Basis of calculation: IEC 62305-3:2024 (Ed. 3.0)
| LPS class | II |
| Method | Rolling sphere |
| Sphere radius | 30 m |
| Rod height above the reference plane | 2 m |
| Protected radius at the reference plane | 10.8 m |
| Perimeter air-termination conductor | 128.0 m on the roof edge |
| Conductor minimum cross-section (Table 7) | 50 mm² tape / 50 mm² round |
| Rod height that best protects the roof edge | 10.0 m |
| Rod spacing at the roof edge (d_edge) | 12.0 m |
| Proposed air-termination rods | 12 |
| Candidate positions considered | 12 |
| Candidate lattice pitch | 13.3 m |
| Roof within a rod's protected radius | 100% |
| Rod coverage proof | exact — every point of the roof shown to lie within a rod's protected radius (no grid; see note) |
| Lateral protection angle α (D.5.2.3.3) | 15° |
| Lateral protected width w = r/10 | 3 m |
§5.2.1: for all types of air terminals only the real physical dimensions of the metal air-termination systems shall be used for the determination of the volume protected. Every protected volume in this design is computed from the entered physical height alone — no enhanced or extended radius is claimed for any device. §5.2.1 also states that radioactive air terminals are not allowed.
§5.2.1: the individual air-termination rods should be connected together at roof level to ensure current division.
An air-termination conductor runs around the roof edge, following the outline: 128.0 m. §5.2.2.1 requires air-termination components to be located at roof level on corners, exposed points and edges, and §5.2.1 requires the individual rods to be connected together at roof level to ensure current division — the roof edge is where both are satisfied at once, and where practice routes the connection. This is not additional material: it specifies a conductor the design already implied.
The rolling sphere always touches the roof edge. That is geometry — it holds for every building and nothing placed mid-roof changes it. D.5.2.2.2 makes a positioning adequate when the sphere touches only the ground and the air-termination system, so a conductor on the edge is what makes the contact *there* a contact with the air termination rather than with the structure.
It protects the edge line only. A conductor lying flush in the roof plane obstructs nothing above it: a sphere coming straight down touches it at one tangent point, and the roof inward of the edge is still the rods' job. Nor is it protected space — an air termination is where the strike is meant to land, not volume that is safe — so the protected volume drawn for this design is the same with the conductor as without it.
Minimum cross-sectional area, Table 7 (§5.6.2) for Copper / tin-plated copper: 50 mm² solid tape or 50 mm² solid round. The Materials section resolves the same table for every LPS conductor, including the stranded option where the table gives one.
The length is the perimeter of the roof outline this design was given, and nothing more: no allowance for laps, joints, fixings, down-conductor connections, upstands or roof plant, and no route around anything on the roof, because no design here knows what is on the roof. It is the geometry to take off from, not a cut length to order.
The roof edge is governed by a different figure from the interior. A sphere resting on the ground beside the building reaches the roof edge from 28.3 m away in plan; a rod tip at 22.0 m above ground is reached from 28.9 m. Rods on the edge keep that sphere off it while they are no more than d_edge = 2·√(a₁² − a₀²) = 12.0 m apart — against the 10.8 m that governs the interior. The two are not the same number and neither substitutes for the other.
d_edge is largest at a rod height of exactly R − H = 10.0 m for this class and building, and falls away on both sides of it. Taller is not better at the roof edge: past 20.0 m a rod of that height protects the edge at no spacing at all, because the sphere that clears its tip clears the roof with it.
These rods carry the roof's interior and nothing else. §5.2.2.1 requires air-termination components on corners, exposed points and edges, and the perimeter conductor above passes through every corner and along every edge — so that requirement is met by the conductor, and the rods answer the one question left: bring every roof point within 10.8 m of a rod. Without the conductor the rods would have to hold the edge as well, and there would be 12 of them here instead of 12.
12 of the 12 lattice positions were kept. The selection is computed the same way for the same inputs, so re-running this design gives this layout again — but it is one covering layout, not the only one, and a rod moved to suit the roof is the engineer's call to make against the same criterion.
