damage stability calculation

Actually it is easy, it does not take more than 2-3 days to a complete stability booklet by hand with a set of Bonjeans and D&Os. I have done it.

As I have said before, do not confuse accuracy with percision. The old hand methods are as accurate as computers without the false security of percision. As someone who was paracticing during the time of GHS and SHCP development from mainframe to PC (and writing my own stability code including porting some modules for the USN ARCHH programs from PRIME to PC), I understand that the reason for modern complexity in subdivision is because of the computers, not that computers are needed to do stability calculations.

Understand that in the days before the PC began to obfuscate engineering practice, a typical merchant ship would only have 8-10 compartments given the damage criteria of baseline to margin line to 1/5 beam. Generally, there was no transverse subdivision (warships and submarines are entirely different subjects and really don't fall under this discussion) because,all in all, asymmetric flooding is not a good idea anyway. So for the 3 required drafts, you only needed 24-30 conditions. Given that the claculation spreadsheets were pre-printed in thoses days (see the '67 edition of PNA or Saunders for lots of examples), it was not hard to pull the measurements off the curves, enter the forms and do the "plug-and-chug". Since multi-modal transport and block construction were starting to dominate shipping, compartment lengths were generally fixed so everything was straighforward. What computerizing the calculations did was to allow "what-ifs?" in the early design stage where many different subdivison arrangements could be used to minimize the tonnage measurements without resorting to shelter decks typical of the break bulkers.

While most modern (say post 1995) software intergrates lines development and hydrostatics nearly seamlessly, that was not true in the early to mid 1980's when programs like GHS and SHCP began to be ported from mainframes to PC's (can you remember when mainframe time cost 10-20 cents a CPU second? and if you screwed up a run, you had to do it again? the next day?). Considerable time/cost savings could be achieved by doing mechanical/hand calculations for stability over digitizing (anybody else remember mechanical integrators? much more accurate than early digital integration.). Given the relatively simplistic damaged stability of the time, calculation by hand was still accomplished and even today, most merchant ship stability is relatively simple and straightforward to do by hand. As the ubiquitousness of PCs increased, more of the calculation began to be automated (early code just mimiced the printed sheets and even printed them out to look like the hand sheets right down to the "checked" initial boxes, and FWIW, you still have to hand check the sheets for data entry errors). Once lines were integrated into stability, it became easy and quick to start attempting to game the stability and tonnage rules during design and so the rules needed to adapt to the increasing ability to game them (FWIW, the rules were always gamed, see the US-UK tonnage wars and the whole whaleback/shelter deck/deck container development).

In this way, it was the computer that lead to more rigorus stability requirements, not that a computer is needed to do stability requirements.

 

It depends on whether you approach flooding as an added weight or lost buoyancy. Generally the classic method is to add weight and free surface to the compartment based upon a legislative specified permability (i.e. 60% for cargo spaces and 95% for voids). This is beacuse with a set of Bonjeans and D&O's it's easy to do the math (see above) and is conserative. There are some programs that try to do an "inside-out" calculation where it determines the new buoyancy and waterplane inertia. These are more difficult because you have know the shape of the buoyant volume in the flooded space.

So the damaged CG would be (initial vertical moment+added vertical moment)/(initial weight+added weight). For most vessel this will result in a rise in CG, though there are exceptions, such as some types of catamarans.

 

Thanks, jehardiman, for your explanations. I have also developed my own software to perform all calculations of naval architecture in modern ships . Of course, stability after damage, the determiníticos method, is covered in my software. I always thought that the method of adding weights was not as accurate as the method that calculates the true floating boat, the position of the new center of buoyancy. With this method, find the equilibrium floatation is not easy, not even with the help of Bonjean .
Clearly what has been done in previous years but now, fortunately , we can work in another way. I think you have to know the history, not as an end in itself, but to build on it. To encourage a beginner to do things by hand does not seem right , it's my opinion. Now, the beginner has to have very clear concepts before he starts pushing buttons on his computer. That's what we should explain here, concepts. Then each using the tool that he likes the best.
In my opinion, to say that stability after damage is easy to calculate, seems inaccurate. For me it is one of the most difficult calculations that a normal (not specialized in certain fields) naval architect can perform. It is comparable to the stability calculations of dredges with open to sea cargo holes.
Cheers

 

Thanks to the beauty of time zones...JEH has beaten me to it and given you a most eloquent reply. Thanks JEH

Additionally, it was a hypothetical example to allow the OP to understand the difference between just a "righting arm/lever" and a "residual" one.

