lead to its touching first line B, whereas some area between lines A and C will still be available for steering. This means that in such cases, satisfaction of the propulsion ability criterion will require a larger installed power than satisfaction of the steering ability criterion, therefore the steering ability criterion will not be relevant for design assessment (although it will be relevant for operation, which is not addressed here). Physically, this means that steering in stern-quartering waves in such cases is possible by increasing forward speed, and such increase will require less power than advance at 6 knots speed in bow seaways, since added power in sternquartering seaways is significantly less than in bow seaways. If, however, the area limited by line C is so big as in Fig. 3 right (which corresponds to steep waves, small rudder or big lateral windage area), so that reducing line A in radius first leads to its touching line C while not crossing yet line B, then the installed power will not be suf­ ficient to keep a necessary forward speed for steering in stern-quartering seaways while still being sufficient to advance at 6 knots speed in bow seaways. In such cases, the steering ability requirement will be relevant for the definition of the required installed power (or for the definition of marginal wave height for a given power) rather than the propulsion ability requirement, therefore, such cases are addressed here in the development of the simplified steering ability assessment. As show re­ sults of comprehensive assessment for many ships in many sea states, in all such cases touching of lines A and C happens in seaway directions close to beam, which is understandable since line C is located between following and beam seaways, line A has smaller radius in beam than in stern-quartering seaways and line C should have a big enough radius so that line A does not cross line B in bow seaway first (since line A has the smallest radius in bow seaways). In other words: critical conditions for steering are more demanding with respect to the required installed power than the propulsion ability criterion only in such cases when they occur in seaway directions close to beam. Consequently, taking, as an approximation, the time-average waveand wind-induced forces in the steering ability assessment in the beam seaway direction instead of the exact critical conditions for steering makes a moderate error in these forces in the majority of cases (less than 20% in 95% of cases), which is acceptable for a simplified assessment. Therefore, the first simplification in the simplified assessment of steering ability is that the time-average wave- and wind-induced forces and moments are evaluated in beam seaway. To validate this simplifi­ cation, steering ability was assessed using the following system of equations (written here for the converged state): 90 Xs þ X 90 w þ X d þ XR þ Tð1

tÞ ¼ 0

90 ls Ys þ lw Y 90 w þ ld Y d

Y 90 w ðlw

(6)

90 Ns þ N 90 w þ Nd

(7)

ls Þ þ Y 90 d ðld

(8)

YR lR ¼ 0

Expressing Ys from eq. (6) as Ys ¼ it into eq. (8) leads to

Y 90 w

Y 90 d

ls Þ ¼ YR ðls þ lR Þ

YR and introducing (9)

Comparing terms of converged solutions of system (5)–(7) shows that ls eLpp =2, lw << ls and ld << ls in critical conditions for steering, Fig. 8, thus eq. (9) can be simplified, Y90 ls Þ þ Y 90 ls Þ ¼ YR ðls þ w ð0 d ð0 lR Þ, or � 90 (10) YR ¼ b Y 90 w þ Yd where b ¼ ls = ðls þ lR Þ

(11)

As a result, the system of equations (5)–(7) reduces to only one equation (5) and check (10). The solution of eq. (5) provides the maximum attainable speed, corresponding propeller rotation speed and thrust and thus defines the maximum available lateral force on the rudder Yav R ; to satisfy the steering ability requirement, this force should be not less than the required lateral steering force defined by eq. (10). Assuming lR � 0:5Lpp simplifies eq. (11) to � � (12) b ¼ ls ls þ 0:5Lpp ;

(5)

90 Ys þ Y 90 w þ Y d þ YR ¼ 0

YR lR ¼ 0

Fig. 7. Ratio PD =Pav D vs. hs according to comprehensive steering ability assess­ ment (solid line) and after first simplification, system (5)–(7), for container ship (top) and tanker (bottom) in full load.

where the upper index 90 means that forces are taken in beam seaway. Fig. 7 compares steering ability assessment results using this simplified system (5)–(7) with the results of comprehensive steering ability assessment using system (1)–(3) for a container ship and a tanker and shows that this simplification is sufficiently accurate. The second simplification stems from the comparison of the levers of the time-average wave- and wind-induced yaw moments with the lever of the calm-water yaw moment in critical conditions for steering. Introduce the levers of the calm-water yaw moment and time-average wind- and wave-induced yaw moments as ls � Ns =Ys , lw � Nw =Yw and ld � Nd =Yd , respectively, and rewrite eq. (7) as

which can also be written as b¼

Ys ls Ns N’s ¼ ¼ ; Ys ls þ Ys 0:5Lpp Ns þ 0:5Ys Lpp N’s þ 0:5Y’s

(13)

Y ’s ¼ Ys =ð0:5ρLpp Tm v2s Þ, N’s ¼ Ns =ð0:5ρL2pp Tm v2s Þ are the coefficients of the calm-water side force and yaw moment, respectively; note that they depend only on drift angle β. Fig. 9 compares results of the steering ability assessment according to 6

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Fig. 10. Marginal significant wave height from simplified steering ability assessment (5), (10) with b ¼ 0:5 (y axis) vs. marginal significant wave height from comprehensive steering ability assessment (x axis) for bulk carriers (BC), tankers (TA), container ships (CV) and general cargo vessels (GC).

results for bulk carriers, tankers and container ships and shows that the resulting approximation provides accurate to slightly conservative results. 4. Level 1 assessment The idea of the level 1 assessment, the simplest assessment level, is to apply pure empirical formulae to directly define high-level output, e.g. the required installed power or required thrust, as a function of main ship parameters. Below are some examples. Minimum power lines (MPL), IMO (2013,2014,2015), define the minimum required installed power in terms of the maximum continuous rating MCR, kW, as a function of deadweight DWT, t, as

Fig. 8. Ratios of levers lw =ls (top) and ld =ls (bottom) in critical conditions for steering (i.e. combinations of forward speed and seaway direction for which PD =Pav D is maximum along line δ ¼ δmax ); different symbol types denote different ships.

