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Thank you George,
Joel
----- Original Message -----
From: "George Huxtable" <>
To: <>
Sent: Monday, August 02, 2004 6:04 PM
Subject: Scaling and stability: Was [Nav-L] 7/8 SCALE SEXTANTS MORE
> 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 , by phone at
> 01865 820222 (from outside UK, +44 1865 820222), or by mail at 1 Sandy
> Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
> ================================================================
