Where your coil
actually looks
Three things decide whether a nugget answers you: where the coil is looking, which way the gold is lying, and whether your pulse gives it time to wake up. Miss any one and you walk straight over it. Everything below is live — drag the sliders.
Read the depths as rough indications, not a spec. The model is anchored to a nominal mid-range detector on average ground. It is not tuned to any particular machine, coil or brand — including our own — and it takes no account of your ground, EMI, timings or how slowly you swing. Real depth can easily be half or double what you see here. Use it to see which way things move when you drag a slider, not as a number to expect in the field.
The Cone
where the coil is lookingYour coil doesn't look straight down in a neat tube. Close under the winding it's wide. Go deeper and the useful patch — where a nugget is still loud enough to hear — pinches down to nothing at maximum depth. Drag the nugget down and watch it go quiet.
Overlap your swings by at least half a coil width. The wide patch you get on shallow targets is a trap — the deep ones sit in a window that shrinks to a point, so a sloppy fast sweep only ever finds the easy gold. Slow down and overlap more when you're chasing depth.
The Lie of the Gold
which way it's sittingMost alluvial gold is flat. A flake lying flat under the coil gives the field a big face to push against, and it answers loudly. Tip that same flake up on its edge and the response can fall away to almost nothing. Worse — flatter gold also fades faster, so it's harder for any timing to catch. Drag the model to spin it.
You can't turn the gold over — but you can cross-sweep the same patch at right angles. A flake that's edge-on to one sweep direction often presents its face to the other. On patchy shallow ground this finds gold that a single-direction grid walks straight past.
The Wake-Up
does the pulse give it timeA PI detector shoves current through the coil, then snaps it off and listens to the echo ringing in the target. Big gold rings slowly — it needs a long push to get going. A short pulse snaps off before big deep gold has properly woken up. That's the trade: short timings hear tiny gold, slow timings reach big gold.
There is no single best timing. Short timings win on small shallow gold and on bad ground, because listening early rejects the slow ground signal. Slow timings win on big deep gold, because they give it time to ring. If a patch has produced small gold on a short setting, it is worth walking again on a slow one — you are not detecting the same targets.
The maths behind it
Coil sensitivity
Because a mono coil transmits and receives on the same winding, reciprocity makes the response to a small target proportional to the square of the coil's own field per amp:
On axis this reduces exactly to S/S₀ = 1/(1 + (z/a)²)³ for coil radius a. Maximum depth therefore scales as z_max ∝ (α·a⁴)^(1/6) — a very weak lever. Doubling target strength buys only 2^(1/6) = 1.12× the depth.
The looking-cone
Far from the coil the field goes dipolar and the half-power width solves (w+3) = 2w⁴ with w = 1+(ρ/z)², giving ρ/z = 0.452 — a half-angle of 24.3°. Near the coil (z/a ≲ 2) the footprint is much tighter, around half a coil diameter, so the cone only opens up properly once you're deeper than about two coil radii.
Pulse charge and decay
For a linear current ramp of duration T at drive V, a target of time constant τ carries a ramp-driven current that saturates as (1−e^(−T/τ)), and then gains a step at switch-off from flux conservation. Combining both and sampling at delay Δ:
For T ≪ τ the bracket collapses to T²/2τ. Note the consequence carefully: at fixed peak current I₀ = VT/L, the signal goes as I₀·L·T/2τ — so halving the pulse length halves the signal on a long-τ target. Voltage does compensate linearly, but only up to whatever your hardware will stand.
Orientation and flatness
A flake responds along its polarizability axes, and for a monostatic coil the response weights go as the square of the field projection:
θ is the angle between the field and the flake's normal, so θ = 0 is lying flat — the strong case, since the field then drives large eddy loops across the full face. Edge-on, loops must close through the thickness, so both α and τ collapse; here α⊥/α∥ and τ⊥/τ∥ are both taken as ≈ 1/(aspect ratio).
Time constant from mass: for a sphere τ ≈ μ₀σr²/π² using σ_Au = 4.1×10⁷ S/m. Flattening at fixed mass gives τ ∝ r·t, and since r²t is constant that means τ ∝ (aspect)^(−1/3) — flatter gold rings for a shorter time, which is why thin flakes are hard for every timing.
What this model does not include
- Ground signal. Soil viscous remanent magnetism has a very long time constant, which is the real reason early sampling exists. None of it is modelled here.
- Real targets have a spectrum of time constants, not one. Single-τ is a teaching simplification.
- Coil inductance and resistance are idealised — the current ramp is taken as linear and unsaturated, which stops being true for long pulses at low drive.
- Solid gold assumed. Real nuggets are porous and often ironstone-bound, so measured ring times run shorter than the figures here.
- Depth figures are indicative only. The whole depth scale hangs off one arbitrary reference point — a 5 g nugget read at 30 cm on an 11″ mono, chosen as an ordinary mid-range figure. It is not a measurement of any real detector, not a claim about any brand or model, and not a claim about our own upgrades. Shift that anchor and every depth on the page moves with it. What survives the shift, and what the page is actually for, is the shape: how depth responds to coil size, mass, lie and timing.
- Ground conditions, EMI, coil type, threshold setting, headphones and sweep speed are all outside the model, and in the field they matter as much as anything in it.
Educational illustration of scaling behaviour. Not specific to any detector, brand or model, not a measure of our own upgrades, and not a depth guarantee.