Radar
Radar (radio detection and ranging) sends very short pulses of microwaves from a rotating antenna and listens for the echo. The echoing target is shown as a bright spot on the screen.
- Range: R = c × t / 2, where t is the time between pulse and echo and c = 3 × 10⁸ m/s. For every 1 µs of delay the target is 150 m away.
- Bearing: the direction the antenna points when the echo comes back.
- Minimum range: the receiver is off while the pulse is sent, so targets closer than c × τ / 2 (τ = pulse length) are missed. A 1 µs pulse gives 150 m.
- Maximum range: limited by the radio horizon, the pulse repetition frequency (the echo must return before the next pulse) and the power.
- Parts: transmitter (magnetron), circulator (one antenna to send and receive), rotating antenna, receiver, display.
- Radar can be fooled by rain clutter and sea clutter; the operator adjusts the gain and clutter controls.
Satellite navigation equipment
A GNSS (global navigation satellite system) such as GPS has about 24 or more satellites at about 20,000 km height. Each sends its position and the exact time. A receiver measures how long each signal took, multiplies by c and finds its distance from that satellite. The receiver sits on a sphere around each satellite. Three spheres cross at two points, and one is clearly wrong, so three satellites give position. But the receiver clock is cheap and a little wrong. A fourth satellite lets the receiver fix its own clock error. So four satellites give latitude, longitude, height and time.
Position can be off by a few metres. Differential GPS (DGPS) uses a fixed station with a known position to send corrections and brings the error to 1 metre or less. India's system is NavIC, Europe's is Galileo, Russia's is GLONASS, and China's is BeiDou. The receiver also shows speed and course over the ground and can give the time of day.
Sonar
Sonar (sound navigation and ranging) uses sound, because radio waves are absorbed within a few metres of sea water, but sound travels far. A transducer on the hull turns an electric pulse into a sound ping (often 20 to 200 kHz, using the piezoelectric effect) and later turns the echo back into an electric signal.
- Echo sounder: points straight down. Depth = v × t / 2, with v ≈ 1500 m/s in sea water.
- Fish finder: the same, but shows fish as marks above the bottom.
- Forward-looking and side-scan sonar: look ahead or sideways for rocks, wrecks and shoals.
- Doppler log: uses the frequency shift of sound reflected from the sea floor to measure the ship's speed.
Sound speed changes a little with temperature, salt and depth, so the instrument is set to a typical value.
Other electronic navigation devices
- Gyrocompass: a spinning wheel that settles on true north. It does not depend on magnets and is not fooled by the steel of the ship.
- Autopilot: steers the ship to hold a course set by the officer.
- Speed and distance log: measures the speed through the water or over the ground.
- AIS (automatic identification system): each ship sends its name, position, course and speed by VHF, so other ships see it on a screen.
- ECDIS: an electronic chart system that shows the map, the ship's GPS position and alarms for shallow water.
- VDR (voyage data recorder): the ship's black box.
Key formulas and definitions
- Radar range: R = c × t / 2, c = 3 × 10⁸ m/s
- 1 µs of radar echo delay is 150 m of range
- Minimum radar range = c × τ / 2 (τ = pulse length)
- Sonar depth: d = v × t / 2, v ≈ 1500 m/s in sea water
- GNSS distance from a satellite: d = c × t (t = travel time of the signal)
- Need 4 satellites: 3 for position plus 1 for clock error
Worked examples
1. A radar echo returns after 80 µs. How far is the target?
R = c × t / 2 = 3 × 10⁸ × 80 × 10⁻⁶ / 2 = 12,000 m = 12 km.
2. A radar uses a pulse of 0.5 µs. What is its minimum range?
R_min = c × τ / 2 = 3 × 10⁸ × 0.5 × 10⁻⁶ / 2 = 75 m. Targets closer than 75 m are not seen.
3. An echo sounder gets an echo after 0.08 s. What is the water depth? (v = 1500 m/s)
d = v × t / 2 = 1500 × 0.08 / 2 = 60 m.
4. A GPS signal takes 0.07 s to reach a receiver. How far away is the satellite?
d = c × t = 3 × 10⁸ × 0.07 = 2.1 × 10⁷ m = 21,000 km.
5. A radar scans so that the next pulse leaves 1 ms after the first. What is the largest range that can be shown without confusion?
The echo must come back before the next pulse: R_max = c × T / 2 = 3 × 10⁸ × 10⁻³ / 2 = 150,000 m = 150 km.
Common mistakes
- Forgetting to divide by 2. The pulse goes to the target and comes back, so the one-way distance is half of speed × time.
- Using the speed of light for sonar. Sonar uses sound, about 1500 m/s in sea water.
- Thinking three satellites are enough in practice. The fourth fixes the clock error.
- Believing radar sees through the horizon. Radar waves go straight, so range is limited by the radio horizon.