Reg,
I recommend the following pair of wonderful articles.
Part one is in HAM RADIO, April, 1977, pp. 52-58. The second in May,
1977, pp. 29-39.
The full reference is: Boyer, Joseph M. (W6UYH): "The
Antenna-Transmission
Line Analog".

Mr Boyer simplifies the antenna analysis by equating parts of the
antenna to transmission lines along the same lines that you have.
Regards
Nat