Looks like Yellowbeard and nrgkits.nz have some good advice. Maybe electronically made a mistake with the x2, a 1/4 wave will always be 1/4 wave when that is what is needed. If you struggle for velocity factor of cables, it's a property of what the dielectric inside is made from and it's construction. All cables with solid polyethylene dielectric will have a similar velocity factor, same goes for semi air spaced (like tv co-ax), polyethylene foam, PTFE. I doubt the difference between 0.66 and 0.68 will make much difference as the formula is only approximate anyway (speed of light rounded to 3x10^8 , then divided by 1,000,000 to use MHz for frequency). I'd go for 0.67 when a back and forth between 0.66 and 0.68 is happening.

A useful reference is here: https://www.electronics-notes.com/artic ... factor.php

I never bothered with J-poles because of having to waterproof a sliding contact (one of those SO239 to two element clamp things). My favourite antennas were the 5/8 groundplane and it's co-linear version - I liked the property of being able to add or remove the top part of the co-linear without the matching changing, and the groundplane to reduce RF below the antenna; where audio equipment was, and there would be all sorts of hum and interference with an antenna that didn't have a groundplane, even at the low power I was using.

I just did electronicallys method of x2 and got perfect swr and 50ohm match.

I've never made a 4:1 co-ax balun, that's why I only mentioned "if that is what is needed" so as not to say for definite when I didn't know, sorry if it caused any confusion. Turns out it is meant to be 1/2 wave, so the x2 is right. I have learn't something new myself now. I didn't want to search the net and just 'look knowledgeable'.

Use denso tape for all your waterproofing, I seen it still being perfect after 10 or 12 years buried in the ground - and this was thick black damp Irish muck it was buried in. Sounds like they are sponsoring me, but denso tape is great shit. There. Find that knowledge on the internet!

Agreed on the Denso tape! Brilliant stuff!

For anyone thats still interested, this months CQ amatuer radio (June 2023 for those viewing this on Dave) has a balun special. It features Guanella and 1/12 wave transformers with equations and Smith charts, and a 70 year old article on the half wave balun that we spoke of earlier in this thread. The file is called cq.amateur.radio.june.2023 - google dat if yer a real pirate!