There exists an important point, however, which is missing here. Taking a step back, the so-called Renner Formula does not originate with Rick Baldassin or Renner, but dates back at least as far as Dr. Pfieffer and even beyond to possibly Kutzing. Pfeiffer's version of the formula* implies the Renner one (virtually identical), but there is a subtle yet critical difference in what Pfieffer is saying versus how we are herein interpreting the Renner version. The Renner version is correct, but potentially misleading. I will get back on this later, possibly with an attached paper or whatever. Yes, the "Renner Formula" as David is using it (and I have used it) states an equality which is mathematically consistent. David's Dip and Aftertouch (AT) calculator agrees with my own, as far as this goes; but it doesn't precisely represent the intended concept per Dr. Pfieffer nor per Renner. Still, for the moment, and RE the Renner version as has been shown in these posts, the idea has never been to arbitrarily assign all four variables of blow, dip, let-off and AT into the right hand expression, but to assign (or at least plug in for a dry-fit) only the three variables of dip, blow and let-off which represent usual and understandable specs of a sort, and then to solve for AT. It should be understood that DIP in this regard must be taken at the very, very end of the key stick, which is presumably where we reckon the total length of the front lever arm. Thus, DIP must be taken there as well and is not related to the front rail punching / pin point of of the key lever. Although by happy coincidence**, solving for AT, as defined as "the exact point where the jack tender makes contact with the let-off button" does, in fact seem "consistent with real world results", yet in a relative way only. However, DIP per Pfieffer does not represent (nor should it per Renner) our complete-through-happy-aftertouch DIP; i.e. the regulation DIP we set as regulators to 10 mm (+ or -). In any case, one real value of the formula is that it makes unavoidably apparent the idea that we do not have carte blanche leeway in increasing the mechanical advantage (MA) of the key-hammer system (making it easier to play, lower inertia, etc.) without taking due regard to the amount of total key dip impacted. Lowering the AR from, say, 6.2 to 5.8 (better MA) would require an increase in dip of something like 1 mm, pushing the total dip to 11 mm required in order to complete the cycle. I have heard of mistakes and abuses being made in this regard that exceed this example. But that is another point. *Pg. 111, The Piano Hammer. If you own this book you might read the whole of the related chapter. **I say happy coincidence, yet it is clear that a geometrical process is in place here. That intricate process, when the jack is tripping the light fandango, is not simple, and undoubtedly requires its very own dip to jack-trip ratio, to be expressed as a ratio of jack rotation to required and related partial dip. Likewise, at the front rail pin and punching, where the key sits at something like a 2 degree angle, and the pin sits somewhere at 15 mm or so behind the very front end of the key, the jack-partial dip ratio is here related. I have not worked out the geometry on this. Later NG David Love<a href="http://www.davidlovepianos.com" target="_blank">www.davidlovepianos.com</a> <div class="gmail_quote"> On Wed, Aug 29, 2012 at 6:47 AM, David Love <<a href="mailto:davidlovepianos@comcast.net" target="_blank">davidlovepianos@comcast.net</a>> wrote: <blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"> <div link="blue" vlink="purple" lang="EN-US"><div>Not to beat a dead horse but FWIW one thing I do notice, with my action model anyway, is that the jack movement (and key movement for that matter) from the point of jack tender contact with the let-off button is about 2.5 – 3 mm which, on my model, translates to about .040” key travel after the point of escapement. So if “aftertouch”, at least in this formula, is based on travel after contact with the let-off button when the jack starts to move horizontally rather than vertically, then the output of my design chart seems consistent with real world results. <div>David Love <a href="http://www.davidlovepianos.com" target="_blank">www.davidlovepianos.com</a></div><div><div class="h5"> </div></div></div></div></blockquote></div>