IEC 62305-1 (rolling sphere geometry)6 min read

Worked Example: Protection Radius of a Single Air Terminal Using the Rolling Sphere Method

A simple geometric check — how far from the base of a 10 m mast does an IEC 62305 Class III lightning protection zone actually extend?

Scenario

LPS protection classClass III
Rolling sphere radius for Class III45 m
Air terminal (mast) height10 m

Step-by-step calculation

Step 1: Confirm the mast height doesn't exceed the sphere radius

h ≤ R?
10 m ≤ 45 m
Yes — the simple single-mast formula applies (if h > R, a mesh/multi-terminal study would be required instead)

Step 2: Apply the rolling-sphere protection-radius geometry

This is the radius at ground level within which the sphere cannot touch the ground without first touching the mast tip — geometrically, a sphere resting on the ground and just grazing the top of the mast.

rp = √(2·R·h - h²)
√(2 x 45 x 10 - 10²) = √(900 - 100)
rp = √800 = 28.28 m

Result summary

CheckRequirementActualStatus
Mast height within sphere radiush ≤ R10 m ≤ 45 m✓ PASS
Protection radius at ground leveln/a (this is the computed result)28.28 m✓ PASS
A single 10 m air terminal designed to Class III provides a protection radius of 28.28 m at ground level — meaning equipment or structures within that radius of the mast base are considered shielded from direct strikes under the rolling-sphere model.

Key insight: Protection radius grows with mast height, but not linearly — doubling the mast height doesn't double the protection radius, because the geometry is governed by a square-root relationship. There are real diminishing returns to just building a taller mast, which is why multi-terminal or mesh-conductor systems are typically more practical than a single very tall mast for protecting a large area.

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Frequently asked questions

What happens if the mast is taller than the rolling sphere radius?

The simple single-mast formula stops being valid once mast height exceeds the sphere radius for the chosen LPS class — physically, the sphere can then roll past the tip and touch a wider area at a different geometry, which requires a full multi-terminal or mesh-conductor rolling-sphere study rather than the single closed-form equation used here.

Why does a higher protection class (I) use a smaller sphere radius than a lower class (IV)?

A smaller rolling sphere radius represents a more stringent protection level — it means the model assumes lightning can strike from a shorter final jump distance, which is associated with lower-current, more localized strikes that are harder to intercept. Class I (20 m radius) is therefore the most protective and demanding classification, while Class IV (60 m) is the least stringent.

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