Gyro errors: speed and course, latitude and ballistic
1The lesson in plain words
A moving ship makes the gyro settle a little off the meridian. Know which way, how much, and which corrector setting removes it.
Speed and course error
Your north–south movement changes the rotation sensed by the gyro, shifting its settling direction away from the true meridian. Only the north–south part of your speed matters. The resulting speed-and-course error is zero on east or west courses and largest on north or south courses. It grows with speed and with latitude. On northerly courses it is westerly: the gyro reads high. On southerly courses it is easterly: the gyro reads low.
The formula
Error size° ≈ V × |cos C| ÷ (15.7 × cos φ). V is speed over ground in knots, C is true course over ground and φ is latitude. The factor 15.7 is 900 ÷ 57.3. The absolute value, |cos C|, gives size: assign W on northerly courses and E on southerly courses. Using speed through water and heading assumes no current or leeway. For your gyro's corrector settings, use the input source specified by its maker.
Worked example
Assume no current or leeway. Speed 18 knots, course 030° T, latitude 45° N. V × cos C = 18 × 0.866 = 15.6. Divide by 15.7 × cos 45° = 15.7 × 0.707 = 11.1. Error ≈ 15.6 ÷ 11.1 ≈ 1.4° W. Uncorrected, your gyro reads about 1.4° high: true heading 030° shows about 031.4°. Setting the speed corrector to 18 knots and latitude to 45° N estimates the correction; verify the remaining error.
Latitude (damping) error
In designs damped by tilting the axis, the gyro settles slightly off the meridian. This latitude error, or damping error, grows with the tangent of latitude and changes sign between hemispheres. A latitude corrector removes it. Other designs do not have it. Your gyro's manual says which kind you have and how the correction is applied.
Ballistic deflection
When you change speed or course, the north–south acceleration acts on the gravity control. The axis is pushed off for a while: ballistic deflection. Schuler tuning sets the natural period to about 84.4 minutes. This helps the axis follow its changing settle point during a manoeuvre, reducing the temporary error. In latitudes up to 60°, A.424(XI) limits errors from a rapid 20-knot speed change to 2°, and from a rapid 180° turn at 20 knots to 3°. Check the heading after major manoeuvres.
2Key data
- Speed-error size (simplified)
- Error size° ≈ V × |cos C| ÷ (15.7 × cos φ)
- Northerly courses
- Westerly error: gyro reads high
- Southerly courses
- Easterly error: gyro reads low
- East or west courses
- No speed-and-course error
- Rapid 180° turn at 20 kn (A.424)
- Error not more than 3°, up to 60° latitude
- Rapid 20 kn speed change (A.424)
- Error not more than 2°, up to 60° latitude
3Key points
- 1
Speed-and-course error depends on the north–south part of your speed and grows with latitude.
- 2
Northerly courses: westerly error, gyro reads high. Southerly courses: easterly error, gyro reads low.
- 3
Set the speed and latitude correctors, or check the automatic inputs, to remove these errors.
- 4
Ballistic deflection after large speed or course changes is short-lived. Check the heading afterwards.
4Frequent mistakes
Wrong: Speed-and-course error is largest on east or west courses.
Right: It is zero on east or west courses and largest on north or south courses, because only the north–south part of the speed counts.
Wrong: Speed error is the same at every latitude.
Right: It is divided by cos latitude, so the same speed and course give a bigger error in high latitudes.
5Practice case & exam keys
No current or leeway: you steam 180° T at 20 knots in 60° N. The manual speed corrector is still at 0 knots. A colleague expects a 2.5° E error and proposes subtracting 2.5° from every gyro reading instead of updating the setting. Do you agree?
Show the answer
The predicted sign and size are right, but the action is wrong. An easterly error is added to obtain true. Set speed to 20 knots and latitude to 60° N under the maker’s instructions, then independently check the remaining error. Do not keep applying the predicted 2.5° after the corrector is updated.
Exam keys
- Speed-error size ≈ V × |cos C| ÷ (15.7 × cos φ) degrees; zero on 090°/270°, largest on 000°/180°.
- N courses → error W (reads high); S courses → error E (reads low).
- Latitude (damping) error ∝ tan φ in tilt-damped designs; ballistic deflection after speed or course changes; Schuler period 84.4 min.
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