# cross curves of stability

Discussion in 'Hydrodynamics and Aerodynamics' started by jeffking, Aug 11, 2012.

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### jeffkingJunior Member

Hello,

In calculating the cross curves of stability what happens when the deck edge goes under water? Is the righting arm calculated as if the vessel simply rotates about the center line at various angles? For example, a barge at 10 - 20 degrees will have the deck edge under water. Yet the cross curves of stability are calculated out to 90 degrees. Or is the new buoyancy equilibrium found then the righting arm? I have a few good naval architecture references as well as several from the internet but this point is not clear to me.

thanks, Jeff

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### DCockeySenior Member

From Principles of Naval Architecture Second Revision Volume I Stability and Strength (1988) pp 79-80:
"Cross curves and righting arm curves are usually prepared on the basis of the assumption that there is a complete watertight envelop consisting of bottom, side shell and weather (or bulkhead) deck." Discussion follows about how superstructures and deckhouses are usually delt with as well as openings in the envelope which could cause down flooding.

There is no need to determine buoyancy equilibrium when doing the calculations to obtain the data to create cross curves of stability. Each curve is for a single heel angle and spans a range of displacements. For each heel angle multiple inclined waterline locations are selected which will cover the required range of displacements. There is no need to determine the precise inclinded waterline location for a given displacement. The set of displacement and righting arm points obtained using the selected inclined waterline locations for the heel angle are used to draw the cross curve for that heel angle. The righting moment for other displacements at that heel angle can be interpolated from the curve.

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### jeffkingJunior Member

Thanks David,

Your answer makes sense - one curve spanning a range of displacements. This enables me to start analyzing the necessary freeboard to meet codes.

Jeff

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