KN curves problem

[kaptcatb]

Hello !
I need big help for my stability calculation . Im trying to calculate stability at different wave crest position along lenght of ship ( ABS , Assessment of parametric rolling ) .

I have calculated Omega (subm.area) , Moment of Omega , Volume , VCB (KB) , BM and Ix ( transv.moment) for 35 stations using excel . Calculations are done for 35 different wave crest positions ( for each 1 wave crest position -> different wave profile = different hydrostatic data at each station ; total 35x35 cases ) .
So now i can calculate metacentric height GM=KM-KG=KB+BM-KG . This means i have GM for any wave crest position .
After this i need to calculate GZ curves .. and here comes the problem
For my ship i have ANY data ( have full technical documentation ) . GZ formula - GZ=KN-KG.sin(Q or Phi;Theta if you prefer) ;
I know KG for any loading condition , but dont know how to calculate KN .

Software -
I have Maxsurf ( stud.editiom or however its call ) and Rhino , but I do not think i will be able to create an accurate model of the real ship ( same volume ; i have done 2-3 ship models in Maxsurf for pleasure , but it is still difficult to form stern and bulbows bow ) .
I have offset data in excel . I see some pdf tutorials for Rhino and know i can import data from table in software . Maxsurf have this options too ?


By hand -
Some formulas i find -
1. direct assessment of GZ ( no GZ )
GZ=GM.sin(Q) - small heel angle ; Q<5 , some says 7,8,15 deg.
GZ=(GM+0.5*BM*tan(Q)^2)*sin(Q) - large heel angle ; Q<25 deg

2. there in forum i see thread where
KN=KM.sin(Q) - small / large angle ? Only for small craft ?

I have expirience with Chebishev ( Чебишев) method , Krilov and Darny ( Крилов и Дарни ) but these calculations I will take a long time for these 35 stations .

Any tips ?

 

[jehardiman]

KN is nothing but the distance from the keel centerline to the buoyancy line of action for any heeled condition. See the attached diagram. For the KN curves you will still need to calculate all the heeled centers of buoyancy for all the different drafts, but you only need to calculate the KN curve once. For all the GZ curves all you need to know is KG, because the curves are related by the following relations from the figure
GZ = XN = KN - KX where KX = KG sin (theta)
so GZ = KN - KG sin (theta) for any KG

Edit to add....Do you get to make the all sided assumption? Or is the hull too shaped? For small angles of heel there are some tricks to calculate the buoyancy shift (i.e. find BB1 and then BB1 cos (theta) equals the shift in the line of buoyancy)

 

[kaptcatb]

Thx for reply sir .
I calculate hydrostatic data using 35 x coords / 32 z coords . I think its enough detailed .
During my 2nd year in school i have task to calculate all hydrostatic data by hand ( by excel ) . KN values are calculated by Krilov and Darny method for large angles of heel . I remember this part took me too long time .. and results was 2 KN curves ( for 2 volumes or draft if you prefer ) for Q=0:90 with step 15 deg .

Now i have same task ( i think ) . I have already calculated BM and KB ( forgot for now , ignore that ships is at wave crest ) . Also i have KG for specific loading condition from ship documentation . So metacentric height is
GM=KM-KG=BM+KB-KG= xx m

Next i need is GZ curves . Equations i know i posted in first post ( same as your ) . I know point B and point M moves during heel . To get GZ curves i need to solve GZ=KG-KN*sin(Q) .. to get new coords of point B and M . Tomorrow i look depth in my book but now i think change in center is -

transv. yB=Int(0 / Q)[BMcos(Q)dQ] ; i think this is KN ( but im not sure) -true ?
vert. zB=VCB(initial) + Int(0 / Q)[ BMsin(Q)dQ]
where (0/Q) is limits

2 easy for solve integrals , but for small step of Q and each Z + for any station ..:idea:.. pfff so much + BM changes @ (Q) . Dont remember the formula for BM change @(Q) but know where to look .
Any other method for GZ calculation ?

Maybe tomorow i will upload some information from my books . Im tired now there is 1clock@night .

p.s.1 - do you guys know Krilov-Darny method i talk ( im not sure "Darny" name is correctly . Have check the google and no good results in first pages .

p.s.2 - For all the GZ curves all you need to know is KG ;;In my case KG=7,89 . Give me GZ pls
good night all

 

[jehardiman]

I know point B and point M moves during heel .

No, you can't use BM to calculate the buoyancy shift unless you assume a small angle, wall sided shape, and no free surface. The point shown on the figure where the line of buoyancy crossed the centerline is not the Metacenter (M). The concept of Metacenter and BM (or GM) is only for initial stability, that is, how much stability the vessel has when floating upright and relative GZ = 0 (i.e. the CG and CB are co-linear wether on CL or not). For each angle of heel, there is a new unique GM, that may be negative, based upon the waterplane inertia at that heel. Negative GM, and the vessel is not stable at that point.

GZ on the other hand, is a measure of untimate stability, the moment that is trying to right the ship if heeled, or roll the ship if using a wave profile. And when used for wave profile calculations, GZ is independent of BM (or GM).

 

[kaptcatb]

I check my books . You sure i cant use BM change to calculate KN ( GZ ) ?
The chapter where i look is called " Stability at large angles of heel " . There are 2 group methods - 1) equal volume WL -Krylov , Darny ; 2) no equal WL - Reynov ( Рейнов ) .
There also some formulas for new position for point B ( most ~ formula in my 2 post ) .

