How to theoretically calculate the floating state and stability of a complex floating body in differ

I know that the hull can be calculated according to the drawing method a little bit, but the complicated shape will be done in this way, the workload will be particularly large.

We're not thinking about using computing software.

 

Do you know of any integration method that does not use a computer? These methods exist and it would be important for you to know them, but, honestly, I don't see the point in doing those tedious calculations by hand.
Do you know the stability criteria applicable to that "complex floating body?" It would also be important to know them.
It all comes down to calculating the weight under the loading condition you want to study, calculating the centre of buoyancy for various inclinations and checking if the stability criteria are met.
The theory necessary for all this is nothing more than knowing the 4 basic mathematical operations, plus the integration of surfaces and applying the principle of equilibrium of a floating object: sum of forces equal to zero and sum of moments equal to zero. That's all (or almost all).

 

You can find the area of sections the old fashioned way. Use Simpsons rule or the Trapezoidal rule. finding the areas of all the immersed sections will allow you to calculate the displacement and give you some clues about where the center of buoyancy is located.

 

Sorry, it took a long time to reply. Because you're right, but I don't know how to answer that. I always want to understand where the difficulty is, what kind of process is the difficulty, can I really not break down the difficulty and keep breaking down until I can solve it?

I only know definite integrals. But the shape of the hull is complex, and the more complex the structure is more complex, so it's difficult. I never found a way to integrate without using a computer.

those tedious calculations by hand can make most ordinary people deeply remember, intuitively understand the calculation results and change rules. For most people, calculating the hull is an insurmountable difficulty, should they give up? No, it's just what they think, they just lack the process that works for them. Even if they don't succeed, it's better than doing nothing. Maybe the process of failure is the mother of their success in other things?

Stability criteria are important, but not necessarily needed every time.

“plus the integration of surfaces and applying the principle of equilibrium of a floating object: sum of forces equal to zero and sum of moments equal to zero. "It's hard, for most people, even smart people, because normal people don't get to see this process, in their lifetime, so they don't know how to do it, It's hard if you don't want to.

 

What bothers me the most is that the water line is constantly changing as the buoyancy changes. For example, if you keep loading and the Angle of tilt changes, the position of the water line is unknown. Because the hull is a complex three-dimensional geometry.

 

I cant imagine doing it by hand.. Even an Excel spreadsheet, with each station and matching volumetric data would be way easier than pen and paper.

 

Sigh....Spreadsheets are called spreadsheets because they mimic the way it was done by hand! <facepalm>

Yes, with a set of lines (Bonjeans are better) and weights you can calculate stability by hand. Yes, most people do it by computer today. Yes, everyone should do it by hand (or in a computer spreadsheet <rolleyes>) once. Yes, it is tedious, but No, it is not hard. FWIW, I'm pretty sure that I can teach a middle school algebra class to do it...and make it fun. The lines of a vessel do not need to be described by continuous functions,. You can do it part and piecewise (like most computer programs), but in actual application there some things you cannot control beforehand and therefore you design for a max-min envelope. (cf water density issues during the MV Stellamare capsize 09 Dec 2004, Albany NY).

I think sun needs to get their head around the concept that Initial Stability (i.e. GM) and Ultimate Stability (i.e. positive righting moment) are different. The Class Rules dictate an Initial Stability so that in moving to a new load case (i.e. through onload/offload or damage) Ultimate Stability is maintained.

 

The process and calculations required to study the stability of a boat can be explained in simple words:
1.- process:

- the weight and CoG of the vessel are determined in the desired loading condition.
- the equilibrium flotation in that condition is calculated.
- compliance with the applicable stability criteria is checked (checking an initial GMt is not enough to say that the boat has sufficient stability)​

2.- calculations:

- the areas of each of the frames are calculated at various flotations.
- these areas are integrated to calculate the submerged volume and its centre of gravity, which is the centre of buoyancy (CoB).
- the longitudinal position of the CoG and the CoB must coincide.
- if they do not coincide, the boat is trimmed a little and the CoB is recalculated and so on until both CoG and CoB coincide.
- once the equilibrium flotation has been reached, that is, once the trim of the ship is known, it is given successive heels and, for each heel and the displacement of the condition under study, the transverse position of the CoB is calculated. When the ship heels, not only the transverse position of the CoB changes but also the longitudinal position.
- the equilibrium flotation is calculated again for that trim and that heel.
- etc, etc.​

Important: the areas and volumes will be calculated by integrating using the trapezoid method, Simpson's method or a similar method.
It will be understood that doing this by hand is not feasible. In ancient times, when there were no computers, to simplify things somewhat, it was assumed that the ship did not change its trim when heeling. But nowadays no regulatory body would allow this simplification.
Having explained all this, I would like to know how those who use spreadsheets manage to determine the equilibrium flotation, the KN values and compliance with the various stability criteria.
All this refers to checking stability by calculations. In small vessels, practical, non-numerical procedures are allowed to check their stability and buoyancy.

