Under the track, bigger fish do draw longer arches
Start with the case the folk rule is built on. Every fish straight under the boat, 25 ft, 20° cone, 2 mph, 85% sensitivity:
| Fish length | Arch length | Pings | Peak echo |
|---|---|---|---|
| 4 in | 0.3 s | 4 | +0.1 dB |
| 8 in | 3.0 s | 45 | +6.1 dB |
| 12 in | 3.8 s | 57 | +9.6 dB |
| 16 in | 4.3 s | 65 | +12.1 dB |
| 24 in | 4.9 s | 74 | +15.6 dB |
| 32 in | 5.3 s | 80 | +18.1 dB |
A louder echo clears the display threshold further out from the centre of the beam, so a big fish is painted across more of the cone and stays on screen longer. Peak echo is how far the strongest return clears the threshold. If every fish swam straight under your transducer, arch length would be a fair size gauge.
Off the track, the same arch can be any size
They don't. A fish off to one side is crossed along a shorter chord of its painted circle and never comes closer to the centre of the beam than its sideways distance allows. Both cut the arch down. Move a big fish out far enough and its arch shrinks to exactly the one a small fish draws dead centre. Every row here draws a 3.0 s arch, the same as an 8-inch fish straight under the boat at 25 ft, 20° cone, 2 mph, 85% sensitivity:
| Fish length | Off track | Arch length | Peak echo | Top reads |
|---|---|---|---|---|
| 8 in | 0 ft | 3.0 s | +6.1 dB | 25.0 ft |
| 12 in | 3.4 ft | 3.0 s | +5.9 dB | 25.2 ft |
| 16 in | 4.5 ft | 3.0 s | +5.8 dB | 25.4 ft |
| 20 in | 5.2 ft | 3.0 s | +5.7 dB | 25.5 ft |
| 24 in | 5.7 ft | 3.0 s | +5.7 dB | 25.6 ft |
| 30 in | 6.3 ft | 3.0 s | +5.6 dB | 25.8 ft |
| 36 in | 6.7 ft | 3.0 s | +5.5 dB | 25.9 ft |
Arch length matches exactly, by construction. The peak echo also lands within a fraction of a dB, and that part is not a coincidence. In this model, how long a fish stays painted and how strong its loudest return is are both set by the same quantity: how far its echo clears the threshold at its closest approach to the centre of the beam. For small angles the two are locked together:
(arch length · speed / 2)² ≈ depth² · (cone/2)² · peak / 6
With peak in dB over the threshold and the cone in radians. Read it as: once you know depth, speed and cone, arch length and echo strength are the same measurement made twice. A second clue about size isn't there to be had. The only remaining difference is the top of the arch: the off-track fish reads a little deeper, because the screen plots slant range. That is a fraction of a foot here, and you don't know the true depth to compare it against.
How exact the twin is depends on the cone
The small-angle lock loosens as the cone widens. Matching a 24-inch fish to an 8-inch one at 25 ft:
| Cone | 24 in fish off track | Peak echo weaker by | Top reads deeper by |
|---|---|---|---|
| 12° | 3.3 ft | 0.1 dB | 0.2 ft |
| 20° | 5.7 ft | 0.4 dB | 0.6 ft |
| 40° | 12.9 ft | 1.6 dB | 3.1 ft |
| 60° | 24.1 ft | 3.3 dB | 9.7 ft |
On a wide cone the big fish has to sit so far out that its echo comes back a few dB weaker and its top reads noticeably deeper. That is a different mark from the small fish underneath, but the difference points the wrong way: the bigger fish comes back weaker, not stronger. Narrow cones make arches more comparable; they do not make them a ruler.
Depth stretches every arch
The beam is wider the deeper you go, so the same fish stays in it longer. Arch length for a fish straight under the track, 20° cone, 2 mph:
| Fish length | at 10 ft | at 20 ft | at 30 ft | at 40 ft | at 60 ft |
|---|---|---|---|---|---|
| 6 in | 0.9 s | 1.8 s | 2.8 s | 3.7 s | 5.5 s |
| 12 in | 1.5 s | 3.1 s | 4.6 s | 6.1 s | 9.2 s |
| 20 in | 1.9 s | 3.7 s | 5.6 s | 7.5 s | 11.2 s |
A 6-inch fish at 40 ft draws a 3.7 s arch; a 20-inch fish at 10 ft draws 1.9 s. Comparing arch lengths at different depths compares the cone, not the fish. Boat speed scales every number the same way: half the speed, twice the length.
What would tell them apart
The missing number is where the fish is sideways. Anything that measures that removes the ambiguity: a second beam aimed differently, or a sonar that draws a picture across the track instead of down it. This page models one downward beam, so it can't show you those; it can only show you why one beam isn't enough.
The same reasoning applies to fish-symbol modes that put a small, medium or large icon on screen. Whatever a unit's algorithm does, a single 2D return gives it the same two clues this model has. We haven't modelled any brand's algorithm and make no claim about one.
What this model leaves out
- Echo strength is fish length squared, nothing else. Real echoes are mostly the swim bladder, and depend on species and on whether the fish shows you its side or its head. That adds several dB of scatter between same-length fish, which makes size calls harder than this page shows, not easier.
- Arch thickness is not modelled as a clue. The strips draw every mark with the same pulse length. On real units thickness also changes with the pulse and with how the fish is oriented; this page makes no claim about it.
- Holding fish, a steady boat, no bottom. Both fish hold still at the same depth and the boat runs a straight line at constant speed. A swimming fish changes arch length; seethe arch simulator for that.
- Smooth Gaussian beam, perfect range compensation, 15 pings per second, our sensitivity scale. The same assumptions as the arch simulator.
- Untested by sonar anglers so far. If your screen disagrees with this,tell us what you see.
More from the sonar model
- Why your fish are lines, not arches The interactive simulator: drag a boat over a fish and watch the mark form.
- Sonar cone coverage calculator How wide the beam is at depth, and how much of it a given fish paints in.
- Why sonar shows fish deeper than they are Slant-range geometry: how much deeper an off-track fish reads, by cone and depth.
- What speed should I drive for arches? Find the speed window where your depth and cone produce clean arches, not dashes or flat lines.