**3. On Calm-Water Manoeuvrability Criteria and Corresponding Standards**

*3.1. General Specifics of Manoeuvring Standards*

It should be noted that the parameters defining the manoeuvring performance of ships for a long time belonged to the first "contractual" group that is at best they were specified in the contract but it was clear that this situation could not last forever. As long as the manoeuvring qualities were related to the navigational safety, in the middle of the 20th century first attempts to establish manoeuvring criteria and to set corresponding standards were undertaken.

Even though ship seakeeping and ship manoeuvrability in some sense can be viewed as two faces of ship dynamics, the differences between possible standardizing strategies in both fields are, however, substantial:


4. While ship mathematical models serving as a basis for standardizing the intact stability may only consider one degree of freedom, i.e., accounting for the roll motion only, this cannot be allowed for the manoeuvring motion where a mathematical model must have at least two degrees of freedom, i.e., the coupled sway and yaw and often also the surge motion must be included. To prevent possible misunderstandings, it should be emphasized that the often-used Nomoto equations, contrary to their appearance, implicitly embrace two degrees of freedom.

Here the verifiability requirement may be very difficult to meet as long as it presumes the possibility to check any manoeuvring criterion in full-scale trials. This is not so easy even with calm-water criteria: high-quality measurements require practical absence of wind which is a rather rare situation and typically full-scale data suffer from considerable uncertainties. The difficulties are becoming even more serious for criteria related to the waves and wind as it is necessary to fix a certain level of external perturbations. This problem was discussed by Dand [26] who expressed the opinion that the requirement of the possibility of a full-scale verification of any particular standard could be lifted. He suggested that "a combination of a simulation model and suitable indices derived from past best practice, be used as a way of assessing manoeuvrability of vessels".

While the number of publications on the intact stability and unsinkability criteria is definitely superior to that on manoeuvring standards, the latter is also quite significant. Rather complete reviews on proposed manoeuvring criteria and standards can be found in [12,22] and the following text is mainly focusing on the sources related to the development and validation of the existing IMO standards [1].

There exists a more or less clear understanding of which calm-water manoeuvring qualities should be standardized although, e.g., Quadvlieg [27] tried to extend the list of standard criteria, aiming at the assessment of manoeuvring prediction methods. In the following, only dlassic, commonly recognized criteria will be discussed.

It is recognized that regarding manoeuvring qualities of surface displacement ships in calm water the following properties are of primary interest:


A ship is assessed as perfectly controllable if it can be characterized by a high level of these two properties at the same time although often one of them may be partly sacrificed. For all purposes, it is important to establish reasonable measures for these qualities.

#### *3.2. Turning Ability*

This quality can be subdivided into the turning ability per se which is also called sometimes the ultimate turning ability and the so-called initial turning ability (ITA).

The (ultimate) turning ability of a ship is its capability to describe a highly curved trajectory in absence of external factors. When the moderate manoeuvring (excluding crabbing and rotation with the help of side therusters) is considered, a very natural measure of the turning ability can be introduced which is the steady turning diameter at full helm non-dimensionalized by the ship length. In reality, the easier to register "tactical diameter" is usually preferred. It is, however, well correlated with the steady turning diameter.

According to the IMO standards, the tactical diameter is required to not exceed 5 ships length independently of the value of that length and of the speed of the ship.

Despite a certain terminological similarity, the initial turning ability is rather different from the ultimate turning ability discussed above: not the path curvature is here considered but the ability of a ship to rapidly change the heading enough. In most cases, the 10 deg heading change is considered, and no helm check is performed. The latter indicates that it does not go about a true course-changing manoeuvre. The meaning of standardizing the initial turning ability consists in preventing temptations to assure good turning ability at large helms at the expense of the inherent stability of the ship and without increasing the effectiveness of the rudder: despite technically good turning abilities such ships will be slow in responses to the rudder deflections or, in other words, they will be not well controllable. The ITA is correlated with both the ultimate turning ability and with the ship directional stability although not in a quite straightforward way. It is clear, however, that a ship with a sufficiently large (say 3–4% of the centreplane area) rudder working outside of the propeller slipstream (a rather typical configuration for naval ships) is very likely to possess, at the same time, perfect directional stability combined with the good turning ability both ultimate and initial. With a smaller rudder in the slipstream the combination of manoeuvring qualities may turn out less favourable and then invoking the ITA criterion can serve as a good remedy against unsatisfactory controllability of the ship.

