Lightning Rolling-Sphere Zone of Protection
The ground area a lightning mast or air terminal shields, by the NFPA 780 rolling-sphere method: roll a sphere of radius R (150 ft standard) over the structure -- lightning strikes wherever it touches, and a mast of height h <= R protects a ground circle of radius d = sqrt(2 R h - h^2). A 30 ft mast with the 150 ft sphere protects a 90 ft radius (about 25,400 ft^2). A single-mast estimate; two masts protect the overlapping zone between them, higher than either alone, and a mast taller than R caps at R with side-flash exposure above. Sizes the zone only, not the down-conductor, bonding, or grounding a complete system needs. NFPA 780 and a lightning-protection engineer govern.
Formula and source
protected_radius = sqrt(2 x R x h - h^2) for mast height h <= sphere radius R (capped at R for h >= R); protected_area = pi x radius^2. R = 150 ft standard.
NFPA 780 Standard for the Installation of Lightning Protection Systems (the rolling-sphere method, 150 ft standard radius), by name; NFPA 780 and a lightning-protection engineer govern.
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