# Definition of KN.

Discussion in 'Stability' started by LP, Feb 11, 2008.

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### LPFlying Boatman

I've been tossing around some cross curve data output from Freeship for a while and not really knowning what I was looking at. I've been looking for a description to KNsin(phi) and have not run across a definative answer. With a little determination I'm thinking I've got a handle on the beast, but would like some confirmation that I'm on the right track.

KNsin(phi) is a righting arm at the keel. (K=keel, phi=angle of heel) N was ellusive to me, but I believe it to be closely related to the metacenter(M). N being the actual point where the heeled center of bouyancy passes through the vertical centerline of the vessel.(?) To find N, I rearranged the equation x=KNsin(phi) and for low angles of heel KN appears to be roughly equal to KM.

I'm attempting to identify the range of positive stability for the boat I'm designing so I want to find the righting moment through all ranges of heel.(?) I then establish GN=KN-KG for use in GNsin(phi) to calculate the actual righting arm. You have to excuse me if my terms are not correct. In this essence, GNsin(phi)=GZ in hydrostatic terms. According to my thinking and calculations, this is true. If my logic is flawed here, I would like a nay or even a yay if I'm doing it right.

Applying mass to the righting arm will then give me the righting moment to be used in counter the heeling force of the sails.

Again, N has been ellusive to me. The design texts I have on have don't mention N and the KNsin(phi) is quite prevalent on the web, but without definition.

The design is for a shallow draft, trailerable, 25' coastal cruiser. Right now, my numbers show negative stability at 105 deg. of heel . I'm showing almost 4600 ft.lbs. righting moment at 35 deg. of heel on a 6.9' BWL with a 2 ton displacement craft. BOA is limited to 8. If my calculations are correct, dropping the CG by 6" will give me positive stability through almost 150 deg. of heel.

I don't know any of you can draw conclusions from those numbers, but I'd like to hear some input.

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### Olavarch. nav.

LP,

your thoughts about the meaning of KN*sin(phi) are perfectly right. N (sometimes indicated with "phi") is indeed the metacentre at heeling angles > 0 degrees; however it's admissible to assume N = M at small angles (say < 5 degrees).

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### LPFlying Boatman

Thanks for the confirmation, Olav.

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### GuillermoIngeniero Naval

This KN thing at Freeship has produced this kind of confusion before. In the noting I'm used to, "N" is the point where the vertical from the metacenter crosses the horizontal from the point "K" at the Base Line for every given angle of heel. The produced curves for every load condition are then called the KN curves (the cross curves of stability).
In the notation I use, KN = KH*sin(theta), being H the point where the vertical from N crosses the longitudinal midship section (which is asumed to coincide with M for small angles of heel).
I find this Freeship notation somewhat confusing.
Cheers.

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### LPFlying Boatman

Guillermo,

Thanks for stopping by. I've drawn up a schematic of what I believe is your decription of the annotations as you use them. At first it lead to more confusion. Would you agree though that your KHsin(theta) is equivalent to KNsin(phi) in freeship? I just need to get some personal clarification so that I have a proper understanding of the relationships involved and, of course, the physics.

Perhaps I'm wrong, but I get the feeling that N is not well defined in the industry.

Thanks

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6. Joined: Mar 2005
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### GuillermoIngeniero Naval

You got my point, LP. Yes, my KHsin(theta) is equivalent to Freeship's KNsin(phi).
Cheers.

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