#### *3.3. Directional Stability*

### 3.3.1. Definitions and Criteria

The directional stability is, in practical terms, the capability of a ship to follow a straight path with moderate yawing, at a low average intensity of rudder orders and without an excessive strain of the human operator (helmsman) [22]. The ship is treated here as a closed-loop system and the course-keeping process is interpreted as continuing mitigation of deviations from the ordered heading caused by low-level excitations from sea waves. On directionally unstable ships this process can be accompanied by selfsustained oscillations whose admissible frequency and amplitude are to be standardized. Even though criteria of this type had been suggested, see, e.g., [28], they appeared to be impractical as the mentioned parameters of oscillations depend also on the parameters of the controller represented in this case by the helmsman. The undesirable influence of the controller is eliminated if the "inherent" stability of the ship with the rudder fixed in its neutral position is considered. Both the practical stability and the inherent stability are correlated: the higher is the degree of the inherent directional stability, the easier and better is the course keeping. However, quantitative criteria of the inherent directional stability are not obvious. The most natural criteria, at first sight, must be associated with the eigenvalues of the mathematical model of the sway-yaw motion linearized around the straight run. It is known that both eigenvalues are always real, and one of them has a relatively small absolute value and can be either positive or negative for different ships. The positive eigenvalue correspond to inherently unstable ships, the negative one—to inherently stable craft and it is obvious that the absolute value can serve as a measure of the stability/instability degree. Even though proposals to use the critical eigenvalue or the corresponding time lag as a stability criterion were made [29], its inconvenience became clear very soon: there is no way to check the value of this criterion directly from the results of full-scale or model-scale trials. As result, most of the proposals were exploiting more practical indirect measures.

#### 3.3.2. Connection with Parameters of the Spiral Curve

The first of such indirect criteria is based on the configuration of the static characteristic (spiral curve) of a ship, which represents the dependence *r* (*δR*) of the non-dimensional rate of yaw or the path curvature *r* on the rudder angle *δ<sup>R</sup>* in a steady turn. When the ship is directionally unstable, this curve possesses a hysteresis loop around the origin and the dimensions of this loop, i.e., its height and/or width can serve as measures of the degree of instability [12,22]. Some specialists believed that only some admissible degree of instability must be specified while all inherently stable ships are equally and unconditionally acceptable [30,31]. However, the stability margin can be very different and, aiming at standardizing directional stability of naval combatants and trying to keep the spiral curve as the main source of information on manoeuvring qualities, it was proposed by Sutulo [22] to standardize the value of the spiral curve derivative at the origin, i.e., d*r* d*δ<sup>R</sup>* ( ( ( *<sup>δ</sup>R*=<sup>0</sup> or of its normalized modification *<sup>δ</sup><sup>m</sup> <sup>r</sup>*(*δm*) · <sup>d</sup>*r* d*δ<sup>R</sup>* ( ( ( *δR*=0 , where *δ<sup>m</sup>* is the maximum rudder angle.

There are reasons to believe that the optimal value of the latter normalized parameter should be 1.0 which corresponds to an absolutely straight spiral curve. This can be viewed as an educated guess but this guess is, however, indirectly confirmed by the fact that all high-speed moving objects, e.g., steady-wing aircraft, are highly linear. The aircraft are not only always inherently stable but typically a certain margin of the so-called static directional stability is required [20]. It is interesting to note that Oltmann [32] also considered a similar though inversed criterion <sup>d</sup>*δ<sup>R</sup>* d*r* ( ( ( *<sup>δ</sup>R*=<sup>0</sup> and he demonstrated invoking multiple full-scale data for unstable ships that this criterion is only weakly correlated with the hysteresis loop width.

