Since the day I have started writing, I get a lot of requests suggesting the topics I should write on.

But do you know which question I have been asked the maximum number of times?

No prize for guessing.

It is this question.

How to know the worst case of damage stability?

Well, It is today that I decided to write on it in detail and explain it.

Are you ready to read the answer to this most mystic question?

Let dive in.

## Requirements of damage stability

A ship that can float cannot always be said to be a safe ship.

It must also be able to remain afloat even after sustaining some amount of damage.

Damage stability calculations are all about getting to know if the vessel will remain afloat after sustaining some damage on its hull.

That is what SOLAS, MARPOL (For tankers) and IBC code (For chemical tankers) does.

All these regulations define two things

- the extent of damage that needs to be assumed.
- Sustainability criteria for the assumed extent of damage

For the vessel to comply with damage stability, it should be able to achieve the sustainability criteria after the assumed extent of the damage.

## Extent of damage

Let us see the defined extent of damage as per various regulations.

### Assumed Extent of damage as per SOLAS

Here is the extent of damage defined in SOLAS for cargo and passenger ships without a double bottom.

Below is the required extent of damage to be assumed for passenger ships

### Damage stability requirements in MARPOL

The required assumed extent of damage defined in MARPOL annex 1 for oil tankers is as below.

### The assumed extent of damage as per IBC code

The required assumed extent of damaged defined in IBC code for chemical tanks is as below

## Damage cases as per the assumed extent of damage

Based on the damage assumption requirements, damage cases are created for the vessel by the class.

You can see these cases in damage stability calculations, either in loadicator or in damage stability booklet.

Here are the few of the damage cases from one of the vessel.

## Damage stability for each damage case

For the vessel to comply with damage stability requirements, for each damage case, the vessel must comply with the damage stability requirements under MARPOL annex 1 (for oil tankers) and under IBC code (for chemical tankers)

What does this mean?

Let us take the damage case 201.

In this case, FPTK, 1W(P) and, 1W(S) are assumed to be damaged.

If after this damage, vessel still complied with the damage stability survival requirements as set in MARPOL, IBC code or SOLAS (as applicable), the ship can be said to be complying with the damage stability with reference to damage case 201.

These calculations need to be done for each damage case and ship need to be complying with damage stability survival requirements for each of these damage cases.

If even one case does not comply then for this stowage vessel will not be complying with damage stability and we need to make changes to the stowage and again check for the damage stability.

Of course, manual calculations are not required and lodicator does these calculations for us.

And after calculations, it just shows us if the for the intended stowage if the vessel is complying with damage stability or not.

## Survival requirements

But what are the required survival requirements?

That is, after the assumed damage under each damage case what all stability requirements vessel need to fulfill for it to be considered complying with damage stability?

Here are the survival requirements as per the IBC code.

And here are the survival requirements as per MARPOL.

Although the MARPOL and IBC code requirements are for oil tankers and chemical tankers respectively, if you look closely there are a lot of similarities in the two requirements.

## Deciding Factors for damage stability compliance

If we need to know the worst case of damage stability, we need to first bring all the deciding factors on the table.

Let us see which are the deciding factors for damage stability compliance.

Look at the survival requirements as per IBC and Marpol and you would know that these are

- The distance from the waterline to the opening through which progressive flooding can take place
- Angle of heel
- range of righting lever curve (GZ curve)
- Residual righting lever
- The area under the GZ curve

Contrary to the belief of many, GM of the vessel does not represent here as a factor for deciding the damage stability.

But as the GZ curve and GM of the vessel has a direct relation, we can say that GM indirectly affects the damage stability.

For the scope of this article, I will not discuss here the relation between GM and GZ. I will leave that for some other day.

So if there is anything that decides the worst case of damage stability it has to be one or more of the above factors.

Which one(s) is that? Let us find out.

## Right Lever, Range under GZ curve, area under GZ curve

What is GZ and why it is important?

GZ is righting lever. It is the force that brings the ship back when inclined to an angle by an external force.

In simple words, the centre of gravity (G) of the ship for a particular condition remains the same.

Whereas the center of buoyancy (B) changes with the heel as the underwater area would change when the vessel is inclined.

This generates a lever (GZ) that brings the vessel back to normal.

GZ would increase as the angle of heel increases because with an increase in the heel the center of buoyancy would shift farther from the center of gravity.