Yet again I must disagree. If a NA is unable to perform a hand calculations of stability (structure) or whatever, then how on earth are they ever going to be able to question the output from a program? One is taught theory at university..which then means study work using hand calculations to support the theory when applying said theory. The same is true when in an office. The NA's I trained up I always encouraged them to give me answers performed by hand first, if they couldn't why not???...it also leads into what is a NA...the master estimator! Being able to estimate quickly and methodically is the key to NA. Absolutes are for scientists and theoreticians, an estimate or general trend is NA. Ergo, do a quick calculation by hand first!.

 

I very much agree, Ad Hoc. One have to know how things are done, and above all, to have clear concepts. Different matter is that you have to do things by hand before doing them with computer. I do not know if I get to express the nuances of what I mean. So, again, I agree with you.
But you will agree with me, I hope, that the calculation of damage stability is not an easy thing to accomplish. This is what interests me emphasize from the begining.

 

Thanks for the uploaded lecture documents. i wonder if you also have the solution for the last three example problem stated here. I am actually looking for those formula to solve it , draft after damage, Trim, heel, and GZ after damage.


I am wondering what would be the formula for calculating metacentric radius BM after damage of 2 tanks.

 

First, excellent replies by JEH and Ad Hoc.

The formula for BM is still the same, whether damaged or intact, that is:

BM = I/submerged volume

Where I is the transverse moment of inertia of the damaged waterplane, having lost the waterplane area of the damaged compartment, and the submerged volume is likewise, that of the vessel with the lost (flooded) buoyancy removed from the intact buoyancy. Obviously, the center of buoyancy is also changed, moving forward or aft, vertically up or down, and even transversely if the damage is not symmetric to the vessel's longitudinal axis. So you determine the remaining intact waterplane area and calculate its moment of inertia, and you calculate the remaining intact volume, divide I by sub. vol. to get the damaged BM. The equation is the same, and the input numbers are different, and the result is referenced from the remaining submerged volume center of buoyancy.

Eric

 

I would 100% agree with that, but to add, NA should be able to program such basic calculations himself. I am not talking about writing FEA or CFD codes, but we coded hydrostatics/stability calculations ourselves. Moreover, we coded hull surface generation and fairing algorithms. For graduation project, I developed both VPP software and structural/weight analysis software to ABS Offshore Yacht guidelines. So it was quite common those days! I am still doing programming of some calculations as many of colleagues here, not waiting for new 'magic software' to come on the market.

 

Thanks Eric and others.

I am now trying to get the static heel angle after the flooding. Tried couple of source but cant find exactly the equation to get the Heel angle after damage (no wind). I found once it can be get from , Heeling moment = Displacement (T) * GM(d) sin (phi) . But where to get the heeling moment ?

 

No solutions or answers in the lecture notes

No solutions or answers in the lecture notes. No doubt members can guide you if you post your calcs here.

 

There are basically two approaches to calculate damaged stability:
- exclusion of compartment, i.e. excluding some volume of hull from calculations;
- loading/taking cargo method

The second one is more suitable for manual calcs. Assume You take the cargo at flooded compartment location, calculate moments and evaluate heel/trim/sinkage. If compartment is likely to have significant free surface, include GM correction. Understood?

 

I am trying to solve the problem of this one, not an school assignment,
the value missing , i am assuming, i am filling up the yellow table. I am following added weight method.

*Alik* i understand the steps need to follow, but i am struggling to get the proper formulae to be used.

 

There is not a direct formula, you have to iterate it.
Do you have the Drafts and Others drawing? Bonjean Curves make it really easy but you can get a good approximation with the D&Os unless you have really strangely shaped vessel. The basic process is

1) Calculate the volume (weight) and CG of the flooded compartment to the current displacement waterline.
2) Calculate the new CG of the vessel
3) Sink the vessel on the D&Os using the calculated added weight (I generally start by only sinking the vessel ~75% of the weight knowing that trim and list will make up the rest).
4) Trim and list the vessel with the D&Os using the added weight and calculated compartment CG (this is your trim and list moments).
5) Re-evaluate the new waterline (this is where the Bonjeans really come in handy, but for most ships the proportions are such that the D&Os will still be accurate) and calculate a change to the original flooding volume based upon the new waterline.
6) Repeat steps 1-5 until agreement (generally 3 sig figs) between the flooded weight and new draft, trim, and list.
7) Calculate final stability using final draft, trim and list remembering to reduce GM for lost waterplane.

This is better described with all the math and drawing look-ups laid out in the two references I listed in post #2.

 

thanks mate !

So far i have calculated the GZ (damaged) = GM (damaged) * sin(phi)

i want to know how i can take the Wind heeling moment into consideration for the final GZ ? and how to get the trim at different angle of heel ?

 

Just draw the heeling arm curve, due to the wind, to each list and calculate the point of intersection with the GZ curve.
As to the trim the boat takes at each list I would also like to know how to calculate it by hand fairly quickly. I guess, using the values ​​of Bonjean, is simple but some additional explanations would be very necessary to us.