Leverage, MOI, mass, distance from fulcrum for piano key mechanism

[jkess114]

TL;DR Summary

Leverage, MOI, mass, distance from fulcrum

I am trying to determine tradeoffs in how piano keys are weighted. Piano hammer weight and the behavior of the mechanical parts in a piano action yields a spread of roughly 5:1 in leverage - every gram of weight added to the hammer adds roughly five grams at the key. Piano keys (the wooden sticks they are made of) are drilled to receive the addition of lead weights to bring the force required to play a note roughly in the 45-50 gram zone.

I have assumed its better to have less mass further from the balancing point of the key stick so the force applied to the key being closer to the weight, has less theoretical chance of initiating flex in the wooden key stick. I doubt with the forces we are talking about here if a standard keystick exhibits appreciable flex, so i am left wondering if I am missing anything else here. It seems to me, less mass further from the fulcrum is essentially the same as more mass closer to the fulcrum in behavior.

Can anyone help help the long-underserved critical thinking section in my noodle?

 

[Filip Larsen]

I know nothing about piano key mechanism, but since you mentioned MOI it feels relevant to mention that adding mass further from fulcrum will result in larger MOI and I assume for a trained pianist such a key would feel heavier and probably, depending on how that mechanism work in detail, also have a longer time to return to neutral .

 

[jkess114]

Moving the mass towards the fulcrum means adding more mass to achieve the same force to move the key. Does this not balance out the increased MOI of 'less weight further from the fulcrum'?

 

[Filip Larsen]

Perhaps you have a diagram or sketch of the piano mechanism you have in mind, if those are not all standard?

 

[jkess114]

They are all standard. I do a lot of piano rebuilding and wind up re-weighting of keys. Its a pretty standard model.... weight at one end, finger presses at the other, lead weights installed somewhere between where the finger presses and the fulcrum. In the bass section this always means multiple weights, the number depending on where and how heavy the selected weights are.

I'm trying to understand any trade-off by having heavier weight closer to the mid point (pivot point), or lighter weight further away from the pivot point. Each method can achieve the same force required to press the key. I'd like to know if there is anything I am missing.

 

[jack action]

More overall mass means more friction. This may make them feel "stickier" for the pianist, thus harder to initiate motion. Or, because friction also acts as damping, less friction may make them "bouncier" since the motion is not decelerated as much, and gives greater oscillation.

I don't know if it would be noticeable, but I know musicians (which I'm not) notice a lot of small details I don't.

 

[jkess114]

Yes, friction is a very important and very fussed-over detail when regulating or rebuilding actions, and for the very reasons you state; there is indeed a sweet spot.

In this specific case, I don't think variations in weight added to the key would change friction much as the majority of the friction in the system comes from the various mechanical connections, rotational bushings, and rubbing friction happening in the parts above the keystick, and also in the fitment of the two guide pins and mortises in each key.

 

[berkeman]

More overall mass means more friction.

You beat me to it.

I'm trying to understand any trade-off by having heavier weight closer to the mid point (pivot point), or lighter weight further away from the pivot point. Each method can achieve the same force required to press the key. I'd like to know if there is anything I am missing.

The only other thing that comes to mind is the material cost of the weights that you are adding. If the lighter weight costs half as much per weight as the heavier ones, you should start with the lighter weights to save material costs. (Although the cost of the weights may be insignificant overall.)

 

[jkess114]

Thank you all for your time and energy.