A deceptively simple structural modification (two span-limiting cloth
straps and some 'extra' pneumatic covering cloth) is part of the vacuum
reservoir used in the Model B Ampico reproducing mechanism.  This system
is found in pianos made after 1928-1929 until about 1941.  The Ampico B
reservoir is functionally similar in construction to others that are
made by the American Piano Company and those by other manufacturers.

As described in the text on page 24 of the 1929 Ampico B service
manual, the B reservoir is a large pneumatic (nominally 9.25" wide by
7.25" deep) fitted with two strong leaf springs which serve to keep it
'open'.  The movable board on this pneumatic is typically 5/8" thick.
The fixed board is also 5/8" thick.

Although not described (or even mentioned) in the Ampico B manual,
the nominal perpendicular distance between the middle of each taut
span-limiting strap and the adjacent central crease in the pneumatic
cloth is characteristically about 1.5".  This is an unexpectedly large
distance (by a factor of at least two) when contrasted with the
corresponding spacing of the strap(s) present on other reservoirs.

This unusual configuration (relatively short span-limiting straps)
invariably requires the use of additional (extra) pneumatic cloth to
cover the reservoir assembly.  Unless there is some other reason for
this configuration, one would not expect the American Piano Company to
'waste' cloth unnecessarily.  From the evidence gathered so far, it may
be that all original Ampico B installations utilized this 'additional'
cloth for the reservoir pneumatic, but why?

The Ampico B reservoir depicted in Figure 12, Reservoir and Action
Cut-out, page 24 of the Service Manual, is shown in an upside-down view
relative to its usual orientation in the piano.  A few B installations
mount the reservoir sideways or at another angle to the vertical.  But
two items are notably absent from the otherwise carefully drawn sketch:
they are the 1.75"-wide cloth straps that limit the maximum opening of
the pneumatic.

It is curious that while those straps are not shown in Figure 12 on
page 24, they _are_ shown on page 4 of the 1929 Service Manual in
Figure 1, Ampico Grand Installation.  The upside-down view in Figure 12
clearly could have accommodated the straightforward display of the two
cloth straps.  Perhaps the illustrator forgot to incorporate them in
the sketch or he thought they were not sufficiently important to
include.  It is also possible that the absence of the straps in the
displayed sketch was intentional.

Nevertheless, it seems natural to consider the fundamental purpose(s)
of the two cloth straps on the Ampico B reservoir.  The 1.75" width of
the straps is quite consistent from one Ampico B reservoir to the next.
But the overall end-to-end length of the straps varies (over a range
from about 4.5" to 5.0") among different Ampico B piano installations.

In his monograph, The Model B Ampico Reproducing Piano: An Illustrated
Rebuilding Guide, Dave Saul cites 4 to 4.5 inches (page 97) for the
span-limited dimension (between inner edges) of the open-end of the
pneumatic.  The maximum span dimension (i.e., without the span-limiting
straps) of the cloth on the pneumatic (between the 9.25"-long inner
edges of the B reservoir) is typically about 5.0 inches.  Taking into
account the 5/8" thickness of the two pneumatic boards, this means that
the total breadth of the pneumatic cloth is about 6.25" when the
pneumatic is maximally open (when the straps are absent).

One explanation for the presence of these span-limiting straps is
to relieve the stress that would otherwise be fully imposed on the
pneumatic cloth (that covers the reservoir pneumatic) by the tension
from the two strong leaf springs.  Such mechanical stress applied
long-term could distort the structure of the reservoir and/or cause
some of the pneumatic cloth glue joints to release their grip.

Another possible explanation is that the span of the pneumatic could
be 'adjusted' somewhat (during installation of the mechanism) to allow
the reservoir assembly to more easily be positioned under the piano
soundboard.  This is useful because many piano manufacturers configure
their mechanical support beams differently.

A third explanation is that the relatively short span-limiting straps
are deliberately incorporated to realize a vacuum regulator (the
reservoir assembly) whose pressure-regulating characteristics are
superior to those that have longer cloth straps or those that do not
include any span-limiting straps.  Let us examine in more detail this
third explanation.

A properly sealed, spring-equipped, bellows-type pneumatic closes
when air is exhausted from its interior.  The motion of the movable
board of the pneumatic is governed by the forces acting on it.  As air
is withdrawn from the sealed pneumatic enclosure, three significant
forces act on the movable board.

The first force is caused by the difference in air pressure on one side
of the movable board relative to the other.  For discussion purposes,
it is roughly constant for a given pressure difference, independent of
the position of the movable board.  The force is given by the product
of the pressure difference and the effective area of the movable board.

The second force is imposed on the movable board by the inward folding
of the pneumatic cloth that covers the bellows assembly.  This force
depends strongly on the position of the movable board during the
closure of the pneumatic assembly.  When the bellows is fully open,
the force is large; as the bellows closes, the force decreases rapidly,
roughly following a hyperbolic curve.  As the bellows closes further,
the effect of the second force becomes small relative to the first
force.

The third force acts in a direction opposite to the first two forces.
It is produced by the spring(s) whose purpose is to keep the pneumatic
open.  The design and fabrication of these springs is a separate
technical issue and not discussed in detail here.

When the pneumatic is fully open, the second force is typically larger
than the first force.  This means that the opposing-force leaf spring
will deflect more than it would if the second force were not present.
Generally, the usual leaf springs used in the reservoir assembly are
linear, i.e., the deflection is directly proportional to the applied
force.

The presence of the (variable-strength) second vacuum-induced force
from the pneumatic assembly has the effect of making the leaf spring
behave as if it were weaker, i.e., less stiff, but only during a
portion of the hinged travel of the movable board.  That portion of
travel occurs when the movable board of the pneumatic is at or 'near'
the fully open position.

