Hammer rake angle, etc.

[James Ellis]

Ladies and Gentlemen:

There was a recent discussion on this list regarding hammer "rake angle",
or whatever you wish to call it, that resulted in questions being asked
about why some pianos, old Steinway uprights in particular, have the hammer
flange centers so close to the strings, and the hammers bored at an angle
to make them perpendicular to the strings at contact.  There were good
reasons for doing this; there still are; and I'm afraid too many modern
makers and technicians have forgotten what they are. 

The hammer may be perfectly perpendicular to the string on contact, but
that does not mean that its crown in moving in that direction when it hits.
 The hammer does NOT move in a straight line.  It swings in an arc.  The
closer the pivot (the flange center) is to the string, the more nearly
perpendicular the motion of the hammer's crown will be to the string at
contact.

Those old guys at Steinway knew what they were doing.  Their objective in
getting the center as close to the string as possible was to make the
hammer's motion when it hit's the string as nearly perpendicular to the
string as possible.  Since it was impossible to put the center on the same
line as the string, they did the next best thing.  They put it as close as
possible, and then tilted the hammer forward on the shank to make it
perpendicular to the string when it hit.

You can illustrate this for yourselves.  Draw a circle.  Let that circle
represent the motion of the hammer crown about the center.  Now draw a
vertical line directly through the center of the circle, and let it
represent the string.  Where the lines intersect will be where the hammer
hits the string, and you can see that it will be perfectly perpendicular to
it.  Now draw another vertical line that is offset from the center, and
that will represent the situation we have in a real piano.  You can see
that the actual motion of the hammer crown when it strikes is NOT
perpendicular to the string, no matter how level the hammer is, or how
perpendicular it is to the string.  The motion of the crown in an upright
will have a downward component as well as a horizontal component because it
will be well forward of the center when it hits.  Moving the center closer
to the string reduces that downward component, and boring the hammer at an
angle brings it back to being perpendicular to the string, even though the
shank will be at an angle.

I am convinced this was the primary reason they did this.  It just makes
good sense.  A "byproduct" of this (someone already alluded to it) is that
it puts the center of gravity a little bit farther back than it would
otherwise be, and gravity assists the spring and bridle strap a little bit
more in repetition.

In a grand, the pinblock is in the way of moving the flange center any
closer to the plane of the string, and it just so happens that the shank
ends up being paralled, or nearly so, to the string when the hammer is in
contact with it.  If the shank and string are parallel to each other, and
the hammer is perpendicular to one, then it's automatically going to be
perpendicular to the other as well.  It's not that there is something high
and holy about the hammer-head being perpendicular to the shank.  It just
works out that way most of the time.  It would be nice if we could put the
hammer flange center right in the plane of the string, but we can't.  The
plate and pinblock are in the way, so we compromise and do the best we can.

There is no mystery here.  This is just plain "plane geometry".  I hope
this helps.

Sincerely, Jim Ellis