approximation (5), (10) with the results of comprehensive assessment (1)–(3) for 15 sample bulk carriers, tankers and container ships; in the simplified assessment, the value of b was taken from comprehensive assessment results in critical conditions for steering as b ¼ Ns = ðNs þ 0:5Ys Lpp Þ. The comparison shows that the approximation (5), (10) provides accurate results, becoming more conservative when PD =Pav D >1 (i.e. cases which are not relevant for the considered problem anyway). In the long term, an empirical formula should be established for b as a function of main ship particulars; a conservative assumption following from the application of the comprehensive assessment to many ships is b ¼ 0.5. Fig. 10 compares results of the simplified steering ability assessment (5), (10) using b ¼ 0.5 with comprehensive assessment

MCR ¼ a⋅DWT þ b;

(14)

constants a and b are defined as 0.0763 and 3374.3, respectively, for bulk carriers with deadweight below 145000 t, 0.0490 and 7329.0, respectively, for bulk carriers with deadweight of 145000 t and more, and 0.0652 and 5960.2, respectively, for tankers and combination car­ riers. The application of eq. (14) with these coefficients was extended to phase 2 of EEDI implementation (up to December 31, 2024), i.e. it is presently applicable to bulk carriers with DWT of 10000 t and more and tankers and combination carriers with DWT of 4000 t and more. Empirical formulae proposed by SHOPERA, see IMO (2016a), based on results of comprehensive assessment for more than 400 bulk carriers, tankers, container ships and general cargo vessels with length between perpendiculars from about 120 m to 320 m, equipped with two-stroke low-speed diesel engines, fixed-pitch propellers and conventional rud­ ders at the standard wave heights from IMO (2013), are formulated separately for the propulsion ability and steering ability requirements as 2 MCR ¼ 0:21C0:5 B Lpp

(15)

MCR ¼ 0:15cR L2pp

(16)

respectively; MCR is the required installed power in kW, cR ¼ Lpp Tm =ð50A*R Þ, A*R ¼ minð2AR =3;ApR Þ, where AR is the total rudder area and ApR is the rudder area in propeller race. Fig. 11 compares these formulae with comprehensive assessment results, indicating that these formulae are conservative but produce significant scatter. Work IMO (2016b) proposed to develop empirical formulation for the required propeller thrust at bollard pull, using results of model tests and numerical simulations of manoeuvres in seaway for sufficiently many ships. In IMO (2016b), turning into seaway (‘heading recovery’) was used as a manoeuvrability criterion, which is similar to the weather-vaning criterion proposed by SHOPERA and therefore, does not

Fig. 9. Ratio PD =Pav D from simplified (5), (10) (y axis) and comprehensive (x axis) assessment of steering ability for bulk carriers (■,▴,▾,●), tankers (▸, ◄,◆), container ships (□,△,▽,○) for significant wave heights from 0.0 to 9.5 m; b is taken from comprehensive assessment results in critical conditions for steering as b ¼ Ns =ðNs þ 0:5Ys Lpp Þ 7

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required installed power (maximum values over all considered ships). The figures mean that, for example, a change in the calm-water x-force by 10% changes the installed power required to fulfil the propulsion criterion by 1.5%. According to these results, most important for the propulsion and steering abilities in adverse conditions are (shown in bold in Table 1) the time-average wave-induced x- and y-forces, calm-water x- and y-forces and z-moment, and the lateral rudder force: an error of about 15% in these components leads to the error in the required installed power of 5%. In the simplified assessment, all methods applied to define input components for the comprehensive assessment can be used as well; note, however, that the number of the required components and the number of the situations in which they are required is significantly reduced (e.g. propulsion assessment requires only longitudinal forces and only in bow wave directions). Besides, it seems especially useful to develop addi­ tional simple empirical formulae (see below) specifically for the simplified assessment, to enable its application in the preliminary design or to simplify assessment in cases with big safety margins. Below, a short overview of evaluation methods is given, see IMO (2016a) and Shigunov (2017) for more details. Note that the aim of this paper is not to select and recommend spe­ cific methods that are suitable for regulatory approval: the advantage of the proposed assessment procedures is that any validated method can be used to define the input elements, thus the designers are in a better position to decide what method is most suitable for the ships that they are designing. Therefore, one of the aims of this section is to check whether evaluation methods are available, in principle, for all required input elements – only in this case the proposed assessment procedures make practical sense – and, besides, provide additional, very simple evaluation methods, to further simplify the simplified assessment procedure.

Fig. 11. Required installed MCR, kW, according to eqs. 15 and 16, y axis, vs. required installed MCR from comprehensive assessment, x axis, for propulsion ability (top) and steering ability (bottom) requirements.

consider propulsion ability and steering ability criteria applied here. Apart from this, i.e. assuming that the empirical formulation is based on the fulfilment of appropriate manoeuvrability criteria, thrust at bollard pull may be a more suitable variable for level 1 formulation than the installed power. Generally, assessment procedures based on empirical formulae may be very useful in practice to easily identify conventional ships with big safety margins, which do not require a more accurate analysis; however, such procedures cannot replace performance-based assessment for ships near the acceptance boundaries or for unconventional vessels. Besides, such procedures are applicable only to ships with parameters within the applicability range of the empirical formulae.

5.2. Calm-water hydrodynamic reactions as

5. Evaluation methods

The calm-water hydrodynamic forces and moment can be calculated

Xs ¼ 0:5X’s ðβÞρv2s Lpp Tm ;

(17)

Ys ¼ 0:5Y’s ðβÞρv2s Lpp Tm ;

(18)

Ns ¼ 0:5N’s ðβÞρv2s L2pp Tm ;

(19)

the prime indicates non-dimensional coefficients. For the comprehensive assessment, these coefficients can be defined with well established and widely available experimental methods or from numerical simulations based on solution of Reynolds-averaged Navier-Stokes (RANS) equations; empirical methods are, in principle, also available and can be used within their applicability limits. (In the sample assessments presented in this paper, RANS-based simulations were used, validated for several ships by comparison with model tests.)

