<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN"> <HTML><HEAD> <META http-equiv=Content-Type content="text/html; = charset=iso-8859-1"> <META content="MSHTML 6.00.2800.1170" name=GENERATOR> <STYLE></STYLE> </HEAD> <BODY bgColor=#ffffff><FONT face="Courier New" size=2> <DIV>Jeez Ric. You go out on a limb </DIV> <DIV>and end up riding a freight train.</DIV> <DIV> </DIV> <DIV>I have to agree with Sarah's physics. </DIV> <DIV>Same force, less mass, more acceleration.</DIV> <DIV>That assumes a constant force, though.</DIV> <DIV>Basically if you speed it up, you push on</DIV> <DIV>it.  If you slow it down, it pushes on you.</DIV> <DIV>So if things are decelerating, then you can</DIV> <DIV>get force out of the key lead.  If</DIV> <DIV>somehow you could get it all moving and</DIV> <DIV>then stop pushing on the key with your </DIV> <DIV>finger, then there could be enough</DIV> <DIV>energy in the key to continue to drive the</DIV> <DIV>hammer home.  Not really how we typically</DIV> <DIV>play the piano though, unless you consider</DIV> <DIV>"striking" the key vs. other types of motions.</DIV> <DIV> </DIV> <DIV>But here's the real rub.  She's got you </DIV> <DIV>riding a train when you should be </DIV> <DIV>riding a bicycle.  </DIV> <DIV> </DIV> <DIV>Let's do a little energy napkin sketch.  </DIV> <DIV> </DIV> <DIV>Energy of mass m moving at velocity v </DIV> <DIV>is (m*v^2)/2.</DIV> <DIV> </DIV> <DIV>So if the key front is moving at speed </DIV> <DIV>1, then a key lead halfway out is </DIV> <DIV>moving at .5, while the hammer </DIV> <DIV>moves at approximately 6.</DIV> <DIV> </DIV> <DIV>If the hammer mass is 10g and the </DIV> <DIV>lead mass is 10g, then the lead </DIV> <DIV>energy is </DIV> <DIV> </DIV> <DIV>(10*.5*.5)/2 = 1.25</DIV> <DIV> </DIV> <DIV>while the hammer energy is </DIV> <DIV> </DIV> <DIV>(10*6*6)/2 = 180!</DIV> <DIV> </DIV> <DIV>That's a ratio of 1:144.</DIV> <DIV>So yes, any energy </DIV> <DIV>remaining in the key when it </DIV> <DIV>bottoms out is wasted, but by far</DIV> <DIV>most of the energy is in the hammer.</DIV> <DIV>And it would appear that adding </DIV> <DIV>a key lead makes less than a 1% change in</DIV> <DIV>the TOTAL inertia (hammer inertia </DIV> <DIV>is effectively much larger because </DIV> <DIV>of the leverage involved).</DIV> <DIV> </DIV> <DIV>Oversimplified - should all be</DIV> <DIV>rotational - and neglects</DIV> <DIV>the inertia of the unleaded key,</DIV> <DIV>but I think it makes the point</DIV> <DIV>that the SW and SWR are far and</DIV> <DIV>away the most important components</DIV> <DIV>of the overall inertia.</DIV> <DIV> </DIV> <DIV>For better repetition though, you </DIV> <DIV>still want low key inertia.  That would</DIV> <DIV>appear - at least based on this example - </DIV> <DIV>to be the chief benefit of assist springs.</DIV> <DIV> </DIV> <DIV> </DIV> <DIV>-Mark Davidson</DIV> <DIV> </DIV> <DIV> </DIV> <DIV> </DIV> <DIV> </DIV> <DIV> </DIV> <DIV> </DIV></FONT></BODY></HTML>