Littoral Steel Trawler Design

I don't see any contradiction to my

Naturally the stability decreases, if for a given waterline area a greater lenght and a lesser beam is choosed.

But if beam, the shape of the cross section of hull and the VCG are given, it should not affect stability, if the lenght ist three times larger.

(May be there are other influences then hydrostatics, so as wind, current or waves.)

 

Stability also depends on the inertia of the waterplane, as you know, which determines the position of false metacentre. The same water line area (I mean same square meters), have a very different (bigger) inertia about the longitudinal axis, if the ratio L / B decreases.
I do not know what to say or how to say it to show that, with the same length, the breadth influences increased and much in increasing stability.
What you say, "But if beam, the shape of the cross section of hull and the VCG are Given, It Should not Affect stability, if the lenght ist three times larger" is not correct because, although no change of breadth, or cross section, or c. of g. position, the inertia of the waterplane does change. What happens is that the variation is much greater if what changes is the value of the breadt. For a rectangular waterplane of length "L" and breadth "B": Ix = (L.B^3)/12. and the position of the false metacentre depends on Ix/V, where V is the submerged volume of the hull and, as you well know, the position of false metacentre does have to do with stability.

 

I don't agree, TANSL.

The Ix = L * B^3 / 12 is straight proportional to L and so is V. Assumed the wetted cross section area is fix.

Therefore the value of Ix/V depends not on L.

As I said above, I don't compare boats with constant displacement and different L:B ratio.

 

OK, Heimfried.