NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Scaling and stability: Was [Nav-L] 7/8 SCALE SEXTANTS MORE
From: George Huxtable
Date: 2004 Aug 2, 23:04 +0100
From: George Huxtable
Date: 2004 Aug 2, 23:04 +0100
Joel Jacobs wrote- >I do >have "Stability and Trim for the Ship's Officer" by La Dadge and Van Gemert >handy. > >On page 35, they move beyond the standard formula Henry presents to the >following: > >Saying "moment of inertia is a difficult term to define simply." and "This >moment which resists motion of an infinite number of moments which are >composed of the product of each elementary area and the square of the >distance from the axis." (simple?) > >I = L x B3 / 12 for a rectangular waterplane > >For non-rectangular waterplanes I = L x B3 x k > >k is a constant that relates to a waterplane coefficient > >They conclude that the moment of inertia "is almost wholly dependent on >breadth of the vessel." ================= This is a bit misleading. They are referring to the moment of inertia of a thin flat waterplane, about a fore-and-aft axis, such as a raft (if it can be said to have a fore-and-aft axis). They assume a constant "surface density": that is, assume that the weight per surface are of the raft stays constant when other dimensions are changed. Robert Gainer was describing a rather different situation, in which the dimensions of a vessel (which could well be a raft) are ALL scaled up in proportion. So, as the breadth of a raft is increased by a certain ratio, so is its length increased by that same ratio, and so is the depth (vertical thickness) of the raft. And so, therefore , is its weight per surface area. Now the moment of inertia of the raft about a fore-and-aft axis is proportional to length x (breadth)cubed x depth. So if you double all the dimensions of that raft, you increase the moment of inertia, about its fore-and-aft axis, by 2x2x2x2x2, the fifth power of 2, which is a factor of 32. Note that before you specify a moment of inertia, you have to specify the axis about which the rotation being considered is going to occur. The moments of inertia about different axes will be very different. But in all cases, when the dimensions of a vessel are all multiplied up by the same factor (so that its shape doesn't change), the value of any moment of inertia will change by that factor to the fifth power (i.e. multiplied by itself 5 times). That's what Robert Gainer was pointing out. George. ================================================================ contact George Huxtable by email at george@huxtable.u-net.com, by phone at 01865 820222 (from outside UK, +44 1865 820222), or by mail at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK. ================================================================