Gyrocompass Explained: How It Finds North and Why Errors Occur

Introduction

The gyrocompass is a north-seeking compass. It works on the principle of the gyroscope, altered so that the gyroscope seeks north. Unlike a magnetic compass, it shows true heading, so it is not affected by magnetic variation or deviation.

Principle of the Gyroscope

The principle of the gyroscope is the law of conservation of momentum.

Law of Conservation of Momentum

The momentum of a system is always conserved unless an external force acts on it. For a spinning rotor this is its angular momentum, and it is what keeps the spin axis steady.

Free Gyroscope

A free gyroscope has three degrees of motion:

• Spin
• Vertical (tilting)
• Horizontal (drifting)

Properties of a Gyroscope

A gyroscope has two properties.

1. Gyroscopic Inertia

The rotor, as it rotates, points in a fixed direction in space. This is called gyroscopic inertia, or rigidity in space.

2. Precession

When a torque is applied to the spin axis, the effect of the torque appears 90° to the torque applied, in the direction of rotation of the spin axis.

Tilting

The angle of elevation or depression of the spin axis above or below the horizon is called tilting.

Drifting

The movement of the spin axis in the direction of azimuth is called drifting.

The Gyro Star

A free gyroscope points in a fixed direction in space. The fixed point it points to is an imaginary star called the gyro star. Because the Earth rotates beneath it, the gyroscope appears to tilt and drift as it keeps pointing toward the gyro star.

The rotation of the Earth makes the gyroscope drift. The tilt is measured from the horizontal, which is set by gravity. At any place on the Earth the gyroscope points to the same fixed point, the gyro star.

Making the Gyroscope North Seeking

To make a free gyroscope point in a fixed direction on the Earth’s surface, a weight is added on the top or at the bottom to counteract the effect of the Earth’s rotation and gravity. A weight on top gives the top heavy effect, and a weight at the bottom gives the bottom heavy effect.

When the axle tilts, gravity acts on the weight and produces a torque. Because of precession, this torque turns the axle sideways toward the meridian, so the gyroscope seeks north.

Damping

A controlled gyroscope is not stable, because it oscillates about the meridian. To reduce the oscillation, another torque is applied at right angles to the first torque, which equally opposes the precession caused by the first torque. The oscillation then dies away and the gyro settles on the meridian.

Errors of the Gyrocompass

A gyrocompass has two errors:

• Speed error
• Latitude error

Speed Error

• OV is the speed and course of the vessel.
• OE is the direction of the Earth’s rotation (east).

When the ship is at 000° and stopped, the gyrocompass points to the north. When it is moving, OR is the resultant and the gyro points toward ON′, causing an error. This is the speed error.

Size of the Speed Error

Step 1: Earth’s eastward speed. The Earth turns 15° per hour, and 1° of longitude at the equator is 60 nautical miles, so a point on the equator moves east at 900 knots. At latitude λ the speed is:

900 × cos λ

Step 2: Ship’s components. On course C at speed V, the ship moves north at V cos C and east at V sin C.

Step 3: The error. The gyro treats the direction at right angles to the resultant as north. So the error δ satisfies:

tan δ = V cos C / (900 cos λ + V sin C)

Step 4: Simplify. V is small compared with 900, so in degrees:

δ ≈ V cos C / (15.7 × cos λ)

Many textbooks round 15.7 to 15. The error is largest on north and south courses, nearly zero on east and west courses, and increases with speed and with latitude. It is westerly on northerly courses and easterly on southerly courses.

For example, at 20 knots on course 000° in latitude 30°, δ ≈ 20 / (15.7 × 0.866) ≈ 1.5° west.

The error is removed by a speed and latitude corrector, set by hand or fed automatically from the log or GNSS.

Latitude Error

Damping in tilt makes the spin axis settle a little east or west of the meridian. This error is proportional to the tangent of the latitude, so it increases with increasing latitude. It is zero at the equator.

More You Should Know

Requirements and Accuracy

A gyrocompass is required by SOLAS Chapter V, Regulation 19, and must meet the performance standards in IMO Resolution A.424(XI). ISO 8728 gives the construction and test requirements. The main accuracy points of A.424(XI) are:

• The settle point error at any heading and at any latitude up to 60° should not exceed ±0.75° × secant latitude.
• The repeatability of the settle point error from one run-up to another should be within 0.25° × secant latitude.
• Under operational conditions, the repeatability of the settle point error of the master compass should be within ±1° × secant latitude.
• Means must be provided for correcting the errors caused by speed and latitude.

Main Parts of the System

The master compass holds the spinning rotor, driven at high speed by an electric motor, and the control and damping arrangements. A follow-up system keeps the outer parts aligned with the sensitive element, so the heading can be read and transmitted without disturbing the gyro. The heading is then sent to repeaters on the bridge and to other equipment such as radar, ECDIS and the autopilot.

Starting and Settling

After switching on, the rotor needs time to reach full speed, and the axis then needs further time to settle on the meridian. Start the gyrocompass well before sailing, following the maker’s instructions, and check that the repeaters agree with the master.

Checking and Naming the Gyro Error

The gyro error is found by comparing the gyro with a true bearing, such as an azimuth of the Sun or a transit bearing:

Gyro error = True bearing − Gyro bearing

• If the gyro reads less than true, the error is east (gyro least, error east).
• If the gyro reads more than true, the error is west (gyro best, error west).

For example, if the true bearing is 090° and the gyro reads 092°, the error is 2° west. Check the gyro error regularly, compare it with the magnetic compass, and record it.

Other Errors

• Ballistic deflection error: a temporary error caused when the ship changes speed or course quickly. It dies away as the gyro settles again.
• Ballistic damping error: a temporary error after a change of speed or course, caused by the damping arrangement.
• Quadrantal rolling error: caused by heavy rolling, and largest on intercardinal headings (045°, 135°, 225°, 315°).

Limits at High Latitude

The gyro finds north using the horizontal part of the Earth’s rotation, which becomes weaker as latitude increases and is zero at the poles. Near the poles the gyrocompass becomes sluggish and unreliable. The accuracy limits in A.424(XI) apply up to latitude 60°.

Modern Gyrocompasses

Fibre-optic and ring-laser gyrocompasses sense rotation with light instead of a spinning rotor. They have no moving parts to wear out, start up faster and need less maintenance.

Gyrocompass Compared with Magnetic Compass

• Gyrocompass advantages: shows true north, has no variation or deviation, and has a strong directive force.
• Gyrocompass disadvantages: needs electrical power, needs time to settle, and has speed and latitude errors.
• Magnetic compass: needs no power and is simple, but has variation and deviation, and is the back-up if the gyro fails.

Conclusion

The gyrocompass turns a spinning rotor into a north-seeking instrument by adding a control weight and damping. Knowing how it finds north, and why speed and latitude cause errors, helps you trust its heading, check it regularly and correct it when needed.