Cross Curves in Freeship

[lewisboats]

Ok...so could someone explain how to interpret cross curves? I understand that the left side is the distance from the keel to the center of buoyancy and the bottom is the displacement. What would an almost flat line for a curve indicate? What do the higher heel angle lines indicate when they curve the opposite direction of the lower ones (humped up instead of sloped down or flat-ish) and why when I put in a single displacement does the graph change to straight lines angling up and to the right...stopping at the displacement set (or as close as the increments will allow).

Steve

PS: Yes I read the manual and from the page to my brain it becomes confusing because KN sin(ø) is a meaningless statement to this non math person. From another thread I found out that this MIGHT be the Transverse Center of Buoyancy at angles of heel but I may not be reading that correctly at all so.....HELP!

15.4 Cross curves.
Stability calculations are provided in the form of cross curves. For a number of heeling angles and
displacements KN sin(ø) is calculated and presented in a graph and table. If only one displacement
is provided the KN sin(ø) curve is displayed. If multiple displacements are provided the graph shows
the standard cross curves. The calculated data can be printed or saved to a textfile.

[Ad Hoc]

The "KN" is on the left hand side of the graph. The Displacement, is on the base of the graph.
You then have a series of curves all plotted at various 'angles'.

Select the displacement of the vessel, then draw a straight perpendicular from the displacement. Where this vertical line crosses the curves of angles, note the angle, and then note the value of KN.

First thought, you need to be sure that KN, is from the baseline/keel of the boat to the metacentre. (not all produced like this).

Then once you ahve the KN data you do the following:

GZ = KN - KG x sin (angle)
where
KN = cross curve ordinate
KG = centre of gravity above datum (Same datum as KN, corrected for free surface effects)
angle = heel angle, from cross curves

So, you draw up a table of the items you have
Angle, going down, and going across you have columns of
Angle, KN, sin (angle), KG x sin(angle), GZ.