Mass Coefficient for Tension Formula

[Ric Brekne]

Hey Joe... 

I found the clue I was looking for at last !..  Combination of McFerrins book and the quote from Pure sound website was what I needed to jog my mind and the light goes on  :)

In McFerrins book where he discusses Tension formula for plain wire he ends up with translating everything to the metric system and shows exactly how to determing what Rhodes terms K in the first formula below. Combining this then with that first formula so as to include wrapped wires, and with any give wire density spec gives the correct formula for all cases.

Grin.... glad thats out of my way.  I can reset my spreadsheet now and look at the same numbers I have in the printouts from these other two guys now, and fine tweak this puppy at last !

Cheers
RicB


Joe

The two variants I'm looking at were calculated by two different 
scalers, both taking into account for Pure Sound density.... but using 
unfamiliar formulas for scaling programs.  The one is just a program 
that is no longer available (the one that uses the Harmonicity 
parameter), and the other by a fellow recommended by Pure Sound.

I'm putting the numbers in the spreadsheet type that comes down from the 
Calculating Technician.  Reading both the articles and the accompanying 
documentation, there is no explanation as to where this figure is to go 
into the formula, or how it is to be translated to whatever measuring 
units are to be used.

Take the Tension formula for example... in the T= ( fLd / K)^2 * (1+ 
A(D^2/d^2)-1).  A is the value for wrap (no explanation given anywhere I 
can find as to how this is ascertained or what exactly it represents in 
terms of measuring units.... its just a number given)  K is even less 
clear... it is defined as just a constant with no reference at all to 
what it stands for, let alone how to ascertain it.

One is tempted without further ado to conclude that K is the mass 
coeficient... but how does one make sure its in the right units ?

Taking the other form for T Rhodes gives in his execution of Roberts 
formulas you have  T =  2(m/6)^2 *(Ld / 7.69)^2 * (1+A(D^2/d^2) -1)

Here K is necessarilly manipulated so as to facilitate a different way 
of dealing with the frequency parameter...  and its corresponding number 
is 7.69  Again no explanation is given so I dont know whether or not 
this is average density of the wire.  And if it is... well then Juan 
gives 7.85... not 7.69

So... if you know just where the average density parameter figures into 
this and the other formulas given by Roberts in the Calculating 
Technician... I'd realllllly like to know :)

Cheers
RicB



     This formula is based on modern piano wire, average density 7,85.
    These data are all hidden within the number: 2514.
    For Pure Sound wire this number is : 2530. (average density: 7,90)
    For Malcolm Rose's wire the number is : 2488. (average density:
    7,769)"

    Ric,
    I read through all of that and finally got to the 2nd from the
    bottom line- - -Voila': it reads average density 7.90!! That's the
    mass coefficient and has to be plugged into the scaling formula to
    get a better picture of what that stuff is all about and how it will
    react in regards to tension and Inharmonicity and Impedance! If you
    didn't do that then whatever you are planning on this piano needs to
    be re-calced, IMO.<G>  :-(
    Best Regards,

    Joe Garrett, R.P.T.
    Captain of the Tool Police
    Squares R I