Virtual Ribs, A new crown support method

[Sarah Fox]

Hi Ric,

Sixty pounds?!  Whoa!  ;-)

You suggest that upwards force on the SB increases stiffness, but that's not
necessarily so.  Stiffness would be the same thing as spring constant, which
would be defined as the amount of force needed to deflect the SB by a given
amount.  So if it takes 100 N of pressure to deflect the SB by 1 mm (just
pulling numbers out of the air, without any clue as to whether they would be
close to anything "real"), we could say the SB has a stiffness of 100 N/mm.
If we make the SB twice as stiff, it would take 200N to deflect the SB by 1
mm.  Now set a 100 N weight atop the SB, and the SB will sink by 1 mm.
Apply 100 N of force from the bottom, and the original position will be
restored.  Apply 100 N of force instead to the top of the SB, and the SB
will sink another mm (all assuming ideal spring properties).  Either way,
the relative movement from 100 N of force will be the same.  Thus, the
addition of the 100 N of weight in no way affects the stiffness of the
assembly.  (Mass loading is another issue, but please ignore it for now.
I'm just talking about stiffness.)

Now let's apply 100 N of pressure to the underside of the SB with an
enormous leaf spring with a stiffness of 100 N/mm (same stiffness as the
SB).  Now, when we apply a 100 N force the SB, the deflection of the board
will be only half as much (0.5mm).  To deflect the SB 1mm, we now have to
apply 200N of force, and thus the combined stiffness is 200 N/mm.  That's
because we're deflecting both the SB and the spring, both of which require
force for deflection.

If we repeat the above experiment by simply attaching the spring to the SB
but not applying any force against the SB from the spring, we'll get the
same results -- a combined stiffness of 200 N/mm.  In other words, force
doesn't matter.

What *does* matter?  What matters is the stiffness of the "spring" that is
attached to the SB.  In other words, what matters is the amount of force
needed to change the position of the "spring" by a given amount.  In the
case of gravity, that force is zero.  (Zero?!  OK, consider two equal
weights attached to a rope, hanging over a frictionless pulley.  Now move
one of the weights up or down.  Yup, zero.) In the case of a leaf spring,
that force is greater than zero and is equal to the spring constant.  If you
want to do the equivalent of the pulley/weight demonstration, tie two
springs to a rope, and fasten the other ends of the springs to two walls,
such that the rope is under tension.  Now move the rope back and forth
(longitudinally).  It takes force, right?

This leads to the final and most important point.  If you want to add
pressure to the underside of a SB to support downbearing, but you DON'T want
to increase stiffness very much, then you need to use a support "spring"
that has a relatively low spring constant (i.e. a spring that's not too
stiff).  In other words, the force needed to compress the spring by a given
increment must be small.  You can still apply the same force.  It would
simply require greater compression of the spring to achieve that force.  But
if the force is more uniform with a given increment of deflection, then the
spring constant is lower, and the stiffness added to the SB is less.

But what about magnets?  Well, they're a bit like springs too, albeit more
nonlinear ones.  It sounds like the ones you're using are potentially adding
LOTS of stiffness to the SB assembly.  That's not necessarily bad, if part
of the objective is to add stiffness.  My only point is that your choice of
device to apply force to the bottom of the SB will determine how much
stiffness you add to the entire assembly.  You can use a weaker spring to
achieve the same force with less added stiffness, or you can use your
magnets to apply the same force with much more added stiffness.  Sometimes
added stiffness is needed.  Sometimes it is not.  If stiffness were
universally good, we'd be casting SBs out of reinforced concrete!

Having said all this, I like your magnets idea.  It achieves the application
of force while at the same time eliminating the potential for resonances.
For instance, if coil springs were used, they might "ring," unless they were
somehow damped.  Of course damping the springs would be a bit like damping
the entire soundboard.  The best application of your magnets idea may well
be with a larger number of magnets spaced at larger distances from the SB.
It is the larger distance that would yield an overall lower added stiffness,
while still supporting the downbearing with the same force.

Peace,
Sarah


----- Original Message ----- 
From: "Ric Brekne" <ricbrek@broadpark.no>
To: "pianotech" <pianotech@ptg.org>
Sent: Tuesday, April 12, 2005 2:05 PM
Subject: Virtual Ribs, A new crown support method


> Hi David
>
> Yes, the soundboard is forced up. Impair movement of the soundboard ?
> Well yes... that is in a sense what supplying stiffness does. One can do
> that in many ways.  Traditionally rib dimensions, thickness of the
> panel, proximity to soundboard termination points... and other
> mechanisms are used yes ??.
>
> But there is no real reason why you cant supply crown support and
> stiffness in other fashions. What I like about this idea is that it
> relies on a kind of virtual beam... not really connected to the
> soundboard physically.  Similiar to Dels idea with valve springs in
> concept, yet no physical contact between panel and the support system
> for the springs. Combined with ribbing either any kind of soundboard
> assembly you can get all kinds of auxiliary support.  In the case of an
> old flat panel, you can restore significantly a condition of crown which
> very closely compares to the origional I would think.  It certainly made
> a big difference in the sound on this beater.  The workable range seems
> to be between 2 and 5 mm seperation.  That ends up being quite a range
> of adjustment in terms of pounds of pressure. What a SB designer can do
> with the idea .... who knows ?
>
> I put two of these on a scale the other day... on mounted on the scale,
> the other forced against it by hand.. I could get fairly easily 60
> pounds of pressure before my hand was not stable enough to hinder
> sideslip.  Magnets have to be alligned pretty carefully when used like
> this.
>
> Cheers
> RicB
>
> Hi Ric,
>
> As I understand it...magnets opposing each other are aligned, one set in
the bridge and one set along the beams
> under the bridge.   The soundboard is forced up?   Is is possible this
would impair movement of the soundboard?
> Are you drilling a hole in the bridge and inserting one of the magnets
there?   Interesting experiment ...
>
> David Ilvedson
>
>
>
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