<!doctype html public "-//w3c//dtd html 4.0 transitional//en"> <html> <body bgcolor="#FFFFFF" style="FONT-SIZE: 14pt; FONT-FAMILY: Arial; BACKGROUND-COLOR: #ffffff">   "Don A. Gilmore" wrote: <blockquote TYPE=CITE> Hi Richard: I'm not sure what the qualifications of your "physics guy" are, but inertia is not even an engineering quantity.  There are no units of "inertia".  It is just a concept regarding the nature of matter.  All bodies with mass have inertia and tend to want to stay at a constant velocity and move in a straight line. </blockquote> Doesnt really matter.... beyond saying that he is regarded by many as an authoritive figure in these matters by many in the PTG. Scary I guess...   any ways ..my point is that one can easily get led astray around here :)  I << believe >> at this point I have things rather sorted out... at least at this stage of things.     <blockquote TYPE=CITE>Though a piano action does a lot of fancy stuff, it still is a captive mechanism.  In other words, up till the point where the hammer is released there is a specific, repeatable relation between key movement and hammer movement.  So for any given position of the key downward, there is a specific angle of the hammer produced.  You could draw a graph showing key movement along the ordinate axis and hammer angle along the abcissa.  And an equation can be determined that describes this curve.  From this equation can be derived all the other equations of motion including those for velocity, acceleration and perhaps even jerk.  These would tell you exactly what that all-important "release velocity" is for any given finger motion. Sounds simple, right?  But "finger motion" is another subject entirely!</blockquote> Grin... wellll lets forget the finger motion for the time being, and what happens after the hammer leaves the jacktop. What I am interested in is finding out exactly how much work is required of the finger to accelerate a given key mass to any realistic velocity for any given top action mass and action ratio... how to manipulate that by changing parameters of key mass, hammer mass and action ratio.  The Stanwood equation goes only a little ways along this road... tho its a good deal farther then what preceeded it.   Sounds to me tho...l like you are suggesting determining an equation through some sort of regression, and taking 1st and 2nd deriviatives to get at  velocity and acceleration for it. If so... yes that much sound rather easy. Why dont we a step through example.. ? :) Cheers RicB <blockquote TYPE=CITE>  Don A. Gilmore Mechanical Engineer Kansas City </blockquote> -- Richard Brekne RPT, N.P.T.F. UiB, Bergen, Norway <A HREF="mailto:rbrekne@broadpark.no">mailto:rbrekne@broadpark.no</A> <A HREF="http://home.broadpark.no/~rbrekne/ricmain.html">http://home.broadpark.no/~rbrekne/ricmain.html</A> <A HREF="http://www.hf.uib.no/grieg/personer/cv_RB.html">http://www.hf.uib.no/grieg/personer/cv_RB.html</A>   </body> </html>