Computing bass string tension from broken wire.

[Richard Moody]

<<<.
 I just got a call that both of those replacement strings
broke. The windings look the same and the overall dimension is the
same as the surrounding strings, but the core wire is size 15 whereas
the surrounding core wires are size 14. Both strings broke at the top
bridge pin.
Michael Musial

>>>>>

I don't think I have seen a string break at the top bridge pin unless corosion.

I would like to throw this out as I haven't tried it yet but do have the
formulas to compute tension by weight. grains per inch.

Trim the broken wire so only the speaking length remains.  Weigh that. Compute
the tension from the weight formulas. If you use a gun powder scale you will get
the direct weight in grains.  You can go to your friendly local gun shop if you
don't happen to have one.

 Take the diameter of the core wire.  Look up its weight in grains per inch
table.  (Reblitz, McFerrin or archives) (or I've got it on a spread sheet with
the formuals ready to work.)
Compute its weight. Subtract that from the weight of the wire.  That is the
weight of the winding.  Knowing the weight of the wire and the weight of the
winding gives you an idea of how much "load" is on the wire.  You can do fun
things like computing what the tension of the wire would be if it was not
wrapped.  Or compare your results with the formulas that have you measure core
diameter and overall diameter.  Or figure out how much an error of 1/16 of an
inch makes.
    It would be a little more difficult to figure out how much weight was added
by measureing the overall diameter as the copper flattens a little as it is
wound on, or so they say.  However the winder should know the length of the
copper wire he put on so the weight of the winding could be computed from that.
That would be a good way to test the accuracy of the formulas that derive the
weight of the copper winding from the over all diameter of the bass string.

Since all tension formulas are derived from a basic formula using mass, using
the actual weight of the wire should be the most accurate determination of
tension.

The univeral formula is      T = 4*F^2*L^2*(W/g)     where W/g   = mass

English    T=F^2*L^2*(W/675356)           W = weight in grains per inch.
    W would be the total weight of the wire (in grains) divided by the length in
inches.

There should be a formula for just the mass without length, but that is for the
engineers or physics students.  Any of those here?


---ric