Moment of Inertia of grand action parts.

[Mark Davidson]

John Hartman wrote:

>I have ways to estimate the MOI of the wip
>and the hammer/shank as well but first I
>wanted to se if anyone else had ideas on
>how to do this.

For hammer & shank I have estimated as follows:

I think Stanwood gives 1.8g as typical SW of shank.  So for purposes of
estimating MOI you can use 2 x 1.8 as the total mass of the shank.  This
helps to correct for the fact that the shank is fatter near the center pin,
but most of the MOI is at the skinny end.  So 3.6g for mass.  Length is the
length from center pin to end of shank, not to center of hammer molding.
Then you can use m*L^2/3 for moment of inertia (stick rotating around one
end).  For hammer, use SW-1.8 grams for mass and for radius measure from
center pin to center of molding 1/2" above shank.  Treat as point mass for
estimating. Add shank and hammer MOIs to get total.

Wippen is harder.

Fortunately due to modest mass and small motion it is less significant in
the end so errors are not as important.  I have used m*L^2/3 for wippen
(same as formula for stick rotating around endpoint), taking the total mass
as m and distance from center pin to jack center as L.  Crude, but puts you
in the ballpark.

Your revised key estimate looks good.  Certainly the key inertia is no
smaller than that.

I made an attempt to relate hammer, wippen and key inertia to total
reflected inertia here:

https://www.moypiano.com/ptg/pianotech.php/2003-August/140901.html


-Mark