However, such "initial tangent" criteria have not gained recognition. One of the causes is that it is difficult to estimate these quantities from full-scale trials that must include the Bech reverse spiral test being rather difficult to execute let alone that the obtained estimates of the derivatives can be highly uncertain. Regarding the fact that most civil ships indeed remain well steerable even at some moderate degree of inherent instability, the dimensions of the hysteresis loop can serve as suitable indicators of acceptable directional stability at least for merchant ships.

However, the analysis based on the spiral curve configuration also has inconveniences related to full-scale trials. The Dieudonné spiral manoeuvre is not the easiest manoeuvre to execute as it requires substantial water area and is long in duration. The presence of wind is especially unfavourable for this manoeuvre as it makes practically impossible reaching the steady turn regime at each rudder deflection. To obtain more or less reliable averaged results in wind, it is necessary to perform at least two full turns at each helm which would increase the duration of the trials to unacceptable values. That is why, while requirements to the parameters of the spiral manoeuvre are formulated in the Explanatory Notes to the IMO manoeuvring standards [33] they were not even mentioned in the main text of the Standards [1] where an alternative in form of overshoot angles in zigzag tests was preferred [34]. However, Norrbin [35] characterized the fact that the spiral characteristic finally did not enter the main text of the IMO standards as "unfortunate".

#### 3.3.3. Connection with Parameters of the Zigzag Manoeuvre

As long as there is no way to establish an analytical connection between the overshoot angles and, say, traditional stability indices, this solution raises, however, the following questions:


As will be seen from the review below, the existing data are rather contradictory and this fact alone was sufficient for stimulating some criticism with respect to the existing IMO standards [1,23,33]. For instance, the data presented in [23] indicated that the relation between the loop width and the overshoot angles is rather rigid: the larger is the former, the larger are the latter. Norrbin [17] discussed the relative importance of the loop width and height and pointed out that the overshoot angles are better correlated with the loop width than with its height. Nikolayev et al. [36] discovered that the correspondence between the overshoot angles and the loop width alone can be very poor but can be improved if the loop height is used as an additional factor.

It is generally recognized that the following 3 overshoot angles adopted as standard measures are significant: the first overshoot angle in the 10◦–10◦ zigzag (OS1), the second overshoot angle in the same zigzag (OS2) and the first overshoot angle in the 20◦–20◦ zigzag (OS3). It is not possible to link analytically the parameters of Kempf's zigzag manoeuvres to other measures of the inherent directional stability, multiple simulations and trials confirm that typically the higher is the directional stability, the smaller are values of the overshoot angles. There is also a direct evidence that reduction of OS1 is beneficial for steering. In particular, such a conclusion was obtained in [37] based on multiple interactive simulations in the conditions of a straight and double-bent channel under influence of current. Many specialists suspected that these three criteria are not of equal significance. For instance, Ræstad [38] came to the conclusion that the necessity of inclusion of OS3 into the Standards was not confirmed by analysis of full-scale data and by polling the seafarers although OS3 is typically considered important as a measure of the turn checking ability. At least, Yoshimura et al. [39], on the other hand, concluded that the OS1 requirement is less restrictive than OS3 while the least restrictive is OS2. At the same time, according to [40] OS1 is the strictest criterion.

