According to IEC 62305-3/2006 Table 6 for all type of LPS [I to IV] the minimum cross section area of copper rods in air-termination system is 78 mm^2.[9.966 mm diameter]
NFPA 780/2011 Table 4.1.1.1.2 Minimum Class II Material Requirements 12.7 mm.
In my opinion, the standards-IEC or NFPA-are the result of many studies and calculations and I don't think you can find a formula-or a program-in order to calculate the minimum air-termination diameter.
The material at lightning stroke arcing current could reach 15-20000 K and in short time a part of the rod will evaporate reducing the rod diameter and height. It depends for how long an air-termination has to withstand the strokes.
A formula proposed by Stanback-for instance-Y=A*I^n [cm^3]
For copper A=13.38/100 and n=1.25 so at 200 kA 65 cm^3 will evaporate in a single stroke but according to Koch it will be only 16 cm^3 [depending on maximum temperature].
According to the Onderdonk’s relation, it is possible that a 10 mm Dia Cu bare conductor with a fusing current of 1083 oC can take 200kA RMS current for a duration of approximately 8 msec.
