I decided to do a bit of follow-up work in the form of a few practical tests on this today.
I wanted to see what the impedance of a 30cm wire antenna would be at 27MHz.
The test I did was done under conditions which were far from ideal, there was no ground plane for the antenna to work against, just the body of the antenna analyser.
So moving the antenna and analyser around on the bench would probably have a big effect on the results, but then this is no worse that what would happen when the original circuit was built, there is no defined ground plane there either.
The pictures in the attachments tell most of the story.
The antenna analyser is an Array Solutions AIM 4170 (Google it), which works in conjunction with some software in a PC.
So, 30cm of wire at 27MHz, in my test setup gave an impedance of 10 Ohms in series with 2pF.
Adding a loading coil of 8 turns on a length of ferrite rod from an old radio antenna changed the impedance to 143 Ohms in series with 8.3pF.
What really surprised me was that this antenna with a loading coil exhibited a resonance at 32.6MHz.
Another turn or two on the coil and it would be resonant at 27MHz.
Coming back to Samys original calculations and ignoring the 8 turn coil and assuming that the antenna impedance would be 50 Ohm, that was not a good assumption.
Allowing for the 8 turn coil with some random piece of ferrite, does give a closer impedance to 50 Ohm, but still quite some way off.
My opinion is that trying to rigorously analyse simple RF circuits such as this is not very helpfull.
JimB