Paul,
On Mon, 13 Aug 2001 15:19:50
larudee wrote:
>Great response, Phil, and perhaps that really is the thinking behind it. If so,
>however, do you really think it works as intended? In the first place, the front flange
>is a sort of I beam itself, with the serif portions of the I being the plate struts on
>either side, which strengthen it. Second, the sans serif portion of the I runs parallel
>to string tension, giving it added strength and stiffness in that direction. Cast iron
>has very little tensile strength, anyway, and if it were capable of giving at all, it
>might be more likely to break.
---
Yes, the front flange does work as a beam. More on that later. Cast iron
does in fact have tensile strength. How much depends on the specific
iron that is being used. At the convention, I went to the Boesendorfer
class and they mentioned that they use 35000 PSI iron. This refers to the
tensile strength (breaking strength) of the material. While not high by
high strength steel standards it is still a respectable number, even by
metal standards. Also, the iron is capable of giving (deflecting) as every
tuner knows. One of the reasons it takes several tunings to stabilize a
piano is because the plate is deflecting under the increased load.
---
>
>Another point to consider is that only a small proportion of the string energy is going
>to reach the front flange and pin block area of the plate. If everything is working
>right, most of it will be absorbed through the bridge, and the next largest portion
>partly reflected and partly absorbed by the capo bar. Only a small remainder will get
>through to flange and pin block.
---
My thinking was that when a string is struck and vibrates then there must
be an periodic increase in tension. When a string of fixed length is
displaced then it seems to me that there must be an increase in tension.
For the fundamental, as the string swings up the tension increases, comes
back to nominal as the string comes back level, and increases again as
the string swings down. This is happening several times a second. Also,
this is happening for all of the partials, just at different frequencies. This
increase in tension must be sustained by the plate. Admittedly, the loads
in question are low and the deflections must be small. But, cast iron has
high damping (by metal standards) and the vibrations are occurring several
times per second, so even a small amount of deflection could perhaps
dissipate consequential amounts of energy. The amount of this deflection
will depend on how stiff the plate and pinblock arrangement are.
---
>
>Even if it does work as intended, we need to remember that the tuning pins are 3 or 4
>times farther above the pin block in a closed design and that string tension is
>therefore exerting that much more leverage upon them. To the extent that string energy
>might be absorbed by the pinblock/plate in an open face design, wouldn't it be at least
>as likely to be absorbed by the flex of the tuning pins in a closed design?
>
>I am to some extent playing devil's advocate here, because I'm sort of half convinced of
>your argument, but would like someone to remove my remaining doubts.
>
>Paul Larudee
---
Good point about the tuning pins. I hadn't considered that. Do you think
that the string is 3 or 4 times further from the pinblock in a closed design?
I had thought perhaps twice. Maybe .25 inch for an open face and an
additional .25 inch for the thickness of the plate in a closed face. To get
some idea of relative deflections I did a few calculations. These are based
on some assumptions about the structure of the open face design and the
structure of the closed face design so they would vary for any specific
pianos in question but hopefully are in the ballpark.
Assume:
Iron E = 18,000,000 PSI
Steel E = 29,000,000 PSI
Maple E = 1,800,000 PSI
Tuning pins are .282 inch diameter
Assume a unit load of 100,000 lbs - I know this isn't a real load, I'm just
using this for a basis of comparison and to keep my deflections from
being so small (too many zeros to the right of the decimal point).
For a tuning pin with string coming off .25 inch above pinblock, deflection of
the string in the direction of load is 0.014 inch
For a tuning pin with string coming off .50 inch above pinblock, deflection of
the string is 0.112 inch
Note that deflection of a cantilever is proportional to the third power (cube)
of the length. If string is twice as high above pinblock then deflection of
the pin at this point is 2 to the third power or 8 times as much. If the string
were 3 times as high above the block then deflection would be 3 to the third
power or 27 times as much.
Assume a plate with an unsupported span (span between plate struts) of
18 inch. Assume the total width (parallel to the string) of the plate in the
pinblock area is 8 inch. Assume the plate and pinblock act as a fixed ended
beam between the plate struts.