The book is not in English . There are many figures and formulas i can give you if interesting . ( im new to forum , long time was only reader . How to upload files ?

 

[TANSL]

kaptcatb,
I do not know if there is something I do not understand, or if I stopped reading anything in previous pots. If what you want is to calculate and plot the curves KN, YOU DON´T NEED AT ALL the center of gravity.
KN values ​​depend exclusively on the shapes of the boat, whatever be its weight or its center of gravity position.

 

[kaptcatb]

kaptcatb,
If what you want is to calculate and plot the curves KN, YOU DON´T NEED AT ALL the center of gravity.

Hello Tansl ,
Where i say KN depends on KG ?? I want KN to get GZ for different Q and /\ . The methods i know will take long time to calculate KN for heel , displ . and for all 35 stations . So i ask for other faster way to get KN .
Is there software where i can only put x,y,z points and get data i need ? Or can you recommend another method ?

http://store.picbg.net/pubpic/BD/5D/bde97bd12e39bd5d.jpg -
Yb,Zb - change of position of CB
Ym,Zm - change of position of M
later i will upload Krylov method .
Good day all

 

[TANSL]

The only way I know is to calculate the position of the center of buoyancy with the boat heeled. We begin by defining the point K, which is at the intersection of the base line with the vertical line traced by amidships, without heeling. You tilt the boat, we calculate the center of buoyancy and draw the perpendicular to the new waterline passing through the center of buoyancy. The distance from point K to said vertical is the KN value for the heel and displacement we are studying. The same procedure is repeated for each list and each displacement we want to calculate.
If there is another method, I do not know.
Modern programs do the calculation on a three-dimensional model which, previously, we had to define. With this model all calculations are performed, and no need for anything, until now, not knowing what the boat weighs or position of its center of buoyancy.

 

[kaptcatb]

You tilt the boat, we calculate the center of buoyancy

How you calculate ( by your method ) volume and Ix for any heel angle ? Cuz if you can calculate BM for heel angle , then you can calculate KN . Do you ignore the received trim from heel ( when ship heel , volume in aft > volume fore => more buoyancy aft => trim @ fore ) . Can you explain detailed how you calculate KN /?

 

[TANSL]

I hope the attached figure helps to clarify the issue.
No need to know the false metacentre and therefore no need to calculate the inertia of the waterline.
All you need is to calculate the submerged areas of the frames to thereby calculate the submerged volume and position of center of buoyancy. To calculate this, simply integrated using Simpson's rule.

 

[kaptcatb]

Hmm .
And how about transverse center of flotation YF ( WL at heel angle cross this point ) ? If you dont know Yf for heel angle , you dont know the position of WL and cant calculate volume ( ship is rotated ( heeled ) arround point F ) ?
Im not sure @ 100%

 

[TANSL]

You put the float where you want.
The process is not to calculate the float (the draft) that has the boat for a certain displacement. It is just the opposite. For each heel :
- You put the float at depth as you want
- Calculate the areas of each of the frames to that depth.
- Calculate the displacement and center of buoyancy.
So you get a first poit for the curve KN values at this heel​​.
Now you change the draft and repeat the procedure. Get a second point of the curve to another displacement, which will come out, but for the same heel.
So until 4 0 5 points. Generally no further.
Choose another heel and go back to do the same.
You repeat this for all heeling you want.
It's very simple but very laborious. And not complicate your life, please, with more things than necessary.

 

[kaptcatb]

You put the float where you want.

where you want .. you talking about point F or ? Positions of F and heel Q determine the underwater volume . Different (not real) volume => incorect KN => incorect GZ .
Also if point F is random .... place this point at B/2 ( board ) , rotate ship at 30 deg . He sink
Following link : for 2 displacement ship is heeled at 0;15;30;45 . See position of point F . Can be calculated but its rly long story .
http://store.picbg.net/pubpic/08/B3/b44889ce9f1f08b3.jpg

So anyway your advice is to leave these calculations and start to create model of ship ?

 

[TANSL]

Forget the point F. It is much simpler.
Draw the floating inclined at an angle alpha, to a certain depth, which you like. That draft, the same for each frame, determines a submerged area of each frame. What displacement are we calculating? : I do not know. We'll find out later.
The integral of the submerged areas of all the frames, to get volume: Now you know the displacement.
The integral of the moments of areas about the after perpendicular, compared to baseline and relative to the center line and get the coordinates of the center of buoyancy.
Knowing B, as I said in my previous post, you calculate KN easily.
You therefore have a point of the KN curve for the heel alpha. And so on.

Of course it is best to start creating the model. But it is very important to know what you are calculating and how it is calculated. Thus, when you have a stability problem you will know what to do, what you have to change, to solve the problem. Otherwise you can never project ships.
There are many people making precious 3D models; the corresponding software processes, and they apparent to be naval architects, but never will be because they have not the ability to get a boat with problems, float correctly.

 

[kaptcatb]

Forget the point F. It is much simpler.

I understand your words about hydrostatic calculations but cant believe your way for calculations have enoug accuracy .. Just seems so easy . To get KN for 1 displacement and Q=0:15:90 with "my" method i need ~3-4 hours ..
Anyway thx for help .

I have another question - i check some books about stability .. and none stated how to calculate KN ( GZ ) . Can you give me link t something with detailed information for KN calculation ?
Have someone heard about Vlasov curves for integration ?