As I mentioned earlier the formula for safe BP% (60%) came from Sanderson as .557*(d^1.667), d in mils which gave me 170 lbs for .031 or US 13 gauge. The actual diameter in mils (.775 mm) is more like .0305 which yields your 166 lbs. I appreciate the clarification on the derivation of the other numbers--practical breaking load and elastic limit. Certainly one doesn't want to exceed the elastic limit without potential and serious tonal repercussions. So if the elastic limit for #13 wire is 178 pounds and if the expected variation in tension while simply tuning is 15 - 20 lbs then it would seem that 155 - 160 lbs would probably be the design limit for that particular wire, as I read it. Beyond that it appears that you run the risk of creating some distortion in the wire leading to falseness at best and breakage at worst. I'm not really trying to make any pronouncements here, just clarify my own understanding of it. I readily admit this is not an area where I have done much research rather I have taken these formulas on faith as provided by those who have delved more deeply into this than I. In the bass it would be logical to assume that a greater margin would needed. David Love www.davidlovepianos.com -----Original Message----- From: pianotech-bounces at ptg.org [mailto:pianotech-bounces at ptg.org] On Behalf Of David Love Sent: Wednesday, April 13, 2011 4:42 PM To: pianotech at ptg.org Subject: Re: [pianotech] Breaking bass string It's the second (excel format). Your 166 lbs versus my 170 lbs is due to differences in rounding english units from metric. I'm using .031" for #13 which is how it's sold here but is slightly different from .775 mm. I'll have to look at the rest of the post later. David Love www.davidlovepianos.com (sent from bb) -----Original Message----- From: John Delacour <JD at Pianomaker.co.uk> Sender: pianotech-bounces at ptg.org Date: Wed, 13 Apr 2011 23:21:50 To: <pianotech at ptg.org> Reply-To: pianotech at ptg.org Subject: Re: [pianotech] Breaking bass string At 09:10 -0700 10/04/2011, David Love wrote: >The maximum safe tension for a given string that I have used is T = >.557d^1.667 representing 60% of the breaking strength, d given in >mils so for your #13 gauge I would come up with .557*31^1.667 which >equals about 170 lbs. That's quite a bit different from your 137 >lbs even if you figure in the differences for metric versus English >diameters. David, your formula is ambiguous. Your first statement of it disagrees with the second. The first would mean to me (0.557 * d)^1.6666666 The second would mean 0.557 * d^1.666666 For mwg.13 (0.775 mm) this would give in the first case 112 lbs. in the second 166 lbs. So which is it? And how is the formula arrived at? At all events it is not possible to use one equation for all sizes because the tensile strength per unit cross-sectional area varies - the thinner the wire, the greater the tensile strength per unit. So for example if the 'mechanical resistance' of 13 mwg is 548 lbs per mm2, 23 mwg. is only 505 lbs. But to continue. So far as I can tell, without spending half an hour puzzling out of what formula yours is a simplification, (0.557 * d)^1.6666666 makes sense and the other does not, because it gives the wrong curve. And if, as you say, this gives 60% of the "breaking strain" (whatever that is!), then, as Del says, this is very conservative. If we raise that to 75% we get figures far more similar to mine and Paulello's... But the breaking strain to start with is not the 'mechanical resistance' or 'nominal breaking load', to use Paulello's terms, that is the tension under which the wire breaks on the testing machine has to be reduced by 25% to arrive at the 'practical breaking load'. The elastic limit of the wire is another 20% below that, in other words it is 80% of the 'practical breaking load', and we need to make sure the tension of the string never exceeds the elastic limit, so we need another margin. To quote from Paulello: "Since Mersenne's work about gut strings until the recent researches by Claude Valette and Christian Cuesta in their book dedicated to vibrating strings, it is generally accepted that a string provides the fullness of its vibrating power when it is stressed to around 60 to 75% of its practical breaking load, or close to its elastic limit (Re). Stressing a string in this way actually limits internal damping and offers the best balance between the fundamental frequency and higher partials." At 09:43 -0700 12/04/2011, Delwin D Fandrich wrote: >For example, the breaking strength of Mapes IG No. 13 gage wire >(U.S., or 0.031"/0.787 mm) ...averages 296 lbs. I have asked Mapes to send me a full list. Perhaps someone here can send me it. Now this is the 'mechanical resistance' or 'nominal breaking load' of the wire. To arrive at the 'practical breaking load' we multiply by 0.75 and get 222 lbs. Multiplying by 0.80 we get 178 lbs. as the elastic limit. We then need a safety margin to be sure the string will not exceed 178 lbs. at any point in its life. By comparison, Paulello's No. 13 would have a 'mechanical' resistance' of about 265 lbs. I stupidly got some of my numbers wrong in my last message. The nominal strength is less than Mapes but not all that much. JD
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