# KN curves

Discussion in 'Stability' started by shrijeet mishra, Mar 31, 2020.

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1. Joined: Feb 2020
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### shrijeet mishraJunior Member

hi everyone
hope all of you are doing good and pray we get out of this pandemic very soon.

i wanted to know the method maxsurf uses for the calculation of KN CURVES.
we just provide displacement range and it gives us back set of curves can someone please provide me the manual method that can be used otherwise or formula used by the maxsurf software.

thank you.

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### jehardimanSenior Member

Maxsurf calculates it directly from the body as it is easier to calculate than GZ. What it represents is the location of a vertical line drawn through the Center of Buoyancy (B) for a given angle of heel and displacement, that is horizontally perpendicular to the Centerline keel.
The "KN curves" are a contrivance used by the IMO and mariners to calculate GZ (the righting arm) from either the cross curves of stability (mostly tankers) or just from the hull form (mostly bulkers). Note that KN curves are not the true cross curves of stability, but a short cut for mariners that allow them to calculate a specific static cross curve of stability (GZ curve) based upon an inclined KG plus a known cargo load.
KN Curve & GZ Curve are different representations of righting arm. GZ is the righting arm with respect to Vertical Center of Gravity (KG), where as KN is the righting arm with respect to Keel (i.e. KG = 0). KN Curve is constant for a vessel at a particular displacement (and trim), while GZ curve will be vary depending on the KG (i.e. loading conditions) for same draft. Once the KN curve is derived for a particular draft, GZ can be easily calculated for any loading condition (any KG) using the formula GZ = KN - KG*Sin(heel) or KN = GZ + KG *sin ΓΈ; where GZ is first calculated in the correct method for large angles of heel for a given displacement.
While this calculation is OK for wall sided, high length to beam ratios, it has a significant limitation in that it does not have a correction for either free surface changes or significant trim (bow or stern). See the discussion here;
Ship Stability - Understanding Curves of Static Stability https://www.marineinsight.com/naval-architecture/ship-stability-understanding-curves-static-stability/

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### shrijeet mishraJunior Member

Thank you so much for giving your precious time in explaining in bringing out the difference between GZ curve and KN curves.

SIR the question coming to the mind is maxsurf uses my model and body to calculate the KN curves as its easy since we do it with respect to keel rather than G which is difficult to find at different point of time. but sir which was the method used earlier when maxsurf came into play. I mean there must be some algorithm or formula fed into the program of maxsurf with help of which it does help us not to calculate. I'd like to know the method or formula used in it. i understood that it uses the model and calculates but like what goes inside the program?!

Kindly enlighten me on this.

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### jehardimanSenior Member

You are making this too hard in your own mind.
KN is a geometrical construct solely dependent on the location of CB in the hull shape at the selected displacement. Do you agree that Maxsurf (along with its add-ins) can correctly calculate the center of buoyancy of an arbitrary shape at any angle of heel? Or, backing up one step further; do you know how to calculate the center of buoyancy of an arbitrary shape using a surface model? Maxsurf uses NURBS surfaces which are then subdivided and/or sub-meshed as needed for calculation.
I personally have not climbed inside the Maxsurf code to see how they do it, but having done it myself for other codes, it is rather straightforward but tedious (unless you can exploit the geometry). The calculation of CB from a mesh has little to do with how KN is determined, you could calculate CB with a planimeter or pixels just as easy.

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### shrijeet mishraJunior Member

yes sir

thank u so much for your valuable time.

sir since my project ship is catamaran its GM is coming out to be high 15-17 m
this makes my ship tender.
how can i reduce its rolling period
like active stabilizers or bilge keels or fins something?!
i have space(cofferdam) in both my demi hulls.
or is there any other method i can adopt without having to go back to resistance calculation due to addition of keel or something extra.
i hope u get my motive ( not actually wanting to that extra work of previous chapters)
ill attach the excel and GA for your better idea sir.

kindly have a look.

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### shrijeet mishraJunior Member

sir also i have query in midship section drawing.
if u have some time to have a look and guide me through this. would be so much obiliged.

thank u sir.

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### jehardimanSenior Member

Why with a GM of over 12m do you think that the vessel is too "tender" and has to a too long a roll period? I would suggest you go back and check your assumptions and math on your period calculation. (Note: periods are often given in units of radians per second, normally using the symbol omega. Period (T) in seconds = 2*pi/omega. In this case large omega means a quick period.) FWIW, most "quick" calculations of roll period assume GZ is approximately equal to GM. This is not the case with a catamaran.
Additionally, be smart about using your tools. Why did you choose a catamaran hull form? What type of motions and stability are expected with your hull form? Do you know the heel angle when the deck edge submerges or you reach downflooding? Computer programs are just power tools, they cut the tree down faster but they don't determine the direction it will fall.

