When a ship becomes damaged, the flooding need not be confined to the immediately ruptured compartments, but may also extend to other compartments due to the presence of pipelines, ducts or other forms of compartment connections. To this end, PIAS is equipped with a number of tools and mechanisms that will be discussed in this chapter.
Background from tools for ship-internal connections in PIAS
If a compartment is damaged in such a way that it is open to sea water then it will obviously be flooded, which can also extend further into the vessel through all kinds of connections between compartments. In stability regulations, the word progressive flooding is sometimes used for this, but we rather avoid this word because it suggests that the flodding continues until it is fatal, which of course is not necessarily the case. Obviously, this process can be modelled in PIAS and computed. There are two facilities for this purpose:
- The first dates back to ±1990 and is called Complex intermediate stages of flooding. This works on the basis of non-uniform filling percentages per compartment, supplemented where necessary by virtual compartment connections. This allows to specify whether there was a connection between two compartments, however, it had no geometry (although it had an optional threshold height, called a ‘critical point’). There was also only a single connection possible between two compartments. In Define compartment connections, a table of such connections can be defined, which is used in damage case generation to co-generate such complex intermediate stages with. This Probdam function has been extended in 2018 and that will also be the last modification to this ‘complex stages’ system. Although it will not be disappear, its further development has stopped, as it has been replaced by consecutive flooding. Complex stages are discussed in more detail in Complex stages of flooding (before 2021).
- The second system was introduced in 2021 and is called Consecutive flooding. It was developed based on the specification New inter-compartment flooding mechanism in PIAS, which was drafted in 2018, in collaboration with a number of key users op PIAS. Consecutuve Flooding works on the basis of the actual geometry of pipes and connections, and can also calculate flooding in time domain.
This chapter discusses the following:
Flooding through ducts and pipes: Consecutive Flooding, after 2020
This system is discussed in the three sections below, viz.:
- The basic operation of the conventional intermediate stages of flooding method in consecutive flooding.
- The basic operation of the time domain computation in consecutive flooding.
- The background of the definition of some pipeline properties in Layout.
This order may appear to be a bit unnatural — because we should first define, before being able to use — but is nevertheless deliberately chosen this way.
With conventional intermediate stages of flooding (“fractional”)
This method was conceptualized given two facts:
- Standard stability regulations apply the concept of “intermediates stages of floodings” of fixed percentages of flooding, i.e 25%, 50%, 75% and 100%.
- Not all compartments are always flooded with the same percentages, i.e. with small connections between compartments the flooding of the connected compartments may lag behind the flooding of the ruptured compartment.
In the elder “compartment connection” method of PIAS the latter is facilitated by so-called “complex stages of flooding”, which support individual percentages of flooding for different compartments. This offered full freedom, however at the cost of significant manual input labour. For the numerous damage cases of probabilistic damage stability this is not practical, so module Probdam offered a specific feature to generate these complex stages, where the binary concepts of “open” and “pipe” (as discussed in Damage cases generation including "progressive flooding") offered a flexibility sufficient for the vast majority of cases, but not for all cases. So, in the consecutive flooding system a novel subsystem for unequal intermediate stages of flooding has been created which is a) flexible, b) based on generation so does not require much user input, and c) works for all PIAS damage stability calculation modules.
This subsystem maintains the notion of “percentual stage of flooding”, because a) this is a fundamental concept in present damage stability regulations, b) therefore this concept is familiar to authorities and classification societies and c) the concept is easy to understand. In order to have a shorthand word for this concept it was labelled “fractional”, because essentially it fills compartments by &;squo;fractions’ of the final volume. So that fraction is the unit, which enables us to introduce an integer “delay” in the flooding of connected compartments. Assume, for the time being, that the percentages of flooding are 0, 25, 50, 75 and 100%, so one fraction corresponds with 25%. If we use a delay of zero (so, no delay), then the flooding of a connected compartment will obviously be the same as for the ruptured compartment:
Fraction ruptured compartment | Fraction connected compartment |
1 (=25%) | 1 (=25%) |
2 (=50%) | 2 (=50%) |
3 (=75%) | 3 (=75%) |
4 (=100%) | 4 (=100%) |
With a delay of 1, there will be a single fraction delay:
Fraction ruptured compartment | Fraction connected compartment |
1 (=25%) | 0 (=0%) |
2 (=50%) | 1 (=25%) |
3 (=75%) | 2 (=50%) |
4 (=100%) | 3 (=75%) |
4 (=100%) | 4 (=100%) |
The last row is added because the filling should always end up with all flooded compartments filled to their final levels.
