what shockwave says is true, i have stated that several times in these sigma4 threads, the vector/sigma will tune with almost any length monopole at least between 27ft and 32ft,
the right length for me is whatever length gives the best signals out at the fringes of my coverage,
the way i determine that is to use a reliable distant vertical fm station and tune for best signal,
i used fm stations about 60 miles from my location, stations i cannot hear on the i10k mounted on the same mast,
i tune at night so locals do not pump my agc and never tune/make comparisons when there is skip messing with signals,
i use a fluke 87 multimeter in min/max record mode to read s-meter voltage plus a large external s-meter, i also have a precision constant impedance 50ohm attenuator so i can take relative gain measurements if i choose to,
using a modulated am signal or ssb makes taking accurate readings or noting small incremental trends as you tune virtually impossible,
you should tune/test with only one antenna errected at any one time, no exceptions for convenience,
the reasons are well documented, observed in my own tests years ago and also mentioned in the sigma4 instructions, getting the best out of anything is never convenient,
i will say it again, you will only find what works best for you by actual on air tests with distant reliable unmodulated stations,
it is also well documented that monopole diameter/taper the relative radial diameter/taper radial spacing and length plus number of radials all effect resonant frequency there is no exact measurement anybody can give you nor is there any requirement to achieve a resonant length,
if you want simple/convenient build an exact replica of a vector, the only version i know to work from my own experience is the old 7/8wave physical version that will outperform any groundplane even in stock form,
radiation angle of sleeve antennas does change with changes in monopole to radial sleeve length ratios, that has been known and used to good effect since the 1940's,
its not about maximising gain its all about putting your signal where it is most effective,
my own tests indicate to me that i am either effecting radiation angle or making large improvements in gain, since i don't believe i am increasing gain by the difference i see in signal on the ft990 and ft767, i suspect i am manipulating radiation angle,
it also makes sense to me that when i told mr cebik what i thought was happening when i made my adjustments he would have said so if it was not likely, on the contrary he said it was very much possible,
i could be wrong but i doubt it