Instructions for recovering the two distinct, same size,
pneumatic sleeve assemblies in an Ampico B reproducing piano are
well documented in Dave Saul's monograph, The Model B Ampico
Reproducing Piano: An Illustrated Rebuilding Guide.  One leather
sleeve is part of the pedal regulator and is directly exposed to
the atmosphere around that device.  The second sleeve is indirectly
exposed to the atmosphere.  It is better protected from the ambient
air because it is housed within the felt-lined wooden enclosure of
the 'distributor block compartment' mounted on the Ampico B pump.

Fortunately, the Ampico B rebuilding instructions include a handy
one-to-one design template for the specialized geometric shape of
the flat surface pattern from which the sleeve can be made.  This
allows the rebuilder to fabricate just the right shape and size of
the sleeve from pouch leather (used originally by the American Piano
Company), which is still the preferred material.

One could determine the shape and size for the sleeve template cited
above by one of three methods, two of which exhibit inherent practical
difficulties.  The first method consists of 'unwrapping' an original
intact (presumably operational) sleeve without damaging any significant
portion of it and laying it out on a convenient flat surface for
trace-and-copy purposes.  In principle, this requires the disbonding
of leather from the central cylindrically-shaped Bakelite slug, the
wood of the regulator body, and the leather itself (the end-to-end
overlap area).

In practice, the near ninety-year-old leather is fragile (because
of long-term atmospheric exposure) and prone to inadvertent tears,
even with gentle handling.  Furthermore, it is disheartening to
destructively disassemble an operational sleeve assembly.  Despite
the practical and conservational difficulties, the unwrapping can be
accomplished, but it is not a recommended procedure.

The second method is an iterative trial-and-error technique where one
makes a guess for the needed shape and size of the leather piece by
'eyeballing' an original sleeve.  Then, one can install the new leather
piece on a bare regulator assembly to see if it works.  Unless one is
very lucky, the first trial solution is typically unsatisfactory.

Guided by the results from the first experiment, a second trial is
implemented.  One continues this procedure until a useful result is
obtained.  With experience, this approach can be effective, but it is
by nature time- consuming and also a source of unwanted frustration.
However, there is a third approach, which is conveniently
straightforward; it is discussed below in some detail.

The motivation for finding another approach was provided by the
observation that the so-called late-A Ampico pump (circa 1927-1929)
incorporated two different-size sleeve pneumatics within its
'distributor block compartment'.  The late-A pump was installed in
several different brands of Ampico pianos, both upright and grand
(notably the Symphonique).  This production variation may have
reflected a need to 'field test' the then-new pump which, in hindsight,
was a precursor to Ampico B technology.

Each of the sleeves in the late-A pump is dimensionally different and
also not the same size as the one encountered in the Ampico B system
(pedal regulator and pump).  Consequently, two new and distinct design
templates are required to fabricate the pouch leather patterns for the
two sleeve pneumatics in the late-A Ampico pump.  No published source
for these specialized contours was readily available.  Could there be
a general way to determine the appropriate contours?  Thankfully, the
answer was yes.

As mentioned by Dave Saul in his rebuilding guide (p. 69), the
wrap-around sleeve before installation in the pedal regulator has
'an appearance something like a cone with its pointed end cut off'.
The resulting 3-dimensional shape is known as a conical frustum.
The exterior curved surface of a conical frustum can always be formed
from a flat piece of flexible material whose planar contour can be
mathematically calculated and drawn in advance.  All that is required
is three readily measured dimensions from an original undisturbed
in-situ sleeve pneumatic.

To accommodate those readers whose ability to visualize a conical
frustum might be limited, consider the ubiquitous lampshade, so
often seen in the form of a tapered light-attenuating decoration,
characteristic of some floor and table lamps.  When there is no
tapering to the geometry of the lamp shade, the shape is a
concentrically hollow cylinder with a thin light-attenuating curved
wall made of paper, linen, plastic, etc.

Two of the three dimensions needed from an original sleeve pneumatic
are: 1) the diameter (d1) of the circle formed by the peripheral edge
of the inward-facing, folded-over, glued-down leather on the outer
surface of the cylindrically shaped moving slug (of Bakelite or wood),
and 2) the diameter (d2) of the circle formed by the peripheral edge of
the folded-over, outward-facing, glued-down leather on the outer planar
surface surrounding the circular hole drilled into the stationary
wooden block.

The third measurement is the longitudinal [in the direction of axial
motion] length (L) of the leather sleeve when the cylindrical movable
slug (Bakelite or wood) is fully extended.  This length measurement
must include the spans of the two folded-over portions (about 1/16"
for d1 and 1/8" for d2) and some extra length (about 1/16") for the
retaining groove in which a thin string is tied.

From these three measurements, determine the product of d1 and L and
then divide the result by the difference between d2 and d1, i.e.,
(d2 - d1).  This number, denoted by R, may be treated as the radius
of a circle to be drawn on a piece of paper.  Then, determine the sum
of R and L, and let that number be the radius of another circle to be
drawn concentric with the first circle on the same sheet of paper.
The plane space between the two concentric circles is called an annulus
or annular ring.

This annular pattern can be traced and then transferred to a sheet
of pouch leather.  After cutting the annular pattern along any single
radius used to form the annulus, an annular band is created.  This
is the correct shape and size of the material from which a portion can
be cut to make the sleeve pneumatic for the dimensions, d1, d2, and L,
previously measured.  The angular portion to be cut out can be
estimated by eye or determined mathematically (see below).

The mathematical determination of the appropriate angular portion of
the annular band to use for the pneumatic sleeve is described here.
Divide the term (d2 - d1), which was calculated earlier, by twice the
value of L, the 'extended length' of the leather sleeve.  The resulting
value is a fractional portion of a full circle, which is 360 degrees or
6.283 radians.

To illustrate by example, if the (d2 - d1)/ 2L calculation is 0.2, then
the corresponding annular band should subtend an angle of 72 degrees.
This angle can be marked on the full-circle annular band with the aid
of a protractor or other angle-measuring device.

This mathematically exact angular determination reflects the ideal
situation where one end of the annular band wraps around, meets, and
merges with the other end precisely, in an edge-to-edge manner.  In
practice, the angle needs to be larger than the predicted value to
provide room for some overlap of the leather ends.  In this way, the
ends of the annular band can be glued together (contact cement or
similar), one end over the other.  Typically, this requires about
1/4" of extra leather.

It is most satisfying that when the above procedure is exercised for
the Ampico B sleeve pneumatic, the resulting pattern is very nearly the
same as the one displayed on page 68 of Dave Saul's Ampico B rebuilding
guide.

Bill Koenigsberg
Concord, Massachusetts