The layout is proved to cover rather than sampled for coverage. Any uncovered piece of roof would be an open region whose border is made of walls and of arcs of the rods' reach, and such a border can only change from one to the other at a corner of the outline, where a rod's reach crosses a wall, or where two rods' reaches cross. A piece with none of those would have to be ringed by a single unbroken circle, which cannot happen inside a closed outline. So that finite set of places decides the whole roof, and every one of them was tested — no grid is involved and nothing between the tested places is assumed. Two limits, stated because the claim is only worth what they leave: a point exactly at a rod's reach counts as outside it throughout, so a point on the boundary of the protected volume is treated as unprotected rather than protected; and where a tested place is a knife-edge contact rather than a gap, its surroundings are probed at a finite number of points to decide whether real area opens there, so a gap narrower than roughly a quarter-turn at that contact would not be reported. Both are properties of the layout as drawn: move or shorten any rod and neither this proof nor the coverage percentage applies until the design is recomputed. That percentage — the "Roof within a rod's protected radius" row above — is not a second proof. It answers the same question on a grid, by code that shares none with this argument, so where this proof closes it can only agree — read it as a check on the tool, not as further evidence about this roof. It is reported with its spacing because it is the number that says how far short a layout falls in the case this proof does not close.
The rod positions above are a proposed layout, computed from the LPS class, the plan outline and the rod height by the positioning rule of §5.2.2.1 — rods on corners, then edges, then the field, on a square grid no coarser than the spacing one rod's protected radius supports. They are not a survey and not an instruction: the engineer may move them, and the coverage figure is what any alternative should be judged against — but the coverage figure and the covering proof are both about the layout as drawn, and a rod moved, shortened or removed voids them until the design is recomputed against the positions actually adopted.
Natural air terminations are not counted. Metal parapets, copings, handrails, ladders and existing masts commonly protect a roof already, and §5.2.5 allows them; none of them is an input here, so the layout may put a rod where something on the roof already does the job. Check the layout against what is actually up there before pricing it.
The coverage figure is measured and not assumed: 960 roof points on a 1.00 m grid, each tested against the rolling-sphere criterion of §5.2.2 — a point is protected when the sphere resting on it cannot avoid touching the air termination, and every one of them is protected — so it reads 100% with no "at least" in front of it. Elsewhere the figure is a lower bound, because the only obstacles counted are the rods above and anything else on the roof can add protection but never remove it; here there is nothing left above it for a bound to allow for. What it remains is the grid's answer rather than the roof's: whether every point of the roof is covered is a different question, and the "Rod coverage proof" row above is what answers it.
§5.2.3: lateral impacts of flashes to the side are considered negligible for structures up to 60 m measured from ground level, and this structure is 20 m. However, the same clause states that elements significantly protruding the facade can be endangered (e.g. balconies, cameras, antennas), and NOTE 2 adds that such elements on structures up to 60 m are rarely endangered. No air termination is *required* on the vertical surfaces at this height — the requirement in §5.2.3 is scoped to structures taller than 60 m — so this is a judgement for the designer, about protruding elements this design does not know about.
D.5.2.3.3 proposes a simple approach for those elements: the positioning is adequate if all parts of the element to be protected are below a surface generated by a straight line at α = 15° to vertical (Figure D.6), with the horizontal width of the protected area limited to w = r/10 = 3 m at class II. α is independent of the class of LPS; only w moves with it. This design states those two quantities and positions nothing on the facade. w is a width limit rather than a facade solution — D.5.2.3.3 offers the method as a supplementary part of protected area, "especially useful just below the roof".
This design does not lay out the lateral air termination. It carries no facade elevation, no balcony, camera or antenna position, and no facade conductor route — the quantities above size that work, they do not specify it.
