Corona Inception Voltage: Why the Shape of an Electrode Decides When Air Starts to Conduct

1. In 60 seconds

• A lightning laboratory cannot reproduce a thundercloud. It reproduces the elementary event — a discharge across a known air gap — and measures it with a reference instrument: the standard sphere gap (IEC 60052).
• That instrument has one job: to tell you at what voltage the air breaks down (BD). It is a metrology tool, built to calibrate high-voltage measuring systems, and its tables contain nothing else.
• In 2016, two Indian researchers (Madhu & Kanchanapalli) ran 250 mm spheres and a point on the same bench, at the same gaps, on the same day, and recorded four quantities instead of one — including the voltage at which the air starts to conduct: the corona inception voltage (CIV). measured
• Their data gives the numbers this page is built on: at 80 mm, a grounded point starts ionising at 24 kV and arcs at 51.8 kV; a grounded 250 mm sphere starts at 45 kV and arcs at 120 kV. Same bench, same day, same air. measured

2. The vocabulary of the electric discharge

When the voltage between two electrodes rises, the air does not fail in a single instant. It walks through stages, and each stage has a name.

Electric field. The force a charge feels, in volts per metre. Air begins to ionise when the local field reaches roughly 3 MV/m (≈ 30 kV/cm) at a surface.

Charge density. The charge per unit area on a conductor. On a smooth conductor it is uniform; on an edge or a point it concentrates. This is why two electrodes of the same size and a different shape do not behave the same way.

Corona / corona inception voltage (CIV). The first measurable step: a local ionisation of the air around the electrode, audible as a hiss, sometimes visible as a faint bluish glow, producing ozone and microamps of current. The voltage at which it appears is the CIV.

Streamers. Ionised filaments launched from the region of the highest field, towards the other electrode. They are the direct precursors of the arc, and they always start where the field is locally the strongest.

Leader / upward tracer. At lightning scale, a streamer becomes a leader: an ionised, heated channel that propagates in jumps. The cloud sends a downward leader; objects on the ground respond by launching an upward tracer. The attachment point is the object whose upward tracer starts first — which is why the onset voltage matters as much as the breakdown voltage.

Breakdown / arc (BD). The end of the process: the air becomes fully conductive, the arc closes the gap, the voltage collapses.

3. The sphere-gap method: the reference instrument

Since 1960 (IEC 60052, taken up by IEEE 4), the sphere gap has been the standard of high-voltage measurement: two metal spheres of known diameter D, a known spacing d, and a breakdown voltage reproducible to ±3 % for spacings below 0.5·D — so reproducible that it is used to calibrate other instruments (voltmeters, dividers, probes).

“Air gaps constructed and used in accordance with this standard represent IEC standard measuring devices in accordance with IEC 60060-2 and are primarily intended for performance checks of high voltage measuring systems.” — IEC 60052:2002, §1 documented

That single sentence says what the instrument is for, and what its tables contain. They contain one quantity: the disruptive discharge voltage. No corona inception, no corona extinction, no point configuration — the standard requires the electrode shanks to be free of sharp edges “in order to avoid corona discharge”: the sphere gap is specified to be corona-free over its range of use. documented — IEC 60052:2002, §§4.2.1 and 7, tables 2–3

That reproducibility is itself an experimental demonstration: the voltage at which air breaks down does not depend on distance alone — it depends on the geometry of the electrodes. If that were not the case, the sphere gap would not be a standard. It is precisely because two smooth spheres of known diameter, properly installed, always break down at the same voltage for the same spacing that they can be used to measure.

The empirical formula of the sphere gap (Ungureanu & Nemțoi, 2014, equation 4, itself drawn from the classical literature) gives the breakdown voltage between two identical spheres:

U = 27.2 · δ · r · [1 + 0.54/√(δ·r)] · (d/r) / { 0.25 · [d/r + 1 + √((d/r+1)² + 8)] } (kV, d and r in cm)

with d the spacing, r the radius of the spheres and δ the relative air density. Numerical check: for 25 cm spheres (r = 12.5 cm) — d = 1 cm → ~30.5 kV (table: 31.0–31.7) ; d = 5 cm → ~137.6 kV (table: 137–138). The formula reproduces the tables to better than ~4 % over 1–16 cm (actual deviations −0.3 % to −3.8 %). theoretical, verified against the tables

