[pianotech] Force equivalents in different actions

[David Love]

Question for you action engineers.

Assume two actions, A. has an AR of 6.5, B has an AR of 5.5.  Strike weight
at note 40 in A is 10 grams.  

Questions:

1.  Can you convert the AR into some value for acceleration?

2.  Since F = M*A, what will the hammer weight at note #40 in B need to be
to produce an equal force to note #40 in A.

3.  Is the relationship a linear one.

The application is as follows:

Assume you convert an old action from a 6.5 AR to a new action 5.5 AR.  You
have decreased the hammer speed by 15% (1/6.5).  Does that mean that an
increase in the SW of the same amount to 11.5 grams is needed in order to
produce the same force with which the hammer strikes the string?  The
relevance is this.  A change in the AR to a higher AR with no change in SWs
will produce more force due to the increase in hammer speed.  The piano gets
louder.  If you want to change the AR to a lower AR but want the force with
which the hammer delivers energy to the string to remain the same, how much
of an increase in mass is required?  The answer I've suggested seems too
simple on the surface (of course we're assuming hammers of equal density and
not consider for the moment the increase in blow distance required for a
lower AR which will increase the force * distance part of the equation.)  

More simply put, does it makes sense that a lower AR will require a heavier
hammer to deliver an equal force and how would you equilibrate that with the
original action if that was your goal.  


David Love
www.davidlovepianos.com