LPDA design

In the design of a log periodic one of the key steps is identifying the avarage characteristic impedance of a dipole. For a typical application see The expression for this is given as 120*ln[(L/D) - 2.25)], where L is the length of the dipole and D the diameter. Does anyone know the origins of this expression, and how it was derived? The only time I have ever seen it is with reference to LPDA design.

Any help would be appreciated.