Are the lengths of radials related to the height of a vertical?

A couple of weeks back I noticed a question on the TowerTalk reflector about making the radials on a vertical the same length as the height, i.e. use shorter radials on shorter antennas.  Something along these lines has been "conventional wisdom" for a long time but I'd never seen any real justification for it.  So I did a quick modeling study and up to a point it does seem to support this idea.  I wrote this up in:

Download radial_system_design_and_efficiency_in_hf_verticals.pdf

While I was at it I took a look at the variation in radiation resistance and ground loss resistance as the radial system and/or ground characteritics were varied:

Download radiation_resistance_variation_with_radial_system_design.pdf

This one is just for fun, I don't think it has much practical application but it may help in understanding how verticals work.