Measuring Antenna Capacitance

...not bad. And now its a small exercise for you to substitude k and a by terms with L und d. Perfect formula for this special case.  

Too few points to select realistic functional dependencies.

(for example: the behavior of parameter "a" is unclear on the interval L=0...20 cm, whether it tends to 1, or to another value)

For practical purposes (in order to obtain intermediate values of "a" and "k"), it is sufficient to have a piecewise linear interpolation or approximation by a 2-nd order polynomial (as anyone likes).