minimum longitudinal righting moment area

Hi guys,

I could use some help on calculating the minimum longitudinal righting moment area according to section H3.1 ISO12217-2:2013. It says:

f) Graph longitudinal righting moment and height to immersion of the foredeck against trim angle.
g) Determine whether or not the foredeck becomes immersed at a trim angle less than 20°. The limiting trim
angle is the lesser of 20° and the angle at which the immersion of the weather deck at the stem (main hull
for trimarans).
h) Determine the limiting longitudinal righting moment and calculate the longitudinal righting moment area to
the limiting trim angle from the graph, and convert to kN⋅m⋅rad by dividing by 57,296.

Does that mean I can multiply angle and longitudinal righting moment and sum these up for all steps?

 

Well, maybe this was the wrong question? :$ Or better placed in stability corner of the forum?

The background: I would like to use a F28 style catamaran for offshore racing. In Europe there are some KL28 catamarans for sale but these have a cat. D designation. Then I was wondering or it would be possible to design a 28 catamaran with cat. A or B by using more modern hull designs from beachcat's.
Before going into extreme designs, I was able to get a Nacra Infusion like design in Freeship. For calculating stability I use ISO12217. Most important questions are:

a) maximum transverse righting lever (par 7.8 rolling in breaking waves)
b) longitudinal righting moment area (par 7.9 pitchpoling)
c) diagonal stability (par 7.10)

I have a background in (electrical) engineering but am not very familiar with marine related mechanics. Ofcourse I read about it, but could use someone looking over my shoulder.

a) that's relatively easy. Could just get cat A by enlarging the beam from 5 to 5,8 m.

b) with Freeship I trim the single hull in steps of 0.1 m and for each step calculate trim angle, and righting arm (distance between trimmed LCB en orginal LCG). Multiplying angle, righting arm and mass(moc)*9,8 gives Nmrad. Deck is at 1 meter which corresponds to 12 degrees. Then I sum up the angle-arm-force products + the little triangles in between: 1/2Δangle * 1/2Δmoment.

For this situation minimum righting moment area is 24 [kNmrad]. Forward I get a 23, Backwards 26. Forward is to low, but can easily be raised by raising the bow 10 cm. Maximum specified angle is 20 degrees so I have some design space there. I have been thinking about taking half the weight because of calculation angle and righting arm on one hull, but this configuration for both hulls. So total weight should be used.

c) The ISO standard describes calculation of metacentric height. Related to higher LCG because of trim angle? In hydrostatics transversal metacentric height is negative? Because of leaking? Therefore I tought of another way of calculation. A lateral angle van 1 degree makes a beam of 4.8 metre go down for 4 cm on one and and 4 cm up on the other end. From hydrostatics calculation a forward trimmed boat (until deck immersion) which goes down 4 cm takes 122 kg to do so. Therefore righting moment is 4,8 * 2 * 122 * 9,8 = 11477 Nm. Neccesary for cat A is 5000 Nm. Double... Seems stranges as the other values are just in range?
The standard: http://jsaf-anzen.jp/pdf/ISO_12217-2_2013(E)-Character_PDF_document.pdf