Yoshimura et al. [39] showed that the correlation between the loop width and the overshoot angles OS1 and OS2 was confirmed by full-scale trials carried out with 50 ships. It can be noticed, however, that the shown correlation was better than in most other sources. Rhee et al. [41] performed a rather detailed study of the width–height correlations. Simulations showed a rather strong correlation with the width and a somewhat weaker one with the height of the loop. At the same time, the full-scale data demonstrated substantially inferior correlation in general and with OS3 it was even practically absent. As to the 10◦–10◦ zigzag overshoots, OS1 correlated better with the loop height while OS2—with its width. Haraguchi and Nimura [42] have found, performing simulations based on tank data, a definitely positive width–angles correlation for pod-driven ships. A good correlation between the loop width and the overshoot angles was obtained by Sohn et al. [43] for a number of simulated ships but Yamada [44] pointed out that his data do not confirm such correlation.

The brief review above might leave an impression that the correlation between the parameters of the hysteresis loop is uncertain as the available data are controversial especially regarding full-scale sea trials data. However, it must be taken into account that such data are always given without uncertainty estimates while the uncertainties may be considerable for measurements taken in real sea conditions. In addition, there is sufficient evidence that the hysteresis loop height though ignored by the existing standards also influences the ship's behaviour in steering and the values of the overshoot angles thus impairing their correlation with the loop width. It must be admitted that detailed study of the influence of the loop width–height relation is still the matter of future research and so far even qualitative discussions such as that by Norrbin [17] are very rare.

However, in practice, there is no doubt that both the loop width and the overshoot angles can serve as reasonable measures of the directional stability of ships and the overshoot angles have the advantage to suit not only unstable but also directionally stable vessels. Remarkably, Ræstad [38] demonstrated using full-scale measurements and questionnaires distributed among seafarers that ships with subjectively abnormal behaviour indeed exhibit especially large overshoot angles.

#### *3.4. Analysis of IMO Criteria of Directional Stability*

The measures of the ship's directional stability used in the IMO standards [1,33] are reviewed and analysed in this subsubsection. It is important to keep in mind that these standards had been devised for calm-water steering.

The measures for the turning ability in IMO standards in terms of the ship length are fixed for all vessels but the required degree of the directional stability depends on the ship reference time *T*ref = *L*/*V*, where *V* is the speed specified in the standards. The stability requirements can be formulated either in terms of the hysteresis loop width (Figure 1) or in terms of the overshoot angle OS1 (Figure 2). The IMO requirements are shown on the plots as a solid line (graphs plotted in dotted and dash-dot lines and the meaning of *L*1,2,3 will be discussed below, in the next section). If the reference time is smaller than 9 or 10 s, the requirement becomes flat. In particular, every inherently stable ship unconditionally satisfies the spiral loop requirement although further tightening of the inherent stability standard for small values of the reference time would seem more natural. However, any extrapolation on the plot for the loop width can only result in unrealizable negative values, see the dotted line in Figure 1 and application of alternative parameters of the spiral curve, such as its initial slope, discussed in the previous section is not compatible with the IMO

standard. At the same time, a reasonable extrapolation can be performed on the overshoot angle plot, see the dashed line in Figure 2.

**Figure 1.** Standards for hysteresis loop width according to IMO standards and alternative requirements.

**Figure 2.** Existing and proposed standards for the first overshoot angle in 10◦–10◦ zigzag.

As to the reference time exceeding 9 s, such ships are allowed to be directionally unstable and only the degree of instability is limited. As the reference time is increasing further, the inherent stability requirements according to the existing IMO standards are becoming looser and looser which looks consistent for manoeuvring in calm water. Constant limiting

values applied again for *T*ref > 30 s are explained by the necessity to have some helm margin at large loop width.

Dependence of the stability criteria on the ship reference time looks quite logical from the viewpoint of the ergatic approach: the smaller and faster is the craft, the higher is the required degree of directional stability. This is explained by the obvious fact that smaller time lags of the controlled object require also smaller time lags of the controller. Even though the human operator is adaptable in a rather wide range of dynamic properties of the controlled object, steering faster and smaller craft requires from the operator a higher degree of concentration and tension which cannot be completely eliminated even after intense and long training.

