Open-Water Characteristics: KT, KQ & Efficiency
How a propeller's thrust, torque and efficiency are made comparable across every size and speed.
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 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.
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.
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.
- T = KT·ρ·n²·D⁴ = 0.18 × 1025 × (2.0)² × 410.06 = 0.18 × 1025 × 4 × 410.06
- 0.18 × 1025 = 184.5; 184.5 × 4 = 738; 738 × 410.06 ≈ 302,626 N ≈ 302.6 kN
- 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
- η0 = (J/2π)(KT/KQ) = (0.667/6.2832) × (0.18/0.030) = 0.1062 × 6.0 = 0.637
- η0 = (J/2π)(KT/KQ) = (0.5/2π) × (0.22/0.035)
- 0.5/2π = 0.5/6.2832 = 0.0796
- 0.22/0.035 = 6.286
- η0 = 0.0796 × 6.286 = 0.500
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
- 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