There are formulas but at VHF there will still be a lot of experimenting to get the coil and whip lengths working together. The placement of the coil along the whip also makes a noticeable difference in the coil specs. Here is a link to a loading coil calculator for 1/4 antennas as an example:
https://m0ukd.com/calculators/loaded-quarter-wave-antenna-inductance-calculator/
Even at HF frequencies where the calculator is intended to be used, there will still be a lot of tinkering with the coil windings to get the antenna to resonate where you want.
A 1/2 wavelength end fed antenna like your whip idea is a very high impedance antenna and you first need a circuit to match the roughly 3,000 ohm impedance of the 1/2 wave whip to your 50 ohm radio, which is not easy. Then you want to shorten the half wave antenna with a coil, which will reduce its efficiency and probably not make it worth using a half wave at that point.
Its much easier to just use a full size 1/4 wave whip, which is around 15 to 20 inches long depending on what part of the VHF band you want. Shortening a 1/2 wave antenna to a similar length will not work any better than a 1/4 wave whip of the same length due to all the efficiency problems you introduce with the coil and a shorter antenna. A full length half wave antenna with a proper 3,000 ohm to 50 ohm matching network will work noticeably better than a full length 1/4 wave if done right, but its going to be at least 3ft long.
prcguy
