Yep you can stick a piece of coax up and make it into an antenna

, the coax dipole has been my go to problem solver for a quick and dirty antenna for years.
As you will find in any " large book on antenna theory" there are a number of different reasons to need either a specific or minimum length feeder....
The reasons in the 27Mhz aerals may be different from the reasons in the VHF areials... they will be two very different designs.
As far as being rough design......hmm....... remember there are also effective radiated power restrictions....so they problay have to design arround unity gain......at VHF a co-linear would problay be the best and easiest design... but that would give a gain above unity...........
If anyone has a donged or broken example of any of these antennae....I would realy like to pull one appart to see what sort of design they are.......I'm sure andy would like a look too
The 27Mhz ones with the single pivot base seem to be a straight helical whip with a coil and cap base tune arrangement in the base.
cheers