5.1. General Comprehensive and simplified assessment procedures require defi­ nition of multiple input elements: time-average wave-induced forces and moments, wind forces, calm-water reactions, rudder forces and propel­ ler characteristics. The proposed assessment procedures allow defining any of these elements separately and, if necessary, with different methods (experimental, numerical or empirical) depending on the needs and possibilities of the designer for particular ship designs. An important question, however, is what accuracy is required when designers define each force component. To quantify the relative importance of the components of forces and moments, the comprehen­ sive assessment was conducted for several ships of different types and sizes using as input the original components of forces and moments and, for comparison, cases where each of these components was changed in turn by 10%. The required installed power to satisfy, separately, pro­ pulsion ability and steering ability requirements in the environmental conditions according to IMO (2013) was defined for the original and comparative cases, and the change in the required installed power due to the 10%-change in the components of forces and moments was calcu­ lated. Table 1 shows the results as the percentage of the change in the

Table 1 Percentage of change of required installed power due to change of each component of forces and moments by 10%. Contributions Propulsion Criterion Calm water Wind (bow) Waves (bow) Rudder Steering Criterion Calm water Wind (close to beam) Waves (close to beam) Rudder

8

x-force

y-force

z-moment

1.5 2.5 3.8 1.0

1.3 0.7 1.4 2.2

2.1 0.6 0.2 0.0

3.0 0.8 1.3 1.5

3.4 1.6 3.0 3.4

3.5 0.2 0.3 0.0

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The simplified assessment for both propulsion ability, eq. (4), and steering ability, eq. (5), requires only longitudinal force, which can be defined by methods approved for EEDI verification (note that this verification must be performed anyway); this solution was proposed in IMO (2017a). 5.3. Wind forces and moment The forces and moment due to wind are expressed as Xw ¼ 0:5X’w ðεÞρa v2w AF ;

(20)

Yw ¼ 0:5Y’w ðεÞρa v2w AL ;

(21)

Nw ¼ 0:5N’w ðεÞρa v2w AL Loa ;

(22)

’;0 Fig. 12. Approximations X90 (△) and X90 w ¼ 0:5X w ρa vs Uw AF w ¼ 2 0:5X’;0 w ρa vs AF (●), y axis, vs. measurements, x axis, of longitudinal wind force in critical conditions for steering.

the prime indicates non-dimensional coefficients, ρa is the air den­ sity, AF and AL are, respectively, the frontal and lateral projected areas above the water plane, and Loa is the overall ship length. The relative wind speed vw and the apparent wind angle of attack ε (measured from the ship centre plane, positive for wind coming from port, Fig. 2) were calculated as vw ¼ (a2 þ b2)0.5 and ε ¼ cos 1(a/vw)⋅sign b, respectively; a ¼ Uw cos(βw β) þ vs cosβ, b ¼ Uw sin(βw β) vs sinβ, and Uw is the absolute wind speed. The coefficients X0 w, Y0 w and N0 w can be defined from wellestablished model tests in widely available testing facilities or from existing empirical data, e.g. Blendermann (2014) and Fujiwara et al. (2006); numerical methods based on RANS or DES (detached-eddy simulations) in full scale are available and increasingly used. In the sample assessments presented in this paper, experimental measurements (for few ships), RANS-based simulations and empirical data from Blen­ dermann (2014) were used. The mentioned evaluation methods can be used both in the comprehensive and simplified assessment procedures. Due to availability of comprehensive empirical data for wind forces, e.g. Blendermann (2014) and Fujiwara et al. (2006), additional simple empirical formulae specifically for the simplified assessment seem rather unnecessary; still, such formulae may be useful and are therefore proposed. In the simplified propulsion assessment, maximum of X0 w in head and bow-quartering wind is required; from available data in SHOPERA and JASNAOE-coordinated projects, a default value of 1.1 was proposed in IMO (2017a) (which is increased to 1.4 for ships with big windage areas of deck cranes to account for shadowing effects in head wind). The simplified steering ability assessment requires the longitudinal and lateral wind-induced forces in beam wind. The longitudinal force due to beam wind strongly depends on the geometry of the windage area of the ship. A consistent approximation for this force would be X90 w � 90 ’;0 ’;0 2 0:5X’;0 w cos ερa vw AF , i.e. Xw � 0:5Xw ρa vs Uw AF (Xw is the coefficient of longitudinal wind force in head wind, conservatively 1.1), which was found to lead to consistently conservative results compared to the lon­ gitudinal force in critical conditions for steering based on measure­ ments, Fig. 12. Empirically, it was found that an assumption X90 w ¼ 2 0:5X’;0 w ρa vs AF provides a sufficiently close approximation, Fig. 12 (not always conservative, but note that this force does not require a high accuracy, since an error of 60% in this force leads to about 5% error in the required installed power, Table 1). The lateral force due to beam wind can be approximated as Y 90 w ¼ 2 ’;90 ρ A U , where Y is the coefficient of the lateral force due to 0:5Y ’;90 a L w w w beam wind (conservatively 1.0); Fig. 13 compares this formula with measurements.

Fig. 13. Approximated lateral wind force in critical conditions for steering divided by measured one vs. ratio of ship speed to service speed.

irregular waves are calculated using the spectral method, Z ∞ Z 2π Xd Sζζ ðω’ÞDðμ μ’Þ ​ dω’ ​ dμ’ Xd ¼ 2 A2 0 0

(23)

(similarly Yd and Nd); Xd (us,μ0 ,ω0 )/A2 is the quadratic transfer function of the time-average wave-induced surge force, assumed to depend on the longitudinal ship speed us, mean wave direction with respect to the ship centre plane μ ¼ βe β and wave frequency ω; A is the wave amplitude, Sζζ is the wave energy spectrum and D is the wave energy spreading function. To define the quadratic transfer functions Xd/A2, Yd/A2 and Nd/A2 for all relevant wave frequencies and directions, model tests can be used; however, such tests require advanced measurements in a seakeeping basin, which cannot be used routinely. Availability of numerical and, especially, empirical methods for the time-average wave-induced forces is one of the most critical issues for practical design and approval, and their development and validation was one of the major tasks in SHOPERA. The results of the international benchmarking conducted by SHOPERA, Shigunov et al. (2018), show significant progress in the development of numerical and empirical methods in the last years and their availability, in principle, for practical and regulatory purposes; however, the results also show that their application should be verified in each individual case. For the sample assessments presented in this paper, the waveinduced forces and moments were defined using numerical computa­ €ding and Shigunov (2015), tions with the software GL Rankine, see So validated in comparison with experimental measurements available for some ships. The simplified propulsion ability assessment requires maximum time-average wave-induced surge force in head to bow-quartering wave

