16 · The counterpoise question: when the right answer is a refusal

Ask any antenna modeler what they want from real-soil support and the answer is a picture: a quarter-wave vertical, base at ground level, over a fan of radials buried a few inches down. momwire serves buried wires. momwire serves ground-contact verticals. Ask it for the two together — a contact vertical over detached buried radials — and it refuses, by name, with a sentence that ends in suggestions.

That refusal is not a missing feature. It is the most-measured single decision in this codebase, and this chapter is the story: three probe campaigns, four candidate physics spellings, two convergence ladders, one feed-addressing erratum that forced the whole thing to be re-derived — and no candidate that converged to a physics the deck can express.

What the deck doesn’t say

Follow the current. At the base of a contact vertical, I(0) is not zero — charge arrives at the interface and must go somewhere. In a deck with no buried wires, momwire’s contact model (chapter 9’s reflection machinery, momwire#151) continues it as a scaled image: a fiction, but a safe one, because every observer is above the ground and the image reproduces what they see. A buried radial breaks the safety: it is an observer inside the soil, parked 15 cm below the fiction.

What should it see? The real system puts the base current into the soil as a spreading conduction current — the physics of a ground electrode. And here the deck goes silent: a spreading current needs an electrode geometry, and “a wire end touching z = 0” doesn’t specify one. A thin wire tip is a terrible electrode — the point-contact spreading resistance is ~1/(4σa), which at σ = 0.005 S/m and a = 1 mm is tens of kilohms. Real installations don’t work that way and real installers know it: the radials are bonded to the vertical precisely so the current has a conductor to spread through. The detached deck asks for the coupling of an electrode it never describes. It underspecifies its own physics.

What the licensed engine can be asked

NEC-5 has no documented spelling for this deck. Its below-ground ground card leaves a wire that ends on the interface with no basis function there — the conductor reads as open-circuited — and its bonding card is documented for decks with no buried wires. A vertical that continues through the surface into a buried hub is served by both engines and they agree to a few percent; a vertical that stops on the surface above detached buried wires is a question the engine’s documented cards do not pose. So there is no engine answer to match here. The question is whether the deck specifies its own physics, and that is what the campaign measured.

The campaign: four spellings, two ladders, one erratum

momwire’s candidate serve was the continuation-consistent spelling: keep the contact fiction on the vertical’s own account (chapter 9’s column, unchanged), couple the buried radial through the designed cross-medium kernels, omit the end terms the fiction cannot support. Laddered to convergence on one and four radials, it converges — to an answer that depends on a spreading current into the soil the deck never describes, and that no external reference can adjudicate.

(An addressing erratum was found along the way: the EX card drives a segment’s far node, not its center, and for a while our cross-engine comparisons fed momwire half a segment from the actual drive point — on a reactive deck that half-segment is worth ~10 Ω. Feed conventions scale as Z², and the lesson is now load-bearing in the test suite.)

Could any added physics pin that spreading current down? Four families, each measured, each excluded for its own reason:

1. Solve the soil current exactly — respell the contact as a real crossing junction. Convergent, served, and a different antenna: that is the bonded deck (below), not this one.
2. A solved stub under the continuation spelling — not a convergent object (its answer is set by the mesh, not the physics).
3. A prescribed line ghost — closable per-deck to 0.001 Ω, but the fitted strength does not transfer between decks (0.48+0.36j on one radial, 0.36−0.07j on four): whatever sink strength the engine’s answer embodies, it is solved per deck, not a physical constant momwire could adopt.
4. A derived Born electrode (hemispherical spreading, first principles) — a measured null.

And the ghost’s fitted strength says why: purely reactive with one collector, gaining a real part as collectors multiply — that is what a real spreading current looks like as radials arrive to intercept it. It is not what any fixed source constant looks like. The physics the answer depends on is exactly the physics the deck never specified. There is nothing consistent to spell.

The refusal, and what it hands you instead

So momwire refuses the detached contact+buried combination — not because the answer is unknown, but because every honest answer depends on a spreading current the deck never specifies, and the stake it would flow through isn’t in your deck. The refusal sentence itself hands you the three served respellings:

• Bond the radials. Respell the screen to rise to the surface and junction-join the vertical at z = 0. The crossing junction is served (one above wire over N below wires, buried-hub spelling included) — and it is what a real installation is.
• Lift the feed. An elevated vertical over detached buried radials is served, converged, and cross-validated against the licensed engine at the 0.2–2 Ω level — the full study is on the antennaknobs site: Buried radials: two engines on the same dirt.
• Solve the buried structure alone.

One last piece of engineering honesty: the refusal is gated in the test suite in both of its copies, with the deck geometry banked beside it, so a change that lifts it fails a test that names the deck rather than quietly serving an answer nobody adjudicated. A refusal this load-bearing doesn’t get to rot.

An engine that answers every deck is wrong somewhere and silent about where. momwire’s bet — the same one chapter 15’s instrument made — is that attributable accuracy beats universal answers: serve what converges, refuse what the deck cannot specify, and leave a measurement trail either way.