[CAUT] Wire Stretch

[John Delacour]

At 11:09 am -0400 27/4/07, Jeff Tanner wrote:

>On Apr 26, 2007, at 7:17 PM, Fred Sturm wrote:
>
>>     Wrapped strings are much closer to breaking point/higher 
>>tension than the neighbor plain wires. The lower tension wires take 
>>much less change in any factor (length, deflection, tension) to 
>>produce a given pitch change than the higher tension wires. Think 
>>about how much turn on the tuning pin it takes to raise that lowest 
>>plain wire 25 cents, compared to what it takes to raise the top 
>>wrapped string the same amount. Think about the same comparison 
>>when you are first chipping to pitch. Crank and crank on those 
>>wrapped strings, where a single yank gets the plain ones to pitch 
>>and past.
>>
>
>But which one stabilizes first?

I think the point Fred makes, which I agree with, is that the plain
wire strings at low tension do not stabilize as regards pitch.  The
most succinct description I know of of this phenomenon comes from
Wolfenden, writing in 1916.

_____________________________

         It is now known from experience that practical equality of tension
      throughout the instrument tends to prevent changes in the tuning due
      to variations in the temperature.  When the tension is equal the
      temperature movements are equal.
         In former days pianofortes were exceedingly sensitive to changes
      of temperature, mainly because the fact noted above was unrecognized
      or disregarded.
         A thermometric movement of a few degrees often sufficed to render
      (in a very short time) an instrument unusable, and had the tuner
      recently paid one of his visits, the discredit of the change was
      charged to him.
         The notes in which the greatest changes occurred, were the lower
      ones which were strung with plain steel wire.
         I have known numerous instances in which the changes in these notes
      were equal to nearly a semitone between midsummer and midwinter,
      while the other parts were relatively stable.
         This was due to the customary very low tension of these notes.
         There seems to be a point in an ascending scale of tension, at
      which the elasticity of the wire is almost suddenly developed (*) to
      an extent we could not anticipate, so that a difference, so that a
      difference, which would be very serious at a general low tension,
      will become more tolerable.
         To make this intelligible, let us suppose an instrument in the
      tension of pitch C is 130 lbs., and that of C two octaves lower is
      only 100 lbs.  This piano will be extremely sensitive.
         But let us now suppose that we can lift the tension so that pitch C
      stands at 200 lbs. and the other at 154 lbs.  While there still
      remains a liability to change, it is much reduced, although the ratio
      of the difference in unaltered.  Covered bass strings, which are
      usually at a rather higher tension, seem immune from this disease.
_____________________________

I have marked with an asterisk the observation that I find most 
interesting in this, namely: -
"There seems to be a point in an ascending scale of tension, at which 
the elasticity of the wire is almost suddenly developed to an extent 
we could not anticipate" -- and I think we would search in vain on 
the WWW for a simple explanation, or any explanation at all, of this 
phenomenon so familiar to piano makers.


>In other words, the plain wire is more "elastic"?

Are you sure you do mean elastic?

>I'm no physicist.  But it just seems like plain wire keeps on and 
>keeps on stretching over the years.

I'm no physicist either but the answer is fundamentally yes, in many 
cases, but there are many factors in play and the mathematics and 
physics of it are highly involved.  Besides that I am not aware that 
any serious specific study has ever been carried out to quantify or 
explain what does happen to patented steel wire (piano wire) under 
the strains to which it is subjected in a piano.  It is worth noting 
too that patented wire of different manufacturers behaves differently.

As we all know, new strings fall in pitch quite dramatically and 
become more and more stable with subsequent tunings.  It is said that 
piano wire is elastic, in other words that any deformation it 
undergoes when strained within its "elastic limit" will be reversed 
when the strain is removed and the wire return to exactly its former 
state.  This is a gross simplification of what actually happens, as 
experience shows.

A few years ago I asked the brother of a friend of mine, an 
extraordinarily brilliant Swiss scientist, about this business of 
initial pitch drop, and he was able to explain it immediately and in 
more detail than I could actually absorb, and his explanation is that 
when the stain is applied the molecules of the steel (which 
incidentally in the case of patented wire is by no means homogeneous) 
very slowly through minute vibrations and displacements, realign 
themselves to achieve for themselves the position of least stress for 
the given new strain, and this leads to a slight lengthening of the 
wire.  When the wire is next re-stretched to pitch, the difference is 
far less between the previous "comfort alignment" and the the 
alignment required for maximum comfort under the slightly higher new 
strain.  Less internal repositioning is thus needed to achieve the 
equilibrium and the drop in pitch is consequently less.

I think the common term for this phenomenon is "creep".

There are then to be considered a) the "true elastic limit" or "limit 
of perfect elasticity" of the wire, and b) the "yield point".  The 
"breaking strain" or "ultimate tensile strength" of the wire is not a 
useful figure for the practical piano maker.

The "true elastic limit" is quite a low figure.  I can't quantify it, 
but it seems probably that most strings on any piano will exceed this 
limit.  Possibly it is beyond this limit that "creep" begins.  A.E.H. 
Love gives for Bessemer steel an elastic limit of 1780 atmospheres 
and a yield point of 2650 atmospheres.  That is to say the elastic 
limit for this material (_not_ patented steel wire, which is very 
different) is 67% of the yield point.

Love (A Treatise of the Mathematical Theory of Elasticity - 1926. 
 From Dover) cites a number of previous researchers and notes an 
experiment by Vicat:- " He found that wires held stretched, with a 
tension equal to one quarter of the breaking stress, retained the 
length to which this tension brought them throughout the whole time 
of his experiments (33 months) , while similar wires stretched with a 
tension equal to half the breaking stress, exhibited a notable 
gradual increase of extension."

There is much other tantalizing stuff in this treatise.  I wish I 
were qualified to read it all, but the reason I have it is that the 
text is highly readable and at moments comprehensible in part even to 
my untutored mind.

JD