(I must humbly admit that I do not know what "Ultimate Stability" is, how it is calculated, or what values the CS recommends for it.
I do not believe that anyone is obliged to maintain the value of "Ultimate Stability", whatever that may be, or any other stability parameter, when changing from one loading condition to another.
Perhaps I am becoming obsolete.)

 

I have learned ship principles and am familiar with the calculation methods of ship buoyancy and stability. However, just the theoretical stuff, such as examples give a lot of information. I was thinking, how to give me little information, I can only calculate from scratch, but I don't know how to start.

 

The calculation, I understand, I've even seen a lot of Newtonian iterations do this. The problem is, when I load the geometry of a complex surface, I know the displacement, but how do I know the waterplane and the inclination? You know when the inclination changes, the waterplane changes, right?

 

Correct.
You need to simulate several inclinations(and probably several drafts) and calculate, just as you do for zero inclination, the CoB. If its longitudinal position coincides with that of the CoG, perfect, otherwise you should simulate another inclination, and so on until you get it right.
If you are going to do the calculations by hand, it is better to forget about complex surfaces and focus on the cross sections of the hull

 

If it gets to be too complex to calculate reliably, perhaps find out what the smallest scalable size is, build it, and use a water testing tank to explore the refinements?

Apologies if this is off topic, just kind of appeals to my pragmatic self..

 

It doesn't scale that way, You would end up doing more than if you had just calculated it directly, since you have to calculate it for the model first then transform it to full size.

I've thought long and hard about this reply, but I call BULLSH*T! A statement like that just shows ignorance of how the calculations were made before the desktop computer made it into design office (circa 1982-9, it was not overnight considering the cost and the fallibility of the programing, as someone who suffered through the original iterations of SHCP, GHS and many main-frame custom programs, )...a time when an engineer's salary $20,125/year and mainframe time was 25 cents/sec...and there were way more "Calculators" and Drafters making 10-15K/year than engineers (if you ignore the civil rights issues, and look at what is going on in the engineering office, the book/movie Hidden Figures pretty well lays it out in a large government engineering office. As late as 1989, human 'Calculators' would check my computer program algorithms.)

Really, everything that is in the modern rules, and more for military vessels, could and was done by "non-computer" methods until well after I started engineering classes in middle school (1972). That is not to say we didn't use "machine tools"; slide rules, mechanical calculators, planimeters, 3-wheel integrators, pre-printed spreadsheets, etc, were all used to develop the Curves of Form, D&Os, Cross Curves of Stability, Tank Capacity Curves, etc. Today computer programs do it just like I/we used to, because they were coded by people who did it that way (at least my submarine docking/undocking stability program, which is still in use after 40 years, did). What a digital computer brings to the calculation is speed, not a better method, not more insight, not even better accuracy (as you never really know the actual shape, water density, and weights and therefore can never really know the actual stability)...just speed. It still slices the hull into discrete sections, still calculates the discrete water planes, still connects discrete solutions with lines to get the Curves of Form.... it just does more of them faster...so it can be less insightful...a power saw rather than a hand saw, but neither is successful without a skilled user to input and interpret the data.

I'm not sure how your instructors addressed the topic, but mine made the distinction between the ability of a vessel to resist heel in the present condition (based on instantaneous GM) verses the final quiescent state of list (based on the alignment of BG). The first allows the vessel to resist perturbations like the seaway, free surface, and suspended loads, the second to prevent capsize. Very few vessels, mostly small sailing yachts have ultimate stability exceeding 90 degrees, and only those vessels designed for self-righting (i.e. lifeboats) go to 180. But that doesn't mean that I can't step on the gunwale of a rowboat than step to the thwart without capsizing the vessel. For that brief moment, the vessel was going to capsize, and would have if I stood there. But it didn't because the waterplane initera resisted the motion, even though the BG couple was way out of alignment. This is similar the the problem of the marble/roller skate on the cambered deck; GM is negative, and the vessel capsizes until the marble/roller skate hits the bulwark, and then the vessel has a list. This is also what killed 18 of 30 crewmen of the MV ROCKNES in 2004; the assumption was made that a damaged compartment would flood instantaneously whereas the slow flood up caused GM to go negative and the ship to capsize.

 

@jehardiman, you have written quite a few incorrect things and, furthermore, with some very rude expressions, so I will avoid wallowing in your mud and I will avoid responding to you.

 

Indeed.
We did all this by hand when at Uni....took for ever, but is not rocket science.
The first time I did this by "computer" was at my first job...we hat a small floppy disc driven computer to do these "hand calculations", via a digitised hull form from a drawn liens plan.
A computer, just does it quicker - that's all.

Yup - there too....basic understanding of stability.