The Zig-Zag Manoeuvre

The standard test that measures not just how a ship turns, but how well it stops turning and holds a course.

Marine EngineeringManoeuvring, Seakeeping & Shafting

⏱️ About 12 min

Illustrative image (AI-generated).

Any ship can be made to turn — the harder question is whether it will settle back onto a heading cleanly once the rudder is centred, or overshoot and wander. The zig-zag test answers exactly that.

💡

The big idea: The zig-zag (Kempf) manoeuvre measures a ship's course-keeping and yaw-checking quality through its overshoot angle, while the steady turning radius R = V/ω relates rate of turn to the geometry of a completed turn.

🎯 By the end, you'll be able to

Describe the zig-zag (Kempf) test procedure and what it measures
Define the overshoot angle and explain what a large vs. small value implies
Relate rate of turn to steady turning radius via R = V/ω
Convert a rate of turn in degrees per second to radians per second

📎 Helpful to know first

Rudder Forces & the Turning Circle

Turning Is Only Half the Job

The previous lesson showed how a rudder develops the side force that bends a ship into a turn. But real ship-handling demands the opposite skill just as often: checking a turn — stopping the yaw and settling back onto a steady heading. A vessel that turns readily but then overshoots, lolls, or wanders before steadying is a poor sea boat and a handful for the helmsman. The zig-zag manoeuvre (also called the Kempf test, after its originator) is the standard way to measure this course-keeping quality.

In a zig-zag test the rudder is put over to a fixed angle (say +10° or +20°) and held there until the ship's heading has changed by a matching angle (say +10°). The rudder is then thrown to the opposite side (−10°) and held until the heading swings back through to −10°, and so on. The ship traces a zig-zag path. The key quantity recorded is the overshoot angle — how far the heading continues past the trigger point before the opposite rudder arrests the swing.

✨ Reading the overshoot angle

A small overshoot angle means the ship responds crisply to opposite rudder: the yaw is checked promptly and the heading settles with little overshoot — good course-keeping. A large overshoot angle means the ship keeps swinging well past the trigger before the counter-rudder takes hold, lazily 'leaning into' its turns — a vessel that will be tiring to steer on a long passage and potentially sluggish in an evasive manoeuvre. Overshoot is therefore a direct, comparative measure of manoeuvring 'liveliness'.

From Rate of Turn to Turning Radius

Once a ship has settled into a steady turn, its rate of turn ω (how fast the heading is changing) and its forward speed V together fix the turning radius R — the radius of the roughly circular path it follows. The relationship is simple kinematics: a body moving at speed V around a circle, rotating at angular rate ω, has radius R = V/ω.

There is one unit trap to watch for. Rates of turn are usually quoted in degrees per second (°/s), but the formula requires ω in radians per second. So before computing R, convert: multiply the rate in °/s by π/180 to get rad/s. A handy feel for scale: a large ship turning at one degree per second at a few metres per second ends up with a turning radius of several hundred metres — a reminder of just how much sea room a big vessel needs.

\[ \omega_{\text{rad/s}} = \omega_{\text{deg/s}} \times \frac{\pi}{180}, \qquad R = \frac{V}{\omega} \]

V is ship speed (m/s); ω must be in rad/s for R to come out in metres. The π/180 factor converts a rate of turn from degrees per second to radians per second.

📝 Worked example: A ship at V = 8 m/s settles into a steady hard-over turn at a rate of turn ω = 1.2 °/s. Find the steady turning radius R.

Convert the rate of turn to rad/s: ω = 1.2 × π/180 = 1.2 × 0.017453 = 0.02094 rad/s
Steady turning radius: R = V/ω = 8/0.02094 = 382.0 m

✓ ω = 1.2°/s = 0.02094 rad/s; R = V/ω = 8/0.02094 ≈ 382 m

✏️ Practice: A ship at V = 7 m/s settles into a steady turn at ω = 1.0 °/s. Find the steady turning radius R (in metres).

Solution

Convert: ω = 1.0 × π/180 = 0.017453 rad/s
R = V/ω = 7/0.017453 ≈ 401.1 m

Check your understanding

1. The zig-zag (Kempf) manoeuvre is primarily used to assess:

By alternately putting the rudder over and measuring how far the heading overshoots before the counter-rudder checks it, the test quantifies how crisply a ship settles onto a course.

2. To use R = V/ω with a rate of turn given in degrees per second, you must first:

R = V/ω requires ω in radians per second; a rate in °/s is converted by the factor π/180.

✅ Key takeaways

The zig-zag (Kempf) test measures course-keeping and yaw-checking; a small overshoot angle means crisp response, a large one means sluggish wandering
Steady turning radius R = V/ω, but ω must first be converted from °/s to rad/s (×π/180)
Even modest rates of turn at ship speeds give turning radii of hundreds of metres — big vessels need big sea room

➡️ So far we have treated the ship as a body that turns on command. Next we step back and catalogue all six ways a ship can move in a seaway — including the rolling motion that dominates comfort and safety.

Want to test yourself on this? Try the Marine Engineering Aptitude test →