Strike motion ratio

[stanwood]

>Thanks to David Stanwood for reposting his cooperative work on leverage.  I
>have found it to be invaluable.

>I would like to see a reposting of his work on strike motion ratio for
others who didn't see it before.

>Tim Coates



Tim found the posting for me and here it is.  Thanks Tim:



Dear Ken,

You mention in a recent posting that the speed of the
hammer with relation to the key is faster when pre-84
parts are used as opposed to post-84 parts, and that you
associate faster repetition with the pre-84 parts.

My comment:

In speaking of hammer speed, I have seen actions were the
contrary is true. It is apparently possible to have one
action with pre-84 Steinway parts that has a slower
movement of the hammer than another action with Post-84
Steinway parts.

When this happens it is because of a difference in the key
ratios of the two actions.  Key ratio can be defined as
the ratio of the downward movement of the key to the
upward movement of the capstan.

Key ratio is a thrashworthy subject.


Allow me to thrash:

Lets sort out some of the variables here.

I refer here to the ratio of hammer movement to key
movement as the "Strike motion ratio".

The strike motion ratio results from the interaction of three
independent levers. The shank, wippen, and key, each with
there own independent lever ratio.


Shank ratio:  Strike point to hammer flange center
              ------------------------------------
              Knuckle contact to flange center


Wip Ratio:    Top of jack to wip center
              --------------------------
              Wip center to heel contact

Key Ratio:   Capstan   to   balance
             -----------------------
             Balance to front of key



If each independent lever ratio is known, the strike motion ratio
may be found by multiplying them together.
(See "The Piano Hammer" by Pfeiffer p108-p111)

To find strike motion ratio, the formula would apply:

Strike motion ratio = Shank Ratio x Wip Ratio x Key Ratio


Lets take a hypothetical example with pre-84 parts where:

Strike motion ratio = 7/1 x 3/2 x 1/2 =  5.3  (pre-84)



Take the same example and slightly change the shank ratio:

where: Shank ratio = 7/1.1  Thereby simulating a change to
Post-84 parts were the knuckle is slightly closer to the
hammer.

Now calculate the strike motion ratio:

Strike motion ratio = 7/1.1 x 3/2 x 1/2 =  4.8 (post-84)

So we see that the Post-84 parts caused a slowing of the
hammer in relation to the key.
***

In these two examples the key ratio was 1/2 or 0.50

However!  In measuring many key ratios I have found that a
ratio of 0.58 is not unusual, especially in the late
Victorian vintage Steinways..

Lets take the post-84 example and substitute the 0.57 key
ratio:

Strike motion ratio = 7/1.1 x 3/2 x .58 =  5.5 (post-84)

This is faster than our first example of pre-84 parts with
a hammer ratio of 5.4.

Lesson: Pay attention to key ratio!

Question:Do the post-84 parts with a 5.5 strike motion ratio repeat better
than the pre-84 parts with a 5.4 strike motion ratio?

Answer: This can only come from years of studying strike motion ratios and
comparing it to qualitative assesment of repetition.

I suggest that the strike weight ratio closely approximates the strike
motion ratio and herein lies an area ripe for study.


David C. Stanwood