<!doctype html public "-//w3c//dtd html 4.0 transitional//en"> <html> Hi folks. I wanted to try and turn this back to the origional question at hand. The origional concern of this was to compare the touchweight characteristics of  various methods of counterbalancing, primarilly lead vs springs. We were looking (compaitively) at two related issues really... the << heavyness >> (which we evidently still havent really defined in terms of physics) of the mass being moved at all possible (reasonable) speeds, and whether or not there exists some << ideal >> amount or range  of key inertia for top action inertia for any given overall action ratio (defined in terms of the Balance Weight Ratio commonly called the Strike Weight Ratio.) i.e... how the action gets up to speed and what the amount and character of the work the fingers need to do to accomplish that. I went into this discussion with the following idea in my mind. The action at balance can expressed as BW + FW  = ((SW x HR x WR) + WW) x KR which means the actions velocity is 0 and the masses being counterbalanced result in a horizontal key... Any force exerted upon the key to accelerate it and the rest the action then should be able to be viewed through this equation.  BW + FW become a <<ground zero>> as it were... a baseline, and ((SW x HR x WR) + WW) x KR define the mass and leverage (effective mass ?) being moved at any given time..... but the weight quanties would have to be translated to their respective moments of inertia, and the changing leverage through out the key stroke would have to be figured. One way to approximate this, I had thought, was to see what sum of BW and FW it takes to balance the key at ten evenly spaced points through the key stroke. Obvioiusly you cant do this with UW and DW measurements, but there are ways of getting around that. Assuming then that you can find this  BW + FW  for these ten positions... you can interprete the resulting change either as changes in "effective weight" or as changes in leverage.... but not both.  If you interpret as changes in leverage... then you have  ten points you can plot on a graph which will show the leverage on the one axis against the position of the key on the other. Useing simple regression math you should be able to find an approximate equation for the leverage throughout the whole keystroke. Yes ?? Once you have that, and moments of inertia for each part it becomes easier to figure the amount of force needed to accellerate an action to any given velocity. <<FW>> seen as key inertia will gradualy reverse from a positive to a negative number as key velocity approaches and exceeds 9.8 m/sec^2. The others <<weights>> will keep the same sign. Ok.. assuming you can do all this... it should be easier to compare assist spring actions with lead counterbalanced actions yes ? Cheers RicB -- 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>  </html>