John Tuttle asks some questions in 130520 MMDigest for which there are
simple answers and complex answers.

Taking the questions in turn:

> 1. Does the square area of the pouch have to be bigger than the
> square area of the valve seat?

The simple answer is "yes".  The reason for this is that the pouch at
rest has to lift the weight of the valve stem plus the weight of the
vacuum force which forces the valve to shut tightly. Five inches of
water gauge is a pressure of 0.185 psi. Consider the pouch as a piston
and its lifting force is, for a one inch diameter pouch,

  Force = pi/4 x 1 x1 x 0.185 = 0.145 lb.f = 2.35 ounce force

The weight of a 'Standard' valve stem, etc., is about 6 grams or 0.2
ounce.  The valve disc diameter is about 0.67 inch.  The downward force
due to the valve disc is:

  = pi/4 x 0.67 x 0.67 x 0.185 = 0.065 lb.f  = 1.04 ounce force.

So the opening force is 2.35 ounce and the force plus mass of the valve
is 1.04 plus 0.2 ounce force; = 1.24 ounce force.

If the valve disc was the same diameter as the pouch, then the pouch
could not lift the valve.


> 2. In terms of physical size, is there a finite point at which
> a pouch and valve are so big that the pressure of the atmosphere
> is not great enough to activate the valve?

The simple answer is the atmospheric pressure has nothing to do
with the lifting of the valve.  The valve lifts because of the pressure
difference between each side of the pouch.


> 3. What is the exact ratio between the size of the bleed and the size
> of the hole in the trackerbar at which the note will fail to activate
> when the trackerbar hole is open to the atmosphere?

The simple answer is "there is no simple answer."  The tracker bar is
connected to the pouch through a long tube.  Outside the tracker bar is
atmospheric pressure.  When the tracker bar is open, air flows through
the port and the tube through the bleed to the vacuum supply.  There is
a pressure gradient along this tube, but ideally this pressure gradient
is small, so that under the pouch, the air pressure is close to
atmospheric pressure.

It is the flow of air through the bleed, which gives rise to an air
flow which increases the pressure gradient along the tube.  This
results in the air pressure under the pouch falling from atmospheric
pressure, to a pressure closer to the vacuum level above the pouch.
This reduction in pressure difference across the pouch reduces the
force development potential of the pouch. From this point of view a
small bleed is to be preferred.


> 4. What is the exact ratio between the size of the bleed and the
> size of the hole in the trackerbar at which the note will fail to
> turn 'off' as fast as it turns 'on'?

The simple answer is "there is no simple answer."  The bleed must
remove the atmospheric air under the pouch when the tracker hole is
covered again, before the valve can shut off.  For reasons of closing
speed, the bleed should be large to extract the air more quickly,
but in question 3 we showed the bleed should be small.  So the bleed
size is a compromise.  The obvious example of bleed sizes, is the
Ampico model "B" where there is a small bleed for turning the valve
on and holding it on, and a larger bleed for exhausting the pouch when
the valve turns off.


> 5. Are there formulas that a person without a degree in physics can
> understand that can be used to accurately determine things like the
> optimum size of a pouch, valve, a bleed, and striker pneumatic?  Or
> was it all done by trial-and-error?

The simple answer is that most things can be understood through quite
simple explanations but design matters involve more rigour.  Bleed
design is a compromise and is affected particularly by pouch material
selection and its leakage stability over time.  In my paper about force
development (in the MMD Archives) I consider such matters as force
development in pneumatic motors.  Such work generally comes along after
the initial experimentation has confirmed an approach, but quantifying
an engineering systems through mathematical models is invariably
necessary for product optimisation.  See

  http://www.mmdigest.com/Gallery/Tech/rumpf_1.doc 

I guess there was some guess work, but the anecdotal evidence relating
to the story of Dr. Hickman's arrival at the American Piano Company,
shows how mathematical modelling is an important part of all product
design and manufacturing.

Paul Rumpf