Inertia, was "Grand Touch"

[ed440 at mindspring.com]

About 2 years ago this question was discussed at great inconclusive length on CAUT.

Probably the most important question was "can the pianist feel a difference?"

No one doubted that weight location could make a difference in the moment of inertia of the key. But the key is a small part of the system.  Other parts, especially the hammer head, contribute their moments of inertia as well.

The question becomes "What percentage of the total of what the pianist feels can be changed by changing the moment of inertia of the key, and what percentage is controlled by the rest of the system? Is it enough to matter?"

Take a look at Stanwood's lever drawing.

Note the 10 gram hammer at the end of the lever that is 5 times longer than the key front. What is the moment of inertia represented by that part of the system?

Now look at the frontweight, 20 grams, at the front of the "0ne unit long" key.

Change that to 40 grams at the "one half unit" location.

That makes a big difference in the moment of inertia of the front end of the system taken alone, but how much change does it make in the entire system?  Is this enough to change the performance response of the piano a perceptible amount?

Ed Sutton

-----Original Message-----
>From: Cy Shuster <cy at shusterpiano.com>
>Sent: Jul 12, 2006 8:12 PM
>To: Pianotech List <pianotech at ptg.org>
>Subject: Re: Inertia, was "Grand Touch"
>
>
>Measuring FW alone won't tell you the dynamic inertia.  50g downweight could 
>be achieved with 50g at the end of a massless key (standard physicist 
>issue), or 1000g right in front of the balance pin, but they'd sure feel 
>different to the pianist.
>
>The front side of the key has the weight between your hands and the fulcrum, 
>like a wheelbarrow.  You could put a cement block up by the wheel in the 
>barrow, and measure the downforce on the handles.  Take out the block, put a 
>much lighter weight right on the handles, the downforce is the same, but 
>moving the handles up and down a foot or so you'd feel a lot more inertia 
>than with the cement block in front (am I right on this, you physicists?).
>
>For reference, Stanwood's "See-Saw Science" (a PDF):
>http://www.stanwoodpiano.com/seesaw.pdf
>
>--Cy--
>shusterpiano.com
>
>
>
>----- Original Message ----- 
>From: "William R. Monroe" <pianotech at a440piano.net>
>To: "Pianotech List" <pianotech at ptg.org>
>Sent: Wednesday, July 12, 2006 4:41 PM
>Subject: Re: Inertia, was "Grand Touch"
>
>
>> Hi Cy,
>>
>> Haven't read Stephen's paper yet.  Will tonight, then, more questions, I'm
>> sure.  However, just my intuitive take with your example.
>>
>> Consider the other option, and how they compare.  I do not dispute that
>> installing weights at the end of the car (key) increase inertia.  I only
>> question whether inertia would be different in the case of hanging a small
>> weight at the end of the car (key) vs. installing slightly more mass near
>> the pivot point.  Since the pianist feels/activates the key somewhere near
>> the end of the stick (for arguments sake), it would seem that the FW of 
>> the
>> key would be the point at which we take a mass reading to compute inertia 
>> in
>> a played key, since some of that mass (regardless of placement) is 
>> supported
>> at the balance rail.
>>
>> Just my musings.  God I love this kind of stuff!  Awful fun to learn from
>> you all.
>>
>> William R. Monroe
>