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    Re: Hybrid Artificial Horizon
    From: George Huxtable
    Date: 2008 Sep 13, 12:30 +0100

    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).
    
    George.
    
    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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