5.4. Time-average wave-induced forces According to existing regulations and proposals, IMO (2012a,2013, 2016a,2017a), time-average wave-induced forces and moment in 9

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directions. In short-crested waves, it is sufficient to use head waves since head waves produce maximum surge force even when the quadratic transfer function is maximal in oblique waves, Fig. 14, whereas if longcrested head waves are used, the added resistance should be multiplied by an empirical correction factor 1.3, see IMO (2017a). In SHOPERA, empirical formulae were developed specifically for the simplified propulsion assessment. The approach developed in Liu et al. (2015) and Liu and Papanikolaou (2016) provides simple empirical expressions for the transfer functions of added resistance in bow waves. A simpler approach, directly providing the maximum time-average surge force in irregular short-crested bow waves, Xd ¼

0:5 2 83Lpp C1:5 B ð1 þ Fr Þhs , see IMO (2016a), is based on computations with method GL Rankine, S€ oding and Shigunov (2015), followed by spectral integration in irregular short-crested waves described by JONSWAP wave energy spectrum with γ ¼ 3:3 and cos2-wave energy spreading and taking the maximum over mean wave headings from head waves up to 60� off-bow and peak wave periods from 7 to 15 s. After work IMO (2016a), extensive computations of added resistance in irregular short-crested bow waves were carried out to develop an improved formula specifically for bulk carriers and tankers for the revised guidelines IMO (2017a); the result, � �0:75 2 Xd ¼ 1336ð5:3 þ vs Þ Bwl T Lpp hs (24)

where vs is the ship speed in m/s, Bwl is the waterline breadth and T is the draught midships, is based on numerical computations for 50 bulk car­ riers, tankers and general cargo vessels with Lpp in the range from 90 to 320 m, CB from 0.78 to 0.87, Lpp/Bwl ratio from 5.0 to 7.9 and Bwl/T ratio from 2.0 to 3.3, at the forward speeds from 0 to 8 knots. Fig. 15 com­ pares these empirical formulae with numerical computations for bulk carriers, tankers, general cargo, container, RoRo and cruise vessels. The empirical formula for transfer functions of added resistance in

Fig. 15. Xd in irregular short-crested head waves of 1 m significant height by empirical formula proposed by SHOPERA, IMO (2016a), (top) and improved formula for bulk carriers and tankers (bottom) vs. numerical computations for bulk carriers, tankers, general cargo vessels (■,▴,▾,●,◆) and container, RoRo, cruise vessels (□,△,▽,○,◊); symbol types differentiate forward speeds.

head waves from Liu et al. (2015) and Liu and Papanikolaou (2016) and the simple formula (24) for the added resistance in irregular short-crested head waves are included as default methods in the joint proposal IMO (2017a). The simplified steering ability assessment requires time-average wave-induced surge and sway forces in irregular short-crested beam waves; for both, simple empirical formulae were developed in SHOP­ ERA, see IMO (2016a), using numerical computations with GL Rankine followed by spectral integration for JONSWAP spectrum with γ ¼ 3:3 and cos2 wave energy spreading, as a maximum over peak wave periods from 7 to 15 s. For the time-average surge force in irregular short-crested beam waves, a simple formula X90 d ¼

2 380Lpp C1:5 B ð0:1 þFrÞhs was developed

in IMO (2016a), where Fr ¼ vs ðgLpp Þ0:5 . Here it is improved as � 2 X 90 83Lpp C0:5 d ¼ B hs ðvs þ 1Þ ðvs þ 3Þ

(25)

Fig. 16 compares these two formulae with numerical computations; whereas the spreading of results of the empirical formulae for X90 d is significantly greater than for the added resistance in head waves, the sensitivity of the final result (required installed power) to the accuracy of the definition of X90 d is much less, thus the achieved accuracy seems acceptable. For the time-average wave-induced sway force in irregular shortcrested beam waves Y90 d , the formula was developed by the author for IMO (2016a); Fig. 17 compares it with numerical computations. Note that this formula was developed to define the maximum force over the peak wave periods used in the assessment procedure, thus it can be applied only near the smallest (and therefore, maximizing the sway

Fig. 14. Added resistance in short-crested irregular waves per significant wave height squared vs. mean wave direction off-bow (top) and in regular waves per wave amplitude squared vs. wave direction off-bow (bottom) for bulk carriers, tankers and container ships at 4 knots forward speed; each line and symbol type correspond to one ship.

force) peak wave period used in the assessment, Tp ¼ 3:6h0:5 s .

10

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Especially important for practical use is the availability of simple empirical methods; Shigunov (2017) validates two such methods, Brix €ding (1998), vs. experiments for a small tanker and vs. (1993) and So RANS simulations for a 14000 TEU container ship. A thorough valida­ tion of available empirical methods in SHOPERA, see IMO (2016a), including their benchmarking together with the JASNAOE-coordinated project, concluded that such methods are, in principle, available for practical use. Figs. 18 and 19 show additional validation examples of €ding (1998) and Yasukawa semi-empirical methods from Brix (1993), So and Yoshimura (2015) (note that all of these methods are based on momentum theory), resulting from this joint work: the lateral rudder force YR for a 14000 TEU container ship in bollard pull in comparison with model experiments and RANS simulations, Fig. 18, and the longi­ tudinal XR and lateral YR rudder forces for a handysize bulk carrier in comparison with model experiments, Fig. 19 (note that rudder forces are defined in the ship coordinate system, Fig. 2). Note that in the propul­ sion ability and steering ability assessment examples in this paper,

Fig. 16. X90 d in irregular short-crested beam waves of 1 m significant height by simplified empirical formula (y-axis) proposed in SHOPERA, see IMO (2016a) (top) and improved formula (25) (bottom) vs. results of numerical method (x-axis) for bulk carriers, tankers, general cargo vessels (■,▴,▾,●,◆) and container, RoRo, cruise vessels (□,△,▽,○,◊); symbol types differentiate for­ ward speeds.

