[CAUT] Stringing equations and friction

[David Love]

At C88 speaking length of 63 mm you are at 98% of the BP.  Reducing the
diameter of the wire doesn't change the BP percentage.  The higher the
tension the more friction because there is more pressure on the bearing
points.  A thinner wire will have less tension and therefore slightly less
friction.  The segments when equalized are at the same tension and BP%
however when you start to pull up the pitch there is a slightly higher
tension in the tuning pin to capo segment until the rest of the string
moves.  Since you are so close to the BP% that likely pushed you over the
edge to where the strings were breaking.  The reduction in friction because
of the slightly thinner wire was probably not a significant factor in that
string making it and the other not.  The difference in tension between #13
and #12.5 is 249 to 224 lbs.  The Mapes wire has a slightly higher BP so
that combined with a bit of dumb luck probably got you there.  Tuning the
piano 1/2 step flat will reduce the BP% at C88 to 88%.  If you believe in
numerology maybe that's a sign.  

David Love
www.davidlovepianos.com


-----Original Message-----
From: caut-bounces at ptg.org [mailto:caut-bounces at ptg.org] On Behalf Of Greg
Graham
Sent: Saturday, December 05, 2009 6:44 PM
To: caut at ptg.org
Subject: [CAUT] Stringing equations and friction

I've always suspected the stringing equations were forgetting something,
namely friction at the bearing points.  

A year or so ago I wrote asking for advice on a piano with a C88 speaking
length of 63 mm.  The #13 Roslau wire I had wouldn't come up to pitch,
usually breaking at the capo.  I tried some #13 Mapes Int'l Gold and got
closer.  Mapes I.G. #12.5 got me to pitch after two tries, with gritted
teeth and squinty eyes.

Here's the rub... literally:  

There is so much tension on that poorly scaled string that the capo develops
grooves as soon as you pull up to pitch.  There is LOTS of friction going
on.  A smaller wire, with less tension, will have less friction.  That
matters when you are talking about strings breaking, doesn't it?

Won't the segment of string between the capo and tuning pin always
experience higher tension and break percentage than the speaking length?

If we reduce bearing point friction, won't we lower the difference in
tension between the two segments, thus allowing less breakage?  

I don't have the answers here.  I'm just the new guy (with a mechanical
engineering degree) looking for guidance and questioning authority.

Greg Graham, RPT
East Stroudsburg, PA