# KN Calculation using KMT values from Hydro data

Discussion in 'Stability' started by mactavish, Jun 4, 2023.

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1. Joined: Sep 2014
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### mactavishJunior Member

Hi<

I just want to ask about the basic approach how to calculate the KN values using kmt from Hydrostatic data.

Is this correct?

Because I have forgotten the long calculation for crosscurves.

I am trying to compare my result vs maxsurf but it's way off...

I am trying to create cross curves.

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### jehardimanSenior Member

Your assumption is correct IF...there is no change in trim, displacement, or water plane (only possible with a cylinder). Therefore, you need to calculate a new KMt for each angle of heel at the desired displacement. I.e. KN10 = KMt10 * sin (10).

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### mactavishJunior Member

On maxsurf its KN values are calculated based on the CoB value.

Is there a simple formula to calculate the CoB of submerged part aside from simpsons?

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### jehardimanSenior Member

By hand?...not really. But a planimeter and some onion skin/tracing paper will make it much easier. Actually, this is all computer programs do...except they do it really, really fast with really, really small sections and waterlines. Learning the old methods gives wonderful insight into how computer programs work.

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### mactavishJunior Member

I'm actually dealing with creating the algorithm for this. Because i'm doing a program to calculate KN.

anyways thank you for your input.

kind regards,

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### Nathan BossettNew Member

The timing of your question is a little amusing to me because I just did hand calcs for this yesterday to validate some software.

If you assume zero trim and a wall sided hull such as a barge and a TCG on centerline, as was common before computers made such calculation-saving assumptions unnecessary, yes.

Notice that as the vessel heels, until the waterline hits a corner such as the deck edge or bilge, the change in volume is represented by two wedges, one on each side, one of them being added submerged volume and the other subtracted.

Sum up the moments of those two wedges (triangles in the 2d pic) to adjust the original submerged volume and compute the new Cb.

Then, calculate your new GZ directly.

Among other books, Intact Stability, Colin Moore, SNAME or Principles of Naval Architecture (also SNAME) have diagrams.

If you're creating software to generate cross curves, you may find it simplest to skip computing KMt entirely unless you specifically need that value in output.

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### TANSLSenior Member

The same goes for any other software or manual calculation. At present, since when the boat heels it also acquires a certain trim (not in prismatic barges), these calculations are not usually accepted if this other movement is not taken into account to determine the true equilibrium floatation. Calculating all of that by hand is not practical.

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### jehardimanSenior Member

So you say you want to create an algorithm and are already using MAXSURF? For a floating vessel of arbitrary shape? As Nathan and TANSL say, there is a lot more going on. You need to move to surface methods if you are going to do this correctly (i.e. why it is called max "SURF"!). If I had a virtual lecture hall with whiteboards it would take me about 10 minutes to explain everything through once; but I don't have the time or the inclination to create a upper level college course over the net; I have beaches to sit on and boat drinks to drink. If you want to make something like MAXSURF or even WAMIT, I would suggest starting with J L Meriam's two very good texts Engineering Mechanics: Statics and Engineering Mechanics: Dynamics paying particular attention to the "engineering potato": i.e. how forces are generated by surface integrals. Then a good book on linear algebra focusing on cross products, dot products, and surface normals. Finally you are ready for PNA and all the other snarky things about buoyancy and stability; statically and in waves.

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