Lightning Protection Formulas: Rolling Sphere
Lightning protection formulas: rolling sphere radius by protection level, protected radius of a vertical air terminal, and the radius at a lower height.
The formulas
| To find | Formula |
|---|---|
| Protected radius at ground level | r0 = √(h × (2R − h)) |
| Protected radius at height hx | rx = √(h × (2R − h)) − √(hx × (2R − hx)) |
| Condition | h ≤ R and hx ≤ h |
R is the rolling sphere radius in metres, h the height of the air terminal above the reference plane and hx the height of the surface you want to protect. The rolling sphere radius depends on the protection level of the system (IEC 62305-3 uses 20, 30, 45 and 60 m for levels I to IV, as in the table below). The standard has the full design rules, and a risk assessment comes first.
Rolling sphere radius by protection level
| Protection level | Rolling sphere radius R |
|---|---|
| I | 20 m |
| II | 30 m |
| III | 45 m |
| IV | 60 m |
Worked example: a 10 m rod, level III
A vertical air terminal 10 m high with R = 45 m. The equipment to protect is 4 m high.
- r0 = √(10 × (2 × 45 − 10)) = √800 = 28.28 m at ground level
- The term at 4 m is √(4 × (90 − 4)) = 18.55 m
- rx = 28.28 − 18.55 = 9.737 m protected radius at 4 m height
Protected radius at ground level by rod height
| Rod height | Level I | Level II | Level III | Level IV |
|---|---|---|---|---|
| 5 m | 13.23 m | 16.58 m | 20.62 m | 23.98 m |
| 10 m | 17.32 m | 22.36 m | 28.28 m | 33.17 m |
| 15 m | 19.36 m | 25.98 m | 33.54 m | 39.69 m |
| 20 m | 20 m | 28.28 m | 37.42 m | 44.72 m |
Frequently asked questions
What does the rolling sphere method do?
It rolls an imaginary sphere of radius R over the structure. Anything the sphere can touch may be struck, and anything it cannot touch is shielded by the air terminals.
Why is the radius smaller at a higher level?
Level I is the highest protection. It uses the smallest sphere, which can slip into more gaps and so asks for more air terminals.
Can I use the formula when the rod is higher than R?
No. For h above R the formula does not apply and the protected radius is limited by the sphere radius. Use the standard.
Does this replace a lightning risk assessment?
No. The risk assessment chooses whether you need protection and which level. These formulas only give the geometry for a chosen level.
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