Quote of the Day
Hard work spotlights the character of people: Some turn up their sleeves, some turn up their noses, and some don't turn up at all.
— Sam Ewing, baseball player
Introduction
FIgure 1: We have had phones for a very long time.
I still work on old copper phone networks, and today I encountered wire specified as "300 pound". I had never seen a specification like this for phone wire before. As I thought about it, this specification seemed very similar to how the diameter of thread is still specified, which is by the weight in grams of a 9000 meters of fiber – a unit of measure called the denier.
In this post, I derive a formula for the diameter of wire specified in terms of weight of annealed copper per mile of distance. This is not a problem, but it does illustrate how our common units of measure evolve over time. In the case of wire, it used to be difficult to measure the diameter of fine wire, but it was easy to measure the weight of given length of material. This simple fact drove the use of this specification.
Analysis
Figure 2 shows my derivation and some worked examples. The derivation assumes the length of copper wire is a long, thin cylinder. I was able to confirm that the actual wire diameter agrees with my calculations.
Figure 2: Wire Diameter Formula with Examples.
Conclusion
Landline phone service had its beginning back in 1876. It is amazing that even today I encounter vestiges of the old system that date back to the early part of the 20th century.