Ric, The short answer is, you're right about isolated weights undergoing the same change in motion. But in the case of keyleads, we're interested in the reaction force perceived by the pianist at the front rail, when he/she applies a force hoping to causes a given acceleration of the key. So the effect of the lever arms on both the acceleration of the lead, and on the reflection of the reaction force back to the pianist's finger at the front rail, must enter into the calculation. The long answer is: Inertia is the tendency of a body to resist a change in velocity, otherwise known as acceleration. The greater the mass, or the greater the acceleration, the greater the resisting force. The governing formula, for linear motion, is F = m*a. (Force equals Mass times Acceleration) The formula we looked at earlier in this string (I=M*r^2) applies to rotating bodies. The rotational formula is T = I*alpha (Torque equals Moment of Inertia times angular acceleration). It's neat 'cause it takes the lever arm lengths into account within the values for torque, moment of inertia, and angular acceleration, but I always get bogged down in the units conversions, lb-in^2, radians/second^2, etc. etc., so where possible I try to see every problem in the linear model. Let's take the key weight example, and we'll round off the numbers to make it easier, if not necessarily correct for your specific piano: (You may find it makes more sense if you sketch this as you read through) The key measures 8" from front rail pin to balance rail pin. You want to increase the keyweight by 4 grams, and are considering putting the weight at 4" (4 grams times 8" divided by 4" = 8 grams required) or at 2" (4 grams times 8" divided by 2" = 16 grams required). Let's let A equal the acceleration of the key, at the front rail pin, for a mezzo-forte blow. The acceleration at 2" would be A times 2" divided by 8", or A/4. The force at 2" would be M * A/4, or 16*A/4, or 4*A. The acceleration at 4" would be A times 4" divided by 8", or A/2. The force at 4" would be M * A/2, or 8*A/2, or 4*A. So, in both cases, the force AT THE WEIGHT is equal to 4*A. But the force felt by the pianist, AT THE FRONT RAIL, is reduced by the leverage: For the weight at 4", the force is reduced by 4" divided by 8", so the pianist feels 2*A. For the weight at 2", the force is reduced by 2" divided by 8", so the pianist feels A. Bottom line, the closer the weight can be placed to the balance rail, the less inertial resistance the pianist will feel. Mike ----- Original Message ----- From: Richard Moody <remoody@midstatesd.net> To: <pianotech@ptg.org> Sent: Saturday, March 31, 2001 1:46 AM Subject: Re: Ideal leading pattern: > >Putting less lead further out will result in more > > inertia than more lead closer in........ > > I thought more mass meant more inertia. Perhaps I lost the meaning of > the terms. Inertia is the "force" needed to move (or change the > motion of) a body? Momentum is the force of a body in motion? > You can balance a lever (Key) with one weight near the end, or with 4 > weights near the fulcrum. Both are in balance but one with 4 times > the mass. Wouldn't the one with more mass require more force to move > it? As piano keys, both would still have the same down weight, but one > would feel harder to press. That would be the key with more mass in > it, right? ---ric? > > ----- Original Message ----- > From: Mike and Jane Spalding <mjbkspal@execpc.com> > To: <pianotech@ptg.org> > Sent: Thursday, March 29, 2001 11:47 AM > Subject: Re: Ideal leading pattern: > > > > Paul, > > > > I believe you are mistaken regarding the inertia. (As a former > machine > > design engineer who recently jumped out of the frying pan and into > piano > > tuning, I have some experience with this). It does indeed vary with > the > > placement of the lead: Putting less lead further out will result in > more > > inertia than more lead closer in. Half the weight, twice as far > out, same > > static downweight, but twice the inertia. (For those of us old > enough to > > remember phonograph records, this is why the counterweight on the > tone arm > > is very large and very close to the pivot point.) Doesn't change > your > > conclusion: all other things being equal, keep the lead near the > pivot > > point. > > > > Mike Spalding > > > > > > ----- Original Message ----- > > From: <larudee@pacbell.net> > > To: <pianotech@ptg.org> > > Sent: Thursday, March 29, 2001 10:15 AM > > Subject: Re: Ideal leading pattern: > > > > > > > David, > > > > > > As a matter of simple physics, it makes no difference whether you > put less > > lead > > > farther away from the balance rail or closer in, with one > stipulation. > > The > > > stipulation is that the key is perfectly rigid and has no > flexibility. > > > Otherwise, both the momentum and inertia will be the same either > way. > > > > > > Of course, we know that the key is not perfectly rigid, so > placement of > > more > > > lead closer in is probably preferable, all else being equal. This > reduces > > the > > > sense of inertia in the key because the part that takes the force > of > > depression > > > has less mass in it than otherwise, and applies leverage to the > part that > > has > > > the mass, closer to the balance rail, after some momentum has > already been > > > gained in the key. Along with the use of cylindrical key > bearings, I > > think this > > > design is part of what Steinway calls its accelerated action, but > I am > > prepared > > > to be corrected. > > > > > > Paul Larudee > > > > > > David Love wrote: > > > > > > > I run into this sort of situation frequently and I would like > some > > opinions. > > > > Steinway model S ca 1936. I am replacing hammers and shanks > only. I > > use > > > > Steinway hammers full taper, Abel shank 16.5 mm knuckle gives me > the > > best > > > > combination of regulation/downweight from which to work. The > strike > > weight > > > > is medium and consistent throughout. Key weight ratio is 5.0. > When I > > > > install the hammers, I will still want to take 2-5 grams off the > > downweight > > > > throughout much of the piano (though it is somewhat erratic) to > get a > > 52-48g > > > > taper. Doing so does not compromise the upweight. The present > front > > > > weight of the keys allows me to add lead without exceeding the > maximum > > > > recommended front weight (according to Stanwood charts). But... > the > > keys > > > > already have a fair amount of lead grouped mostly toward the > balance > > rail. > > > > Though the front weight is not excessive, the keys themselves > weigh a > > lot > > > > because of the amount of lead in them (e.g. C16 = 163g , C40 = > 144g, C64 > > = > > > > 133g). I have the option of adding a small lead, or removing > two or > > more > > > > large leads from near the balance rail and replacing them with > one large > > > > lead out toward the front of the key. The latter will produce a > more > > > > conventional leading pattern--and involves a lot more work. > > > > > > > > My questions are: > > > > > > > > 1. Which one will produce a better feel? > > > > 2. Will the difference be significant? > > > > 3. Do front weight parameters change with the overall length of > the > > key: > > > > i.e., is the allowable front weight greater for a model D than > for a > > model > > > > S, or there other factors. > > > > 4. What additional information will be helpful in making a > quantifiable > > > > decision? > > > > > > > > David Love > > > > > _________________________________________________________________ > > > > Get your FREE download of MSN Explorer at > http://explorer.msn.com > > > > > > > > > >
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