The IMO-adopted standardizing numerical values of the manoeuvring criteria are a result of intense and long research work and of multiple discussions carried out over many years. So, it can be saidthat they represent some acceptable compromise [34]. However, they should not be viewed as a kind of dogma and alternative values of the manoeuvrability measures were proposed not only before but also after the interim and even definitive standards were approved. For instance, in one of the earlier proposals [45] it was suggested to allow the hysteresis loop width not exceeding 4 degrees as a measure of an acceptable degree of instability for all ships independently of the reference time. A number of values of the parameters of the hysteresis loop proposed from 1959 to 1987 were listed by Norrbin [17]. Li and Wu [41] suggested to consider manoeuvring criteria as fuzzy variables but this suggestion did not have any impact apparently because it was unclear how to use fuzzy requirements in a document of legal nature.

Yoshimura et al. [39] analysed full-scale data for 50 ships and came to the conclusion that OS2 should be increased by 5 deg and OS3 should be defined as doubled OS2 while in fact it was fixed at 25 deg which looked too strict for ships with *T*ref > 12 s. On the other hand, Rhee et al. [41] suggested easing the overshoot angles requirements for small *T*ref having pointed out that the smaller ships are easier to operate in narrow waterways without considering, however, external disturbances. Sohn et al. [43] performed interactive simulations in a narrow waterway under the action of wind and current and discovered that in discordance with the IMO standards ships with larger *T*ref and with the same loop width were more difficult to steer (Nishimura and Kobayashi [46] came to similar conclusions). Alternative flat standards, 20◦ for OS1 and 40◦ for OS2 independently of the *T*ref value, were proposed in [43] on the basis of subjective assessments and data on mean rudder deflections. Another flat standard for only OS1 was proposed by Oltmann [32]: the suggested value of 17◦ was close to the average of the IMO standard over the whole *T*ref interval. In theory, a lower speed must not impair either the turning ability or the directional stability in calm conditions although such effect was traced by Yasukawa et al. [47] in the case when the propeller loading was substantially reduced. However, as the reference time of the ship *T*ref = *L*/*V* at a lower operational speed *V* becomes larger, the standard related to the stability will be easier to meet according to the existing IMO requirements (Figures 1 and 2).

It is worth noting that the ship reference time can serve, to some extent, as an indirect measure of the degree of powering: the smaller is *T*ref, the better powered is the ship. Hence, according to the existing IMO standards, the less powered is the ship, the less directionally stable it may be. Of course, such simple and general parameter as *T*ref is not capable to account for all specifics reflecting the capability of this or that ship to withstand adverse conditions but in general it captures that capability fairly enough to be used in first-level standards: the smaller is *T*ref the faster is the ship at the same length and, in general, the higher is the disposable power. All specifics related to the characteristics of the propulsion complex (different configurations can reveal very different reactions to augmentation of the resistance) should be accounted for in higher-level criteria or, even preferably, within special design and simulation procedures.

Looser directional stability requirements for larger and slower ships have always been considered beneficial for the designers as in this case good turning ability can be achieved with less effective steering devices. However, when external loads of any nature, roughly independent of the ship speed, are taken into consideration, it can be expected quite the opposite: as the proper hydrodynamic forces on the ship hull and the rudder are roughly proportional to the square of the speed, a more effective steering device must be required. In other words, if one needs to keep the resisting capacity of a ship to given external factors at a lower speed, one must stimulate installation of a more effective steering device. Stimulation can be achieved by augmenting the directional stability requirements without easing (or maybe even with tightening) those for the turning ability. This task is always feasible although not always very easy.

Possible solutions for a single-screw vessel could be:


It is expected that all these solutions may presume augmentation of maximum deflection angles as compared to the orthodox 35 degrees. Of course, these solutions make the steering complex heavier, bulkier and more expensive but this is inevitable as a definite improvement of the steering ability has its price.

#### **4. Accounting for Adverse Conditions and External Perturbations in**