And with a delay≥4:
Fraction ruptured compartment | Fraction connected compartment |
1 (=25%) | 0 (=0%) |
2 (=50%) | 0 (=0%) |
3 (=75%) | 0 (=0%) |
4 (=100%) | 0 (=0%) |
4 (=100%) | 1 (=25%) |
4 (=100%) | 2 (=50%) |
4 (=100%) | 3 (=75%) |
4 (=100%) | 4 (=100%) |
This was an example of a single connection between two compartments. But also cascaded connections are supported by nature, take for instance this configuration of three compartments and two connections (with each a delay of 1):
Three serially connected compartments
Fraction comp1 | Fraction comp2 | Fraction comp3 |
1 | 0 | 0 |
2 | 1 | 0 |
3 | 2 | 1 |
4 | 3 | 2 |
4 | 4 | 3 |
4 | 5 | 4 |
Also more complicated topologies are allowed. The delay factors for the different paths might contradict, but that poses not a real dilemma, because the smallest fraction determines the actual flooding, which is a sound logical consequence of the underlying assumptions. For example this case:
Four connected compartments
Fraction comp1 | Fraction comp2 | Fraction comp3 | Fraction comp4 |
1 | 0 | 0 | 0 |
2 | 1 | 1 | 1 |
3 | 2 | 2 | 2 |
4 | 3 | 3 | 3 |
4 | 4 | 4 | 4 |
Delay factors are given for each pipe segment (which is a connection between two joints or compartments, without any branch inbetween). That enables a pipe topology and delay factors such as:
Many connected compartments, with varying delay factors
Which will lead to eleven different stages of flooding (including the final stage).
That's the basic idea. And how realistic will modelling method be? Just as realistic as the whole presumption of fixed percentages of flooding, as imposed by all major damage stability rules. For added flexibility PIAS goes one step further, by allowing multiple (to a maximum of three) delay factors per pipe segment. In most cases a single delay factor will suffice, but even more complex scenarios than presented in this section can be modelled with combinations of factors.
Finally, a remark on the percentages of flooding as used in the examples of this section. As demontration, multiples of 25% have been used, but you will certainly be aware that in PIAS the number of intermediate stages of flooding is user-defined, as well as the percentage of each stage. So, where we have used multiples of 25% here, in reality for this percentage the user-defined flooding percentages will be applied.
In time domain
This functionality will be released about mid-2021. This manual section is still to be elaborated.
Hydrodynamic parameters from pipes and piping systems
The piping geometry and connectivity can be defined in combination with the internal (i.e. compartment) geometry, with module Layout. This is discussed in Pipe lines and piping systems. In order to keep data of the same categories as much together as possible, the flow-related choices and parameters will be discussed in this section.
Fluid flow resistance factors
Frictional resistance from pipes lines
Frictional resistance through pipes is in the essence a complex issue. In practice, however, there are a number of practical methods and parameters in use, and in PIAS we have chosen to implement some of them:
- The (cross-sectional) shape. Choice of round or square, the most common shapes.
- The cross-sectional dimension. If round then diameter, of square then edgelength. In meters, as commonly used in PIAS.
- The (dimensionless) resistance coefficient. Three common methods are implemented in PIAS:
- According to IMO resolution MSC.362(92), where the frictional resistance per meter length is 0.02 ÷ hydraulic diameter.
- With a user-specified Darcy-Weisbach coefficient, where the frictional resistance per meter of length is that coefficient ÷ hydraulic diameter.
- With a user-specified resistance coefficient per meter of length.
Fluid outlet energy loss
The resistance of fluid flowing through a pipe consists of two components. One is the frictional resistance, and the other one is due to the energy loss of the fluid outflow at the pipe outlet. The latter one simply follows from the fact that the fluid travels with some velocity through the pipe, and hence carries kinetic energy. After outflow (into a reservoir, or into the open air) that velocity vanishes, so the energy content also has gone. This is inevitable, also in a frictionless world. This phenomenon should be included — once, not twice. Unfortunately the different IMO regulations are not consistent in this respect. There are three IMO regulations involved, res. A266 (1973), MSC. 245(83) (2007) and MSC. 362(92) (2013). In A266 and 362 this outflow loss is included implicitly, while in 245 a energy loss factor should be included explicitly, in combination with frictional resistance coefficients of the piping configuration.