For the open plate pinblock:
Assume plate flange is 1 inch deep and 3 inches wide. Pinblock is 5 inches
wide and 1.5 inch deep. Deflection at center of beam for 100,000 lb load
is 0.044 inch.
For the closed plate pinblock:
Assume front and rear plate flange are 1.5 square inch in area. Assume
pinblock is 7.5 inch wide and 1.375 inch deep. Deflection at center of
beam for 100,000 lb load is 0.0048 inch.
Some things to note here:
The closed face pinblock and plate are about 9 times as stiff as the
open face pinblock and plate for the dimensions given here.
However, the tuning pin flexibility for the taller pin overshadows the
plate and pinblock deflection. So, the total string deflection for the
open face block with the less flexible pin will be less than the much
stiffer closed face block with the more flexible pin.
A couple of things I'm not sure about:
The unit load that I used was very large. Actual string load is much
smaller. Also, the deflections we're talking about here are not from
string load but from deviation from nominal string load (increase in
tension due to vibration) which are probably smaller still. Would the
tiny deflections caused by this much load be enough to cause
consequential energy dissipation? I don't know.
The closed face pinblock arrangement is much stiffer than the open
face pinblock arrangement for the dimensions used here. If the string
speaking length terminations somehow put a 'lock' on the string so that
the string is seeing the stiffness of the plate and pinblock but not the
stiffness of the tuning pin then perhaps the closed face arrangement
would be the less flexible of the two. Once again, I don't know if it
works this way.
At this point I also need more convincing to believe that the closed
face pinblock arrangement really is superior to the open face pinblock
arrangement in terms of power.
Phil
---
Phillip Ford
Piano Service & Restoration
1777 Yosemite Ave
San Francisco, CA 94124
>
>Phillip L Ford wrote:
>
>> As I see it, with a closed face pinblock, the plate in the pinblock area
>> is acting as a beam - a Z section beam if you will (like an I beam with
>> a couple of pieces of flange missing). The plate flange against which
>> the pinblock bears is one flange (or cap) of the Z and the upstanding
>> flange at the front end of the plate (along the stretcher) is the other
>> flange (or cap) of the Z with the portion of the plate over the pinblock
>> acting as the web of the Z beam. The presence of this web allows
>> the entire section to work as one beam. If this web is not there (as
>> in an open face pinblock) the two flanges work independently as separate
>> beams. The bending stiffness of these two independent beams is
>> substantially less than the bending stiffness of the entire section
>> working as one beam. In practice, on an open face pinblock, the
>> flange against which the pinblock bears will be the only flange
>> working (resisting bending) with the front flange in effect doing nothing.
>> So, there should be less deflection of the pinblock in the direction of
>> the string load with a closed face pinblock than with an open face
>> pinblock. What effect this has on the tone and on tuning stability
>> would probably depend on just how massive the pinblock and plate
>> structure of the open face pinblock in question are. I can imagine
>> it could have an affect on power, as some of the string energy
>> would be used in flexing the pinblock and plate.
>>
>> Phil
>>
>> ---
>> Phillip Ford
>> Piano Service & Restoration
>> 1777 Yosemite Ave
>> San Francisco, CA 94124
>>
>> On Mon, 13 Aug 2001 07:28:29
>> larudee wrote:
>> >List,
>> >
>> >Does anyone have any ideas about why so few manufacturers use open face pin
>> >blocks? Cost is a major factor, of course. Leo Duricic of Bechstein says that it
>> >takes a master craftsman 11 hours to fit a block in an open face plate vs. 3 for
>> >the closed face. However, precision robotic manufacturing techniques such as those
>> >used by Yamaha and others should be capable of greatly narrowing that difference.
>> >
>> >Leo also says that the closed type produces more power, which is why their concert
>> >size instruments recently switched to that design. I don't buy that. Bechstein
>> >invariably uses agraffes in the entire scale with open face blocks but is now using
>> >a capo bar with the closed blocks in their concert instruments. I think that this
>> >a more likely factor in power production. Bosendorfer, which pairs open face
>> >blocks with a capo bar, agrees.
>> >
>> >Are there any other performance or design considerations that might lead
>> >manufacturers away from open face blocks?
>> >
>> >Paul Larudee
>> >
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