Lightning Striking Distance (Rolling Sphere Radius)

A lightning leader descends in steps of a few tens of metres, and for most of its journey it has no idea what is beneath it. Then, at some height, the electric field between the leader tip and something on the ground becomes large enough for the final jump, and at that moment the flash commits to a target. The distance at which this happens is the striking distance, and it is the single geometric fact on which all conventional lightning protection is built.

It depends on how much charge the leader is carrying, which shows up afterwards as the peak current of the return stroke. IEC 62305 uses $r_s = 10\,I^{0.65}$, with $r_s$ in metres and $I$ in kiloamps. A weak flash commits late and close; a powerful one commits early and from far away.

The constant is unit-bound, and this is the trap. The 10 means ten metres per kA^0.65 — it is not a dimensionless number and it does not survive a change of units. Feed the same relation a current in amps and the answer is wrong by a factor of $1000^{0.65} \approx 87$. This page therefore pins kiloamps on the current variable in both unit systems, because kA is the only unit in which the published relation, and every published protection level, means anything.

What the number is for is the rolling sphere. Imagine a sphere of radius $r_s$ rolled over the structure and the ground around it, touching whatever it touches. Every surface the sphere can reach is a surface lightning can reach; every volume it cannot enter is protected. That is the entire method, and it is why air terminals are placed where they are placed — not to "attract" lightning, but to be the thing the sphere touches first. The standard defines four Lightning Protection Levels with spheres of 20, 30, 45 and 60 m, and those four numbers are precisely this relation evaluated at 3, 5, 10 and 16 kA and then rounded: 20.4, 28.5, 44.7 and 60.6. Reproducing them is the best check there is that the relation has been written down correctly.

Read the relation backwards and the protection level's real meaning appears. A 45 m sphere corresponds to about 10.1 kA, which is exactly why LPL III is described as intercepting flashes down to 10 kA. Anything weaker has a shorter striking distance, can slip inside the sphere, and can attach to a surface the method has declared protected. That is not a flaw being hidden; it is the residual risk the level explicitly accepts, stated as a current rather than as a probability. Choosing a higher level means choosing a smaller sphere, which means more air terminals more closely spaced, which means catching weaker flashes.

The honest limits. The electrogeometric model is an engineering abstraction fitted to field observation and laboratory long-spark work, not a derivation from field theory; different published versions use different coefficients and exponents, and the scatter in the underlying data is wide. The peak current of a future flash is unknowable — it is a broad distribution with a median near 30 kA and a long tail, so a protection system is designed against a percentile of that distribution and never against certainty. And the model treats the striking distance to a structure, to a mast and to flat ground as if they were the same, which more detailed treatments do not. None of that makes the method wrong. It makes it a method, with a stated residual risk, which is what a standard is.