Fig. 17. Y 90 in irregular short-crested waves per significant wave height d squared from simplified empirical formula (26) (y axis) and numerical method (x axis) for the shortest peak wave periods used in the assessment.

Y 90 d ¼

n � �5 o 540Lpp h2s 1 þ Tp CB 1 Lpp1=2

1

(26)

5.5. Rudder forces The specifics of the considered problem is that rudder works at a large angle and low forward speed in a race of a highly-loaded propeller. To define rudder forces, experimental methods are widely available, including well-established methods, not requiring expensive facilities and thus suitable for design and approval. Numerical methods (RANS simulations) are also, in principle, available, IMO (2016a).

Fig. 18. Lateral force on rudder YR, N, vs. rudder angle according to models from Brix (1993) (S€ oding-Brix, solid line) and Yasukawa and Yoshimura (2015) (JASNAOE, dashed line) vs. experiments (▪) and RANS simulations (△) for three propeller rotation speeds for 14000 TEU container ship in bollard pull. 11

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Fig. 19. Longitudinal (left) and lateral (right) forces on rudder at three values of propeller load coefficient Cth ¼ 8T=ðπρu2a D2p Þ according to models from Brix (1993) (S€ oding-Brix, solid line), S€ oding (1998) (S€ oding-ONR, dash-dot line) and Yasukawa and Yoshimura (2015) (JASNAOE, dashed line) vs. experiments (▪) for handysize bulk carrier; note that rudder resistance at zero rudder angle is shown as zero since it is included in calm-water hull resistance Xs in eq. (1).

method from Brix (1993) was used. In Fig. 18, the lowest propeller rotation speed (top plot) corresponds to propeller loading relevant for steering ability assessment. Both methods from Brix (1993) and Yasukawa and Yoshimura (2015) provide decent lateral force, although they do not reproduce the asymmetry of the lateral force with respect to the rudder angle (the same relates to the other propeller rotation speeds) since they do not model rotational ef­ fects in the propeller race. The middle and bottom plots in Fig. 18 correspond to higher loading of the propeller than relevant for the steering ability assessment. The model from Brix (1993) predicts the lateral force very well; the model from Yasukawa and Yoshimura (2015) provides slightly non-conservative results (i.e. it over-estimates the lateral rudder force). RANS results are slightly conservative. In Fig. 19, the top plots (the lowest propeller rotation speed) corre­ spond to too low loading of the propeller than loading relevant for the steering ability assessment. Both models from Brix (1993) and Yasukawa and Yoshimura (2015) provide close, slightly conservative (i.e. they over-estimate the resistance) longitudinal force on the rudder compared €ding (1998) show to the measurements. Models from Brix (1993) and So close (and conservative, i.e. under-estimating the measurements) results

for the lateral force, and model from Yasukawa and Yoshimura (2015) shows non-conservative results (note, however, big scatter of experi­ mental results for this case). The middle plots in Fig. 19 correspond to propeller loading relevant for the steering ability assessment. Models from Brix (1993) and Yasu­ kawa and Yoshimura (2015) show close results for the longitudinal force, slightly conservative (over-estimating experiments) at medium rudder angles. The lateral rudder force is predicted very well by models from Brix (1993) and S€ oding (1998) while over-predicted (i.e. non-conservatively predicted) by the model from Yasukawa and Yosh­ imura (2015). In the bottom plots in Fig. 19, the propeller loading is too high to be relevant for the steering ability assessment. Here, the method from Yasukawa and Yoshimura (2015) provides close (slightly conservative) predictions of the longitudinal rudder force compared to experiments, whereas the method from Brix (1993) provides much too conservative results. The lateral rudder force significantly differs between the €ding (1998), both of which signifi­ methods from Brix (1993) and So cantly over-estimate the experiments; the method from Yasukawa and Yoshimura (2015) provides the best results for the lateral rudder force between the three methods, although still non-conservative. 12

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These results show that the methods from Brix (1993) and Yasukawa and Yoshimura (2015) are suitable as simple empirical methods for rudder forces in propeller race for propeller loadings relevant for the steering ability assessment; moreover, since both these methods are semi-empirical, their parameters (hull-rudder and propeller-rudder interaction coefficients) can be fine-tuned for particular designs for practical use in regulatory approval. The simplified steering ability assessment requires definition of the maximum available lateral steering force Y av R , which depends on the maximum attainable forward speed and the corresponding propeller thrust, defined by eq. (5), thus this assessment needs rather accurate models for rudder forces. On the other hand, the simplified propulsion assessment requires only the added resistance on the rudder due to manoeuvring in bow-quartering seaway; proposal IMO (2017a) suggests 3% of propeller thrust as a default conservative estimate. Fig. 20, showing additional resistance on the hull and rudder due to propeller overload at various drift and rudder angles, confirms the additional longitudinal force on the rudder due to propeller overload of about 3% of propeller thrust at 20� rudder angle.

From the so found advance ratio J, KQ is found from the open-water propeller curve KQ(J), the propeller rotation speed is found as nP ¼ ua/(J DP), and the required delivered power is defined as PD ¼ 2πQnP ¼ 2πρn3P D5P KQ ðJÞ, where Q is the propeller torque. Therefore, the required power in seaway depends not only on the resistance increase but also on the change in the open-water propeller characteristics and hull-propeller interaction coefficients in waves, about which it is very little known presently. The required delivered power PD ¼ PE =ηD ¼ Xt vs =ηD ;

(27)

where PE ¼ Xt vs is the effective power, PD ¼ 2πQnP is the delivered power to the propeller, Xt is the total resistance and

ηD ¼ ηH η0 ηR ;

(28)

is the propulsive efficiency, with the hull efficiency ηH ¼ ð1 tÞ=ð1 wÞ on the thrust deduction fraction t and wake fraction w, the relative rotative efficiency ηR ¼ Q0 =Q, defined as the ratio of the propeller tor­ que in open water Q0 to propeller torque behind ship Q, and the openwater propeller efficiency

5.6. Propulsion characteristics

η0 ¼ Tua =ð2π Q0 nP Þ ¼ KT J=ð2πKQ Þ

Propeller thrust is found from equation (1) and (4) or (5) using a known thrust deduction fraction t. From the found thrust, the advance ratio J is defined from the relation T ¼ ρu2a D2P KT ðJÞ =J2 (ua ¼ us (1 w) is the propeller advance speed and DP is the propeller diameter), using a known open-water propeller curve KT(J) and a given wake fraction w.