PIAS offers you this choice. It can be given in a user setting, in Layout, labelled ‘Processing of outlet losses’ (please see General piping settings), with binary choice ‘Explicitly user-defined by means of resistance coefficients’ or ‘Implicitly taken into account’. Please ascertain to set this switch in accordance with the resistance coefficients you assign to the pipe line components, and with this background in mind:
- In A266 en 362 the resistance coefficient formula is \( 1 / \sqrt{ 1 + \sum{K} } \). This factor 1 in the denominator in all likelihood represents the pipe outlet energy loss. In PIAS this is implemented so that it is only included for pipe ends that exit into a compartment or into seawater, and where actual outflow occurs (i.e., not inflow).
- In MSC.245 the formula reads \( 1 / \sqrt{\sum{K} } \), where the result may not be taken smaller than 1. To give the user maximum freedom, that limitation to 1 is intentionally not included in PIAS. The user himself must ensure that the resistance coefficients are specified conscientiously (and, incidentally, only applies the factor of 1 for pipe ends where actual outflow occurs).
- If you find it confusing that multiple types of formulas are used in the various IMO rules, and that the background of this factor 1 is not even properly explained then you will find an ally in SARC.
Damage stability criteria to be applied
When assessing the stability of a damage with a cross flooding device, the question may arise “what are the applicable stability criteria”? Those for final stage or those for intermediate stages of flooding? In a time domain calculation this can be linked to an equalization time, but for a calculation with conventional intermediate stages of flooding that information is missing. To allow the user to influence this, PIAS has a facility to specify whether a pipe is large or small. These terms ‘large’ and ‘small’ have no relationship to the exact pipe size, but only to the choice of stability criteria to be applied, in this way:
- Whith ‘large’ the cross flooding is assumed to be quick, so intermediate stages are thus checked against the user-specified criteria for intermediate stages of flooding. If those are not defined, then the criteria for final stages are used, as there is nothing else.
- With ‘small’, the flooding process is considered to occur slowly, so that also the intermediate stages are tested against the stability criteria for the final stage.
As mentioned earlier, this mechanism applies only to the conventional intermediate stages of flooding. For a time domain calculation, the choice on which criteria to be applied depends on the time required for equilization, which can be set at TODO reference.
Layered definition of flow-related parameters
For the purpose of damage stability calculations, many properties of pipe components can be specified, such as dimensions and coefficients. Because many pipes will be similar it can happen in practice that one is typing in the same numbers over and over again, and nobody likes that. In order to increase the ease of use in this respect, PIAS is therefore equipped with the feature to specify some of those parameters in ‘layers&rsquo. So, a parameter can explicitly be ‘not specified’, which will make PIAS to look for the corresponding parameter in a higher layer.
- The pipe resistance coefficient, as discussed in Frictional resistance from pipes lines, is initially taken to be as specified for that pipe section (which is in a segment). If not specified at that level, then the coefficient that applies to the network to which this pipe belongs is taken. If that is not specified either, then PIAS will look one level higher, to the default given in the general pipeline settings (see General piping settings). If it is not specified either then the pipe is considered free from resistance.
- The component resistance coefficient is initially taken as specified for that component. If not specified at that level, the default specified in the general pipeline settings is taken. If that is not specified either, the component is assumed to have no resistance.
- The resistance coefficient of a connection is analogous to that of a component: if it is specified for that particular connection, then it is used, and otherwise the default.
- For the other resistance parameters (shape & size), those asspecified for that pipe, component or connection are taken in the first instance. If these are not specified, then the parameters as defined with their network are taken. If that is not specified either, then PIAS looks one level higher, at the default shape and dimensions of the system where this thing belongs to. If those are not specified either, then the thing is assumed to have no resistance. There is deliberately no global default for shape and dimensions, because in general there will be no standard pipe size for the ship as a whole. For a particular system, e.g. ballast or sounding pipe system, on the other hand such a standard may exist.
- A time-domain calculation is performed with a fixed time interval, in seconds. This can be specified globally at the general settings for damage stability calculations (see TODO ref to chapter), but it is also possible to set a so-called ‘overruling time interval’ per piping network. If this is used, it prevails. This mechanism offers the user the possibility to apply a longer interval in networks with small pipes than with large ducts.
Clearly, this system is designed to minimise user input. Indeed, one can specify a default at a certain higher level (e.g. at the level of a piping system) and leave all the items below it which correspond to that default to ‘not specified’. Only the exceptions then actually have to be given individually.