| Rod | x (m) | y (m) | h (m) | r_p (m) |
|---|---|---|---|---|
| 1 | 0.00 | 0.00 | 2.00 | 10.77 |
| 2 | 0.00 | 24.00 | 2.00 | 10.77 |
| 3 | 40.00 | 0.00 | 2.00 | 10.77 |
| 4 | 40.00 | 24.00 | 2.00 | 10.77 |
| 5 | 0.00 | 12.00 | 2.00 | 10.77 |
| 6 | 13.33 | 0.00 | 2.00 | 10.77 |
| 7 | 13.33 | 24.00 | 2.00 | 10.77 |
| 8 | 26.67 | 0.00 | 2.00 | 10.77 |
| 9 | 26.67 | 24.00 | 2.00 | 10.77 |
| 10 | 40.00 | 12.00 | 2.00 | 10.77 |
| 11 | 13.33 | 12.00 | 2.00 | 10.77 |
| 12 | 26.67 | 12.00 | 2.00 | 10.77 |
| Perimeter | 128 m |
| Preferred distance between down conductors | 10 m |
| Down conductors | 13 |
| Largest gap between adjacent conductors | 9.85 m (of the even spacing this design proposes) |
IEC 62305-3:2024 §5.3.3 requires only that an attached LPS have not fewer than two down conductors. Distributing them around the perimeter is stated as a recommendation, explicitly subject to architectural and practical constraints, and both equal spacing and the Table 5 distances are preferred values rather than limits. The count above is derived from the preferred distance for this class, which is the conservative reading; a layout that departs from it is a departure from a preference, and the design records it as one.
Fit a test joint on each of the 13 down conductors at its connection to the earth termination, openable for measurement and closed in normal use (§5.3.6).
| k_i (class) | 0.06 |
| k_c (current division) | 0.44 — 13 down conductor(s) |
| k_m (material) | 1 — Air |
| Length l | 20 m |
| Required separation s at the air-termination tip | 0.648 m |
| Point considered | 20 m above ground |
| Down-conductor spacing c | 9.85 m (assumed equally spaced) |
| Per-level k_c | level 1: 0.337, level 2: 0.177 |
| Required separation s (general) | 0.309 m |
| Simplified comparison | 0.528 m (general saves 42 %) |
s is a distance at a point, and this design has two worth quoting. §6.3.1 measures l from the point where the separation distance is to be considered, along the air termination *and* the down conductor. The figure above is for the down-conductor run; at the tip of the rod the path is longer and the current has not yet divided among the down conductors, so k_c = 1 over the rod (Annex B, Figure B.4 a) — the values of k_c are considered from the point of strike). Separate any metal installation by the figure for *its own* elevation; this design carries no position for any metal installation, so it cannot say which applies where — a proposed rod layout locates the air termination and nothing else. The governing figure below is the larger of the two, because a single distance applied everywhere has to be the worst case.
General approach assumes all down conductors interconnected by ring conductors at the stated spacing (§5.3.4, Figure B.3).
The segment sum runs to the earth termination (bonding at ground level only — conservative). Where the internal installation is bonded at a ring level, only the segments above that level apply (Figure B.3, cases a–e).
Every internal metal installation closer than s to a down conductor must be bonded or the distance increased.
This separation distance is not altitude-corrected. §6.3.2 requires a correction for an LPS installed at high elevations, following IEC 60071-2. Site elevation is not an input to this tool and no correction has been applied, so where the site is at elevation, read §6.3.2 against it and adjust s accordingly.
s is the one figure in this design that the finished drawing can correct. Everything else above is fixed by the class and the building; s is computed from the conductor run length and, on the general approach, from the down-conductor and ring spacings — and the values used here for those are stated defaults, not measurements of a layout. Two of them can move s the wrong way: k_c1 grows with the down-conductor spacing c, and rings further apart than assumed make the computed s non-conservative. Once the layout is drawn, re-run this design with the measured figures.
| Arrangement | Type B (ring electrode) |
| Soil resistivity ρ | 1500 Ω·m |
| Minimum length l_1 | 19.0 m |
| Ring requirement | mean radius of enclosed area r_e ≥ 19.0 m |
| Effective ring radius r_e | 18.6 m (from footprint, ring ≈ 1 m out) |
| Ring criterion | not met — additional electrodes required |
| Additional electrodes | 13 × horizontal ≥ 0.4 m, or vertical ≥ 0.7 m |
The minimum lengths may be disregarded where an earthing resistance of the Type A arrangement below 10 Ω is achieved — measured at a frequency different from the power frequency and its multiples, to avoid interference (§5.4.2.2).