(29)

Eq. (28) shows that ηD changes in waves due to, first, change in η0 (due to change in the propulsion point, i.e. advance ratio, due to

added resistance, and due to change in propeller characteristics KT(J) and KQ(J) near the free surface) and, second, change in hull-propeller interaction coefficients ηR and ηH in seaway. The open-water propeller characteristics change in waves, see e.g. Faltinsen et al. (1980) and Nakatake (1976), due to wave generation by the propeller when the submergence of the propeller shaft centre is less than about 1.5 of the propeller radius. Further emersion of the propeller leads to its emergence and ventilation, when the submergence of the propeller shaft is close to the propeller radius, as well as splashing of propeller blades into water, see Wagner (1925). These effects occur, however, in heavier sea, at lower draught or at higher forward speeds than those relevant here. The relative rotative efficiency ηR can both increase and decrease in waves; results of tests in Moor and Murdey (1970) and Nakamura and Naito (1977) do not allow drawing conclusions about the influence of waves on ηR. Measurements in regular waves of various lengths and heights up to 3.6 m height (for a ship with Lpp of 221 m) in Valanto and Hong (2017) show that ηR remains almost constant, equal to its calm-water value. Regarding the change in ηH in waves, Moor and Murdey (1970) and Nakamura and Naito (1977) report decrease in thrust deduction with increasing wave height and increasing pitch motions. Several studies, e. g. Faltinsen et al. (1980), suggested that propeller overload in calm water produces a similar decrease in t if the thrust loading coefficient CTh corresponds to that in waves, which makes the definition of t in waves very simple. On the other hand, Faltinsen et al. (1980), Moor and Murdey (1970) and Nakamura and Naito (1977) also report increase in wake velocities due to wave-induced ship motions, thus both nominator and denominator in ηH increase in waves and the total change of ηH in waves is uncertain. In Valanto and Hong (2017), change of η0 and ηD is measured in regular waves of various heights and lengths; the largest change, occurring at the wave length of about 1.09 of ship length (wave height to wave length ratio about 1.5%), corresponds to a decrease in η0 of about 8% and decrease in ηD of about 9%, i.e. the decrease in ηHηR is only about 1% (which is less than accuracy of measurements); thus loss of propul­ sive efficiency ηD can be explained entirely by the loss of the open-water propeller efficiency η0 due to the change in operation point, whereas ηH and ηR are almost constant and equal to their calm-water values. Note, however, that the tests in Valanto and Hong (2017) were done at higher forward speed and in lower waves than those relevant here, and that the

Fig. 20. Additional resistance on hull (blue dashed lines, empty symbols), rudder (red dash-dot lines, empty symbols) and hull and rudder together (solid black lines, filled symbols) due to propeller overload, non-dimensionalised with respect to propeller thrust, vs. propeller load coefficient at drift angles 0, 7.5, 15� (■,▴,◆,respectively) at rudder angle 0� (top) and at rudder angles 0, 10, 20� (■,▴,◆,respectively) at zero drift angle (bottom). (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.) 13

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wind resistance was not considered; consideration of these factors should increase propeller loading and thus further reduce the thrust deduction fraction t.Whereas it is easy to conduct additional towing tests or numerical simulations with overloaded propeller in calm water to define the thrust deduction in seaway, Fig. 20, such tests cannot define the change in wake fraction due to waves and ship motions, and thus may lead to a non-conservative estimate of ηH. In ITTC (2018), which concerns, however, more moderate sea states than those relevant here, thrust identity method is used and the open-water propeller characteristics, wake fraction and thrust deduction are taken from calm-water tests. In ITTC (2002), concerning more severe sea states, which are rele­ vant also here, three procedures are analysed, one from which, the direct power method is recommended. In this method, transfer functions of power in regular waves are measured directly at the model self-propulsion point, thus the propeller characteristics and hull-propeller interaction coefficients in waves are implicitly consid­ ered, although for a slightly more loaded propeller (namely, at the model self-propulsion point; however, calm-water power is corrected for scale effects). Similarly, in the second, torque and rate of rotation method, transfer functions of the change in torque and propeller rotation speed are defined from model tests in regular waves at model self-propulsion point. In the third, thrust method, transfer functions of thrust increase are defined from model tests in regular waves at the model self-propulsion point – thus, this method requires propeller character­ istics to define added power in waves, which are taken as the open-water propeller characteristics in calm water. Note that none of these three methods is suitable for the problem considered here since added resis­ tance due to wind and rudder operation cannot be taken into account. The thrust identity method is also mentioned in ITTC (2002) as one of methods under discussion: in this method, added resistance due to waves is calculated from the transfer functions measured in regular waves, thus wind resistance and other resistance components can be simply added. However, definition of the required power in this method requires propeller characteristics and hull-propeller interaction co­ efficients, which are defined in calm water. Note that accurate definition of propeller characteristics and hullpropeller interaction coefficients in seaway for design and regulatory approval concerning manoeuvrability in adverse conditions is presently not critical, since with the presently available knowledge, ship designers will not try to optimise these characteristics to fulfil the minimum power regulations; therefore, some simplifications are possible until more knowledge is available. Therefore, in the joint proposal IMO (2017a), thrust identity method is used to define the added power in adverse conditions, and the open-water propeller characteristics and hull-propeller interaction coefficients are recommended to be defined by the methods approved for EEDI verification, i.e. presently, from calm-water propulsion and resistance tests (so that no additional work is needed since EEDI verification is required anyway); in IMO (2013), also empirical formulae are proposed for the thrust deduction fraction and wake fraction, based on calm-water values. In the examples of assess­ ments presented in this paper, calm-water values were used.

