Doug Dawson did some marvelous estimates regarding plane sole flexion (I'm 
going to assume that's a real word), based on certain assumptions:

>   We'll assume the
>   sole is concave from end to end by some measure, and that during
>   use to sole is initially supported at the front and back ends,
>   and moreover that the downwards force applied through the tote
>   is centrally located, i.e. roughly in a spot equidistant from the
>   front and back edges.

The only problem is, how dows one apply force *downwards* at the iron, for 
purposes of determining sole flexion, when the hands are located at the 
front ball and the tote, which are some distance away?  Even if one pressed 
down like the devil with both hands, that wouldn't suppress the concavity, 
if any, halfway between the places where downward pressure is applied.  The 
downward force applied to the tote, for example, would be felt, at most, at 
the bottom of the tote, so the principal flexion would occur between the 
bottom of the tote and the back end of the plane, and similarly for the 
downward force on the ball.  Assuming that one applies sufficient force to 
drive the sole flat to the surface at these two points, the concavity would 
remain, to some lesser degree, between these pressure points (i.e., around 
the mouth).  Ain't nobody pressing down on the iron.  Of course, the depth 
of cut of the iron will also result in downward force, flattening the sole 
further.  I suspect that any useful modeling of the forces involved in this 
situation will call for higher mathematics.

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Michael D. Sullivan, Bethesda, Maryland, USA
mds@a... / avogadro@w... / 74160.1134@c...
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