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### shrijeet mishraJunior Member

sorry sir.

ship will be stiff i forgot and wrote in hurry.

but i didnt get the 2nd part of your reply. deck edge immersion is given by maxsurf.

but that is not the issue to be catered.
if ship is stiff for an ambulance with quick period its a design problem and need to be taken care of.

request to know if some ideas u have to share and guide me to implement it in my project.
in last reply i did attach the excel stating the equilibrium condition of each loading conditions. in that it is visible that the case.

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### jehardimanSenior Member

I assume that this is a university design project which is supposed to teach you something.
Ok, I will play your professor.
1) Your project requirement was for a water ambulance. This included a roll period requirement.
2) You selected/were required to use a catamaran hull form when you should know that catamarans are stiff transversely for their displacement.
3) After working through your design, the roll period is too short. Surprised? Why?
4) You may fail your project....Congratulations! You have just gained experience!

Really, experience is what you get when you don't get the outcome you want. Can tell me, and your professor/client, what drove you to select a catamaran of the dimensions you now have (22.3m x 8.16m x 0.9m)?

At this point, without a total redesign of the hull form, there is nothing to do but raise the effective KG of the vessel (add ballast high) and/or reduce the effective GM (add big roll tanks); neither which is suited for a weight sensitive catamaran hull form. Or, pull out a clean sheet of paper and start over. Don't feel sad, this happens from time to time (and very often in university projects), see the 1986 USS MIDWAY refit issues.

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### shrijeet mishraJunior Member

haha
thank you for taking it in lighter note

i tried to make an ambulance which is light weight so GRP and thus reducing the draft as if can go in shallow regins the max possible and in regions of island in india it might be very helpful
and catamaran because it will give me enough deck space and stability
but yes in end of stability chapter i found the period of roll not favourable.

yes im trying to convince the proffesor stating that the cofferdam which i am having i can use it for increasing G or reducing roll by using it anti rolling tanks and stabilizing.

i hope this reason suits apt.?

any other suggestion would u like to give me for avoid to start from scratch beacuse i have 3 weeks to submit and degree.

thank you once again

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11. Joined: Aug 2004
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### jehardimanSenior Member

Realistically, without starting over, all you can do is attempt to decrease GM. To do this while still keeping the same house arrangement and principle dimensions try the following.
1) add an roll damping tank on the bridge deck aft of the conn or even on top of the conning house. This will raise KG as well as lower GM
2) make the hulls draft deeper and/or add displacement low in the hull, this will lower BM by increasing submerged volume as well as lowering KB. It also adds displacement to account for the roll damping tank weight.
3) Make the hulls narrower, this will lower BM by reducing Iwp. Just watch your WP area to prevent making a heave problem.
IMHO, you really should do all three. My personal opinion is that the hulls are too wide inboard for their distance apart. Have you checked for choked flow between the hulls? I would flatten the keel, increase draft aft, harden the bilge aft and reduce the half-beam on the inner hull sides, while trying to avoid MPU and structural arrangement issues. I doubt that those changes will affect powering that much because those hull really aren't that slender.

I know that you have spent a lot of time on this and have a lot of yourself tied up in your senior design (I know I did). Talk with your professor. The ability to identify in writing the issues with a project is just as important as completing a project. Either way you learn something that will help you in the future.

So to quote Enrico Fermi about conducting experiments: There are two possible outcomes: if the result confirms the hypothesis, then you've made a measurement. If the result is contrary to the hypothesis, then you've made a discovery. It is no good to try to stop knowledge from going forward.

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### shrijeet mishraJunior Member

haha the quote got me smile
its true.

sir
i couldnt understand the third method u mentioned.

id actually put forward these methods and work upon something or other to get it as per requirement.
it was really nice to learn from you sir.
looking forward for many such learning experience from you.

thank you alot sir.
stay safe.

13. Joined: Aug 2004
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### jehardimanSenior Member

Basically, your hulls are presently symmetrical, often in catamarans the inner hull side is much less shaped than the outer side. Read this paper with attention to Appendix A and B. https://www.nap.edu/read/5870/chapter/48

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### shrijeet mishraJunior Member

thank you so much

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