complexity equations and significantly less input elements than the comprehensive assessment. The simplest assessment, level 1, relies on empirical formulae to define the required installed power as a function of main ship parameters. Level 1 assessment, as a pure empirical procedure, is applicable only to the vessels similar to those for which it was developed; still, it shows significant scatter even for such vessels (note, however, that alternative ideas, e.g. using bollard pull instead of installed power as in IMO (2016b), may lead to better results). The simplified assessment is a compromise between simplicity, flexibility and accuracy: the analysis is simple and may use simple methods to define input elements while remaining open for high-accuracy input elements if necessary. However, due to the simplifications involved, this procedure is conservative. The comprehensive assessment allows the best accuracy but requires extensive input – three components (surge and sway forces and yaw moment) of calm-water forces for drift angles from zero up to about 20� , wind forces for 0–180� apparent wind directions and wave-induced forces for 0–180� wave directions at all relevant wave frequencies, as well as rudder forces and propeller characteristics. The proposed comprehensive and simplified assessment procedures allow defining any of the input elements separately and with different methods (experimental, numerical or empirical), depending on the needs and possibilities of designers and administrations. Experimental methods are established and available in sufficiently many facilities world-wide for the evaluation of calm-water, wind, rudder and propeller forces, whereas measurement of the time-average wave-induced forces and moments needs advanced measurements in a seakeeping basin and therefore, cannot be used routinely. Numerical methods are available, in principle, for calm-water, wind, rudder and propeller forces; again, their availability for the time-average wave-induced forces is one of the most critical issues, see Shigunov et al. (2018). The availability of empirical methods is especially important for practical design and approval. The studies by SHOPERA and the JASNAOE-coordinated project concluded that such methods are in principle available for practical use for calm-water reactions, wind forces and rudder forces; empirical methods for the time-average waveinduced forces and moments again require attention. Thus, the avail­ ability of numerical and empirical methods for wave-induced forces is critical for the practical implementation of the proposed assessment framework. An important question is the overall uncertainty of the resulting procedures and practical ways to deal with this uncertainty. Level 1 shows high uncertainty, which can be compensated only by its addi­ tional conservativeness. For both the comprehensive and simplified assessment procedures, the greatest uncertainty stems from the differ­ ence between the real operation, strongly depending on human de­ cisions (such as ordering a tug, waiting at anchor, leaving dangerous area or searching for a shelter), and design assessment criteria (pro­ pulsion, steering and weather-vaning criteria considered here). The second greatest source of uncertainty is introduced by the step from the assessment criteria to the practical assessment procedure, i.e. here the omission of the time-dependent wave-induced forces and reducing the assessment to time-average characteristics, which sim­ plifies not only the hydrodynamic forces but also transient reactions of the engine and propeller in waves. This simplification, although widely used, has not been validated conclusively so far (note validation of the comprehensive assessment in comparison with model tests and for an accident example in Shigunov, 2018). One more error is introduced in the simplified assessment due to the reduced number of assessment cases and simplified equations compared to the comprehensive assessment. Since the development of the simplified assessment was the aim of this paper, it was validated here in comparison with the comprehensive assessment; Figs. 5, 6, 9 and 10 show that this error is rather moderate and conservative. The final source of uncertainties are the methods that are used to define the input elements for the comprehensive and simplified

6. Discussion The proposed flexible approach to the assessment of ship’s manoeuvrability under adverse conditions allows choosing between various procedures, ranging from advanced assessment, which is required for cases with large uncertainties, to simple procedures, suffi­ cient for most conventional vessels. Three levels of complexity are considered: the most accurate level 3, comprehensive assessment, allows the best accuracy; even in this procedure, the designer does not have to use expensive evaluation methods to define the input elements and can choose between experimental, numerical or empirical methods. A less complex level 2, simplified assessment, still considers the physics of the problem but applies a reduced number of assessment situations, reduced 14

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assessment procedures. Since the accuracy of the input can (and must) be verified in the regulatory approval, this uncertainty is controllable. This concerns also the dedicated simple empirical formulae that were developed here specifically for the simplified assessment (the included validation examples show that their accuracy is sufficient). The uncertainty introduced by the time-averaging assumption can be quantified by comparison of the results of comprehensive assessment with transient model tests or numerical simulations (note, however, that this is difficult to do in irregular short-crested waves combined with wind and taking into account the need for accurate statistical estimates). On the other hand, verification of the gap between the real operation and practical criteria is not possible in a strict sense. Nevertheless, a pragmatic solution to address this gap (which also addresses the un­ certainty due to time-averaging) is possible: as long as the criteria and assessment procedures concern relevant ship characteristics for manoeuvrability in adverse conditions (i.e. parameters of the steering and propulsion systems) and treat them in a correct way, these un­ certainties can be compensated by fine-tuning the standards (here, the wave height and wind force up to which the ship should satisfy the proposed criteria to be considered as safe); this fine-tuning can be done by applying the assessment procedures to a sufficiently big number of existing vessels, taking into account accident statistics and individual accidents, see IMO (2016a) and Shigunov (2018): the standards should be adjusted in such a way that the resulting assessment appropriately differentiates safe and unsafe ships.

assumptions used in the assessment procedure (use of time-average characteristics and, in the simplified assessment, also reduced number of assessment cases and simplified equations) and the uncertainties of methods used to define input elements. The latter uncertainty is controllable; the uncertainty introduced by the simplified assessment is evaluated in this paper, and the remaining uncertainties (i.e. un­ certainties due to simplifications in criteria and assessment procedure) can be pragmatically addressed by fine-tuning the standards (the wave height and wind force up to which the ship should satisfy the proposed criteria to be considered safe) in such a way that the resulting assessment appropriately differentiates safe and unsafe ships. Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgements This work was partly supported by the Collaborative Project Energy Efficient Safe SHip OPERAtion (SHOPERA), Grant Agreement 605221, cofunded by the Research DG of the European Commission within the FP7 Thematic Priority Transport. References

