The Eternal Squire wrote:
All,

I'm currently considering a design for making a steampunk radio. I
just
had an idea for the VFO that I want to run by those who have a far
better grasp of the abstract mathematics of harmonics than I do.

Suppose I have a DC motor running steady at 1000 RPM. Through a
X100 set of planetary gears I create a shaft spinning at 20,000 RPM,
which is pretty much the upper limit for small drills anyway. On
the
shaft is a disk that is an etched circuit board with a star pattern,
that is,
500 conductors etched radiating from the center to the edge of the
disk.

***
20,000 rpm, so how many revs a second?
20000 rev/minute x 1/60 minutes/second = 333 rev/second
How many spokes?
333 rev/sec x 500 spokes/rev = 167000 spokes/sec

Now I have a wiper that is laid across the edge of the disk to make or
break contact with the outside of the star pattern, with 12 Volts DC
potential on the wiper. Assuming the shaft was conductive and made
firm contact with the center of the star pattern, should I see a 10
Mhz
square wave, suitable for say a switching mixer?

No, you would see a 167kHz square wave, with plenty of odd harmonics:
500 kHz, 833kHz, 1170kHz etc.

Question: How bad are the phase noise and harmonics likely to be?

The harmonics speak for themselves. Mechanical rotation is hard to keep
constant.

Thanks in advance,

The Eternal Squire

You'rte most welcome

Brian W