About Lightning Protection (Rolling Sphere) Calculator
The lightning protection calculator implements the rolling-sphere method, the geometric basis of the air-termination design in IEC 62305-3 and NFPA 780. An imaginary sphere of a fixed radius is rolled over the structure and its air terminals; wherever it touches is a point a downward leader could strike, and the volume the sphere cannot reach is protected.
The sphere radius depends on the chosen lightning protection level, LPL I (20 m) being the most stringent and LPL IV (60 m) the least, or it can be derived directly from the minimum peak stroke current with R = 10 * I^0.65. For a single vertical air-terminal mast the tool computes the protected radius at ground, rp = sqrt(2*R*h - h^2), the protected area, the recommended mesh size and the protection angle, so you can size and space air terminals for a given level of protection.
How It Works
- Pick how the rolling-sphere radius is set: a lightning protection level (LPL I=20 m, II=30 m, III=45 m, IV=60 m) or a minimum peak stroke current, which gives R = 10 * I^0.65 metres for a current in kiloamperes.
- Enter the air-terminal (mast) height above the protected plane and the structure height. The protected radius at ground follows from the rolling-sphere geometry: rp = sqrt(2*R*h - h^2) while the mast is shorter than the sphere radius.
- When the mast height reaches the sphere radius the protected radius is capped at R, because a vertical rod cannot protect a circle wider than the sphere it deflects.
- The tool also reports the mesh size for the chosen LPL (5, 10, 15 or 20 m) and the protection angle, which decreases as the air terminal gets taller and is not applicable above the rolling-sphere radius.
Worked Example
A structure is protected to LPL II, giving a rolling-sphere radius R = 30 m. A vertical air-terminal mast 10 m tall protects, at ground level, a circle of radius rp = sqrt(2*30*10 - 10^2) = sqrt(600 - 100) = sqrt(500) = 22.36 m, a protected area of pi*22.36^2 = 1571 m^2. The mesh-method grid for LPL II is 10 m. Raising the mast to 30 m would make h equal R, so the protected radius is capped at 30 m and the protection-angle method no longer applies.
Formulas
- Rolling-sphere radius by LPL
R = 20 (I), 30 (II), 45 (III), 60 (IV) metres- Radius from peak current
R = 10 * I^0.65- Protected radius of a mast
rp = sqrt(2*R*h - h^2) for h < R; rp = R for h >= R- Protected ground area
A = pi * rp^2
Standards & References
- IEC 62305-3 (protection of structures against lightning)
- NFPA 780 (Standard for the Installation of Lightning Protection Systems)
- IEC 62305-1 (general principles, peak current vs. LPL)
Frequently Asked Questions
What is the rolling-sphere method?
It is a geometric design technique in which an imaginary sphere of a fixed radius is rolled over a structure and its air terminals. Any surface the sphere touches can be struck by lightning, while regions the sphere cannot reach are deemed protected. The radius is set by the chosen protection level or peak stroke current.
Why does a higher protection level use a smaller sphere?
A smaller sphere reaches into more crevices and touches more of the structure, so it intercepts strokes of lower peak current. LPL I uses a 20 m sphere to capture weaker, harder-to-intercept strokes, giving the highest level of protection; LPL IV uses a 60 m sphere and protects against only the larger strokes.
How is the protected radius of an air terminal found?
For a single vertical mast of height h with a rolling-sphere radius R, the protected circle at ground has radius rp = sqrt(2*R*h - h^2) as long as h is less than R. Once the mast reaches the sphere radius the protected radius is capped at R, because the sphere itself limits how wide a zone one rod can shield.
When should I use the mesh or protection-angle method instead?
IEC 62305-3 lets you combine three methods. The protection angle suits simple, low structures; the mesh method (5 to 20 m grid by LPL) suits flat roofs; and the rolling sphere is the most general and applies to complex shapes and tall structures where the angle method is no longer valid.