I have been asked by Robbie Rhodes to expand upon the subject of flapper type tracker adjusters, that was briefly touched upon in an earlier submission about the Æolian Themodist piano. Several variations of this method of paper tracking adjustment is commonly found in many (but by no means all) player pianos, including most Æolian products, earlier Ampicos, as well as later Æolian 116-note organs.
These are most easily understood by examining the single ear system used in very early Æolian pianos. This consists of a single 5/32" elbow with a reduced sized end facing the left edge of the roll. A small orifice is drilled in the plugged outer end of the elbow. A light flapper, or "ear" is arranged to rotate, such that when the edge of the paper pushes it outwards, its other end moves to uncover the hole in the elbow. A very light spring normally keeps this in the closed position. Often the whole assembly is located behind the tracker bar, with only the "paper detecting" end protruding through a hole in the bar.
The assembly is tubed to a pneumatic which, when under vacuum, tends to move the paper away from the finger. Linkage is included which usually causes the entire right roll chuck shaft to shift to the left when the pneumatic collapses, against the force of the left roll chuck spring. Other arrangements, such as moving both the take-up spool and the roll, or moving the tracker bar (along with the detector assembly) to the right and leaving the paper alone, are also known.
The pneumatic is also tubed to a constant supply of vacuum; often the
main reservoir manifold. A medium sized bleed is in this path. On my 1912
Themodist, this bleed is accessible by pulling off the supply elbow, and
measures 0.029" diameter., using the "buttered sewing needle and micrometer"
method. But its absolute size is not important, but rather its relationship
to the elbow orifice size, as I explain below.
Figure 1 shows this arrangement in a highly schematic manner, with the size of the flapper valve detector assembly greatly enlarged.
The basic operating principle of this design is the concept of "two orifices in series", so elegantly exploited later by Hickman in the Ampico B. When any fluid flows from a high-pressure regime (atmosphere in this case), to a lower pressure regime (the pump, here) through two restrictions in series, both restrictions create their own pressure drop in the fluid. The sum of these two pressure drops, neglecting the insignificant loss in the lines, must necessarily equal the total pressure difference between the source and the discharge of the system. The space between the restrictions assumes an intermediate pressure somewhere between the high and low ends. Both restrictions have the same flow through them at any moment, but the amount of pressure drop that each one imposes on that flow need not be the same, but is rather dependent on each individual restrictions own "capacity". That capacity is highly dependent on the size of the hole.
In one case, where the flapper nozzle is fully open, and the hole in the nozzle is a larger than the bleed, the flow to the supply is comparatively large. But there is little pressure loss at the nozzle compared to the loss across the smaller supply bleed. The pressure inside the pneumatic is therefore close to atmospheric, and the pneumatic can not exert enough force to move the roll.
In another case, where the flapper is close to the nozzle opening, the capacity at that point is greatly reduced, and the total flow through both orifices is likewise reduced. The capacity of the supply bleed remains the same as before, but with the flow through it reduced, it imposes far less pressure loss on the stream. Most of the total pressure loss now occurs at the comparatively small nozzle opening. Thus the pressure in the pneumatic is now low, close to the pump vacuum, and can move the roll easily.
The extreme case is where the flapper closes the nozzle completely. Now there is now no flow at all, and therefore no pressure loss at the bleed. The maximum pump vacuum is "trapped" in the pneumatic, and it can exert its maximum possible force.
Now to put some numbers to the matter. The general formula for flow through any restriction is:
PRESSURE LOSS = K * C * FLOW2,
where K is a whole bunch of constants, and C is a measure of the restrictions capacity. For a round hole, C is approximately (11 * d2) where d is the hole diameter in inches. Since for two restrictions in series, both flows are equal (it doesn't matter what these flows actually are), all the constants and the flow drop out, the analysis reduces to:
PRESSURE LOSS1 = PRESSURE LOSS2
or PRESSURE LOSS1 = d22
d22 d12 PRESSURE LOSS2 d12
Or to put it another way, for two orifices in series, the ratio of pressure losses between them is inversely proportional to the ration of their diameters squared. This analysis makes some simplifying assumptions, first that the components of K are equal for both holes. This is not absolutely true, but most of the differences are second-order effects due to their different absolute pressures. In most player and organ work where the usual pressure ranges are 10 to 40 in. WC out of over 400 in. WC of absolute pressure, such errors can safely be ignored. Also C is somewhat dependent on the detailed shape and form of both the orifice and the channel in which it is located. But where the hole is small compared with its surroundings, the relationship between hole area and capacity holds up well enough for this illustration.