7. Conclusions

Blendermann, W., 2014. Practical Ship and Offshore Structure Aerodynamics. Technische Universit€ at Hamburg, Arbeitsbereiche Schiffbau. Brix, J., 1993. Manoeuvring Technical Manual. Seehafen Verlag, Hamburg. Faltinsen, O.M., Minsaas, K.J., Liapis, N., Skjørdal, S.O., 1980. Prediction of resistance and propulsion of a ship in a seaway. In: Proc. 13th Symp. Naval Hydro. Fujiwara, T., Ueno, M., Ikeda, Y., 2006. Cruising performance of a large passenger ship in heavy sea. In: Proc. 16-th Int. Offshore and Polar Engineering Conf., vol. III, pp. 304–311. IMO, 2002. Standards for Ship Manoeuvrability, Resolution MSC, vol. 137, 76. IMO, 2010. Report of the Working Group on Energy Efficiency Measures for Ships, MEPC 60/WP.9. IMO, 2012. Consideration of the Energy Efficiency Design Index for New Ships – Minimum Propulsion Power to Maintain the Manoeuvrability in Adverse Conditions, Paper MEPC 64/4/13 Submitted by IACS, BIMCO, INTERCARGO, INTERTANKO and OCIMF. IMO, 2012. Background Information to Document MEPC 64/4/13, Paper MEPC 64/INF.7 Submitted by IACS. IMO, 2012. Interim Guidelines for determining minimum propulsion power to maintain the manoeuvrability of ships in adverse conditions. IMO Circ. MSC-MEPC.2/Circ.11. IMO, 2013. Interim guidelines for determining minimum propulsion power to maintain the manoeuvrability in adverse conditions. IMO Resolution MEPC 232 (65). IMO, 2014. Amendments to the 2013 interim guidelines for determining minimum propulsion power to maintain the manoeuvrability in adverse conditions. Res. MEPC.232(65). IMO Resolution MEPC 255 (67). IMO, 2015. Amendments to the 2013 interim guidelines for determining minimum propulsion power to maintain the manoeuvrability in adverse conditions. Res. MEPC.232(65), as amended by Res. MEPC 255(67). IMO Resolution MEPC 262 (68). IMO, 2016. Results of Research Project “Energy Efficient Safe Ship Operation” (SHOPERA), Paper MEPC 70/INF.33 Submitted by Denmark, Germany, Norway and Spain. IMO, 2016. Study on Minimum Power Requirements (MacRAW), Paper MEPC 70/INF.28 Submitted by the Netherlands. IMO, 2017. Draft Revised Guidelines for Determining Minimum Propulsion Power to Maintain the Manoeuvrability of Ships in Adverse Conditions, Paper МЕРС 71/ INF.28 Submitted by Denmark, Germany, Japan, Spain and IACS. IMO, 2017. Progress and Present Status of the Draft Revised Guidelines for Determining Minimum Propulsion Power to Maintain the Manoeuvrability of Ships in Adverse Conditions, Paper МЕРС 71/5/13 Submitted by Denmark, Germany, Japan, Spain and IACS. ITTC, 2018. Recommended Procedures and Guidelines 7.5-02-07-02.8: Calculation of the Weather Factor Fw for Decrease of Ship Speed in Wind and Waves. ITTC, 2002. Recommended Procedures and Guidelines 7.5-02-07-02.2: Prediction of Power Increase in Irregular Waves from Model Experiments in Regular Waves. Liu, S.K., Papanikolaou, A., Zaraphonitis, G., 2015. Practical Approach to the Added Resistance of a Ship in Short Waves. ISOPE, Hawaii, USA. Liu, S.K., Papanikolaou, A., 2016. Fast approach to the estimation of the added resistance in head waves. Ocean Eng. 112, 211–225. MAN, 2014. B&W G60ME-C9.5-TII Project Guide. Electronically Controlled Twostroke Engines, Edition 0.5. Moor, D.J., Murdey, D.E., 1970. Motions and propulsion of single screw models in head seas, Part II. TINA, 112.

The introduction of EEDI raised the need to norm (standardise) ship’s manoeuvrability under adverse conditions, which requires definition of assessment criteria and corresponding measures and standards. The research projects conducted by IACS, EU (SHOPERA) and JASNAOE proposed steering ability and propulsion ability criteria as minimum re­ quirements for manoeuvrability of ships in adverse conditions, related to the installed power. This paper addresses evaluation of these criteria in practical design and regulatory approval, keeping in mind that the problem of manoeuvrability in adverse weather conditions is very difficult and presently dealt with only in few advanced research centres worldwide. A flexible assessment framework is proposed, which includes three alternative levels of complexity: the most accurate comprehensive assessment (level 3) allows the best accuracy but requires a big number of input elements; a less complex simplified assessment (level 2) involves a reduced number of assessment situations, reduced complexity equations and significantly less input elements; the simplest assessment (level 1) relies on empirical formulae to define the required installed power directly as a function of main ship parameters. Another factor contributing to the flexibility of the proposed assessment framework is that any input element, required in the comprehensive and simplified assessment procedures, can be defined separately and with different methods (either experimental, numerical or empirical), depending on the needs and possibilities of designers and administrations. Experimental, numerical and empirical methods are, in principle, established and available for all input elements apart from the time-average wave-induced forces and moments: their experimental definition requires expensive measurements in a seakeeping basin, whereas numerical and empirical methods for them are only developing. Especially useful for practical design and approval is the availability of simple empirical formulae dedicated specifically for the simplified assessment; several such formulae are developed and validated in this paper for wave- and wind-induced forces and rudder forces. The uncertainty of the resulting procedures and practical ways to deal with this uncertainty are discussed. The uncertainty of the empir­ ical level 1 assessment can be compensated only by its excessive conservativeness. For the comprehensive and simplified assessment procedures, the uncertainty stems from simplifications in criteria, 15

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