reducing hammer weight

[Nick Gravagne]

-----Original Message-----
From: pianotech-bounces at ptg.org [mailto:pianotech-bounces at ptg.org] On Behalf
Of William Monroe
Sent: Wednesday, September 10, 2008 9:28 PM
To: Pianotech List
Subject: Re: reducing hammer weight

Hi Nick,

...
Would you mind expanding upon your last paragraph below??

Thanks,
William R. Monroe

> Hi William,

> ...
> In addition, our statically determined weight adjustments, i.e., the usual
> downweight/upweight gram tests, is one thing; but the dynamic result of a
> hammer of either more weight or less weight flying toward the strings at
> high velocity is something else again. The dynamic inertial values are a
> function of the static, but are of significantly higher magnitude.
>
> Regards,
>
> Nick Gravagne, RPT

Hi William,

Think of the tire on your car. It must be balanced or it will wobble at high
speeds but won't be noticeable at very low speeds. This is because
rotational dynamics or dynamic inertia "feels" the spinning mass in a much
more intensified way. The guy at the tire shop finds the out-of-balance
points by use of a dynamically controlled spin-balancer and makes
corrections by clipping small weights on to the wheel. 

The usual DW and UW touchweight tests we make are static, and although
revealing much needed information they only suggest what the pianist is
likely to feel when the entire system is in operation at varying speeds.
Mass in motion, whether in a straight line or rotational (as with piano
actions), always implies inertia as a force to be reckoned with. 

Now we have no real convenient method to measure dynamic or rotational piano
action inertia, thus our simple static tests will have to do, and in fact
they do reasonably well. This is to say that a direct measurement of the
dynamics would not yield anything critical that our static tests don't
already suggest. But having said that it is interesting to realize the
generalized physics of inertia, that rotating mass is the product of the
mass times the radius (of the rotation) squared (m r^2). 

But what we are really looking for is torque (T) since it includes the
factor of acceleration (A) giving us the desired formula T = (m r^2) A. Here
we clearly see the direct relationship of acceleration to torque in that
increases to A are directly proportional to increases in T. But static tests
have no acceleration (the slow hammer rise due to 50 grams of downweight is
negligible). 

Also note that inertia is considered to be reflected back to the initial
cause or source. Inertial force is less about output and more about
feedback, which again is torque in a rotational system. In our case inertia
is reflected back to the pianist's finger and is perceived as a force
required to get things moving --- the higher the acceleration of the finger,
the higher the reflected inertial force is felt by that finger.

Graphed out on an x-y coordinate system the dynamic ratios, based on a
spread of static ratios of 4.8 to 6.2, form a segment of a classic y = x^2
parabola indicating that the ratios increase exponentially (although the
curve is not classic exponential). Simply stated, higher dynamic ratios mean
more serious inertia at harder hammer blows. And as the ratios increase the
reflected inertial force felt at the key follows suit. This is not merely an
additive process but rather a classic nonlinear function and linked process.

I am working to include actual data in my own programs, spreadsheets and
graphing programs. 

All this is to say what we already know, i.e., that in addition to
maintaining overall action ratios we must pay special attention to the
following five items:

1.	Hammer mass: The weight of the hammers, particularly the moldings (I
prefer as much felt-to-wood ratio as I can get). The usual prepping of
tailing, side tapering and (sometimes) enlarging the cove, along with
general cleaning of the felt should suffice in most cases. I am not a big
fan in heavy removal of felt in order to lighten hammer mass.
2.	Keystick ratio: is held close to 2 to 1 or better.
3.	Hammer center-to-knuckle core spread: it should work for a
particular application. 17mm is something of a safe industry standard, but
does not have to be rigidly adhered to depending on the knowledge and skill
of the practitioner (see recent PT Journal pg. 13 RE Bruce Stevens' brief
explanation of a very skillful use of the old-style S&S 15.5mm knuckle
spread). In fact, closer spreads, say 15.5 or 16 or 16.2, or 16.5mm will
yield increased hammer speed for a given dip and hammer blow.
4.    Key leads: use as few as possible to get the job done. Recall the
3-2-1-none general rule; i.e., 3 leads in the bass, yields to 2 leads in the
tenor, yields to 2 in the treble, yields to none in the high treble. But
don't get hung up as this "rule" is often violated as it cannot always work
for all action ratios and parts weights.
5.	Dip: playing with ratios is fine, but changes will impact the
required key dip necessary for aftertouch to function. In general and
theoretically, every 1/2mm increase in hammer center-to-knuckle core spread
will require an additional 0.32mm increase in key dip for aftertouch to
function. Thus a change from 15.5mm to 17 will require a dip increase of
almost 1mm. Of course, one could split the difference using less dip in
combo with a slightly reduced hammer blow. 

Action supply kits are handy tools with which to work out a recipe, to
"break the code". Once there, then "plug and play"! 

Keystick bending and overall too-soft compaction and recovery of felts,
leather and contact points are also items to consider, but that is a story
primarily about efficiency and secondarily about ratios and forces.

Ciao for now...

Nick