Bridge pin angles

[Phillip Ford]

>Phil,
>
>So.. you are taking the position that upward pressure by the bridge 
>surface simply increases sidebearing and there by more friction, and 
>that the increased upward pressure by the bridge on the string is 
>more then countered by that increased friction ?

As the bridge pushes the string further up the pin then the 
sidebearing angle increases and static friction should increase 
accordingly.  It's probably not significant.  Ron mentioned an .011 
inch rise of bridge relative to pin.  I haven't run any numbers to 
indicate what the increase in sidebearing would be for that amount of 
rise, and I probably won't, since you don't seem to like numbers.

My 'position' is that when the string is sitting on the bridge cap, 
with what I take to be more or less standard sidebearing and bridge 
pin angles, and with a coefficient of friction based on what I take 
to be standard materials for bridge pins and strings, and with 
assumed surface finishes based on my own observation, and assuming a 
standard downbearing angle, and assuming what I thought was a 
reasonable bearing area, that for the string to move up as the bridge 
cap moves up due to humidity, the stress on that bearing area would 
exceed the capability of hard maple and would crush.  I ran this 
number because we have all observed that bridge caps crush (I think 
there's no disagreement on that at least) and Ron N was offering the 
explanation that the bridge cap moves up relative to the pin from 
humidity change and the string wasn't able to move up with it, 
resulting in crushing of the cap.  I decided to run a number to see 
if this explanation seemed plausible.  If the result of that calc had 
been that bearing stress was 100 PSI, then I would have said, hey 
Ron, I hate to tell you this, but ...  What I found was that, for the 
assumptions that I made, the indication was that the cap would easily 
crush.  This didn't prove that Ron was right, but the important thing 
was, it didn't prove that he was wrong.  I shared that calc with the 
list because I thought it might add something to the discussion and I 
thought that some might be interested.

That is the essence of the scientific method.  Propose a hypothesis 
for how something works and then try to prove it wrong.  You never 
prove something right.  Ask a scientist if some theory is right and 
he will tell you that it just hasn't been proved wrong yet.

I have tried to be completely open about the assumptions that I am 
making and the calculations that I am doing.  That is so that anyone 
may refute me if they wish.  If you think my assumptions for bearing 
angles, for friction coefficients, for assumed bearing area, etc. are 
wrong, then refute me, and indicate what you think would be correct. 
If you think that I am wrong in assuming static friction for this 
situation because string vibration will break the static friction and 
allow the string to climb up the pin, then say so, and say why.  If 
you think there's something wrong about the simplified model or 
representation of the situation then say specifically what it is.  So 
far no one has done that.

>If that were the case, then my little brass plate experiement below 
>would fail.   And it doesnt.

What brass plate experiment?  You told us to install a brass plate on 
top of a bridge, put it into service, and bang on the note a lot. 
What's the experiment?  What does it demonstrate?  What's the 
criteria for pass or fail?

>  Yes I have done it, along with a few other experiements about 
>things that are not supposed to be happening according to the 
>numbers perspective.  I'm a practical oriented person. Instead of 
>simply looking at what I think should be happening, I try and find 
>ways of seeing what actually is happening.

That sounds like a reasonable approach.  Perhaps you could share the 
results of some of those experiments with us rather than telling us 
that we're wasting our time discussing it and running numbers.

>   You can get the same condition of pins off the bridge cap with a 
>brass surface.

What condition?  Pins rising relative to the bridge cap?  So what? 
It's still the same bridge pin and still a wooden bridge.  Putting a 
little piece of brass on top hasn't changed that.  I don't recall 
anyone stating that they thought pins didn't rise over time.  Roger 
offered one explanation for the rising pin due to the wooden bridge 
pushing it up from the bottom.  That sounds plausible to me.  Might 
be right, might be wrong.  I don't know as I haven't conducted a 
battery of experiments to disprove it.  But I'm glad he shared the 
idea and chose to participate in the discussion.  I'm not going to 
criticize him for failing to offer reams of experimental data to back 
up that conjecture.

>
>I personally believe the focus of this discussion is all wrong. 
>Instead of trying to prove a pre-thought-out idea by use of what 
>must neccessarilly be an incomplete model,  why not simply construct 
>a whole set of experiements to find out exactly what happens under 
>varioius controlled situations first ? Then go about trying to 
>explain.

Perhaps you could tell us what experiments you propose?

>   So far it's painfully obvious no one really knows for sure why 
>exactly strings can find themselves away from the bridge surface in 
>the various situations they do.

I think this discussion started when a few people mentioned (me being 
one of them) that they thought that strings could be above the bridge 
caps, because they had observed that strings, on being tapped down, 
exhibited a noticeable down movement.  Ron N argued that it was not 
possible for the string to be completely off the bridge and that this 
was a local effect at the notch edge.  That's when I ran my first 
number, to try to disprove what he said.  Which I did, for the 
assumptions that I made, which was a string above the bridge acted on 
by static forces - if anything I was trying to make your case for 
you, that a string could be off the bridge, rather than trying to 
'prove' that it can't.  He argued, plausibly, that at least one of my 
assumptions was wrong, the assumption of a static situation.  He 
argued that a dynamic situation would cause the string to seat 
against the bridge cap.  I haven't as yet been able to show him to be 
wrong.  If there was some reasonable calculation that I could do to 
try to disprove this I would, but I don't know of one.  So, I'll need 
physical evidence.   If someone finds a piano with a string sitting 
above the bridge, such that it can have a feeler gage inserted under 
it in the middle of the bridge, then he would be shown to be wrong, 
at least for certain situations.  By making observations about that 
particular piano we might start to learn what those situations are. 
I intend to do some checking around with a feeler gage as time 
permits.  Others have indicated that they would too.

Since you're the one that seems to be most adamant that strings can 
be above the bridge, why don't you prove Ron wrong by posting a 
picture of a string above a bridge and a picture of a feeler gage 
stuck under it?

>  And, despite this lack of knowing... we are witness to numbers 
>being used to attempt to <<prove>> that one and only one basic 
>reason exists for this, and that represents essentially a destroyed 
>bridge cap.
>...
>Cheers
>RicB
>

To reiterate, I haven't tried to 'prove' that a damaged bridge cap 
causes a string to be above the bridge cap.  I have only been 
unsuccessful (at least I haven't been told otherwise) in disproving 
that a string could crush itself into a rising bridge cap.  If you're 
able to disprove this, then please share the explanation with us and 
we'll throw rocks at you.

As an additional note I might add that numbers are a way of 
communicating, just as words are, but are illuminating in some 
situations where words are not.  In the way that I assume people 
don't object to me using words to have a discussion, they don't 
object to me using numbers to have a discussion.  If you would prefer 
that I refrain from sharing numbers or calculations with the list 
I'll be happy to send them only to those who indicate that they would 
like to see them.

Phil Ford