Hello kb4qaa, No we are not just dealing with high power transmission lines.The surge impedance formula is also useful and used to work out varying vertical diameters with height and for included loading coils and capacity hat systems and is accurate down to 0.64"D and is also useful for these types of antenna system calculations.
So yes surge impedance indeed.
My original question is not how to tune a vertical mobile antenna. That was an attempt to answer to k0bg retort and sorry I was sidetracked lol

It is about whether or not the cap hat addition to an exacting system is feasible to consider as a worthy addition to when one already has in operation an optimised Hustler mobile antenna.
To g7die: Dx Engineering MM-1? I did not mention a brand, hmm I was Not referring to it but since you mentioned it yeah might be a perfect solution for my installation slap it in ya know? Rather than building a shunt inductor at the feed point.
Geeze those young and lazy newbies "well when I was your age!"
Anything you can do I can do better.

73