<!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 6.00.2800.1276" name=GENERATOR> <STYLE></STYLE> </HEAD> <BODY bgColor=#ffffff> <DIV><FONT face=Arial size=2>Hi Mark,</FONT></DIV> <DIV><FONT face=Arial size=2></FONT> </DIV> <DIV><FONT face=Arial size=2>I agree with your napkin sketch, but = this brings into question the psychophysical concept of a "just noticeable = difference" (JND) -- the magnitude of difference that can just be detected by a human observer.  I am not very well versed in somatosensory (touch) characteristics (being an auditory person), but JNDs are typically on = the order of 1/256 of the stimulus magnitude -- not *exactly* 256, of = course.  However, the 8-bit word worked out well for encoding things such as = brightness, as 1/256 is about a JND for brightness.</FONT></DIV> <DIV><FONT face=Arial size=2></FONT> </DIV> <DIV><FONT face=Arial size=2>This leads to your napkintop = example.  Would a 1 percentish change in inertia be noticeable?  Probably, = yes.  Would it be very significant?  Probably not.  </FONT></DIV> <DIV><FONT face=Arial size=2></FONT> </DIV> <DIV><FONT face=Arial size=2>Would a 3% change (15 g off of BW, = from 30 g of leading at a halfway point) be noticeable?  Yes.  = Would it matter?  Yes, it would likely give the pianist some edge.  = There are certainly pianists who like the spring assist for *some* reason.  = At the very least, they notice the difference in the way the piano = plays.</FONT></DIV> <DIV><FONT face=Arial size=2></FONT> </DIV> <DIV><FONT face=Arial size=2>Now many pianos that are balanced in = the traditional manner.  Some key leading is located way out on the = front end of the keystick.  Now the key lead inertia becomes even more = significant -- 6% of total inertia to achieve 15 g off of balance weight.  More of = an edge.</FONT></DIV> <DIV><FONT face=Arial size=2></FONT> </DIV> <DIV><FONT face=Arial size=2>But using the halfway-point leading, = consider the leading consequence of adding a gram to the hammer and 12 g of leading = to the halfway point on the keystick to compensate for the additional BW.  = NOW we're talking about a 10% ratio of additional key inertia to additional = hammer inertia, which is becoming more significant still.</FONT></DIV> <DIV><FONT face=Arial size=2></FONT> </DIV> <DIV><FONT face=Arial size=2>Does 10% matter?  Does 5% = matter?  Well, does a pianist notice BW inconsistencies of 2 or 4 or 5 g between keys = during soft playing?  That's roughly the same degree of difference.  = It would probably take a more advanced pianist to care, granted.</FONT></DIV> <DIV><FONT face=Arial size=2></FONT> </DIV> <DIV><FONT face=Arial size=2>Even so, your napkintop sketch is very illuminating.  I frankly hadn't expected the ratio to be = that high!</FONT></DIV> <DIV><FONT face=Arial size=2></FONT> </DIV> <DIV><FONT face=Arial size=2>Peace,</FONT></DIV> <DIV><FONT face=Arial size=2>Sarah</FONT></DIV> <DIV><FONT face=Arial size=2></FONT> </DIV> <DIV><FONT face=Arial size=2>  </FONT></DIV> <BLOCKQUOTE dir=ltr style="PADDING-RIGHT: 0px; PADDING-LEFT: 5px; MARGIN-LEFT: 5px; = BORDER-LEFT: #000000 2px solid; MARGIN-RIGHT: 0px"> <DIV style="FONT: 10pt arial">----- Original Message ----- </DIV> <DIV style="BACKGROUND: #e4e4e4; FONT: 10pt arial; font-color: = black"><B>From:</B> <A title=mark.davidson@mindspring.com href="mailto:mark.davidson@mindspring.com">Mark Davidson</A> </DIV> <DIV style="FONT: 10pt arial"><B>To:</B> <A = title=pianotech@ptg.org href="mailto:pianotech@ptg.org">Pianotech</A> </DIV> <DIV style="FONT: 10pt arial"><B>Sent:</B> Friday, December 12, 2003 = 8:49 PM</DIV> <DIV style="FONT: 10pt arial"><B>Subject:</B> Adjusting wippen = assist springs</DIV> <DIV><FONT face=Arial size=2></FONT><BR></DIV><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><FONT face=Arial></FONT> </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><FONT face=Arial></FONT> </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><FONT face=Arial></FONT> </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><FONT face=Arial></FONT> </DIV> <DIV> </DIV> <DIV>-Mark Davidson</DIV> <DIV> </DIV> <DIV> </DIV> <DIV> </DIV> <DIV> </DIV> <DIV> </DIV> <DIV> </DIV></BLOCKQUOTE></FONT></BODY></HTML>