Inertia

[Stephen Birkett]

Welcome back...

D.Stanwood wrote:
> Inertia is a function of mass and velocity.  My system describes mass as
> strike weight and velocity as strike ratio in terms that are usable by piano
> makers and technicians.
>
For piano hammers `inertia' also means *moment* of inertia i.e. how
the mass is distributed with respect to the pivot. I know D.S. is
aware of this, but some of the others on the list may not have the
physics background to be aware of the difference. Easiest analogy is
to consider rotating a 10kg mass attached to a 1m piano wire...then
try the same with a 3m wire. The mass is the same in both cases but
the second has an increased moment of inertia...much harder to
accelerate up to speed, but also harder to stop and does more damage
if you hit something.

> Hammers have evolved to an upper limit that is very
> well defined by the weight of Steinway concert grands and which correlate
> very closely with my "full" projection zone.  Is there an argument with what
> is used on 90% or so of all performance pianos?
>
Seems that the hammer head mass has evolved empirically to match the
string mass in an optimal way, not necessarily an upper limit in the
sense of the action. My project may shed some light on this matching
of hammer and string. A heavier hammer will require more torque to
accelerate it toward the string, or the same torque will give less
velocity. The torque (force applied x distance from point of
application to the pivot axis) can be increased by moving the
point of application away from the pivot (think of why the doorhandle
is always as far as possible from the hinge side). The familiar F = ma
equation in this case is T = M x A, where T is torque, M is moment of
inertia and A is angular acceleration. So if hammer mass goes up, the
moment of inertia will also go up (unless you use shorter
shanks)...to get the same velocity at the string requires more
torque, either by increasing the force (harder action) or by moving
the point of application toward the hammerhead (more keydip).

[David: Do you have some sample data on hammer/shank masses, string
gauges, shank lengths, leverage ratios etc. that you could pass on to
me...perhaps a `heavy' and a `light' piano for comparison. Are you
aware of any variation in shank length?]


Stephen Birkett (Fortepianos)
Authentic Reproductions of 18th and 19th Century Pianos
Waterloo, Ontario, Canada
tel: 519-885-2228
fax: 519-763-4686