Numerous observations in industry, and published valve capacity tables confirm this old rule of thumb. For a "valve" consisting of a round hole covered by a flat plate; the capacity varies fairly linearly, from zero when the hole is tightly covered, to about 85% - 90% of the open hole capacity, when the distance from the flapper to the face of the nozzle is ¼ of the nozzles diameter. Further opening of the flapper causes the capacity to go to 100% in an irregular way.
For the following examples, I have assumed the bleed diameter to be 0.029", and the nozzle diameter to twice as big; 0.058", and the pump pressure to be 20 in. WC.
Example 1: The nozzle is fully open; the pressure drop ratio, bleed-to-nozzle is 0.000841/0.003364. Ratioing the bleed loss vs. the total drop available, there is only about 4 in. WC vacuum in the pneumatic.
Example 2: The flapper is 0.001" from the nozzle, reducing its capacity to 6.9% of its open value. The pressure ratio is now 0.000841/0.000232. Now there is about 15.6 in. WC vacuum in the pneumatic.
Although this apparatus may appear to work as an on-off switch, either moving the roll to the left, or allowing it to float back to the right, it is in fact a true analog positioner, able to come into equilibrium between the vacuum force in the pneumatic, and the opposing idler shaft spring force, anywhere within its very narrow span (1/4 the diameter of the nozzle). One would suppose a system with such a high gain would tend to be unstable. What apparently saves the system from hunting or breaking into oscillation, is the friction inherent in the roll shifting mechanism, which adds damping, as well as the relatively large capacity of the actuating pneumatic, which introduces a "time constant" due to the time it takes to fill or empty.
Very similar systems are used in industrial pneumatic or hydraulic control, to accurately position something large or heavy like a valve shaft, in reference to a weak control signal. Also, the highly repeatable relationship between the nozzle gap and the measured intermediate pressure, was once used a lot in for high-accuracy automatic machine part gauging. "Flapper-Nozzle Control" is a term that is unusual in the MM field, but it is the standard term used industrially, so I take the liberty to introduce it here for such analog devices. This is done to make the distinction between flapper-nozzle control, and "Pallet Control". In pallet control, some mechanical device in a player piano lifts a pallet covering a tube leading to a valve, thereby triggering some specifically on-off mechanism.
NOTES ABOUT THE ONE-FINGER DESIGN
The one-finger design works well enough, but it accurately locates only the left edge of the paper. If the roll is trimmed a little bit narrow or wide, or has gotten wider due to high humidity, the right edge may be far enough out of alignment to cause mistracking at the treble end. On later Æolian 116-note organs with automatic tracking, and many 176-note organs as well, where the closely spaced (1/12") perforations demanded precise roll centering, a knob was fitted that enabled the operator to adjust the lateral position of the detector assembly. The rolls had a printed or punched center line, which could be aligned with the centering arrow in the spool box, or with lines scribed on the tracker bar.
THE TWO-FINGER DESIGN
Most player makers, including Æolian, abandoned the one finger system early on, and replaced it with a system consisting of two opposing detector assemblies, one for each edge of the roll. These were connected to two opposed actuating pneumatics, whose movable boards were linked together to move as one. Figure 3 shows this arrangement schematically.
In this system, the two pneumatics work exactly the same way as in the one-finger. However, the force exerted by the linked pneumatics is difference between the forces generated in each pneumatic. Since this "sum" is likely to be less than the absolute force generated in a single-ear system, these pneumatics were made about 1-1/2 times larger than the ones used for the one-ear system, to allow for this.
The system assumes an equilibrium where the paper is approximately midway between the two detector assemblies, with each ear orifice open just enough to allow its pneumatics force to balance the force generated in the opposite side, with enough left over on the side which will push the paper in the correct direction. Of course, if the paper is far enough out-of-whack to the right, for example, to require a large leftward push to correct, the two flapper gaps will not be equal. The left flapper will have to be more fully closed to create a larger force in the right pneumatic. However, since the effective measuring range of each ear assembly is only ¼ of the nozzle diameter (0.0145" in my example), this error is not enough to cause mistracking even at its maximum magnitude.
