In the interest of getting past at least some of the mix of variously rationalized opinions on the subject, I would request some help in the form of input from the various folks on the list with engineering backgrounds, regarding fundamental physical principals. Let's open-source this sucker and produce some straightforward math from known data that rationally answers some basic questions which are obviously still in doubt. I know this will have no effect whatsoever on those who don't believe in science and math, who insist that this doesn't prove anything, nor tell you how the piano will sound, etc, but for some of us it may throw some light on the basic structural forces involved - which is the reason I'm starting this. I'd appreciate constructive ideas and critique as a reality cross check to get as close as possible to the real stuff, should anyone interested in trying to define the real stuff care to participate. I need math corrections if I did something wrong too. This is not an attempt at modeling all the details of what makes a soundboard work, merely the most significant structural loading and stress estimate. Any claims to the contrary will be dismissed as febrile ravings. In the interest of using a measurement system most familiar to most of the list participants, I'll start this in inches and feet for linear dimensions and pounds for weight and compression. E=modulus of elasticity. Considering Sitka spruce at 1,570,000 Lin=rib length in inches H=rib height W=rib width Pt=panel thickness Pw=width of panel between ribs (half way from the last, to half way to the next) Pc=panel compression psi Rad=crown radius in feet Cr=crown height P=load in pounds B=total string bearing load of all unisons supported by this rib (Pw range) D=deflection Bearing load per string is the sine of the angle times string tension (close enough) To find crown height for a given radius Cr = (rad*12)-((rad*12)^2-(Lin/2)^2)^0.5 To find radius for a given crown height Rad = (((Lin/2)^2+Cr^2)^0.5/(2*Cr))/12 Deflection under load D = (Lin^3*P)/(4*E*W*H^3) Load required for a target deflection P = (4*E*W*H^3*D)/Lin^3 Panel compression psi necessary to produce given deflection - how much unloaded crown P is obtained with above equation Pc = ((P*(Lin/2))/((H+Pt)/2))/(Pt*Pw) Any corrections, comments, or additions so far? Ron N
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