You analysis of the accordion roughness' effect is relative to the wavelength. I have no idea of the relationship, but my brother whom has designed antenna systems for military aircraft and patented antenna designs schooled on the fact that the formulas we all love and use are WRONG!

However, the formulas we use work well because we typically use relatively thin radiating elements compared to the wavelength, often significantly less than 1% of the operating frequency. The correct formula is surface area of the radiating element NOT LENGTH.

To you and I building wire, Yagi, and loop antenna with skinny radiating elements length ends up being very close to the surface area. However, design an antenna for a cellphone from a thin plate or part of an aircraft fuselage and the length formula starts falling apart, especially at the higher frequencies.

I didn't bother learning the correct formula as it is a little more complex.. I think it may come up when you start building fractal shaped antennas, such as were used in WWII by underground operatives using the lead frames stained glass windows in churches as radiating elements. The surface area formula may become relavent to magnetic loops with radiating loops with very thick radiators.

N4VEP