Buried radials: two engines on the same dirt

Buried radials are the reason a lot of people keep NEC-5 around: it models wires inside real soil, and the counterpoise under a vertical is the classic case. momwire serves the same class — a Sommerfeld half-space with the wire’s fields solved inside the lower medium — so for the first time we can put the same antenna, the same dirt, the same card file through both engines and compare printed impedances.

This page is that comparison, done the careful way: convergence ladders on both sides (never single meshes), matched drive points, and every number below taken from printed engine output against momwire’s served answers. The class under test is the elevated-detached family: a vertical whose base sits above the ground (0.25–1 m), over one or four detached 5 m radials buried 15 cm deep, in average soil (ε_r 13, σ 0.005 S/m) at 7 MHz. Neither engine has a wire touching the interface here, so both are solving the same well-posed problem — real parasitic coupling through the soil, the Yagi mechanism pointed downward. (Why not the base-on-the-ground deck? That one is a different story, and momwire refuses it on purpose — see the counterpoise question on the momwire primer.)

The drop-in table

momwire’s EZNEC-dialect seam runs NEC-5 deck text directly — same cards, zero hand-translation, feed addressing included:

python -m momwire.eznec vertical-radials.nec printout.txt

Here is the resonant family (21 m center-fed vertical dipole, lower tip 0.25 m up, radials as labeled) through both readers of the same file. The engine columns are its own refinement ladder (×1 = 22 segments on the vertical, then ×3, ×8) plus the Richardson-extrapolated limit; “seam ×3” is momwire solving the identical ×3 card:

deck	seam ×1	seam ×3	engine ×1	engine ×3	engine ×8	engine → limit	|seam ×3 − limit|
no radials	100.54+19.70j	100.62+20.01j	98.74+12.28j	100.06+17.77j	100.42+19.21j	100.64+20.08j	0.07 Ω
1 radial	100.46+19.94j	100.55+20.25j	98.89+13.08j	100.21+18.62j	100.56+20.07j	100.76+20.95j	0.73 Ω
4 radials	100.09+20.43j	100.18+20.74j	98.84+14.56j	100.15+20.14j	100.50+21.60j	100.70+22.49j	1.82 Ω

The momwire columns are converged in quadrature, not just in mesh

An earlier version of this table was computed at n_qp_pair = 4, momwire’s cross-edge quadrature default when the study ran (August 2026). That mattered more than routine bookkeeping: momwire#760 had, at the time, read the cross-edge error at a lossy-soil interface as falling only as 1/n_qp — on momwire’s side only, and growing with the number of buried members meeting at a junction. Same side, same direction, and the same ordering as the residual in the last column, which made that residual unfalsifiable from this page. (That first-order reading was later corrected — the error is superalgebraic on every shipped deck, and the C/q was the bottom of one ladder read as a rate — but the correction does not change what had to be done here: sweep it.)

It has now been swept, q = 4 through 128, and the columns above are the converged answer (identical at 32, 64 and 128). The residual is not quadrature. Quadrature is worth 0.10 Ω on the four-radial deck — and 0.10 Ω on the no-radial deck, which has no buried wire at all. It is a common-mode shift, so it cannot produce a residual that grows by 1.75 Ω across that same span, and it does not: the four-radial-minus-no-radial spread was 1.75 Ω at n_qp_pair = 4 and is 1.75 Ω converged.

The delta instrument in the disagreement section is unaffected to four decimals, by the same cancellation.

Reproducing these rows: on a deck like this one — wire below the interface — momwire now chooses n_qp_pair = 32 for itself rather than the free-space default of 8, so the rows reproduce without setting the knob at all. The web UI leaves it on auto for the same reason, and sends nothing. Pin a number only to reproduce a specific older run; n_qp_pair = 8 was the shipped value before momwire 0.47.0 and lands within 0.02 Ω of the converged values above. Measured in antennaknobs#1068, default per deck since momwire#863.

Two things worth absorbing before any conclusion:

1. The engine’s coarse print is 7–8 Ω from its own converged value on this deck (98.74+12.28j at ×1 against 100.64+20.08j at the limit). A single-mesh cross-engine comparison on this class measures discretization error, not physics. Ladders or nothing.
2. Once both sides converge, the no-radial decks agree to a fraction of an ohm, and the residual grows with radial count — 0.07 → 0.7 → 1.8 Ω. That ordering is not noise; it is the one genuine disagreement this study found, and it gets its own section below.

Converged-vs-converged, the full panel

Running both engines’ ladders on the whole family (heights 0.25, 0.5, 1.0 m; no-radial reference, one radial, four radials) and extrapolating each side’s own ladder:

• Resonant family (~95–100 Ω): no-radial decks agree to 0.19–0.22 Ω; one radial 0.29–0.44 Ω; four radials 1.13–1.53 Ω.
• Insulated-base family (10 m vertical fed 4.67 m from the top, |Z| ≈ 960): 0.26–1.17 Ω converged — 0.03–0.12 % on a thousand-ohm reactive deck.

These panel columns come from momwire’s native builder rather than the seam above, and they are already converged in quadrature: n_qp_pair = 4 and 128 agree to 1.2e-4 Ω on all nine combinations, with q = 2 as a live control that does move. The sweep described above does not shift them.