Time steps, and stability computations in time domain
Complex stages of flooding (before 2021)
Preliminary remark: as mentioned in the introduction to this chapter, PIAS now has two systems that can be used to account internal flooding between compartments. The subject of this section's system, complex intermediate stages, was in development until ±2020 and was then replaced by the more advanced Consecutive flooding system, see Flooding through ducts and pipes: Consecutive Flooding, after 2020.
This section a number of distinct facilities will be discussed:
- When necessary PIAS takes into account intermediate stages of flooding. Normally these stages are equal within a damage case for all damaged compartments. With this option a mechanism is available to define the intermediate stages of flooding more specifically, especially according to IMO regulations for seagoing passenger vessels.
- Special kinds of openings can be defined for which it will not be assumed that the vessel will immediately sinks when flooded, but for which the procedure described at the previous bullet will be adopted. Two types of such openings are available: internal openings, which connect the compartment with another compartment, and external openings, which connect a compartment with the sea.
- To define whether damaged compartments have the same level of liquid or not in intermediate stages of flooding.
- Calculation of cross-flooding times.
- The use of this function for the calculation of Ro-Ro ferries with water on deck (abbreviated to STAB90+50).
In each module for damage stability of PIAS, with the exception of the computation of floodable lengths, damage cases are defined at least by defining which compartments will be flooded for that case. This is discussed at Input and edit damage cases, where in the menu bar the [Flooding stages] function is included. When this fuction is used the following option menu appears:
Specify calculation type, number of intermediate stages and other parameters
The first option in this menu concerns the calculation type. There are four types of calculation:
- Non-uniform intermediate stages of flooding. This type must be used if intermediate stages of flooding (expressed as percentage of the final stage) are not equal for all compartments. For this calculation type, at the second line the number of intermediate stages can be defined, with a maximum of 12. The final stage of flooding should not be defined because it is included automatically.
- Intermediate stages with equal levels of liquid, or intermediate stages with unequal levels of liquid. The background of the equal level of liquid is discussed in Intermediate stages with global equal liquid level, however, that setting there is global. In this option you can set this property for each damage case individually.
- Time calculation for cross-flooding arrangements. With this option for each time step it is determined how much water enters a compartment, and what time a complete flooding of a compartment requires. For this calculation type also the time step and maximum number of time steps must be specified. The time step is used as an integration step in the calculation and this step must not be too large.
Finaly, this menu also contains the parameters ‘aft boundary damage’ and ‘forward boundary damage’, which are only relevant a calculation according to STAB90+50, in order to calculate the residual freeboard. Please bear in mind that the freeboard is derived from the deck line, from which the definition method is discussed in Deck line.
Specify intermediate stages and critical points, with calculation type `Non-uniform intermediate stages of flooding'
After selecting this option the following input screen appears which contains all damaged compartments:
Damage case Compartment | Connected with | Via critical point |
| | Length | Breadth | Height | SB&PS |
DEF | - | - | - | - | - |
PQR | Seawater | 10.123 | 8.123 | 6.123 | Yes |
STU | PQR | 23.123 | 8.123 | 6.123 | No |
XYZ | STU | 43.123 | 8.123 | 6.123 | No |
A critical point defines an internal opening between two damaged compartments. The compartment will only then be flooded (with the percentage of flooding in a certain intermediate stage) when the level of liquid of the compartment in `Connected with' is higher than the critical point. When for a critical point the column ‘SB&PS’ is set to ‘Yes’, than that point exists on SB and on PS (with an equal breadth from CL). The same mechanism is applicable to critical points if ‘Connected with’ is set to ‘Seawater’.
The mechanism contains three limitations:
- Weathertight openings cannot be taken into account, but of course weathertight openings may be specified as usual in Hulldef .
- A compartment which can be flooded through a critical point may not contain any liquid in intact condition.
- With the combination of critical points and intermediate stages of flooding the following mechanism applies:
- If the calculation is made without ‘global equal liquid level’ the procedure is as might be expected, that is, that every compartment has its own percentage, and its own level of filling. The compartment which can only be flooded through a critical point will only be flooded if the liquid level of the corresponding compartment exceeds the height of the critical point.
- A calculation with ‘global equal liquid level’ is ligically inconsistent with the concept of ‘critical point’. Therefore, for the question whether a compartiment is flooded through a critical point is solely determined at the final stage of flooding, and this condition (flooded yes/no) is also used at intermediate stages, regardless the actual liquid level at the critical point.
