length / diameter / tension relationship, was Upright and Grand rims, was: Impressive Steinway Upright

[Mike and Jane Spalding]

Tony,

You asked why not make them longer AND thinner.  I was merely trying to point out that you can make them thinner, but you can't make them longer, because THAT will quickly cause the tension to exceed its maximum safe percentage of breaking strain.

A85, 6cm long, size 13,         53% of breaking strain.
A85, 6cm long, size 13.5,     53% of breaking strain.
A85, 7cm long, size 13,        72% of breaking strain.
A85, 7cm long, size 13.5        72% of breaking strain.

hope that helps,

Mike

----- Original Message ----- 
From: Tony Caught <caute@optusnet.com.au>
To: Mike and Jane Spalding <mjbkspal@execpc.com>; Pianotech <pianotech@ptg.org>
Sent: Monday, September 16, 2002 8:23 PM
Subject: Re: Upright and Grand rims, was: Impressive Steinway Upright


> Yes Mike but if you make the string longer at the same frequency and the
> string is thinner and at the same frequency, its another ball game.
> 
> An A85 note of 13.5 gauge that is 6CM long has a 60% of maximum tension of
> 79 kilo and is in tune at 71 kilo. 8 kilo below max recommended tension.
> An A85 note of 13 gauge that is 7CM long has a 60% of maximum tension. of 75
> kilo and is in tune at 91.52 kilo.  16.52 kilo above maximum tension.
> 
> The question was
> 
> "Why does the high treble scale not have slightly thinner, somewhat longer
> strings? It seems to me that the short speaking lengths would contribute to
> lack of sustain, excess hammer sound vs. musical tone, difficulty in tuning
> etc"
> 
> The %ages have nothing to do with it.
> 
> Regards
> 
> Tony Caught
> caute@optusnet.com.au
> 
> 
> ----- Original Message -----
> From: "Mike and Jane Spalding" <mjbkspal@execpc.com>
> To: "Pianotech" <pianotech@ptg.org>
> Sent: Monday, September 16, 2002 10:58 PM
> Subject: Re: Upright and Grand rims, was: Impressive Steinway Upright
> 
> 
> > Alan, Tony,
> >
> > An interesting property of the equations is this:  At a given length and
> frequency, the percentage breaking strength of the steel wire is constant.
> You can vary the wire size to play with tension, inharmonicity, power and
> impedence, but the percentage breaking strength does not change.
> >
> > FWIW
> >
> > Mike Spalding RPT
> 
> 
>