GZ curve is the curve drawn for the length of the righting lever (GZ) against the angle of heel.

The area under the GZ curve at an angle of heel is simply the area of the curve from 0 deg heel to that angle of heel.

The significance of the area under the GZ curve is that it represents the amount of work required to bring the ship to that angle of heel.

In other words, it will also be the force available to bring the ship back to its original position or the force available to counter the external force that is causing the ship to heel.

### GZ and damage stability

So when a ship is damaged and is arrived at equilibrium, one thing we want is it to have some dynamic stability to withstand the usual weather conditions.

In simple words, in damaged conditions, if the vessel does not have any dynamic stability then a slight increase in the heel due to weather conditions can capsize the vessel.

The minimum dynamic stability required after the assumed damage cases is defined in MARPOL and IBC.

I do not have the calculations to show how severe weather conditions the vessel can survive with these minimum values required as per MARPOL and IBC code.

But we can believe that IMO came to these values to ensure that the ship can withstand normal weather conditions at sea.

## The distance from the waterline to the opening through which progressive flooding can take place

Apart from GZ and related criteria, there are one more criteria that are required to be fulfilled for the vessel to comply with damage stability.

This is…

*“The distance from the waterline to the opening through which progressive flooding can take place”.*

And it is required that

*The final waterline, taking into account the sinkage, heel, and trim, shall be below the lower edge of any opening through which the progressive flooding can take place.*

So after the damage and when the vessel has arrived at the equilibrium, the openings like air pipe and other openings that are not water-tight must be above the water line considering

- it does not apply to the opening of the compartments that are already flooded
- if any opening is below the waterline, the compartment needs to be assumed to be flooded for damage stability calculations.

So if you note, a small distance of even 5cms between the waterline and the opening is considered in compliance.

What if we have a swell of more than a few meters?

Even when we are complying with the damage stability requirements, the compartment can get flooded in this case and everything changes.

GZ and other values that were complying with damage stability with this compartment intact will now change and may not comply anymore.

## The worst case of damage stability

Finally, I come to the concluding part.

The damage stability requirements have defined the minimum required criteria for each element.

Except for the distance of waterline from opening through which progressive flooding can take place.

This is a critical factor too.

If the distance is too small, the vessel will still comply with the requirements but the whole scenario will change if the compartment gets flooded through this opening because of weather conditions.

So the worst case of damage stability is the one that has the least distance from the waterline to the opening through which progressive flooding can take place.

## Example of the worst case of stability

I know now you would like to see an example for the worst case of stability.

Let us take this as step by step.

### Critical openings

The first thing we need to know is the critical opening for the ship.

These are the openings through which progressive flooding can take place and these are identified by the classification society.

If you are on a vessel, do some homework to find the list of these openings. These must be either in your approved loading conditions booklet or damage stability booklet.

Here is the list of the critical opening of one of the vessels.

### Damage stability calculations

Damage stability calculations demonstrate if the vessel’s stowage would comply with the damage stability requirements.

And as one of the requirements is that the critical opening must be above the waterline, the damage stability calculations are supposed to give the distance from the waterline to these openings.

Here are the damage stability calculations for one of the vessel.

The last column (Opening immersion) gives the distance from a critical opening (the one with the least distance for that damaged case).

It also gives the identification of the opening for each case (in the above it is given as the identification number of that opening).

So looking at the above calculations can you guess the worst case of damage stability?

Did you say “Damage case 301″ in which has the least distance of the critical opening (no 40) from waterline (0.12m)?

Let us scroll to the next page of the damage stability calculations for this same loading condition to see if you are right.

Bingo. You are absolutely right. It is damage case 301 indeed.

You see this loading computer identifies the “most severe damage case” and provides the information in one section.

But if your loading computer does not do that then you can identify the most severe damage case by looking at the distance of critical opening from the waterline.

But there is one more thing that you need to be careful about.

You need to check if the damage case with the least distance of critical opening from the waterline is not assumed to be flooded.

If it is assumed to be flooded, then the distance of this opening from the waterline would not matter and we need to look for the next most severe case.

For example, look at this damage stability calculations.

Which would be the most severe damage case in this?

You would probably say, damage case 408 with the least distance of 0.25m for opening # 46.

The opening no 46 is *Air vent for E/R cofferdam (S)*.