Ring in contact with the soil for at least 80 % of its length, buried ≥ 0,5 m deep, about 1 m from the external walls (§5.4.3).
Vertical electrode lengths above include the 0,5 m that §5.4.3 adds to every vertical electrode on top of the l_1-derived figure; horizontal lengths carry no such addition.
Connect the additional electrodes to the ring where the down conductors connect, as equidistantly as possible.
| LPS conductor material | Copper / tin-plated copper |
| Solid tape, minimum | 50 mm² |
| Solid round, minimum | 50 mm² |
| Stranded, minimum | 50 mm² |
| Air-termination rods | 176 mm² solid round |
| Earth-electrode material | Copper / tin-plated copper |
| Earth rod (solid round) | Ø 15 mm |
| Earth rod (tubular) | Ø 20 mm |
| Buried earth conductor | 50 mm² |
| Earth plate | 500 × 500 mm |
All LPS components (conductors, rods, electrodes, clamps) shall meet IEC 62561-2 mechanical/electrical/corrosion requirements (Table 7/8 note a).
Air-termination rods where mechanical stress such as wind loading is not critical may be reduced to 9,5 mm diameter, 1 m long (Table 7 note c).
Copper solid round 50 mm² (8 mm Ø) may be reduced to 28 mm² (6 mm Ø) where mechanical strength is not essential; reduce fastener spacing accordingly (Table 7 note b).
A buried copper earth electrode shall not be used in contact with the structure's steel members, pipes or piles — corrosion (Table 8 note g).
| Bonding conductor material | Copper |
| Bars ↔ bars / bar ↔ earth termination | 16 mm² (Table 9) |
| Internal installations ↔ bonding bar | 6 mm² (Table 10) |
Install the main bonding bar in the basement or at ground level, accessible for inspection, and connect it to the earth-termination system (§6.2.2 a).
Structure length 40 m exceeds 20 m — use a ring bonding bar or several interconnected bonding bars (§6.2.2 a).
Bond additionally at every point where the separation distance s of the section above cannot be kept (§6.2.2 b). Keep bonding connections as direct and straight as possible.
Live conductors of internal systems are bonded via SPDs — coordinate per IEC 62305-4.
| People within 3 m of down conductors | yes (assumed) |
| Assessment | Protection measures required |
| Touch-voltage measures | Insulate exposed down conductors to 100 kV, 1,2/50 µs impulse withstand (e.g. ≥ 3 mm cross-linked polyethylene), or apply physical restrictions / warning notices |
| Step-voltage measures | Equipotentialize with a meshed earth-termination system, or apply physical restrictions / warning notices within 3 m of the down conductors |
The insulation withstand voltage should be considered in wet conditions (§8.1). Signage shall conform to ISO 3864-1.
Alternative exemption: a measured contact resistance within 3 m of the down conductors of at least 100 kΩ also brings the hazard to a tolerable level. §8.1 c) sets that over the area of a typical footprint (0,02 m²) for touch voltage; §8.2 c) states the 100 kΩ for the soil surface layer without giving an area. A 5 cm layer of insulating material, e.g. asphalt, generally achieves it (§8.1 NOTE 2 / §8.2 NOTE 1).
| Site environment | Sensitive internal systems / high occupancy |
| Visual inspection | every year |
| Complete inspection (incl. electrical testing) | every year |
Also inspect: during construction (components that become concealed), after LPS installation, after alterations or repairs, and after a known or suspected lightning strike to the structure (§7.4).
Periodic checks: deterioration and corrosion of air-termination elements, conductors and connections; earthing resistance of the earth-termination system; condition of connections, equipotential bonding and fixings (§7.4).
Testing on a 14–15-month cycle is acceptable where earth-resistance readings across different seasons are wanted (D.7.2.2). Consider improving the earthing system when measured resistance rises over successive inspections.
