Moment of Inertia of grand action parts.

[Mark Davidson]

John Hartman wrote:

> Have you plugged in the MOIs? It looks like the shank and hammer
> contribute about 12 times or more of the total I as felt at the key. If
> the formula is right it shows how unimportant changes to the key MOI is
> in relation to overall efficiency. Also, if there is any benefit to
> pattern leading it is not to make the action feel even from note to
> note. Adding lead to the key is not the big evil commonly thought unless
> it has some effect on repetition.
>
> I think we are going to find that the biggest problem with increasing
> the mass of the action parts is the losses due to bending and compliance.

Obviously depends on your assumptions about hammer weight and SWR, but I
have come up with about 87-81% of the reflected inertia in the hammer/shank,
12-16% in the key, 1-3% in the wippen (range from bass-treble).

Pretty much the same conclusions about leading, except... there seems to be
a lot of anecdotal evidence to suggest a noticeable difference in feel
between a more-leaded action versus a wippen assisted action (with same SW,
SWRs, BW).  Haven't quite worked that out to my satisfaction.  Too many
people out there with lots of rebuilding experience saying there's a
difference. Probably has to do with how each part starts moving/flexes as
things compress at the start of the keystroke.

> I still need to complete the kinetic model of the action but I can see
> ahead to the next step. Maybe you are already there. Is there a way to
> convert the kinetic forces developed at different levels of play into
> static loads. Then we can see how these loads bend the shank and key. It
> would be great if this could lead to a formula for finding the terminal
> velocity of the hammer.

I think I see what you're asking.  The upward force at the capstan on the
wippen heel would the torque on the key (key front radius * (finger - BW -
friction) divided by the capstan radius.  This force is the input on the
wippen.  The torque on the wippen is this force * wippen heel radius.  See
where this is going?

-Mark