Open-Water Characteristics: KT, KQ & Efficiency

How a propeller's thrust, torque and efficiency are made comparable across every size and speed.

Marine EngineeringPropellers & Propulsive Efficiency
⏱️ About 16 min
Open-Water Characteristics: KT, KQ & Efficiency — illustration
Illustrative image (AI-generated).

A 6-metre propeller and a 2-metre propeller of identical geometry produce wildly different thrust at the same shaft speed — yet they share a single thrust-versus-speed curve. The trick that makes them comparable is non-dimensionalisation, and it is the foundation of everything that follows.

💡
The big idea: Measured in uniform open water, a propeller's thrust and torque collapse onto universal non-dimensional coefficients KT and KQ when plotted against the advance ratio J, and the open-water efficiency η0 = (J/2π)(KT/KQ) rises to a single peak — so a small model propeller can predict a full-scale propeller of the same geometry.
🎯 By the end, you'll be able to
  • Define the open-water test and explain why propeller performance is measured in uniform inflow
  • State the non-dimensional thrust and torque coefficients KT and KQ and compute thrust and torque from them
  • State and apply the open-water efficiency η0 = (J/2π)(KT/KQ)
  • Read the qualitative shape of the KT–KQ–η0 versus J open-water diagram
📎 Helpful to know first

The Open-Water Test

Before a propeller ever meets a hull, its basic performance is measured in isolation. In an open-water test the propeller is mounted on a drive strut and towed through undisturbed (uniform) water at a known speed of advance Va, while it is turned at a known shaft speed n. At each combination of Va and n the testers record the thrust T, the torque Q required to turn the shaft, and the advance ratio J = Va/(nD). Plotting the results against J gives the propeller's open-water characteristics — its performance fingerprint, independent of any particular hull.

'Open water' means uniform inflow: there is no hull ahead of the propeller, no wake, no thrust deduction. That isolation is deliberate. It lets one propeller's intrinsic quality be compared with another's, and it gives the clean baseline that the hull-interaction factors of Lesson 3 will later modify. The open-water efficiency η0 measured here is the propeller on its best behaviour; behind a real hull it will be nudged up or down by wake and thrust deduction.

\[ K_T = \frac{T}{\rho\, n^{2} D^{4}}, \qquad K_Q = \frac{Q}{\rho\, n^{2} D^{5}} \]
T in newtons, Q in N·m, ρ in kg/m³, n in rev/s, D in m. KT and KQ are dimensionless; D⁴ appears in KT (a force ∝ area × dynamic pressure) and D⁵ in KQ (a torque ∝ force × lever arm).

Why Non-Dimensional Coefficients?

Thrust and torque by themselves are useless for comparing propellers, because they change with size, speed and water density. A 6-metre propeller and a 2-metre propeller of identical geometry will produce wildly different thrust at the same shaft speed — but the same thrust coefficient KT. Non-dimensionalising strips out the scale: dividing thrust by ρn²D⁴ (the natural force scale of a rotating disc in a fluid) collapses a whole family of geometrically similar propellers onto a single KT-versus-J curve. The same trick with ρn²D⁵ collapses torque onto a single KQ curve.

That is the whole point: a propeller's open-water curves are a property of its geometry and pitch ratio, not its absolute size, so a model propeller tested in a basin can predict a full-scale propeller of the same geometry. Once KT and KQ are read off the curve at the operating J, thrust and torque at any scale follow by inverting the definitions: T = KT·ρ·n²·D⁴ and Q = KQ·ρ·n²·D⁵.

\[ \eta_0 = \frac{J}{2\pi}\,\frac{K_T}{K_Q} \]
J is the advance ratio; 2π converts per-revolution quantities; KT/KQ is the ratio of useful thrust work to the torque work put in. η0 is the open-water (propeller-alone) efficiency.
Open-water characteristics: KT, 10·KQ and η0 plotted against advance ratio JThree curves versus J. KT falls steadily from left to right. 10·KQ falls on a similar, slightly lower trend. η0 rises from zero at J = 0, peaks near J ≈ 0.6, then falls back toward zero at high J.advance ratio JKT, 10·KQ, η001.0KT10·KQη0

A line chart with advance ratio J on the horizontal axis (0 to 1.0) and coefficient value on the vertical axis. Three curves are shown: KT (blue) falling steadily from upper left to lower right; 10·KQ (light blue) falling on a similar but slightly lower trend; and η0 (amber) rising from zero at J = 0 to a peak near J ≈ 0.6, then falling back toward zero at high J. The efficiency peak is the design target.

