<div dir="ltr"><div>Everybody's taking a run at explaining so I want a turn, too. I want to elaborate a little on what Don said.</div><div><br></div><div>F = ma^2</div><div><br></div><div>That's </div><div><br></div>
<div>force = mass times acceleration squared</div><div><br></div><div>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. </div>
<div><br></div><div>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. </div>
<div><br></div><div><br></div><div>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. </div>
<div><br></div><div>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. </div><div><br></div><div>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. </div>
<div><br></div><div><br></div><div><br></div><div>Dean</div><div><br></div><div>Dean May cell 812.239.3359 </div><div><br></div><div>PianoRebuilders.com 812.235.5272 </div><div><br></div><div>Terre Haute IN 47802</div>
<div><br></div><div> </div><div><br></div><div><br></div><div>-----Original Message-----</div><div>From: <a href="mailto:pianotech-bounces@ptg.org">pianotech-bounces@ptg.org</a> [mailto:<a href="mailto:pianotech-bounces@ptg.org">pianotech-bounces@ptg.org</a>] On Behalf Of Don Mannino</div>
<div>Sent: Monday, September 29, 2008 8:36 PM</div><div>To: 'Pianotech List'</div><div>Subject: RE: What's all this I hear about Inertia ?</div><div><br></div><div>David,</div><div><br></div><div>Sometimes when we try to simplify things too much, we find out that we forgot some things.</div>
<div><br></div><div>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.</div><div><br>
</div><div>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.</div>
<div><br></div><div>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.</div><div><br></div><div>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.</div>
<div><br></div><div>Don Mannino</div><div><br></div><div>-----Original Message-----</div><div>From: <a href="mailto:pianotech-bounces@ptg.org">pianotech-bounces@ptg.org</a> [mailto:<a href="mailto:pianotech-bounces@ptg.org">pianotech-bounces@ptg.org</a>] On Behalf Of David B. Stang</div>
<div>Sent: Monday, September 29, 2008 11:48 AM</div><div>To: <a href="mailto:pianotech@ptg.org">pianotech@ptg.org</a></div><div>Subject: What's all this I hear about Inertia ?</div><div><br></div><div>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:</div>
<div>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.</div>
<div><br></div><div>In summary:</div><div><br></div><div>Two items of the same weight have the same inertia here on Earth. Period.</div><div><br></div><div>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.</div>
<div><br></div><div>But we all know that a key with less weight in front has more dynamic range.</div><div>The key, pardon the pun, is the rigidity.</div><div>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.</div>
<div><br></div><div>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.</div><div><br></div><div>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.</div>
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