And the assumed damaged compartments in damage case 408 are: 5W(P), SP(P), E/RFORDM, S/G RM, FWT(P).

The opening no 46 comes under one of these damaged compartments (E/RFORDM). So we need to neglect this while choosing the most severe damage case.

In this case, we need to look for the next most severe damage case and so on till we have a damage case where the distance is the least and the compartment of the critical opening is not already assumed as flooded.

In the above example, this would be damage case 108 as the most severe damage case.

## Conclusion

It is not a statutory requirement for the masters to know about the most severe damage case.

However, SIRE requires masters to be aware of that.

Surely the factors that decide the compliance with the damage stability requirements need to be the one that decides the most severe case of damage stability too.

And these factors are

- GZ and other associated data
- angle of heel
- the distance of critical opening from the waterline

IMO has already defined the minimum required criteria for the first two factors but not for the third one.

This is the factor that decides the most severe case of damage stability.

The damage case that has the least distance of the critical opening to the waterline will be the most severe damage case.

The most severe damage case need not be the same for all loading conditions.

It can be different for different loading conditions but more often there will be one damage case that would appear as the favorite for most of the loading conditions.

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### About Capt Rajeev Jassal

Capt. Rajeev Jassal has sailed for over 20 years mainly on crude oil, product and chemical tankers. He holds MBA in shipping & Logistics degree from London. He has done extensive research on quantitatively measuring Safety culture onboard and safety climate ashore which he believes is the most important element for safer shipping.

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### 26 Comments

Thank u sir . Very well explained.

Thanks Ilyas...

Excellent Sir. Just what I was looking for. The confusion has been finally cleared as to which to choose from the Criteria .. Least GZ , greatest angle of heel or dist of opening to the waterline. So it is the dist of the opening nearest to the waterline which will decide the worst damage case. Thanks again Sir..

Glad you found it useful Satyajit...

Sir the chapter above has clarified many doubts and confusions however in the above case kindly also advice how it will be known that the compartment is considered to be flooded.

Each damage case assumes some compartment to be flooded. Which compartments are assumed to be flooded in each damage case is provided in damage stability booklet.

Thank you sir.

Thanks Yogesh...

THANK YOU VERY MUCH SIR, FOR THE EFFORTS. YOU CANNOT IMAGINE THE HEIGHT OF SATISFACTION I GOT AFTER READING THIS ARTICLE(SELF EXPLANATORY).

Great to hear that Harbinder...

SIR WHAT DO WE UNDERSTAND BY DECK IMMERSION COLUMN IN DIFFERENT CASES THE +VE & -VE ? VALUES AND THE NUMBER NEXT TO IT.

-ve means that deck line is immersed. +ve means deck line is not immersed. The number gives the distance of the deck line to the water line.

First of all thanks a lot for this beneficial information, it refreshed my knowledge as chief officer on chemical tankers.I can barely see the importance of deck immersion however as far as I am concerned, the GZ value should be also considered as well as deck immersion value. During the calculations, I always firstly consider the value of GZ. I mean I always choose the least GZ value result as worst case if I am right ? Could you please confirm if it is true all the time ?

We do not need to consider the value of GZ as if GZ is less than the required value then vessel is not complying with the damage stability and there is no need to know the worst case of damage stability becuase we need to first correct the stowage to the one where damage stability is complied with.

We need new topics !!! ;)

Sir...your explanations are the best...Appreciate your effort...Best wishes!!!

Thank you sir and well explained ,

Thousands of thanks captain...many Years looking for a explanation like this...

Very nicely explained sir Thank you sir

Great article sir ....want you to write more on probabilistic method...as you have already write on it...but need to know more...from where they get required subdivision index...subdivision length n all that

Thank you sir, Very well explained great work.

Thank you Sir for your effort in explaining a topic frequently asked by the SIRE inspectors. It was sought for since a long time specially on ships where loadicator isn't fitted with damage stability calculations.

superb, salamat

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It is always a pleasure to read your articles sir. Just want to clarify .. as it is mentioned that worst case of DS will depend on the least distance from the waterline of any critical opening that is not already assumed to be flooded ... Will it not matter that the critical opening is serving which compartment ... For eg 5S wbt may be a much smaller tank as compared to 4S wbt ... Will it not affect the result if the critical opening serves 5s or 4s ? Thank you for your efforts sir ...

It won't matter as far as it is a critical opening...