Moment of Inertia blah blah blah

[pianolover 88]

Don't let the modified subject line give you the wrong idea.  Yes, sometimes 
a subject gets beaten to death, or in this case, "reduced to the 
rediculous". But I haven't been this entertained by the list participants in 
quite some time. I think we all need a good, long and hearty belly laugh 
every now & then; and this thread is doin' the trick! Thanks.


Terry Peterson





----Original Message Follows----
From: "Mark Davidson" <mark.davidson@mindspring.com>
Reply-To: Mark Davidson <mark.davidson@mindspring.com>,   
Pianotech<pianotech@ptg.org>
[link redacted at request of site owner - Jul 25, 2015]
<pianotech@ptg.org>
Subject: Re: Moment of Inertia of grand action parts.
Date: Sun, 28 Dec 2003 10:14:57 -0500

John Hartman wrote:

 > Have you plugged in the MOIs? It looks like the shank and hammer
 > contribute about 12 times or more of the total I as felt at the key. If
 > the formula is right it shows how unimportant changes to the key MOI is
 > in relation to overall efficiency. Also, if there is any benefit to
 > pattern leading it is not to make the action feel even from note to
 > note. Adding lead to the key is not the big evil commonly thought unless
 > it has some effect on repetition.
 >
 > I think we are going to find that the biggest problem with increasing
 > the mass of the action parts is the losses due to bending and compliance.

Obviously depends on your assumptions about hammer weight and SWR, but I
have come up with about 87-81% of the reflected inertia in the hammer/shank,
12-16% in the key, 1-3% in the wippen (range from bass-treble).

Pretty much the same conclusions about leading, except... there seems to be
a lot of anecdotal evidence to suggest a noticeable difference in feel
between a more-leaded action versus a wippen assisted action (with same SW,
SWRs, BW).  Haven't quite worked that out to my satisfaction.  Too many
people out there with lots of rebuilding experience saying there's a
difference. Probably has to do with how each part starts moving/flexes as
things compress at the start of the keystroke.

 > I still need to complete the kinetic model of the action but I can see
 > ahead to the next step. Maybe you are already there. Is there a way to
 > convert the kinetic forces developed at different levels of play into
 > static loads. Then we can see how these loads bend the shank and key. It
 > would be great if this could lead to a formula for finding the terminal
 > velocity of the hammer.

I think I see what you're asking.  The upward force at the capstan on the
wippen heel would the torque on the key (key front radius * (finger - BW -
friction) divided by the capstan radius.  This force is the input on the
wippen.  The torque on the wippen is this force * wippen heel radius.  See
where this is going?

-Mark

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