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How is the amount of force required to deflect a piano wire calculated? I want to find this so I can calculate how much downbearing force a single and/or set of strings will give at a specific deflection distrance.

Thanks,

Multiply the sine of the angle by the string tension for downbearing force. For example the sine of 1 degree is .0175. So, if you have a deflection of 1 degree and a string tension of 160 pounds then:

160 x .0175=2.8

It's fairly straightforward math.

Edit:
Of course in theory it's simple but in practice it's a complex system and theoretical downbearing is almost never what the actual measured downbearing ends up being.

OK that helps! I was thinking it was more complicated than that. I thought the diameter (gauges) would give some variation through A0-C88. But maybe it's just not a significant difference?