An arch is range over time
A fish finder measures one thing per ping: how long until the echo comes back. That time is the slant range to whatever sent it, straight line, any direction inside the cone. The screen plots that range down the page and time across it, one ping per column.
Now move the boat over a fish that is holding still. As the fish enters the front of the cone it is a little further away than its depth. Directly underneath, the range is its true depth. Leaving the back of the cone, it is further away again. Far, near, far: that is the arch. Its top is the real depth; its tails are the cone's geometry.
range = √(depth² + along² + sideways²)
So an arch needs three things at once: the distance between boat and fish has to change, it has to change fast enough to curve but slow enough to take more than a few pings, and the fish has to be painted far enough from the centre of the cone for the range to change by something you can see. Each setup below breaks one of them.
Why you get a line instead
- Boat stopped. Parked boat, holding fish: the range is the same every ping, so the screen draws the same range forever. This is why fish under a boat at anchor, or on the ice, show as horizontal lines.
- Fish keeping pace. A fish moving with the boat at the same speed is the same as both standing still. Anything that follows the boat, such as a fish tracking a trolled bait, draws a line.
- Dead slow. The arch is still there, but the fish takes so many pings to cross the cone that a one-foot rise gets spread across most of the screen. It reads as a line with drooping ends. Speed up, or slow the scroll.
- Gain turned down. Only the loud middle of the beam paints, so the fish is drawn only while it is nearly straight below, where the range hardly changes. Turn the sensitivity back up and the same fish grows tails.
- Cone edge. A fish off to one side is only clipped by the edge of the cone. The boat crosses a short chord of it and the range barely changes: a short, flat smudge, drawn deeper than the fish really is.
The reverse also holds. A fish swimming under a parked boat draws an arch, because what matters is relative motion, not who is moving. Ashallow fish at running speed crosses the beam in a few pings and leaves a dash.
How long a fish stays in the beam
The arch's width on screen is how long the fish spends in the cone. For a fish straight under the track, holding still, with a 20° cone measured to its nominal edge:
| Fish depth | 0.5 mph | 1 mph | 2 mph | 3 mph | 5 mph |
|---|---|---|---|---|---|
| 10 ft | 4.8 s | 2.4 s | 1.2 s | 0.8 s | 0.5 s |
| 20 ft | 9.6 s | 4.8 s | 2.4 s | 1.6 s | 1.0 s |
| 30 ft | 14 s | 7.2 s | 3.6 s | 2.4 s | 1.4 s |
| 40 ft | 19 s | 9.6 s | 4.8 s | 3.2 s | 1.9 s |
t = 2 · depth · tan(cone/2) / speed. Deeper fish make wider arches because the cone is wider down there. Multiply by your unit's ping rate for the number of columns.
The cone has no hard edge
The cone angle on a transducer box is a convention: the angle where the beam has lost a fixed amount of power. Manufacturers do not all use the same cut-off. Sound keeps going past it, just weaker. Whether a fish out there gets painted depends on how loud its echo is and how much gain you are running. A big fish at high sensitivity paints well outside the printed cone; a small one at low sensitivity only paints near the middle. The same fish, same pass, draws a long curved arch or a short flat mark depending on one knob. Thecone coverage calculator works out both widths, printed and painted, for any cone, depth and fish.
In this model the nominal edge is where one-way power is down 3 dB, the beam falls off as a Gaussian, and the echo is counted twice (out and back). A 12-inch fish at 75% sensitivity paints exactly to the nominal edge.
Fish at the edge read deeper than they are
Because the screen plots slant range, anything off-axis is drawn at its distance, not its depth. A fish at the edge of the cone shows up deeper than it is. Near the middle of the cone the error is small. On a wide cone it is not:
| Cone angle | Fish really at | Screen shows | Error |
|---|---|---|---|
| 10° | 20 ft | 20.1 ft | +0.1 ft |
| 20° | 20 ft | 20.3 ft | +0.3 ft |
| 40° | 20 ft | 21.3 ft | +1.3 ft |
| 60° | 20 ft | 23.1 ft | +3.1 ft |
shown = depth / cos(cone/2)
The dead zone near the bottom
The bottom straight below you is the closest bottom there is, and it comes back far louder than any fish. Every echo from further than that lands in the bottom band. A fish close to the bottom near the edge of the cone is further away than the bottom directly under you, so it gets drawn into the bottom, not above it. Load the dead zone setupto see a fish that is there and never shows.
Over a flat 30 ft bottom, a fish at the nominal cone edge disappears into the bottom band when it is within this height of the bottom:
| Cone angle | Hidden within |
|---|---|
| 10° | 0.1 ft of bottom |
| 20° | 0.5 ft of bottom |
| 40° | 1.8 ft of bottom |
| 60° | 4.0 ft of bottom |
height ≤ bottom · (1 − cos(cone/2)), before the pulse length (about 0.5ft here) makes it a little worse. Wider cones find more fish and hide more of the ones on the bottom.
What this model leaves out
- One target, flat hard bottom. No schools, no timber, no slope, no soft bottom. A sloping bottom moves the dead zone; a soft one makes the bottom band thinner and weaker.
- Echo strength is fish length squared, nothing else. Real target strength is dominated by the swim bladder and depends on species and the angle the fish is presenting. Two fish of the same length can differ by several dB.
- Gaussian beam, no side lobes. Real transducers leak some energy at wider angles, which can paint strong targets well outside the main cone.
- Perfect range compensation. Units apply time-varied gain so a fish reads equally bright at any depth. This model assumes it works perfectly and ignores absorption, so frequency only enters through the cone angle you pick.
- Fixed ping rate and scroll.15 pings per second, one column each. Real units change both with depth and settings, which changes how wide every arch is drawn.
- The sensitivity scale is ours. 75% is 0 dB of gain here and each percent is 0.36 dB. Your unit's percent means something else.
- Untested by sonar anglers so far. The geometry is textbook. Whether the screen looks right to someone who reads one every weekend is a question we haven't answered yet. If it looks wrong to you, tell us what you see on yours.
The lure side of the site works the same way: The Fish decides whether a lure gets eaten and says why not, and How it works documents that model the way this page documents the sonar one.
More from the sonar model
- Sonar cone coverage calculator How wide the beam is at depth, and how much of it a given fish paints in.
- Can you tell fish size from an arch? Why a bigger fish off to the side draws the same mark as a small one underneath.
- 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.
- 83 kHz vs 200 kHz: which frequency should you use? Frequency sets cone angle, not depth limit. See coverage and target-separation tradeoffs side by side.