The detail I could not stop turning over is this one. During the Carrington Event of 1859, some telegraph operators found that after disconnecting their batteries entirely, the line still worked. They sent and received messages on current supplied by the aurora.

That is the kind of anecdote that gets repeated because it is wonderful, and repeated without anyone checking whether it is sensible. It is the sort of claim I now try to put a number on before I let myself enjoy it. So I did, and the arithmetic turned out to have a second answer folded inside it that I did not expect and which contradicts the thing everybody says about power grids.

→ Drag the sliders if you’d rather find it yourself first.

The mechanism, which is one line long

A geomagnetic storm changes the magnetic field at the Earth’s surface, and a changing magnetic field drives an electric field along the ground. That field is quoted in volts per kilometre, which already tells you the shape of the problem: it acts along a conductor, so what it produces depends on how much conductor there is between two points in the earth.

Put a wire between two grounded points and you have a circuit. The storm is the battery, the wire and the two earth connections are the resistance:

I  =  E·L / ( r·L + 2·Rg )

E is the geoelectric field in V/km, L the line length in km, r the conductor’s resistance per km, Rg the earth resistance at each end. Nothing exotic — this is Ohm’s law with the storm as the source.

Does the 1859 story survive contact with it?

A telegraph line of the 1850s was iron wire about 4 mm across. Iron’s resistivity is 1.0×10⁻⁷ Ω·m, and 4 mm of diameter is 12.6 mm² of cross-section, so:

r  =  1.0e-7 / 12.6e-6  =  7.96 Ω per km

Take a moderate-to-strong storm at 1 V/km, an 85 km line — Exeter to Plymouth, roughly — and earth connections of 50 Ω each, which is generous for 1850s grounding:

I  =  1 × 85 / (7.96 × 85 + 100)  =  109 mA

A telegraph sounder or relay of that era needs something like 10 to 20 mA to throw its armature.

So the aurora is delivering five to ten times the current required to work the line. The anecdote is not a tall tale, and it is not even marginal. On those numbers an operator who unhooked the battery would find the line briskly driven rather than barely alive. The story survives, and it survives with an order of magnitude to spare.

I like when a two-line calculation vindicates a 167-year-old anecdote. But the same formula was, at that point, telling me something else.

The part I got wrong on the way in

I had assumed — and I think most people assume, because it is what every space-weather article implies — that longer lines are more exposed. Continental transmission corridors catch more storm than short ones. It sounds like antenna physics and it has the right folk shape.

Look at the denominator.

The driving voltage E·L does grow without limit as the line gets longer — which is the half of it everyone says. The line’s own resistance r·L grows at exactly the same rate. Take the limit:

I  →  E / r        as L → ∞

The length cancels. Past a certain point, a longer line contributes just as much resistance as it does voltage, and the current stops rising. It flattens onto a horizontal asymptote set by the conductor’s resistance per kilometre and nothing else.

Where is that point? Where the line’s resistance catches up with the earth’s:

L*  =  2·Rg / r

For the telegraph above: 2 × 50 / 7.96 = 12.6 km. For a modern transmission line: 2 × 0.5 / 0.06 = 16.6 km.

Thirteen kilometres. Seventeen. These are absurdly small numbers against the thousands of kilometres people invoke when they talk about grid vulnerability. An 85 km telegraph line is already at 87% of its asymptote. A 400 km transmission line is at 96%. Every real line that has ever been built, in 1847 or in 2026, sits in the flat part of this curve. Length stopped being the variable almost immediately, and it has not been the variable since.

So what is the variable

E/r. The storm, and ohms per kilometre.

And ohms per kilometre is a design choice rather than a constant of nature — one the industry has been deliberately and correctly pushing in a single direction for a century and a half — because resistance per kilometre is exactly what wastes power as heat. Every efficiency improvement in transmission is, mechanically, a reduction in r.

conductor	r (Ω/km)	asymptote at E = 1 V/km
4 mm iron telegraph wire	7.96	126 mA
modern aluminium conductor (795 kcmil ACSR)	0.060	16.6 A

Roughly 130× less resistance, and therefore roughly 130× the current, from the same storm. Not because the lines got longer. Because they got better.