Two limits of the formula are worth remembering, because they explain what the tables do:

• As the radius r becomes very large, the term 0.54/√(δ·r) tends to 0 and the denominator to 1: the voltage tends to U ≈ 27.2 · δ · d — the uniform-field limit (~27 kV/cm peak, the classic 30 kV/cm dielectric strength of air). The larger the sphere, the more uniform the field in the gap, and the closer the breakdown voltage gets to that limit.
• As the radius r shrinks, the breakdown voltage falls: the field concentrates on the small sphere, and breakdown starts at its surface well before the uniform-field limit can be reached.

3.1 The official table — IEC 60052:2002, 250 mm spheres, one sphere earthed

U50 disruptive discharge values, kV peak — AC 50 Hz, full lightning impulse and negative switching impulse, DC of both polarities (standard conditions 20 °C, 101.3 kPa) documented — IEC 60052:2002, Table 2:

3.2 The classic tables — two spheres at high voltage (symmetric gap)

kV peak, 20 °C, 760 torr (= 101.3 kPa), AC / DC / impulses, accuracy ±3 % for spacings below 0.5·D documented — classic tables, identical to the original BS/IEC tables:

Reading — the effect of diameter: at a fixed spacing, the breakdown voltage rises with the diameter of the spheres and then saturates as the field becomes quasi-uniform. At 10 cm spacing: 248 kV (25 cm spheres) → 263 (50 cm) → 266 (100 cm) → 267 kV (200 cm). At 5 cm spacing the saturation is already reached at 25 cm — 137–138 kV whatever the diameter. The standardised diameters run from 2 to 200 cm (2 / 5 / 6.25 / 10 / 12.5 / 15 / 25 / 50 / 75 / 100 / 150 / 200 cm) documented.

The 207 kV in bold — two 250 mm spheres at 8 cm, which is the 80 mm gap used throughout this page — is the reference value the calculator is calibrated on (§6).

4. Madhu & Kanchanapalli, 2016 — from one number to four: the corona, measured

Madhu, V., & Kanchanapalli, B. — “Measurement of Air Breakdown Voltage Using Standard Sphere Gap Method”, Journal of Electrical Engineering — measured — Read the full study (PDF, 6 pages)

Same hardware — 250 mm spheres, one electrode earthed — with one difference: they raised the voltage slowly and watched. At each spacing from 5 to 80 mm they recorded four successive events: the corona inception voltage (the hiss), the visible corona, the corona extinction voltage, and the breakdown voltage. Conditions: AC 50 Hz, 31.1 °C, 760 mmHg (= 101.3 kPa), absolute humidity recorded; measured values corrected back to standard conditions (20 °C, 101.3 kPa) with the air-density factor Kd and the humidity factor Kh = K^w — the correction procedure IEC 60052 itself prescribes.

They then ran three more electrode shapes at the same spacings, on the same bench, the same day: sphere–point (sphere at high voltage, point earthed), point–sphere (point at high voltage, sphere earthed) and square-section rod–sphere.

Onset and arc, side by side, on the same bench (kV) measured — arc values corrected to standard conditions, onset values as measured:

Note on the absolute scale. The bench reads 0.58 × the reference tables (120.0 kV against 207 kV at 80 mm; 51.8 against 89) — most likely an RMS rather than a peak reading. The correction the authors applied (Kd, Kh) fixes their test conditions, not this offset. Their ratios are reliable; their absolute volts are not — which is why the calculator carries their ratios over to the reference scale, and never the reverse. measured + hypothesis on the cause

The two quantities no standard tabulates. The bench recorded two more, and neither exists in IEC 60052 — both are read on the same measured column as the onset figures above. The corona extinction voltage, measured as the voltage is brought back down: at 80 mm the 250 mm sphere goes out at 28 kV, far below the 45 kV at which it started. The relation holds at every spacing and in all four configurations — the extinction voltage is always below the inception voltage measured; once the discharge has started, the space charge it has already deposited sustains the field that a cold gap would not have theoretical. And the visible corona: around the point a faint glow appears a few kilovolts above the onset (24 kV → 31 kV at 80 mm), while on the 250 mm sphere it was never seen, at any spacing — detected, measured, and invisible measured.

