Scanning sonar

The sonar sweeps from −30° to +30° and back. It measures the distance to the first surface along an ideal, infinitely narrow sound ray. There is no background wall. No hit within 5 m means no echo; 5 m is only the range limit. The circle has a radius of 0.37 m. The equilateral triangle has sides of approximately 0.58 m and a height of 0.50 m. Both can be moved. Where objects overlap in bearing, the nearest surface is detected. Points update only when a new measurement is taken at that bearing, including after moving or hiding an object.

Sampling: The angular step Δθ is the spacing between adjacent measurement bearings. The measurement rate (ping rate) fₚ is the number of transmitted measurement pulses per second; each ping yields at most one distance value here. It is neither the sound frequency nor the electronic sampling rate of the received signal. The beam sweeps at a constant 20°/s: 3 seconds each way, 6 seconds for a return sweep. Angular step and ping rate are linked: Δθ = ω / fₚ, with ω = 20°/s. Changing either value adjusts the other. Coarse sampling can miss small objects. Changing a setting clears the plot and starts a new scan. A smaller angular step gives denser spatial sampling. Actual angular resolution also depends on beam width; range resolution depends on bandwidth and pulse shape, among other factors. These effects are not simulated.

Small clutter objects: Six fixed objects, each 3.6 cm in diameter, produce geometrically calculated echoes when a measurement ray hits them. Their initial positions lie between coarse measurement bearings: at 2 measurements/s they are missed; at 40 measurements/s they are detected unless a nearer object obscures them. Unwanted echoes from real objects are called clutter here. They are neither random measurement noise nor false echoes created by a high ping rate. A higher rate reveals more detail but can make the display less clear without selecting relevant targets. Coarse sampling can also detect small objects when they lie at suitable bearings. Colours identify known model objects; a real sonar does not automatically recognise their shapes or identities from these colours.

Echo ranging: r = c · Δt / 2, where c is the speed of sound and Δt is the round-trip travel time. Here r is calculated geometrically; sound travel time is not animated. Every geometric hit is assumed to produce a detectable echo. Actual detectability depends on size, material, orientation, wavelength and receiver threshold, among other factors. Range noise is optional; finite beam width, diffraction, multipath and angle-dependent echo losses are omitted. This is a simplified model of sonar using sound, not radar using electromagnetic waves.

Measurement uncertainty: When enabled, each new hit receives an independent normally distributed distance error with zero mean and standard deviation σ = 0.015 m + 0.01 · r. At 3 m this is 4.5 cm; about 68% of errors lie between −σ and +σ. This illustrative choice does not model a specific sensor. Values are clipped to the 0–5 m range. The scene still shows the actual surface; the plot and readout show the noisy measurement. Noise does not create echoes where there is no hit. Toggling this option clears the plot and starts a new sweep.