Can anyone explain what this << =20 >> crap is all about... I'm getting that in a lot of posts now from pianotech... almost half the sentences come through with that at the end... very irritating...? RicB Phillip Ford wrote: > Let's do a little energy napkin sketch. =20 > > Energy of mass m moving at velocity v=20 > is (m*v^2)/2. > > So if the key front is moving at speed=20 > 1, then a key lead halfway out is=20 > moving at .5, while the hammer=20 > moves at approximately 6. > > If the hammer mass is 10g and the=20 > lead mass is 10g, then the lead=20 > energy is=20 > > (10*.5*.5)/2 =3D 1.25 > > while the hammer energy is=20 > > (10*6*6)/2 =3D 180! > > That's a ratio of 1:144. > So yes, any energy=20 > remaining in the key when it=20 > bottoms out is wasted, but by far > most of the energy is in the hammer. > And it would appear that adding=20 > a key lead makes less than a 1% change in > the TOTAL inertia (hammer inertia=20 > is effectively much larger because=20 > of the leverage involved). > > Oversimplified - should all be > rotational - and neglects > the inertia of the unleaded key, > but I think it makes the point > that the SW and SWR are far and > away the most important components > of the overall inertia. > > For better repetition though, you=20 > still want low key inertia. That would > appear - at least based on this example -=20 > to be the chief benefit of assist springs. > > -Mark Davidson > > --------- > > You make an interesting point about energy. I can't agree with you > about inertia though. You seem to be implying that key inertia is > relatively insignificant in the total inertia picture. This is > counter to my experience. I know that I can easily lead up a key so > that the action is unplayable. I also know that if I take an action > that has a ton of lead in the keys, and make some changes to it, > without reducing SW, so that the amount of lead in the keys has been > reduced, that it will make a marked difference in the way the action > plays. On the other hand I can increase SW rather significantly, and > while noticeable, it won't render the action unplayable. > > To do some different math let's assume: > > SW = 10 g > > Hammer CG is 13 cm from its center > > WW = 18 g > > Wippen CG is 7 cm from its center > > Assume SWR of 5 - For a massless key this would imply 50 g of lead > (or whatever) at the measuring point, which we'll assume is 23 cm > from the key balance point. > > Inertia of hammer about its center = 10 x 13 x 13 = 1690 g cm^2 > > Inertia of wippen about its center = 18 x 7 x 7 = 882 g cm^2 > > Inertia of key lead about its center = 50 x 23 x 23 = 26450 g cm^2 > > The key doesn't look so insignificant to me. Admittedly this is a > severe example - the key itself has no distributed mass and the lead > is all concentrated out at the end. But still, if the key inertia is > insignificant then these should be quibbles. The hammer assumes high > velocity from the key input because of all the leverage. I don't see > that all the leverage is affecting the hammer inertia though. To > accelerate the hammer, a torque has to be applied to the hammer > shank. This torque is being provided by jack force at the knuckle. > This force is being reacted back through the mechanism to the > capstan. If you want more acceleration then more force has to be > applied by the capstan. The magnitude of the force is going to be > dependent on the action geometry. But changing this geometry > (changing the amount of leverage) isn't changing the inertia of the > hammer and shank, but changing the force at the capstan that's a > manifestation of its inertia. Its inertia is still small compared to > that of the key. > > Phil Ford > > -- > Phillip Ford > Piano Service and Restoration > 1777 Yosemite Ave - 130 > San Francisco, CA 94124 > _______________________________________________ > pianotech list info: https://www.moypiano.com/resources/#archives -- Richard Brekne RPT, N.P.T.F. UiB, Bergen, Norway mailto:rbrekne@broadpark.no http://home.broadpark.no/~rbrekne/ricmain.html http://www.hf.uib.no/grieg/personer/cv_RB.html
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