It is an engineering objective that the force-opposing spring behave
in a linear manner throughout the entire range of motion of the movable
board.  To illustrate, one can design the vacuum regulator more easily
with a linear spring than one which is nonlinear.  In addition, with
a linear spring the performance of the regulator can be predicted in
advance.  This avoids a time-consuming trial-and-error experimental
implementation process.

There is a way to prevent the geometrically-induced (which is
vacuum induced) spring nonlinearity (when the spring behaves more
weakly) described above from occurring.  It is to configure the vacuum
regulating pneumatic so that it cannot operate 'too close' to the fully
open condition of the reservoir.  This circumstance can be realized by
incorporating 'sufficiently short' span-limiting straps at the open end
of the pneumatic assembly, which, in turn, requires some 'extra'
pneumatic covering cloth.

Fabricating the pneumatic reservoir in this manner assures that the
force-opposing leaf spring behaves in a more nearly linear fashion.
That is, the spring will not suffer the apparent effect of behaving
more weakly (less strong) during the initial portion (say about 1/4 of
the unconstrained pneumatic span) of the closure of the movable board.

In principle, one could introduce a specially-designed, 'counteracting
effect', nonlinear leaf spring that compensates directly for the
apparent geometrically-induced nonlinearity of the spring.  An advantage
of this approach is that span-limiting straps would not be needed and
that it would not be necessary to incur the expense of the 'extra'
pneumatic covering cloth required for the span-limiting configuration.
This is probably not a cost-effective way to address the problem, but
it could work.  The simpler the solution, the better.

You may ask what could happen if the span-limiting Ampico B reservoir
design were not utilized.  Then, the leaf springs would behave as if
they were nonlinear (in this case, weaker) over a portion of their
operational range.  Nonlinearity in dynamic systems can give rise to
many undesirable effects, one of which is the potential introduction
of unintended oscillations.  (Some other effects are jump resonance,
frequency islands, limit cycles, and unpredictable chaotic behavior.)

In terms of Ampico performance, the absence of span-limiting reservoir
straps can manifest as unwanted audible pneumatic oscillations.  This
annoying symptom has been observed in original and rebuilt Ampico A
installations, where the pump reservoir usually does not employ the
span-limiting pneumatic design.  The immediate cause is sometimes
traced to problems with the main vacuum pump, the vacuum regulation
assembly (reservoir), air leaks from the pump distributor block, or
stack pressure regulation devices.

The Ampico B reservoir design does require the addition of two small
span-limiting cloth straps and some extra pneumatic covering material
for the regulator pneumatic.  This is a small price to pay for assuring
oscillation-free function and possibly improved vacuum regulation for
the Ampico B reproducing piano.

In hindsight, it is not surprising that various aspects of the entire
Ampico B mechanism revolve around the benefits of linear system design
and implementation.  Clarence N. Hickman, the designer of the Ampico B,
clearly understood that one should build with functional pneumatic
elements whose individual behaviors were as linear as possible over
a broad dynamic range.

This same Hickman 'attention to detail' characteristic is also seen
in the late (1928-1929) Ampico A pump where a purely linear-operation
sleeve pneumatic is used.  Such late-A Ampico pumps were commonly
installed in the Symphonique grand piano in the time frame 1928-1929.
In that late-A pump, a long-throw (1-5/8") sleeve pneumatic replaced
the pre-1928 Ampico A design which incorporated a conventional
hinge-pneumatic amplifier (decidedly nonlinear over about one quarter
of its dynamic range).

The experienced Ampico rebuilder will know that span-limiting straps
were previously incorporated on vacuum reservoirs used in some early
Ampico A and Stoddard Ampico installations.  But those straps did not
constrain the open-end span of the corresponding reservoir pneumatic
to the extent observed in typical Ampico B configurations.  On those
installations, the shortest middle-of-the-strap to pneumatic-cloth-crease
distance was about 1/2" to 3/4".

This comparative observation suggests that the earlier Ampico A straps
were incorporated for another reason, e.g., to relieve stress on the
reservoir's pneumatic cloth covering when the piano was not operating.
At the time (before 1926 or so), it was probably not clear to anyone
that further limiting of the open-end span (with shorter constraining
straps) could improve the dynamic characteristics of the reservoir
itself.

Clarence Hickman likely predicted or discovered that seemingly esoteric,
but important bit of pneumatic information.  His design for the Ampico
B striker pneumatics and their open-end span-adjustment capability
shows that he was aware of the significant initial nonlinear force
associated with the vacuum-activated closure of a hinged pneumatic.
He may have employed that knowledge in the design and fabrication of
the Ampico B reservoir by utilizing the span-limiting cloth straps
(and extra pneumatic cloth) to effectively suppress the vacuum-induced
weakening of the reservoir's leaf springs.

Based on the Ampico B reservoir discussion above, one might conjecture
that there should be an analogous pneumatically-induced effect in the
functioning of the Duo-Art expression box that is central to the
reproducing piano system made by the Aeolian Corporation.  After all,
it is known that at reduced vacuum levels (when Theme and Accompaniment
regulators are almost fully open), it is often difficult to adjust the
expression box to minimize the occurrence of dropped-out softly-played
notes without having other notes play too loudly.

One has to wonder if Aeolian's introduction of their fan-accordion
reproducing system in 1928 was motivated in part by soft-note playing
problems.  Such difficulties could be associated with the 'spring
nonlinearity' in the vacuum regulation characteristics of the
'conventional' Duo-Art expression box.

It appears that Aeolian did address this problem earlier with a
different approach, i.e., by enhancing the intensity of (boosting the
vacuum level) softly played notes under certain operational conditions.
But that is a totally different story.

Bill Koenigsberg
Concord, Massachusetts