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Hello Isaac (and everyone):
Let me give you a concise grounding in how geometry and balancing =
affects the inertial properties of an object.
As I mentioned before, moment of inertia is due to a mass rotating at a =
distance from a pivot and is proportional to this mass and to the square =
of the distance from the pivot point. Simple; right? Well as long as =
the mass has no physical size you're doing just fine. =20
Now let's talk about a metal rod spinning about one end. metal at the =
middle of the rod is at one distance from the pivot and metal at the end =
of the rod is at a larger distance, so the mass in the rod affects the =
moment of inertia more and more as we go outward from the pivot point, =
in fact it is affected as the square of the distance. If you think =
about it, it gets scary. No matter how small a piece of the rod we take =
into account, it still has some finite size and one end of the piece is =
farther from the center than the other. But we have to have some size =
(volume) or we have no mass! We would have to consider an infinite =
number of pieces that are infinitely small and add their m.o.i.'s =
together to get the total! =20
Impossible? Well, that's what calculus is for. By using integral =
calculus we can do this infinitesimal sum (that's literally what =
calculus is for) and come up with a nice, neat little formula for =
calculating the m.o.i. of our rod. It turns out that it is a simple =
little algebraic equation. Now this equation is only good for a =
cylindrical rod pivoted at its end. For other shapes and pivot points =
we would need to derive a different formula.
"Now, Gilmore, how the hell is this helping me?" Well, now you have a =
general idea of what affects an object's m.o.i. So when you go playing =
around with an object's geometry, you'll know what you're doing. Just =
remember that more mass or a wider radius both increase the m.o.i. and =
the radius is the more extreme of the effects since it is squared. If =
you are using small leads you can probably just assume that it is =
approximately a point mass and figure its addition to the overall m.o.i. =
by using m x r^2. Remember also that a mass' angular location has no =
effect on its moment of inertia...only radius. So a lead weight can be =
located anywhere on an object as long as it is the same distance from =
the pivot.
Now, about balancing. You can use a counterweight to "counter" the =
effects of gravity by creating a teeter-totter effect. But this weight =
can only increase mass and m.o.i. It just depends on what your goal is. =
If you are worried about the weight of the hammer and its effect on key =
pressure you can counterweight and partially, or completely eliminate =
the weight. But even with no weight at the key, the m.o.i. will =
determine what happens when you try to accelerate the object.
Don A. Gilmore
Mechanical Engineer
Kansas City
----- Original Message -----=20
From: Isaac sur Noos=20
To: College and University Technicians=20
Sent: Sunday, December 21, 2003 5:21 AM
Subject: RE: Touch Weight
Vince,=20
I believe that you are also changing the moment of inertia with =
changes in regulation parameters , attack angle of the keys, height of =
the centers - while it does not make sense at first.
I concur to say that the leading of the keys is not the way the action =
can be lightened, or make heavier, it is quite simple to experiment with =
leads using double sided tape and normal cylindrical leads, you can =
experiment on many kind of setups.
I believe that the action mass may match the pianists hand weight so =
to be comfortable, finding the way to express those parameters in =
numbers should certainly be useful.
Best Regards.
Isaac OLEG
Pianotech=20
=20
Isaac OLEG
accordeur - reparateur - concert 19 rue Jules =
Ferry
94400 VITRY sur SEINE =20
oleg-i@noos.fr tel:=20
fax:=20
mobile: 033 01 47 18 06 98
33 01 47 18 06 90
033 06 60 42 58 77 =20
=20
=20
=20
=20
Powered by Plaxo Want a signature like this?=20
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Add me to your address book...=20
-----Message d'origine-----
De : caut-bounces@ptg.org [mailto:caut-bounces@ptg.org]De la part de =
madelyn mrykalo
Envoy=E9 : dimanche 21 d=E9cembre 2003 03:10
=C0 : College and University Technicians
Objet : Re: Touch Weight
James Ellis <claviers@nxs.net> wrote:=20
Touch weight and inertia are NOT the same thing at all. "Tough =
weight" is
merely a measure of static force. "Inertia" is a dynamic quantity.
Neither is front weight the same thing as moment of inertia, which =
I have already said.
That's why putting more leads closer to the center of the keys
will result in less "KEY" inertia. You will have to use more lead, =
but the
"key" inertia will be a little bit less. However, the keys are NOT =
where
most of the total action inertia comes from. It comes from the =
hammer
heads out on the ends of the shanks, because that's where the =
(mass x
velocity squared) is concentrated.
All I'm saying is that moving the leads closer to the centers of =
the keys
is not going to buy you very much, because that's not where most =
of the
total action inertia is coming from in the first place.
But then that is the only place we can change the moment of =
inertia, unless we lighten the hammer.
What it will do is
weaken the keys, especially if you drill more holes, plug holes, =
etc.
That's probably not going to be a problem.
Those two things are about all it will do for you, other than just =
making
the keys heavier in the middle. So, before you haul off and re-do =
a whole
set of keys, drilling more holes, adding more leads, plugging =
holes, and
moving all the leads closer to the center, remember: It won't buy =
you very
much towarding lowering the overall action inertia, because that's =
not
where it's coming from, but it will definitely weaken the keys.
If we are going to change the front weight anyway, because we are =
also changing out hammers, the MOI might as well be dealt with then too.
Merry Christmas, Jim Ellis
_______________________________________________
caut list info: https://www.moypiano.com/resources/#archives
Vince Mrykalo
University of Utah=20
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