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Lightning Protection Design

Rolling Sphere Method · NFPA 780 / IEEE 998

When to use: Check whether a mast or shield wire of height h shields an equipment/point below it using the rolling sphere method — a sphere of radius R "rolled" across the ground and over the mast/wire tip. Anything the sphere can touch, other than the mast/wire tip itself, is exposed to a direct strike. Substation shield-wire and mast placement per IEEE 998/1243 uses this same geometry.

Preliminary educational check only. Final lightning protection system design per NFPA 780/IEEE 998 requires a qualified engineer's full analysis, including tower/structure interaction, ground grid coordination, and site-specific risk assessment.

Shielding Geometry
ft
equipment top
ft
mast/wire to point
ft
Key Formulas
(R−h)² + r² = R² (sphere on ground & mast tip)
r_ground = √(h(2R−h))
r(y) = √(h(2R−h)) − √(y(2R−y))
valid for 0 ≤ y ≤ h < R
shielded if x ≤ r(y)
Protected Radius at Ground
80.0
ft
Protected Radius at Point Height
27.3 ft
at y = 15 ft above ground
Results
MethodSingle vertical mast
Mast/wire height h40 ft
Rolling sphere radius R100 ft
Point horizontal distance x25 ft
Point height y15 ft
Protected radius at ground80.0 ft
Protected radius at height y27.3 ft
Margin (r(y) − x)2.3 ft
✓ SHIELDED
point within rolling-sphere protected zone
✓ VALID
geometry requires 0 ≤ y ≤ h < R
References
NFPA 780 — Standard for the Installation of Lightning Protection Systems
IEEE 998 — Guide for Direct Lightning Stroke Shielding of Substations
IEEE 1243 — Guide for Improving Power Line Lightning Performance
IEC 62305-3 — Protection Against Lightning: Physical Damage & Lightning Protection Levels I–IV

About the Lightning Protection Design Tool

This tool applies the rolling sphere method — the shielding analysis method used by NFPA 780 and, for substations, IEEE 998/1243 — to check whether a mast or shield wire shields a piece of equipment or point below it from a direct lightning strike. It computes the protected radius at ground level and at the actual height of the protected point, then compares that radius against the point's horizontal distance from the mast or wire.

How the rolling sphere method works

Picture a sphere of radius R rolling across the ground and over every mast, shield wire, and rooftop point on a site. Any point the sphere can touch — other than the tip of a mast or the top of a shield wire — is exposed to a direct strike; points the sphere cannot reach, because a taller mast or wire tip gets in the way first, are considered shielded.

For a single vertical mast of height h, the sphere touches both the ground and the mast tip simultaneously at a horizontal distance r_ground = √(h(2R−h)) from the mast — this comes directly from the right-triangle relationship (R−h)² + r² = R² for a sphere of radius R resting on the ground (center at height R) and grazing the mast tip. The same construction generalizes to any point at height y below the mast tip: r(y) = √(h(2R−h)) − √(y(2R−y)), valid for 0 ≤ y ≤ h < R. A point at horizontal distance x and height y is shielded when x ≤ r(y).

For a shield wire strung between two masts, this tool applies the same 2D cross-section geometry to compute the protected width on each side of the wire, treating the span as effectively straight — it does not account for catenary sag, which reduces the effective wire height (and therefore the protected width) toward mid-span on long spans.

Choosing a rolling sphere radius

NFPA 780 sets a standard rolling sphere radius of 150 ft (45.7 m) for ordinary structures, with a smaller, more conservative 100 ft (30.5 m) radius commonly applied to facilities containing hazardous or flammable materials, or to critical equipment where a tighter protected zone is warranted — the choice substations typically make per IEEE 998/1243 shielding guidance, since a smaller sphere radius yields a smaller protected zone and therefore a more conservative (safer) design. Internationally, IEC 62305-3 defines four Lightning Protection Levels (I–IV) with corresponding rolling sphere radii of 20/30/45/60 m (approximately 66/98/148/197 ft) — Level I is the most stringent (smallest radius, smallest protected zone).

Limitations — read before use

This tool checks a single mast or an idealized straight shield wire against a single protected point using only the geometric rolling sphere construction. A complete lightning protection system design per NFPA 780 or a substation shielding study per IEEE 998/1243 must also account for multiple masts/wires and their combined protected zones, shield-wire sag and dynamic swing under wind and fault current, tower/structure grounding and interaction with the station ground grid, the shielding failure rate and stroke current distribution for the specific site, and any applicable lightning risk assessment. Always have a qualified engineer perform or review the complete design.

Frequently asked questions

What is the rolling sphere method?

A geometric lightning-shielding analysis method, adopted by NFPA 780 and (for substations) IEEE 998/1243, that models the reach of a lightning stroke as a sphere of a defined radius rolling across the ground and over every mast, shield wire, and structure on a site. Any point the sphere can touch, other than a mast tip or shield-wire top, is considered exposed to a direct strike.

How do I choose the rolling sphere radius?

NFPA 780 uses 150 ft as the standard radius for ordinary structures and 100 ft for facilities with hazardous/flammable materials or critical equipment — substations commonly use the more conservative 100 ft value per IEEE 998/1243 guidance. IEC 62305-3 offers four internationally defined Lightning Protection Levels (I–IV) with radii of 20/30/45/60 m if you need to reference that framework instead.

Why does a smaller rolling sphere radius mean more conservative protection?

A smaller sphere can reach closer to the ground next to a mast or wire before its curvature carries it away, which shrinks the protected radius at every height. Choosing a smaller R therefore requires masts/wires to be taller, closer together, or more numerous to shield the same equipment — a more conservative (safer) outcome.

Does this tool replace a full lightning protection system design?

No. This is a preliminary educational shielding check using idealized single-mast or single-wire geometry. A complete NFPA 780 or IEEE 998/1243 design must evaluate the combined protected zones of every mast and wire on site, shield-wire sag and swing, ground grid coordination, and a site-specific lightning risk assessment — all performed by a qualified engineer.

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