Record all inspection and test results and keep them with the LPS design documentation for the property manager (§7.4).
| Step | Formula | Values | Result | Reference |
|---|---|---|---|---|
| Rolling-sphere radius | r = r(class) | class II | 30 m | IEC 62305-3:2024 §5.2.2, Table 2 |
| Rod protected radius (rolling sphere geometry) | d = √(h·(2r − h)) | h = 2 m, r = 30 m | 10.8 m | Rolling-sphere geometry, IEC 62305-3:2024 §5.2.2 |
| Perimeter air-termination conductor | l = perimeter of the roof outline | 4-sided outline | 128.0 m | IEC 62305-3:2024 §5.2.1, §5.2.2.1 |
| Rod spacing that protects the roof edge | d_edge = 2·√(h(2R − 2H − h)); best at h = R − H | R = 30 m, H = 20 m, h = 2 m | 12.0 m (best height 10.0 m) | Rolling-sphere geometry at the roof edge, IEC 62305-3:2024 §5.2.2 |
| Proposed rod layout | s ≤ s_max = √2 · r_p; rods on corners, edges, then the field | r_p = 10.77 m, s_max = 15.23 m | 12 rods selected from 12 lattice positions at 13.3 m | IEC 62305-3:2024 §5.2.2.1; rolling-sphere geometry |
| Measured coverage of the rod layout | protected ⟺ dist((x, y, H + r), air termination) < r | 960 roof points at 1.00 m spacing | 100% protected | Rolling-sphere criterion, IEC 62305-3:2024 §5.2.2 |
| Rod height needed to match the class mesh on a square grid | h = r − √(r² − (w_m/√2)²) | w_m = 10 m, r = 30 m | 0.85 m | Rolling-sphere geometry, IEC 62305-3:2024 §5.2.2 |
| Lateral protected width | w = r / 10 | class II, r = 30 m | 3 m | IEC 62305-3:2024 D.5.2.3.3, Figure D.6 |
| Down-conductor count | n = max(2, ⌈perimeter / spacing⌉) | perimeter = 128 m, spacing = 10 m (class II) | n = 13 | IEC 62305-3:2024 §5.3.3, Table 5 |
| Separation distance (simplified) | s = k_i · k_c · l / k_m | k_i = 0.06, k_c = 0.44, l = 20 m, k_m = 1 | s = 0.528 m | IEC 62305-3:2024 §6.3.2, eq. (6), Table 13 |
| Separation distance at the air-termination tip | s = k_i / k_m · (1 · h_rod + k_c · l) | k_i = 0.06, k_m = 1; k_c = 1 over the 2 m rod (the current has not divided at the point of strike), then k_c = 0.44 over l = 20 m | s = 0.648 m | IEC 62305-3:2024 §6.3.1, eq. (5); Annex B, Figure B.4 a) |
| k_c per level (ring-interconnected down conductors) | k_c1 = 1/(2n) + 0.1 + 0.2·∛(c/h₁); k_c2 = 1/n + 0.1; k_c3 = 1/n + 0.01; k_c4… = 1/n | n = 13, c = 9.8 m | k_c1 = 0.337, k_c2 = 0.177 | IEC 62305-3:2024 Annex B, Figure B.3 |
| Separation distance (general approach) | s = k_i/k_m · Σ (k_cn · l_n) | k_i = 0.06, k_m = 1; Σ = 0.337·10 + 0.177·10 | s = 0.309 m | IEC 62305-3:2024 §6.3.1, eq. (5); Annex B |
| Minimum electrode length | l_1 = l_1(class, ρ) | class II, ρ = 1500 Ω·m | l_1 = 19.0 m | IEC 62305-3:2024 §5.4.2, Figure 5 |
| Type B ring criterion | r_e ≥ l_1 | l_1 = 19.0 m | r_e ≥ 19.0 m | IEC 62305-3:2024 §5.4.2.3, eq. (1) |
| Effective ring radius | r_e = √(A/π), A = (L+2)·(W+2) | L = 40 m, W = 24 m | r_e = 18.6 m | IEC 62305-3:2024 §5.4.2.3 (r_e of the enclosed area) |
| Type B additional electrodes | l_r = l_1 − r_e ; l_v = (l_1 − r_e) / 2 + 0.5 m | l_1 = 19.0 m, r_e = 18.6 m; + 0,5 m per vertical electrode (§5.4.3) | l_r ≥ 0.4 m or l_v ≥ 0.7 m, × 13 | IEC 62305-3:2024 §5.4.2.3, eq. (2)/(3), §5.4.3 |