For a class of antenna that people actually build — a vertical raised a little above its buried counterpoise — the two independently-derived, independently-coded formulations land within an ohm or so of each other, and within a fraction of an ohm when no buried wire is present.

The feed lesson (it scales as Z²)

Getting that agreement required matching drive points, not just geometry, and the cost of getting this wrong is worth naming because it bit us during this study.

A feed convention difference behaves like a small parasitic capacitance at the drive point: ΔZ ≈ −jωC·Z². On a resonant deck (|Z| ≈ 100) a half-picofarad of feed-region difference is invisible — a quarter of an ohm. On the insulated-base family (|Z| ≈ 960) the same convention difference is tens of ohms: momwire’s own three feed spellings spread ~26 Ω among themselves there, and mis-locating the drive by half a segment costs ~14 Ω. (We measured exactly that: an addressing convention put our comparison feed half a segment from the engine’s actual drive node for a while, and every high-Z comparison inherited the offset until it was found and fixed.)

Practical rules that fall out:

• Compare engines raw only on resonant decks. On reactive decks, compare at matched drive points and expect the feed-region convention to show at the Z² scale.
• On high-impedance decks, momwire’s knot feed (split the wire at the driven node, drive across the join) is the spelling that matches engine feed conventions; the smooth point feed differs by the parasitic-C class above.

The buried-radial coupling, three ways

Correction (2026-09-09). An earlier version of this section reported the engine’s buried-radial coupling at 2.8–5.2× momwire’s and attributed the gap to the engine’s below-ground fields. The engine column had been captured with its ground card’s two fields transposed — the setting its manual documents as not usable when wires go below the surface, the same capture defect found later on the buried-dipole decks. Re-run under the documented card, the two engines agree on the coupling to about 0.01 Ω on every deck and every mesh rung, and the attribution is withdrawn. The printed near-field observation below is unaffected by the card and is kept as a measurement; the inference that was drawn from it is not.

Subtract each engine’s no-radial reference from its radial decks at matched meshes and the feed convention cancels entirely. What remains is each engine’s opinion of the buried-radial coupling itself — and, under the engine’s documented below-ground card, they agree:

deck	height	engine ΔZ	momwire ΔZ
1 radial	0.25 m	−0.080+0.238j	−0.07+0.24j
1 radial	1.0 m	−0.038+0.094j	−0.04+0.09j
4 radials	0.25 m	−0.448+0.727j	−0.45+0.73j
4 radials	1.0 m	−0.208+0.303j	−0.21+0.30j

The engine values are the ×8 rung (176 segments on the vertical) and move by under 0.01 Ω from ×1 to ×8; the no-radial reference does not move at all between the two ground-card settings, which is the control that says the card touches only the buried conductors. A third reading landed on the same numbers in September 2026: momwire’s sinusoidal-Galerkin solver, which shares no fill code with its B-spline solver below the interface, gives −0.0746+0.2401j and −0.4499+0.7290j for the two 0.25 m decks — the B-spline values to four decimals.

The effect is small — single ohms at most on these decks, dominated by reactance, shrinking with height — and all three readings say so.

One printed-output observation survives from the earlier version, as a fact about the engine’s near-field tables on this deck class and nothing more. Against empymod, the open-source electromagnetic reference for layered media, momwire’s below-ground fields match to 0.5 %, with depth-decay profiles identical to three decimals (1 / 0.679 / 0.422 / 0.207 down the 0.15–2 m ladder at 1 m radius — both instruments). The engine’s printed near-field tables for the same points decay more slowly with depth (1 / 0.602 / 0.326 / 0.286) and at 2.5 m radius are non-monotonic (1 / 0.601 / 0.198 / 0.398). Those tables print the same under either ground-card setting. They are not the coupling: the impedances above are what the engine solves, and on those the two agree.

What to take away

• The elevated-detached class is served and cross-validated: same card files through both engines, converged agreement at the 0.2–2 Ω level, sub-ohm where no buried wire is present.
• Radial effects on an elevated vertical are genuinely small — single ohms at 15 cm depth, shrinking with height. If your feed is clear of the ground, your radials are a second-order refinement, and either engine will tell you so.
• Quote ladders. On buried-soil decks the coarse-mesh prints of either engine can sit many ohms from that engine’s own converged value.
• The buried-coupling delta agrees between the engines to about 0.01 Ω under the documented ground card (correction above).
• Since this page was written (September 2026) the below-ground reference has changed from another engine to a measurement: momwire gates Brown, Lewis and Epstein’s 1937 buried-radial screens, and its second reading underground is the same solver at a different basis degree. The validation page carries the current state.
• Where the two engines stand below ground (September 2026). On the 1937 geometry NEC-5’s radial-count law has the measured shape, steep at low radial count and flat past about thirty, and on a bonded-base vertical over buried radials the two engines agree to a fraction of an ohm in resistance. The NEC-5 column in the drop-in table above was captured with one setting of the engine’s ground card; with its documented below-ground setting the buried-radial decks move by up to 1.7 % in impedance — the same size as the coupling itself, which is why the coupling section carries a correction and the drop-in table’s converged agreement (0.2–2 Ω) does not change.

The companion piece on the momwire primer — the counterpoise question — covers the deck this page deliberately avoided: the vertical whose base touches the ground over detached buried radials, why that deck underspecifies its own physics, and why momwire refuses it rather than answering it a few ohms wrong.