- If unequal percentages of flooding have been defined here, then the switch ‘Equal liquid level’, as dissussed in Intermediate stages with global equal liquid level will be ignored.
With the text cursor on a specific compartment, and prssing <Enter>, the next input screen appears in which the percentage of filling for a certain intermediate stage of flooding for that compartment can be defined, for example:
Compartment XYZ |
Percentage of filling | Water on deck | Stage Number |
25 | No | 1 |
50 | No | 2 |
75 | No | 3 |
100 | No | 4 |
100 | No | 5 |
100 | No | 6 |
A calculation with all compartments filled with 100% does not have to be defined, because this is the final stage of flooding which is calculated automatically.
Water on deck
According to the rules of the ‘Agreement concerning specific stability requirements for Ro-Ro passenger ships undertaking regular scheduled international voyages between or to or from designated ports in North West Europe and the Baltic Sea’ (Circular letter 1891), as adopted on 27-28 February 1996. A.k.a. as ‘Stockholm agreement’ and by EU directive 2003/25/EC 2003 also applicable to amongst others the Mediterranean. The core of the regulations is an additional amount of water on deck, dependant on the residual freeboard. To include the effects of water on deck:
- If necessary, specify the significant wave height, as discussed in Significant wave height for SOLAS STAB90+50 (RoRo).
- Define all spaces above deck as compartments.
- Define the deckline ( Deck line).
- Specify the correct permeability for damage stability for the compartments above deck.
- Include the relevant deck compartments in all damage cases.
- For each damage case define a complex stage of flooding, where all compartments below deck are flooded by 100%, and all above deck compartments are marked with ‘Yes’ in the column ‘Water on deck’.
- At each damage case two calculations are made: One with the upperdeck compartments damaged, without extra water on deck, and one with the upperdeck compartments intact, with a fixed amount of water (which moves with heel and trim). At the last calculation in the last column marked ‘%’ the height of the extra amount of water can be read.
Specify intermediate stages and critical points, with calculation type `Time calculation for cross-flooding arrangements'
This calculation type is aimed at the very simple case of a compartment connected to sea water via a pipe or hole which has fluid flow resistance. Much more complex systems of pipes and connections can be addressed with Consecutive Flooding, see Background from tools for ship-internal connections in PIAS.
After chosing this calculation, a list of compartments is presented, where for each compartment can be specified:
- Whether the compartment is flooded through a cross flooding arrangement. If that is not the case the compartment is always filled for 100% (or, in other words, the water level inside is always equal to the sea water level).
- If the compartment is flooded through a cross-flooding arrangement, also the product of cross-section area S (in m^{2}) and a dimensionless speed reduction factor F must be specified. These parameters, as well as the calculation method for F, are further elucidated in IMO res. MSC.362(92). This PIAS computation of cross-flooding times is discussed with the menu where it can be invoked, in Calculate cross-flooding times.
Output
In the output of the deterministic damage stability (with Loading) with complex intermediate stages, the percentage of flooding is not printed in the heading but in the table with weights per compartment. For the intermediate stages of flooding of the computations of maximum allowable VCG' (as discussed in Maximum VCG' damaged tables and diagrams) only the number of the intermediate stage is printed.
Underpinning of damage stability computations during flooding
Underpinning at Consecutive Flooding (after 2020)
Three subsections, which are further to be elaborated:
- Particulars of flooding process with percentages of filling.
- Particulars of flooding process in time domain.
- Computation of stability (at larger angles), for both of these methods the same.
Underpinning at Complex Stages (before 2021)
While searching through decades-old documentation for the program approval by classification societies, we still came across the phrase that the damage stability calculation of PIAS includes the free-to-trim effect. A bit overdone to repeat that message, but just to be sure: it still does, also in Consecutive Flooding.
The method of calculation in intermediate stages of flooding is simple in the essence, with the following steps:
- For each set inclination angle, for the final stage of flooding the ship's floating position (= draft and trim) is determined, as well as the weight of ingressed sea water in each compartment. -At each intermediate stage of flooding of X%, linear interpolation is performed per compartment between the weight in intact condition (0% intermediate stage) and in fully damaged condition (100% intermediate stage). With those weights per compartment, the floating position is calculated at that gradient. And the righting moment.