Ideally, the detector assemblies ought to be placed far enough apart so that one flapper is closed, and the other is 0.0145" open, with a standard music roll at average relative humidity, 11.25" wide, is in place. In practice, they are usually set about ¼ of a track width (0.03") farther apart. That way, rolls of normal width, or a little narrower, may wander slightly with both nozzles nearly closed, but not enough to cause mistracking. Rolls that are a little wide (a much more usual situation, due to humidity) will then fully engage the centering mechanism, and will still track
Realistically, one can not measure or set these ideal dimensions. One just sets the position of the detector assemblies by trial and error, using several average rolls as a guide, until an adjustment which works with most of the them is found.
NOTES ABOUT THE TWO-FINGER DESIGN
The two-ear system works amazingly well, considering its rather narrow theoretical measuring range. However, rolls that are much too wide or too narrow, will cause both flappers to be either fully closed or fully open. In this case, the system has no information on which to guide its corrective action. Then the roll has to wander much further before any difference in flapper position registers, and the resultant action may not be enough to make the correction. Several other methods of tracker adjustment were developed to correct this problem, which I will touch upon only briefly.
Perhaps the most elegant method was to connect the ears together with a pantographic (scissors) link. The resultant of this linkage measures only the center position of the paper regardless of its width. This measurement, rather than the position of the ears themselves, was used to trigger the corrective action. Both the Simplex mechanical (fish pole) tracker and the Ampico B used this approach.
The Standard system used the relative uncovering of a pair of holes in the tracker bar, rather than flapper nozzles, to create the balance of pneumatic force to adjust the roll position. This system too, has a narrow range, but Standard cleverly allowed for this. Two pairs of detector holes were provided in the tracker bar. One pair took care of narrow-to-normal width rolls. A second pair, spaced slightly farther apart, handled wider rolls. When both of the normally spaced holes were fully covered by a wide roll, the action was logically switched to the wider pair.
Ampico made its rolls with unusually wide perforations. They can tolerate a little more mistracking, and the detector assemblies on an Ampico A can be set slightly farther apart than usual.
Æolian apparently recognized the problem as well. On most Æolian and Duo-Art pianos with double flapper-nozzle tracking, the detector assemblies are wholly exposed, in front of the tracker bar, instead of being behind the bar with only the ears protruding. The assemblies are arranged so they can swivel around the point where they are connected to the tracker bar, using a shoulder-screw and spring washer. Although firmly held in place, they can be moved by hand. The user, confronted with a stubborn or miss-trimmed roll, or an unusually humid day, can reposition the ears to correct the situation.
CENTERING THE ROLL DURING REROLL
Æolian added a further refinement, which is seen in most middle-period instruments. Another potential defect of both the one and two-ear systems is that they are powered from the pump, and therefore are active at all times, during play and reroll. If everything is working right, and the axes of the tracker bar and both spools are perfectly parallel, the paper should end up as a neatly aligned roll on the takeup spool. Then it shouldn't matter if the tracker is still active during reroll. But nothing happens perfectly every time. So it was thought desirable to deactivate the tracker adjuster, and firmly fix the roll at the center of its range of motion during reroll. Figure 4 shows the simple arrangement that fulfills both of these objectives.
A pouch cutout block is placed in each of the sensing lines. During play, they are sucked open, allowing the measured signal to act as described above. During reroll, the cutouts are vented, closing the sensing lines and deactivating the tracking mechanism. With no flow through the orifices, both pneumatics now are under full vacuum.
The force produced by a pneumatic is not simply a function of its board area and vacuum. The tension on the cloth due to the external pressure produces an additional force tending to pull the pneumatic closed. This force can be considerable, and is greater, the farther the pneumatic is open. The force of a pneumatic is a function of both the vacuum inside, and the amount that it is open.
The only way that two opposed pneumatics can generate equal, balancing forces with the same vacuum level, is if both are open the same amount. Thus during reroll both pneumatics try to close to the same gap, and the shifting mechanism goes to almost exactly half-way over; only off dead-center by the amount needed to produce the small net force to the left to hold the spool in the center.
6 Oct. 1999 06:14:03 -0400