Wilderness Keyboard wrote:
"See Guide to Transmitter Range from Artsci---."

See the 19th edition of the "ARRL Antenna Book" pages 23.5 and 23.6.

Eqn. 3:

Dmiles = 1.415 sq rt Hfeet

This can be rewritten:
D = sq rt 2H

Wasn`t it Albert Einstein who wrote something like: "Don`t make things
any more complicated than necessary?"

Solutions to Eqn 3 are plotted in Fig 6.

Example: 20 ft gives 6 miles. The approximate sq rt of 40 is 6 miles.

Example: 50 ft gives 10 miles. The approximate sq rt of 100 is 10 miles.

Example: 200 Ft gives 20 miles. The approximate sq rt of 400 is 20
miles.

Etc., etc., etc..

Best regards, Richard Harrison, KB5WZI