What's all this about inertia?

[Dean May]

Everybody's taking a run at explaining so I want a turn, too. I want to
elaborate a little on what Don said.

F = ma^2

That's

force = mass times acceleration squared

David is partially correct because when the only acceleration we are talking
about is gravity and everything is static, then the force=weight=mass, i.e.,
the weight is the downward force and it is equal to the mass. But as soon as
we start accelerating the object then the force (in our case the resistance
felt by the finger) definitely is increased by an increase in the overall
mass.

The keystick is a rotating mass system, rotating around the fulcrum of the
balance rail. Assume the keystick has zero mass and we add 100g at a point
250mm behind the balance rail and 50g at a point 250mm in front of the
balance rail. The touch weight at the front (250mm from the balance rail) is
50g. When it comes to accelerating this key we must add the front and rear
weights which comes to 150g to figure our inertial force.


Compare to a second key with 1000g at the rear point and 950g at the front.
It's touch weight is also 50g. However when accelerating this key our
inertial force is calculated using 1950g. So even though its static
downweight is the same, its inertial force is more by a factor of 13. Huge
difference.

Key weights closer to the fulcrum will have lower effect on rotating
inertia, key weights further out will have a greater effect on rotating
inertia.

In the piano action inertial differences are even more pronounced with
different hammer weights because of the key ratio, i.e., the amount of
hammer travel being 5-6 times greater than the amount of key travel.



Dean

Dean May             cell 812.239.3359

PianoRebuilders.com   812.235.5272

Terre Haute IN  47802




-----Original Message-----
From: pianotech-bounces at ptg.org [mailto:pianotech-bounces at ptg.org] On Behalf
Of Don Mannino
Sent: Monday, September 29, 2008 8:36 PM
To: 'Pianotech List'
Subject: RE: What's all this I hear about Inertia ?

David,

Sometimes when we try to simplify things too much, we find out that we
forgot some things.

One problem that you did not consider, I think, is that inertia when a mass
is rotating is calculated quite differently than when that same mass is
simply set in motion in a straight line.

I like to use the playground teeter-totter as an example.  You can balance
it by placing identical amounts of mass on either end.  It doesn't matter
how much mass you put there, it will always be in balance - the downweight
(if there were no friction) would be zero.

But two masses of one kilogram would be much easier to get moving than two
masses of 100 kg. The more massive balance would be much harder to get
moving.

Also, if you move those two masses equally towards the pivot point, so that
they were very close to the pivot, then felt the resistance to movement at
the ends of the lever, you would find it much easier to move again - as if
the mass had been removed.  This illustrates that the leverage affects the
inertia, even though the mass has not changed.

Don Mannino

-----Original Message-----
From: pianotech-bounces at ptg.org [mailto:pianotech-bounces at ptg.org] On Behalf
Of David B. Stang
Sent: Monday, September 29, 2008 11:48 AM
To: pianotech at ptg.org
Subject: What's all this I hear about Inertia ?

There seems to be a lot of confusing talk in the piano tech world about "key
inertia". I was confused, too, until I went back to my physics textbook and
found:
Inertia by definition means resistance to acceleration, and (at speeds lower
than the speed of light or so) inertia and mass are identical.  And weight
is proportional to mass on the surface of a particular planet.

In summary:

Two items of the same weight have the same inertia here on Earth. Period.

If a perfectly rigid key weighed 1000 pounds overall but were balanced to
have a certain down-weight, it would behave and feel the same as any other
rigid key with the same down-weight.

But we all know that a key with less weight in front has more dynamic range.
The key, pardon the pun, is the rigidity.
When I press a key I am wasting energy for a very small amount of time when
I am overcoming the weight (i.e. inertia) in the front of the key because it
bends. There would be less wasteful bending and more dynamic range if there
were less weight in front. Correct me if I'm wrong here, but I think the
concept is as simple as that.  No need to fabricate a giant experimental
contraption and write a multi-part journal article about it.

Another aspect of this is time: the weight can change over the duration of
the key press. This is why damper regulation can be important. But, again, a
simple concept.

I think a lot of us are confused about this stuff when we don't really need
to be.  The hard part is figuring out how to engineer a key to behave at its
best.
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