Any confusion with the formulas as shown in emails below exists with the (key dip - aftertouch). You cannot arbitrarily assign a number of your choosing to this value, although from a practical regulating standpoint this is often done. The idea of the overall transmission (or action) ratio is that the component ratio of (hammer travel - let off) to (key dip - aftertouch) is that of the product of the (output levers) to that of the (input levers). My studies assign input levers as effort arms and output levers as resistance arms. So, if we designate: W = (hammer travel - let off) S = (key dip - aftertouch) H = rear key lever arm resistance (key out) Rs = whippen lever arm resistance (whippen out) K = hammer lever long arm resistance (hammer out) V = front key lever effort (key in) Ra = whippen lever arm effort (whippen in) N = hammer lever short arm effort (hammer in) The relationship, then, of W / S should be that of the product of Resistance Arms / Effort Arms. But note that S (key dip - aftertouch) implies a calculated value, not an arbitrary one. In order to isolate S the formula works out thus: S = (product of Effort Arms times W) / (product of Resistance Arms) Once the theoretical value of S is isolated; the Action ratio can be calculated. So, using some values from a Kawai action model: W = 46 mm - 2 mm = 44 mm) S = (10.5 - aftertouch) H = 126 V = 245 Rs = 94 Ra = 67 K = 141 N = 18.25 (Jack to knuckle contact taken at half stroke) S = (V x Ra x N x W) / (H x Rs x K) = (245 x 67 x 18.25 x 44) / (126 x 94 x 141) = 7.89 mm which is the theoretical key dip minus aftertouch. Thus aftertouch = 2.61 mm. Said another way; dip prior to aftertouch is 75% of the key stroke, while aftertouch accounts for the remaining 25%. Given this, the ratio of W to S is equal to the ratio of lever arms thus: W / S = 44 / 7.89 = 5.58 and the ratio of the products of the RAs / EAs = 5.575. The ratios not only agree, but they define the Action Ratio at half stroke. Now, the so-called aftertouch value of 2.61 mm seems odd, but it is important to realize that the measurement for this (if we can call it that) begins the exact moment that the jack tender makes contact with the let-off button in a well regulated action, and continues to the a solid bottom at full key dip. In addition, if the aftertouch value is far off from the theoretical remember that In any case, measurements aside, this is how the ratios interact. For more, see Pfeiffer's The Piano Hammer pages 110 and 111. It is necessary to work the formulas and read a few things between the lines as some of the info references his other book The Piano Key and Whippen. Nick Gravagne, RPT Piano Technicians Guild Member Society Manufacturing Engineers Voice Mail 928-476-4143 _____ From: pianotech-bounces at ptg.org [mailto:pianotech-bounces at ptg.org] On Behalf Of David Love Sent: Tuesday, January 05, 2010 3:48 PM To: joegarrett at earthlink.net; pianotech at ptg.org Subject: Re: [pianotech] Action Ratios Has to do with where the energy comes from and goes just to be sure you're being consistent with the ratio orientation. Key in is the distance from key front to balance rail, key out is balance rail to capstan contact; wippen in is capstan to wippen center, out is wippen center to knuckle contact point (balancier); shank in is flange center to knuckle contact and out is knuckle to tip of hammer or shank hammer center line (I see it done both ways and I'm not really sure why one over the other). David Love www.davidlovepianos.com From: pianotech-bounces at ptg.org [mailto:pianotech-bounces at ptg.org] On Behalf Of Joseph Garrett Sent: Tuesday, January 05, 2010 2:00 PM To: pianotech Subject: Re: [pianotech] Action Ratios David Love submitted a formula: " (keyout/key in) x (wippen out/wippen in) x (shank out/shank in) = (blow distance - letoff)/(key dip-aftertouch)" David, Please explain the Keyout/keyin, wippenin/wippenout and shankout/shankin terms. Either I've been sleeping too much lately or those are terms I've never encountered. (Probably the former.<G> Regards, Joe Joe Garrett, R.P.T. (Oregon) Captain, Tool Police Squares R I -------------- next part -------------- An HTML attachment was scrubbed... URL: <http://ptg.org/pipermail/pianotech.php/attachments/20100105/27adb875/attachment-0001.htm>
This PTG archive page provided courtesy of Moy Piano Service, LLC