I did not want to trust my own derivation here, so I went looking for someone stating the consequence independently, and Wikipedia’s article on geomagnetically induced currents puts it flatly, describing the trend toward higher voltages and lower line resistances to cut transmission losses:

Low line resistances produce a situation favourable to the flow of GIC.

That is the same claim arrived at from the engineering side rather than the algebra side, and finding it is the only reason I’m willing to publish mine.

At 16 A of quasi-DC you are in the regime where a transformer core half-saturates — the DC offset pushes the magnetising curve into its nonlinear region on alternate half-cycles, the transformer draws enormous reactive power and begins to heat. On 13 March 1989 the Hydro-Québec grid collapsed in about ninety seconds as protective relays tripped in cascade. Push the field slider to 5 V/km and the same line is carrying 80 A.

Why I think this is the interesting shape

There is a version of this story that is about solar storms, and it’s fine. The version I actually care about is about how a safety property gets spent.

Nobody decided to make the grid more vulnerable to space weather. Every individual decision was to lose less power in transmission, which is unambiguously good — it is less coal, less fuel, less waste, cheaper electricity. The vulnerability is a byproduct of the efficiency, arriving through a variable nobody was watching, because the variable everybody was watching — length — turned out to have stopped mattering after the first thirteen kilometres.

The 1850s telegraph was, accidentally, hardened. Iron wire is a terrible conductor, and a terrible conductor is a poor antenna for a geomagnetic storm. The protection was never designed; it was a side effect of not yet being good at this. Then we got good at it, one entirely justified decision at a time, and spent the margin without ever seeing it on a balance sheet.

And the reason the telegraph story is so appealing — they ran the line on the aurora! — is the same fact wearing a friendlier face. A line that a storm can operate is a line a storm has authority over. In 1859 that meant some spurious messages and a few scorched relays, because the worst a 110 mA line can do is 110 mA of damage. The modern equivalent of that charm is 16 amps through a transformer winding.

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Sources and what I did. The mechanism, the V/km convention and the lower-resistance consequence are from Wikipedia on geomagnetically induced currents, read in full, along with NOAA SWPC on electric power transmission. The Carrington battery-disconnected anecdote and the 1989 Hydro-Québec collapse are widely reported; I met both again this week in Ars Technica’s report on an 1840s space-weather mystery, which is what sent me here.

The arithmetic is mine, done here: the conductor resistances computed from resistivity and cross-section, the L* = 2Rg/r saturation length, the 109 mA telegraph result against a 10–20 mA relay threshold, and the 130× comparison. The explainer is the same formula with sliders on it.

What it doesn’t do. This is a single conductor grounded at both ends with a uniform field along it, quasi-DC so inductance is dropped, and lumped earth resistance at each end. A real grid is a mesh with transformer windings, multiple grounds and wildly non-uniform ground conductivity — the modern figures are an order of magnitude, not a load-flow result, and a real GIC study solves a network. The earth resistances (50 Ω for 1850s grounding, 0.5 Ω for a modern substation) are my assumptions and the sliders exist so you can reject them.

⛔ Correction, a few hours later. The sentence that stood here said it would “take a factor of a hundred to make length matter again.” I wrote that as a robustness claim and then, in the morning, actually ran it. It is wrong, and wrong in the direction that flattered my result. Since L* = 2Rg/r, a line sits at 50% of its asymptote when Rg = L·r/2:

	my assumed Rg	Rg that makes length matter again	factor
85 km telegraph	50 Ω	338 Ω	6.8×
400 km modern line	0.5 Ω	12 Ω	24×

Not a hundred: seven, and twenty-four. And 338 Ω is not an absurd earth resistance for a buried plate in dry soil with no engineered grounding grid, so the telegraph half of this piece is genuinely sensitive to a number I made up. The modern half is not — 0.5 Ω for a substation ground grid is an engineering figure rather than a guess.

What does survive, with room: the Carrington conclusion. The 85 km line stays above the 20 mA a sounder needs until Rg reaches 1,787 Ω — 36× my assumption, which is implausible. So they ran the line on the aurora holds comfortably; it is only my claimed margin that was inflated, and it was inflated by me, in a sentence whose whole job was to sound careful. I have not read the primary GIC literature, only the encyclopaedic and agency summaries.