Re: Force Versus Distance of a Pneumatic
By Craig Brougher, forwarded by Robbie Rhodes
|[ Begin forwarded message -- note: Craig _IS_ a subscriber to our group
From email@example.com Fri Mar 22 10:02:23 1996
Date: Fri, 22 Mar 96 18:04:57 UT
From: "Craig Brougher" <firstname.lastname@example.org>
To: "Robbie Rhodes" <email@example.com>
Subject: FW: Force VS Distance of a Pneumatic
Many years ago I too calculated something like this and as I recall, the way I did it involved the cotangent (?) of half the angle of the fold to a plane parallel to the pneumatic leaf (I think). Whatever it was, I realized it probably wasn't correct except for positional static measurements since a piano key's force is computed with IMPULSE data, not force data, but that you need this data to compute the resulting impulse. You know, the F(dt) derivations. Then I hit on a method of measuring it exactly, but never built one. I'll explain in a minute.
Having forgotten most of that stuff by now, but substituting a "feel" of experience, I have learned that the soft pedal rise should ideally be equivalent to about the second intensity in a Duo-Art. If I put both on at the same time it should even out to no change in loudness, but will be more reliable in striking the notes than zero intensity is.
The Duo-Art is a good measurement because its curve is linear with the intensity steps and the box can be set up so that the linearity is amazingly true. I have many charts of pianos over the years, and have found out that setting an expression box according to the simplistic method called for in the manual is an ideal but mostly wrong system. It is actually the place to begin, but will not be the setting you end up with, and there are many other things to diddle with as well. It's a real "contraption" and amazing that it could work reliably at all.
The purpose is to give us an understanding of what D/A considered to be an equivalent soft pedal. The joke is that when this high of a rise is achieved, the piano often would lighten its dampers to the degree that some notes will partially sustain. So then you either have to retension the damper springs or lower the hammer rail until the notes no longer ring through.
The Ampico B suggests an ideal hammer rail lift of 1" for most pianos. In the manual, pg. 29, they set the rail up to be equivalent to (the first) two intensity steps. So, looking back to pg. 20, the first two intensities on the "Normal" curve equals a vacuum change of about 1.5" H2O. When you measure through the strings to the raised hammers in an Ampico, you should measure 7/8" on average. That means, you have a 1" rise. D/A was sloppy in this regard. Very few Duo-Arts can you get to raise that much without ring-through.
If you really want to find out what the TRUE playing force of a pneumatic is at different start points in its travel, why not set up this test:
1. Mount a pneumatic with a pitman arm striker and guide on a stand.
2. Adjust a block valve to drive it such that any increase in the valve
gap does not cause an increase in the force of the pneumatic.
3. Mount a adjustment screw below the pneumatic to raise the movable leaf.
4. Operate this with about 20" of regulated vacuum.
5. Build an impulse gauge, which is basically a marble in a tube that
can rise, but can't return until you release it. Calibrate the gauge
in one of many ways, for example, you can operate the "marble" with
a teeter-totter thing on which you drop a calibrated weight from
precise heights onto the other end of your teeter-totter. The
product moment of the calibrated weight and height should be
recorded by the "marble" with a mark on the tube.
Here's the trick: We know that F=m dv/dt. Fdt=mdv. (d is an incremental or differential segment that can be integrated to see the whole pie if you want to. Otherwise, just leave it off and you get the correct equation for each special case). Since mdv=d(mv), then Fdt=d(mv). [This is analogous to the work and energy model of Fds=d(1/2m x v-squared). s is a displacement ]
Fdt is the impulse of the force in cgs--dyne.sec, or in engineering it is lb.seconds. [Momentum is gm cm/sec or slug.ft/sec. 1 slug =1 lb.sec-sq/ft. ] This is important because the impulse of the resultant force is equal to the change in momentum! We know that v=d/t, so as long as acceleration is constant (g) the resultant momentum is a direct function of distance. That makes it directly proportional to moment, as long as you are speaking of scalar measurements in line with gravitational force.
So since pianos don't play on their sides while whirling around, we'll be safe to say that our force is directly proportional to the weight of the marble times the distance it rises in the tube.
Instead of a marble, consider a little thing that looks like two heavy disks sprung together such that it jams instantly when starting down, but collapses together just enough that it can rise without much friction. And the friction it does have is compensated for when you calibrate it. Then by leaning the tube a little, it falls back down the tube. Or, think of a flat vertical board marked off for the experiment. On each side are two tracks and in the tracks ride four small rollers that jam coming down but will fly up. I'll leave it up to your own mechanical brain to devise the thing. You'll probably come up with a much better one that that.
Let me know what you decided to do. I've found that all the figgerin' to the contrary, you never know anything for sure until you actually test for it.
(Message sent Sat 23 Mar 1996, 00:28:54 GMT, from time zone GMT-0800.)