Touch weight

[David Love]

The easiest way to use this stuff is by algebraically manipulating
Stanwood's equation of balance to isolate certain variables and then plug
in the appropriate matches from his published charts.  You can get these
charts from his website: www.stanwoodpiano.com  

For example:

The equation of balance is:

BW + FW = (KR x WW) + (R x SW)

BW = balance weight
FW = front weight
KR = key ratio
WW = wippen strike weight
SW = strike weight
R = strike weight ratio

The most useful algebraic manipulations are

R = (BW + FW - (KR x WW))/ SW

and

SW = (BW + FW - (KR x WW))/R

The procedure is to first  take sample measurements to determine what R is
for the existing action.  You will need a platform and a gram scale for
this.  

By using Stanwood's published charts of FW maximums and SW zones, you can
then input data to determine what SW curve will work best for a given
action (R) based on targeted BW and FW maximum.  You can do this for any
sample note and extrapolate the rest of the SW curve from there.  

For example.  If your action yields an R of 5.5 by sample measurement, you
can determine the maximum SW for that system from a sample note.  If we use
note 40, for example, the maximum FW (according to Stanwood charts) is 30
grams.  If your targeted balance weight is 40 grams, then simply plug in
the remaining numbers to determine what the maximum SW for note 40 can be. 
KR and WW you have from your measurements.  Lets assume that WW is 18 and
KR is .52.   It would look like this:

SW = (40 + 30 - (.52 x 18))/5.5

or

SW = 11.02

As you can see, a higher R will lower the allowable strike weight.  

That represents the maximum strike weight (without assist springs) that can
be used without exceeding the FW maximums.  That number corresponds to zone
10 (1/4 high) in Stanwood's strike weight chart.  Subtract the shank strike
weight from the strike weight (1.8 grams if a Renner shank is used) to
determine what the hammer weight should be.  So on note 40, the maximum
hammer weight that you can use without exceeding FW weight maximums for a
BW of 40 in this system is 9.2 grams.  Use the zone in the published chart
that corresponds and taper the hammers to achieve those weights.  Pretty
easy.  

Now this is for the maximum front weight.  You may not wish to have the
keys leaded to the max to keep inertia down in which case you can reduce
your FW maximum to, say 80% of the front weight max.  Many old Steinway
actions seem to come in around that number.  They also tend to have Rs that
are around 6 or higher.  As you can see, with a higher R, a lower FW max
and even a lower BW target, the maximum strike weight will be much lower. 
This is important to know if you are replacing hammers on an older
Steinway, for example, without changing other parts or modifying leverage
points.  It is also useful in determining why that newer Steinway needs so
much lead.  Usually the problem lies in the KR.  A higher key ratio
(capstan located too far back) will raise the overall ratio.  As an aside,
also keep in mind that if you are modifying the KR, it is not enough to
simply change the number to, say .50 and recalculate.  The new capstan
position will change your measured UWs and DWs and the resultant R from you
sample.   Should you decide that your overall ratio is too high (in the
case of a total action rebuild) and wish to change it, then you will have
to determine how a change in the knuckle position or capstan position will
effect R.  Once you determine that, you can use the same methodology
outlined above to determine your new hammer weights.

David Love
davidlovepianos@earthlink.net