|String Code||Mass per Unit Length||Diameter in mm|
The middle column shows the linear denisty or mass per unit length of dAddario Phosphor Bronze wound acoustic guitar strings. These values are have been converted to g/m from the lb/in values given by d'Addario in their own 'catalog supplement/string tension specifications'. The last three digits of the string codes (first column) correspond to string diameters in thousandths of an inch and these have been converted to millimeters in the right hand column.
Wound acoustic guitar strings depend on their steel core for their strength and elasticity. Steel music wire has a modulus of elasticity of around 210 GPa and a tensile strength (yield) ranging between1590 and 2750 MPa depending on certain factors (see MatWeb.com AMS 5112 specs).
The relationship between the diameter or of the core and the diameter of the winding will vary from one manufacturer to the other for any given string diameter and will also vary from between approximately 3/1 for thinner gauges and 1/1 for larger gauges.
Typical values would be:
String diameter 0.024 = 0.014 core + 0.005 winding
String diameter 0.053 = 0.018 core + 0.0175 winding
Where the winding and the core are of the same diameter of the core represents one third of the overall diameter of the string, the surface area of the core then accounts for approximately 11% of the cross sectionnal area of the string.
Based on this the modulus of elasticity of the wound string would be somewhere in the region of 23 GPa and its strength will also be proportionnaly less. The maximum tension recommended by d'Addario corresponds to approximately 160 MPa, equivalent to 11% of 1454 GPa.
For string calculation purposes of the relative density of each string can be determined from the mass per unit length and the diameter as given in the table, 23 GPa and 160 Mpa for elasticity and yeild strength respectively may be regarded as 'ball park' figures for the larger diameters (most likely to be used on a harp). These values would vary for any particular string depending on the relative size of the core and its mechanical properties but should be close enough to represent an average wound string and enable reasonably reliable calculations. For the smaller gauges the core to winding diameter ratio can be estimated based on the above figures.