5. Reading the data

5.1 The like-for-like comparison

Both series share the same 250 mm sphere at high voltage, the same spacings, the same day, the same correction. The only thing that changes is the shape of the grounded electrode.

At the same distance, in the same air, an object’s shape alone shifts the voltage at which it starts conducting by a factor of ~2, and the voltage at which it arcs over by a factor of ~2.3. measured

5.2 Onset and arc: the ratio is not constant

At 5 and 10 mm no CIV was recorded at all, in any of the four configurations: the gap went straight to breakdown. When the field is nearly uniform, the discharge has no separate beginning — onset and breakdown are the same event. This is also why a “corona-free” reference instrument (§3) is possible, and why it cannot serve as a corona experiment. measured + theoretical

5.3 What holds, whatever the configuration

1. Hierarchy. Point < sphere–point < sphere–sphere — and it survives swapping which electrode is at high voltage: the point–sphere series starts ionising at 22 kV at 80 mm against the sphere's 45 kV. The sharp electrode always starts first, the large sphere always last. measured + documented
2. Saturation with size. Enlarging the sphere raises the breakdown voltage until the field between the electrodes becomes quasi-uniform, approaching ~27 kV/cm × spacing — the dielectric strength of air. At 5 cm, 25 cm spheres and 200 cm spheres are indistinguishable (137–138 kV). documented — the uniform-field limit of §3, measured.

6. Run the numbers yourself

The interactive block sits here. It takes a configuration (point / equal spheres / asymmetric spheres), a sphere diameter up to 250 mm, and a gap range (10 - 80 mm) or an explicit list, and returns one row per gap with three columns:

The exact method behind that last column. The calculator does not use the empirical formula of §3, but the exact electrostatic solution: the maximum surface field is obtained by summing the image charges of the two spheres (method of images, solution of Laplace’s equation), and breakdown occurs when that field reaches the critical surface field E_crit = 31.65 kV/cm (Peek radius correction), calibrated exactly on the reference value for two 250 mm spheres at 80 mm — the 207 kV of §3.2. The empirical formula serves as an independent cross-check. calculator method

The point column deserves its own word. It is not a model: it is the 2016 bench’s measured sphere–point curve placed on the reference scale (all seven tabulated points match the measurement to better than 0.2 %). And that is forced, not chosen: the method above, which reproduces the sphere tables to about 2 %, fails completely for a point. At a realistic tip radius of 0.5 mm it returns a few kilovolts where the bench measured ninety; to make it fit, the “point” would have to be a 52 mm ball. Breakdown at a sharp electrode is governed by streamer propagation, not by a surface-field criterion. The same instrument that defines the volt for industry therefore says nothing about a sharp electrode: what a point does has to be measured.

The calculator’s headline answers, for reference:

7. Evidence status — what is established, estimated, or ours

8. References

Primary

1. Madhu, V., & Kanchanapalli, B. — “Measurement of Air Breakdown Voltage Using Standard Sphere Gap Method”, Journal of Electrical Engineering (jee.ro) — 250 mm spheres, four configurations, 5–80 mm, CIV / visible corona / extinction / BD. — Read the full study (PDF, 6 pages) (the source of every CIV figure on this page)

Standards and tables

2. IEC 60052:2002 — Voltage measurement by means of standard air gaps (3rd edition; 1st edition 1960).
3. IEEE Std 4 — High-Voltage Testing Techniques.
4. Sphere-gap reference tables, two spheres at high voltage (20 °C, 760 torr = 101.3 kPa).

Method

5. Ungureanu, C., & Nemțoi, L. M. — “Peak Voltage Measurements Using Standard Sphere Gap Method”, Advances in Electrical Engineering, Hindawi, 2014 — source of the empirical formula of §3. (Its own 150 mm sphere measurements are not used on this page.)

Continue reading

• Tesla’s lightning protection method — why a rounded protector does not attract lightning
• US Patent 1,266,175 — the full 1918 text
• Tesla Has New Pointless Lightning Rod — The Electrical Experimenter, October 1918
• The Fallacy of Franklin’s Pointed Lightning-Rod — The Electrical Experimenter, February 1919