Doppler Log Explained: How Ships Measure Speed

Introduction

The Doppler log is a bridge instrument that measures a vessel’s speed over ground (SOG) and speed through water (STW). It works on the principle of the Doppler shift in frequency.

What Is an Acoustic Wave?

An acoustic wave is a sound wave: a vibration that travels through a medium by alternately squeezing and stretching the particles of that medium. It needs something to travel through, such as air or water, and it carries energy from one point to another without the medium itself moving along with it.

Radio waves do not travel well through sea water, but sound does. That is why ships use acoustic waves to “see” under the surface. In sea water, sound travels at roughly 1500 m/s, which is the standard value built into marine instruments. In reality the speed changes slightly with temperature, salinity and pressure.

Shipboard instruments such as the echo sounder and the Doppler log use ultrasonic frequencies, well above what the human ear can hear (typically in the range of about 50 to 200 kHz). Using a high frequency keeps the transducer small, gives a narrow beam, and avoids picking up the low-frequency noise of the propeller, the engine and water rushing past the hull. The trade-off is that higher frequencies lose strength faster in water.

How Is an Acoustic Wave Produced on a Ship?

Two parts of the instrument work together to create the sound:

1. The oscillator (pulse generator) produces electrical pulses at the chosen frequency.
2. The transducer, fitted in the ship’s hull, converts those electrical pulses into sound waves and sends them into the water.
3. When the sound hits the seabed or the water layers, it bounces back as an echo. The same transducer picks it up and converts it back into an electrical signal.
4. An amplifier strengthens this weak signal, and the display unit processes it into a reading.

Piezoelectric Transducer

This type works on the piezoelectric effect. Crystals such as quartz, or specially made ceramics, produce an electric current when they are squeezed, and they also change shape when an electric current is applied to them. In a transducer the crystal sits between two steel plates. An alternating current makes the crystal expand and contract rapidly, and that vibration creates the sound wave. When an echo hits the crystal, it is squeezed in the same rhythm and produces a small electric current. Doppler logs use piezoelectric transducers.

Magnetostrictive Transducer

This type uses a ferromagnetic material such as nickel or iron, wound with copper wire to form a coil (solenoid). When current flows through the coil, a magnetic field forms and makes the metal expand and contract, which produces sound. When an echo strikes the metal, its magnetic properties change, and this induces an electric current in the coil.

The Doppler Shift

The Doppler shift is the apparent change in the frequency of a wave caused by the motion of the observer, the source, or both. A familiar example is the change in pitch of a siren as an ambulance passes you.

How a Doppler Log Works

A Doppler log has a transducer that emits an acoustic wave and measures the frequency of the returning echo. Because the transmitted and received frequencies are both known, the vessel’s speed can be calculated:

f_r = f_t × (c + v cos α) / (c − v cos α)

• f_r is the frequency received
• f_t is the frequency transmitted
• c is the speed of sound in water (about 1500 m/s)
• v is the speed of the vessel
• α is the angle of the transmitted beam

The Janus Configuration

A single transducer also picks up errors caused by the vertical motion of the ship: pitching, heaving and even rolling. To avoid this, modern ships use the Janus configuration, in which two transducers are fitted, one forward and one aft. Each transmits at an angle of 60° (forward and aft respectively). Here α is the angle between each beam and the horizontal, which is the same α that appears in the formulas.

With two transducers, the vertical motion of the ship cancels out and only the horizontal motion remains. Speed is then calculated from the difference between the two received frequencies:

v = c (f_r1 − f_r2) / (4 f_t cos α)

Proof: Why the Vertical Motion Cancels Out

Let the ship move forward at speed v and, because of heave, move vertically at speed w (upward positive). Take α as the angle between each beam and the horizontal. For speeds much smaller than c, the Doppler formula reduces to f_r − f_t ≈ 2 f_t u / c, where u is the component of the ship’s velocity along the beam.

Step 1: Forward beam. It points forward and downward, so the ship’s forward motion carries it toward the target and its upward heave carries it away:

f_r1 − f_t = (2 f_t / c) × (v cos α − w sin α)

Step 2: Aft beam. It points backward and downward, so forward motion now carries it away from the target, and heave still carries it away as well:

f_r2 − f_t = (2 f_t / c) × (−v cos α − w sin α)

Step 3: Subtract.

f_r1 − f_r2 = (2 f_t / c) × [(v cos α − w sin α) − (−v cos α − w sin α)]

f_r1 − f_r2 = (2 f_t / c) × 2 v cos α = 4 f_t v cos α / c

Step 4: Rearrange. The w sin α terms are identical in both lines, so they disappear, and we are left with:

v = c (f_r1 − f_r2) / (4 f_t cos α)

In words: heave moves the ship toward or away from the seabed along both beams by the same amount, so it shifts both frequencies in the same direction. Forward motion shifts them in opposite directions. Taking the difference keeps the forward speed and removes everything the two beams have in common. Pitching works the same way to a very good approximation: it makes one beam steeper and the other shallower by the same small angle δ, so the result is only multiplied by cos δ, which is almost exactly 1 for normal pitch angles.

The same Janus arrangement can be used athwartships to measure the vessel’s athwartship (sideways) speed, which is very useful while berthing.

The transducers used in a Doppler log are piezoelectric. If the Janus configuration is used only fore and aft, it is a single-axis system. If it is used both fore-and-aft and athwartships, it is a dual-axis system.

Modes of Operation

Bottom Track (Ground Track)

In this mode the log measures speed over ground by bouncing sound off the seabed. It works only in limited depths, up to about 200 m. Beyond that the echo becomes too weak to measure.

Water Track

A moving ship displaces a large volume of water, forming layers that act as a good reflecting surface for the sound waves. These reflections give speed through water. For water track to work, the ship should have about 10–30 m of water under the keel.

Sources of Error

Transducer orientation

The beam must be set at the correct angle (60°). The speed formula depends on that angle, so any mounting or alignment error feeds straight into the reading.

Oscillator frequency

The oscillator must be accurate and constant. The log compares the frequency it sent with the frequency that comes back, so a drifting oscillator creates a false shift.

Propagation velocity of the sound wave

The speed of sound varies with temperature, salinity and pressure. The log uses a preset value of 1500 m/s, so in other waters it makes a small error.

Ship motion

Pitching, heaving and rolling change the beam angle and add vertical movement to the readings. This is the reason modern ships use the Janus configuration with two transducers.

Inaccurate comparison frequency

Speed is calculated by comparing the received frequency with the transmitted one. Any inaccuracy in measuring the received frequency becomes an error in speed.

Side lobes

Besides the main beam, a transducer also sends out weaker side beams. If a side lobe dominates over the main beam, for example by hitting a strong reflector, the reading is distorted.

Conclusion

The Doppler log is one of the most useful speed-measuring instruments on the bridge. It gives both over-the-ground and through-the-water speed, and in a dual-axis Janus setup it also supports precise manoeuvring in port.