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    Re: Hybrid Artificial Horizon
    From: Gary LaPook
    Date: 2008 Sep 13, 15:42 -0700

    I like George's idea of a ring shaped "catamaran" type of float. Rather
    than trying to make one yourself, just go down to the toy store and buy
    a plastic ring of the right size and mount your mirror to it. The toy
    manufacturer's will  make the ring more symmetrical than you would be
    able to do. You might want to add the screws that I mentioned before to
    three places around the circumference of the ring to use to trim it to
    eliminate any error in COG which would cause the ring to not float
    horizontally. For calibration purposes, figure our the time when Polaris
    is crossing your meridian since it is then at a fixed altitude for 45
    minutes which will allow plenty of time for trial and error adjustments
    of the float, see my previous posts about this.
    George Huxtable wrote:
    >Gary wrote-
    >| Your floating box works because the surface of the water is horizontal
    >| and, you hope, that the box will float so as to remain horizontal also.
    >| This will only work if the box is absolutely symmetrical so that its
    >| center of buoyancy is exactly above its center of gravity (COG) when the
    >| mirror is exactly horizontal, a tough thing to achieve.
    >No, not tough at all, really, especially in the case of a raft.
    >Given such a box, its centre of gravity is fixed. Not so, its centre of
    >buoyancy, which is the centre of gravity of the water it displaces. If the
    >vessel tilts, the centre of buoyancy  shifts. With a flat raft-shape of
    >little depth, the centre of buoyancy shifts much faster, for the same degree
    >of tilt, than for other vessel shapes. So it is more resistant to tilt than
    >is another shape of vessel (or, at least it is until a gunwale immerses).
    >An even more stable shape is a catamaran construction, with its buoyancy at
    >the extreme edges, which is why I was suggesting a sort-of ring-shaped cat.
    >Of course, it's true that the flotation plane will only be exactly
    >horizontal if the centre of gravity is aligned with, and below, the centre
    >of area, but the raft shape is more forgiving of any divergence from this
    >ideal than are other shapes.
    >Gary is comparing two very different sorts of stability; what naval
    >architects refer to as "form stability", which depends on the shape of the
    >vessel , and applies a righting lever which depends on tilt between the
    >vessel and the water surface, and "ballast stability", which applies a
    >righting lever which depends on the tilt of the resulting pendulum from the
    >vertical. In still water, the situation Ken is considering, those tilts are
    >the same (but, by the way, in waves, when the sea-surface is not horizontal,
    >they are not). The two extreme cases are the raft, for form stability, and
    >the fisherman's float or deep-sea buoy, for ballast stability.
    >In practice, all vessels combine those two characteristics, in different
    >proportions, from the sailing dinghy or Thames barge or cat (form) to the
    >racing keelboat (ballast).
    >contact George Huxtable at george@huxtable.u-net.com
    >or at +44 1865 820222 (from UK, 01865 820222)
    >or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
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