# Cross Curve for Small Displacements (4 tonne marine buoy)

Discussion in 'Stability' started by henrynel, Mar 5, 2013.

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### henrynelNew Member

Hi I'm new to this forum. I was wondering if anyone could briefly explain how to calculate the stability on a marine buoy which i'm designing as part of a 2nd year project.

From various articles I've read it seems possible to calculate the initial stability using basic geometry which is valid for an inclining angle up to 10 degrees. I've done this shown that the metacentre lies above the centre of gravity. Hence stable.

However for further angles (>15 degrees) it appears you need to either use software or cross curves to obtain a stability curve. Ideally i'd like to use cross curves however I can't find any which have a displacement <15000 tonnes? (The marine buoy i've designed is 4 tonnes) Can anyone advise me on this topic?

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### DCockeySenior Member

How do you think that the displacement affects the process of calculating the curves?

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### gonzoSenior Member

The horizontal distance between the Center of Flotation and the Center of Gravity will give you the righting arm. The math is the same for 10 degrees or 90. You can do it for several angles, make a graph and then interpolate if you need intermediate values.

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### jehardimanSenior Member

And unless it is a drifting buoy, the effect of the mooring makes everything different. Go get a copy of Buoy Engineering by Henri Berteaux of WHOI, John Wiley & sons 1976 or his 1991 re-write. Should be in any good technical library

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### gonzoSenior Member

The mooring acts to effectively lower the CG. It can be viewed as a ballast keel.

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### henrynelNew Member

I tried doing that:

Angle Centre of Buoyancy x-direction/m
0 0
2 0.0329
4 0.06587
6 0.09901
8 0.132
10 0.16609
12 0.20021
15 0.25185
20 0.33181
25 0.39577
30 0.44131
35 0.47482
40 0.50089
45 0.52213
50 0.53932
60 0.56325
70 0.57817
80 0.58618
90 0.58852
100 0.58521
110 0.57516
120 0.55832
130 0.53448
140 0.49949
150 0.44179
160 0.3235
170 0.16001
175 0.07939
180 0

Is that correct with maximum righting arm at 90 degrees, and zero at 180? Looks a bit too trivial

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### henrynelNew Member

i have had a look for this book in my university library however no copy exists. at present another design team member is looking the mooring. he did mention that there could be a lot of slack and that the buoy could invert completely.

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### henrynelNew Member

i don't think it should matter? so why is there no cross curves for 4 tonne displacements?

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### DCockeySenior Member

Could be correct. It depends on the shape of the buoy. How did you determine the center of buoyancy position?

What are you studying?

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