[pianotech] crown and radius

[pianoguru at cox.net]

On Sun, Jun 14, 2009 at 11:09 PM , Gene Nelson wrote:
> This bridge location mark is where the high points will ideally be.

This is a common notion, the the high point of the bridge should be 
centered under the bridge.  I disagree with this concept.  If every rib 
had its high point under the treble bridge, those ribs, following the 
curve of the bridge and extended to the perimeter of the rim would 
dictate ripples in the soundboard going from rib to rib.   To avoid this 
"ripple" the high point of each rib must follow a straight line in front 
of, but close to the treble bridge.  I prefer to create in CAD 3D 
modeling, a soundboard curved to my liking, projecting the ribs to the 
soundboard surface, and this defines the radii of the ribs.

Ron N wrote:
>> If your crowns are uniform radius circle segments, the high points 
>> couldn't be anywhere other than in the rib center.

This assumes that the elevations of the ends of the rib are the same, 
which they are not, as I and others would have it.  If the termination 
of the rib is higher at one end than the other, the high point of the 
rib shifts from center toward the higher terminus of the rib.  This has 
nothing to do with how the radius of rib is cut, but how the rim is 
machined to correspond to the crown of the soundboard.

Regarding the cutting of the radii in the ribs, forget about where the 
high point will be.  That is irelevent to the arc of the ribs.  The only 
concern in cutting the ribs is at what point will the rib be at its 
thickest, once the arc is cut.  Some would say that it should be 
thickest under the bridge.  I would say that it should be thickest at 
its center.  To me, it's like a roof truss.  To deliberately take the 
lower member of a roof truss, and make it slopped higher on one side 
than the other makes no sense.  It would better support the load of a 
heavy snow if it connects to the other two members of the triangle at 
the lowest practical point on each side.  The same is true of piano 
ribs, having the thickest point at the center.

Frank Emerson