Freeship cross curves notation. Puzzled.

Hello,

I think i understand what KN curves are, their relation to GZ etc.

I think free ship cross curves diagram shows us KN distance in meters in different displacements and heeling angles.

However in Freeship cross curves diagram, Y axis of diagram is not labeled as KN(m), but instead KN(sinø)[m], which I (incorrectly?) read as KN * sin(ø). Why is Y value labelled like this? What is purpose of "sin(ø)" bit? It seems to me that resulting KN values on graph are not multiplied by sin(ø) and if they were, i don't understand the purpose.

This stuff doesn't let me sleep at night. I think i just miss something obvious here and hope this question makes some sense to you? Sorry for such specific question about one detail, I'm just trying to learn and understand everything as systematically as self-taught amateur can.


P.S. Have been reading this forum for past year or so, the amount of information and friendly community amazes me. I enjoy learning from you guys. Thank you.

 

I think the reason simply is a different terminology. Look at this sketch:

M is the initial metacenter, M(phi) is the real metacenter, depending on phi (heel angle), and N is the apparent metacenter, the point where the plumbing line of M(phi) intersects the midships plane.

 

Heimfried, thank you very much, it makes perfect sense now.
My mistake was to assume that GZ and KN lines were the same throughout the literature.

Thanks again.