# [78-L] how long is it?

Per Ahlin Per.Ahlin at abc.se.invalid
Sun Sep 25 13:25:37 PDT 2016

```This is an approximate solution.

A recording of exactly 3 min at exactly 78 rpm
will consist of 3 x 78 = 234 revolutions.
The circumference of a circle of radius r is
2 x pi x r. Assume that the radius varies from
5 to 1 inches. The average radius is 3 inches.
The total length is approximately:
234 x 2 x pi x 3 = 4411 inches.

Per Ahlin

> I just got an interesting question from a friend who has nothing to do
> with 78s! He asked: "If a record didn't go round  and round but a 3
> minute (groove) went straight,  how (long would the groove be)?"
>
> To which I replied: "There's got to be a math formula for this - how
> does one figure out the length of a decreasing spiral over 2 radial
> dimensions? First, you'd have to know the pitch of the groove - that's
> how many lines per inch along a radius the groove makes. Secondly,
> you'd have to measure the inside and outside radii of the spiral. I
> think that's all that is needed to plug into a set formula. Someone in
> 78-land will know this. I'll ask."
>
> Anyone?
>
> Malcolm