Inertia, was "Grand Touch"

[William R. Monroe]

Vladan,

I don't have my book handy, is this the formula for tangential MOI, or
linear?

I'm assuming tangential.

Also, I would question your results (in a friendly way).  I would think you
would be taking the mass reading for the formula at the front of the key, as
you would take FW.  Thus, Mass would be mass of the keystick, not mass of
the individual lead.  In this case, regardless how much mass you use (more,
near the balance hole, or less near the front), the Mass as measured at the
front of the key is going to be the same, thus, equivalent inertia at the
front of the key.

Comments?

William R. Monroe

----- Original Message ----- 
From: "V T" <pianovt at yahoo.com>

> I=m*r^2
>
> I=moment of inertia
> m=mass of the lead
> r=distance from the balance rail hole to the lead
>
> Note that the formula takes the square of "r".
>
> Now, let's look at our options for lead placement.
> Suppose that we can use a 12 gram weight placed 10 cm
> away from the balance rail hole to get the desired
> balance weight.  As an alternative, we could also use
> a 24 gram weight placed 5 cm away from the balance
> rail hole and still have the same balance weight.  Is
> there a difference between the two?
>
> Yes, there is.  Looking at the formula above, the
> inertia increases with "r" squared.  In the first
> case, the inertia will be 12*10*10=1200 gcm.  In the
> second case, the inertia will be 24*5*5=600 gcm.
> Placing the 24g weight 5cm away from the balance rail
> hole reduced the moment of inertia by 50%.  That's a
> lot.  You can minimize the inertia by placing the
> weights closer to the balance rail hole and increasing
> the amount of lead accordingly so that the balance
> weight meets the target.
>
> There is a fundamental trade-off between balance
> weight and key stick inertia.  If we add a lot of lead
> to make the balance weight low, the action will feel
> very light, but only when you move the key slowly.  If
> you try to play a loud note, all that lead will have
> to be accelerated and the key will feel heavy.
>
> If you put very little (or no) lead into the key and
> accept a high balance weight, the action will be heavy
> when you measure it with your weights, but it will
> feel light when you play fast/hard/loud.
>
> The question is: What is better?  My own preference is
> for a heavier balance weight with less inertia.
>
> Vladan