<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"> <html> <head> <meta content="text/html;charset=ISO-8859-1" http-equiv="Content-Type"> <title></title> </head> <body> <meta content="text/html;charset=ISO-8859-1" http-equiv="Content-Type"> <title></title> <meta content="text/html;charset=ISO-8859-1" http-equiv="Content-Type"> <title></title> Hi Folks. Been mulling over a lot of whats been written and looking back at Stephen Birkets article and it struck me that we could use these cute new key inertia measuring jigs Mark and John have worked out to do exactly what Birkets article suggests. According to Birkkets paper there a few key expressions  based on the following diagram. <img src="cid:part1.02070200.00080907@grieg.uib.no" alt=""> The breakpoint acceleration is <img src="cid:part2.05090309.08000105@grieg.uib.no" alt=""> and <img src="cid:part3.03020401.00050308@grieg.uib.no" alt="">   For the Breakpoint force we have.   <img src="cid:part4.03040507.00030808@grieg.uib.no" alt=""> <img src="cid:part5.04000102.08070402@grieg.uib.no" alt=""> Now   Fst is the exact force we need to exceed in order to get the key moving. This is the same thing as  BW * g So.. Fst = BW * g then  Mrk = (BW * r) + mrb. which means that the only unknown in any of these expressions is Ik (which we can measure with our MOI jigs) since we can calculate Mrk directly from BW, r, and mrb. So what do we get if we measure and figure these expressions out. Jo !! we get  2 points on the force for accelleration graph.. and using 9th grade geometry we know that  (y-y1) = a(x- x1) is the solution for finding a 1st degree equation  when two points are known. What we get is Stephens (Fst, a)  ( Fbr, a1) In other words....; <img src="cid:part6.04040501.05010606@grieg.uib.no" alt=""> is the equvilant of <img src="cid:part7.08040308.05000208@grieg.uib.no" alt=""> Or... since Fst = BW * g and Mrk = (BW * r) + mrb. we have as our two points.. (x,y) (x1,y1) <img src="cid:part8.08030703.05020902@grieg.uib.no" alt=""> All of which we can easily measure directly without having to rely on knowing the MOI for the (already) leaded key. We only need Ik for a reference (unleaded) key from which, together with a BW specification, we can  decide which  combinations of  m and rb... ie key mass and its radius from the balance rail pin, will yield desireable  points on the acelleration for force graph. As long as we can assume that lead evenly distributed about a certain point will to a reasonable degree behave as the point mass used in Birketts equation... we have basically a new equation of balance.... and one that directly accounts for key MOI. Mrk = (BW * r) + mrb Yes ??? Cheers RicB </body> </html>