The open-water diagram: KT and KQ both fall with J, while η0 rises to a broad peak then falls. A propeller is matched so its normal operating J sits on or near that η0 peak.

Reading the Open-Water Diagram

The open-water diagram plots three curves against J. The thrust coefficient KT falls steadily as J rises: at low J the blades grip hard (high angle of attack, lots of thrust) and at high J they run nearly feathered (little thrust). The torque coefficient KQ falls on a similar, slightly steeper trend — it is often plotted as 10·KQ so it shares the same vertical scale as KT. The open-water efficiency η0 starts at zero when J = 0 (the propeller is turning but producing thrust with no useful forward work), rises to a broad peak somewhere in the middle of the operating range, and falls back toward zero at high J as thrust collapses.

That efficiency peak is the design target. A well-matched propeller is chosen so that the ship's normal operating J sits on or near the peak of its η0 curve — running a propeller far below its peak wastes fuel in excessive slip, and running it far above starves it of thrust. The numbers in this lesson's worked example sit at J = 0.667, near a typical peak.

📝 Worked example: A propeller of diameter D = 4.5 m turns at n = 2.0 rev/s in seawater (ρ = 1025 kg/m³), operating at advance ratio J = 0.667. The open-water chart gives KT = 0.18 and KQ = 0.030 (with D⁴ = 410.06 and D⁵ = 1845.28). Find the thrust T, the torque Q, and the open-water efficiency η0.
  1. T = KT·ρ·n²·D⁴ = 0.18 × 1025 × (2.0)² × 410.06 = 0.18 × 1025 × 4 × 410.06
  2. 0.18 × 1025 = 184.5; 184.5 × 4 = 738; 738 × 410.06 ≈ 302,626 N ≈ 302.6 kN
  3. Q = KQ·ρ·n²·D⁵ = 0.030 × 1025 × 4 × 1845.28 = 0.030 × 1025 = 30.75; 30.75 × 4 = 123; 123 × 1845.28 ≈ 226,970 N·m ≈ 227.0 kN·m
  4. η0 = (J/2π)(KT/KQ) = (0.667/6.2832) × (0.18/0.030) = 0.1062 × 6.0 = 0.637
✓ T ≈ 302.6 kN; Q ≈ 227.0 kN·m; η0 ≈ 0.637 (63.7%)
✏️ Practice: At an operating point J = 0.5 the open-water chart gives KT = 0.22 and KQ = 0.035. Find the open-water efficiency η0.
Solution
  1. η0 = (J/2π)(KT/KQ) = (0.5/2π) × (0.22/0.035)
  2. 0.5/2π = 0.5/6.2832 = 0.0796
  3. 0.22/0.035 = 6.286
  4. η0 = 0.0796 × 6.286 = 0.500
✨ Where the efficiency peak comes from

The rise-and-fall of η0 is a tug-of-war. At low J the propeller makes thrust but wastes energy churning water (high slip, low efficiency); at high J it runs cleanly but makes almost no thrust. The peak sits where useful thrust per unit of torque work is greatest — a little slip, but not too much. This is why choosing the right pitch and diameter for a ship's operating speed is the central problem of propeller–hull matching in Lesson 4.

Check your understanding

1. In the open-water test, the propeller is tested:
'Open water' means no hull ahead of the propeller — uniform inflow — so the propeller's intrinsic performance can be measured without hull interaction.
2. The torque coefficient KQ is non-dimensionalised with ρn²D⁵ (not D⁴ like KT) because:
Torque is a force times a lever arm (length), so its natural scale carries one extra power of D compared with thrust — hence D⁵ for KQ versus D⁴ for KT.
3. At J = 0.667 the open-water chart gives KT = 0.18 and KQ = 0.030. The open-water efficiency η0 = (J/2π)(KT/KQ) is approximately:
η0 = (0.667/6.2832) × (0.18/0.030) = 0.1062 × 6.0 ≈ 0.637.
✅ Key takeaways
  • The open-water test measures a propeller in uniform inflow, giving a hull-independent performance fingerprint
  • KT = T/(ρn²D⁴) and KQ = Q/(ρn²D⁵) collapse geometrically similar propellers onto single curves versus J
  • Open-water efficiency η0 = (J/2π)(KT/KQ) rises to a peak then falls; a propeller is matched so its operating J sits near that peak
➡️ Open-water efficiency is the propeller alone — but a propeller never works in open water. Next we put it behind the hull and see how wake and thrust deduction reshape its effective efficiency.
Want to test yourself on this? Try the Marine Engineering Aptitude test →