- In this way, the term “intermediate percentual stage of flooding” is understood in a literal sense; it is precisely the percentual interpolation between 0% and 100%. This way provides continuity between 0 and 1% and between 99 and 100%.
- This calculation scheme is complicated a bit by a disturbing regulatory element, which is that in general for the determination of tank volumes the stability rules assume a permeability (μ) of 98%, while for damage stability the μ never needs to be taken higher than 95%. Particularly annoying and physically untenable, but a fact of life, which PIAS hides away by also interpolating the μ linearly between 0% and 100% stages of flooding, so that also in this respect continuity is achieved at 0→1% and at 99→100%.
- If a damaged compartment and an adjacent compartment are connected by a threshold or something similar then that can prevent the connected compartment from flooding. This can be specified as a so-called critical point — please refer for that to Specify intermediate stages and critical points, with calculation type `Non-uniform intermediate stages of flooding'. In intermediate stages of flooding, such a critical point behaves like a yes/no switch; at each angle of inclination, the final stage of flooding determines whether the critical point becomes overflowed, and if so, the connected compartment is filled in intermediate stages with the usual percentages, as if that whole critical point did not exist. And if the critical point does not overflow at 100% then the connected compartment is not filled at all in intermediate stages.
This scenario will not always represent reality, but it is the best fit for the dogma of the “fixed percentual intermediate stage of floodingt”. Those who do not agree with this approach will have to choose a more adequate scenario, e.g. a calculation in the time domain.
Two more details are worth knowing about the calculation method:
- It was mentioned above that with each inclination angle, location is determined, as well as the righting moment. The righting lever — GZ or GN'sin(φ) — is obviously that moment divided by the displacement. For that displacement, PIAS has a choice, see Righting levers denominator.
- As described, floating position GZ are determined at fixed inclination angles. The equilibrium angle is not calculated directly, it is determined by (nonlinear) interpolation on the GZ curve, viz. that angle at which GZ is zero.
Effect of internal openings on the GZ-curve
How does PIAS deal with an internal threshold or pipe which is submerged, and hence allows transfer of water, at an angle of heel which is beyond the static equilibrium? Take for example the GZ-curve as sketched below, where at angle P the upper edge of a partial bulkhead overflows, leading to the filling of an adjacent compartment and hence a deteriorated stability. It will be undebatable that the GZ will initially follow curve A, until angle P is reached, where a greater amount of ingressed water will lead to reduced curve B. However the question is what happens on the “way back”, i.e. with decreasing angle of heel? The water will not fully flow back over the bulkhead, so a curve more or less as indicated by C can be expected. And the subsequent question is which curve to use for the verification of GZ against stability criteria, A+B or C+B?
GZ-curve with internal opening submerged at angle P
In PIAS the past decades A+B has always been used — numerous calculations have been issued at classification societies and shipping inspections, and approved — based on the reasoning that the notion “way back” is never properly addressed, neither in literature nor in regulations. A few more arguments can be made in favour of this choice:
- The example above is expressive, but counter examples also exist. Take the GZ-curve as sketched below, with the partial bulkhead now immersed at an angle P which is much larger. If the vessel is subject to IMO's Intact Stability Code then the maximum heel for criteria evaluation is 50° — the weather criterion — while angle P is much larger than 50°. So, this loading condition meets all stability criteria long before P is reached, and there will not be a reduced C-branch.
- Will 50° then be the determining angle? In many cases not, because dynamic stability equality (area A=B from the weather criterion) may have been reached at a much smaller angle. So, the possible branching of the GZ-curve should be related to the applicable stability criteria, one way or another.
- Assume now that at the same large angle P not an internal opening overflows, but instead an external opening (e.g. a ventilation inlet), which sinks the ship. Then beyond P the GZ curve will vanish, so also branch B. If one would argue that with an internal opening branch C should be taken, then the same reasoning should be applied external ones. However, with branch B also C has vanished, so using this branch will render the whole GZ-curve non-existent. Nobody — user, researcher, authority nor classification society — has ever suggested such a ‘solution’, because it would be unrealistic.
GZ-curve with internal opening submerged at larger angle
Supported by these arguments, it was chosen to keep the computation method for this subject in PIAS as it always has been. Please understand that this is an implementation choice, not the irrevocable result of the modelling method in PIAS. So alternative choices could be made, if there would be a reason for that, such as a generally accepted convention. Other reasons could be clear and unambiguous guidance by rules or regulations or unified interpretations from institutions, ssuch as IMO, IACS or national authorities.