Stripping the Ship Away: What Open Water Means

At one instant on passage, four numbers describe our reference ship's propeller and no two of them agree. The Panamax bulker, about 75,000 tonnes deadweight, is making 14.0 knots through the water, 7.202 m/s. The water arriving at her propeller disc is moving at 4.897 m/s. The propeller is pushing with 704 kN of thrust. The same hull towed at the same speed with no propeller behind it needs 577 kN. Two speeds, two forces, all four correct and none of them interchangeable. Ask what that propeller's efficiency is and the only honest first answer is a question back: efficiency of what, reckoned against which pair?

(Our reference Panamax is a teaching hull with round numbers, and her 577 kN is light for her size: a real Panamax at 14.0 knots needs nearer 680 kN. Every force and power hung on that figure in this course is therefore about 15 per cent lighter than a real ship's, and her propeller a little more lightly loaded, and so a little more efficient, than a real one would be. The definitions and the method do not change.)

The subject gets out of that hole by taking the ship away.

What open water takes away

Open water is the condition in which a propeller advances along its own axis into water that nothing has disturbed. There is no body ahead of the disc, so the inflow runs parallel to the shaft and is the same at every point of it. The disc is deep enough that the free surface neither makes waves nor lets air down the low-pressure side of a blade. The blades work below cavitation inception, so no vapour is present. Nothing else is specified, and nothing else is allowed in.

It is a definition by subtraction, and each subtraction removes a real effect. Behind a hull the inflow is sheared: a blade passing 12 o'clock, up in the thick boundary layer under the stern, meets much slower water than the same blade at 6 o'clock, and the difference arrives once a revolution as a swing in angle of attack. The propeller's own suction also lowers the pressure over the afterbody, so a hull being pushed needs more force than the same hull on a towrope, 704 kN against 577 kN. That gap is the thrust deduction fraction, t = 1 - 577/704 = 0.180, a statement about the stern rather than about the propeller.

Neither effect belongs to the wheel, and both change if you change the ship. A measurement made with the hull in place is a measurement of the pair, and it travels to no other vessel. The open-water condition is the only one in which the answer is repeatable, transferable and a property of the bronze itself. That is why the characterisation is done alone first, and why every basin report begins there.

The price is that reality has a hull. An open-water curve is not the end of the calculation but the reference the interaction terms are defined against, and defining them is the job of our course The Propeller Behind the Hull.

The speed the propeller actually sees

A hull drags a following current along with it, so the water entering the disc is slower than the ship. The speed of advance Va is the speed of that water relative to the propeller: equivalently, the speed at which this propeller would have to advance in open water to be doing the job it is doing here. It follows from ship speed through the Taylor wake fraction w:

Va = V · (1 - w)

where V is the ship's speed through the water in metres per second and w is dimensionless. For our Panamax, w = 0.32 at the design draught, so Va = 7.202 × 0.68 = 4.897 m/s.

The 2.3 m/s between them is not a rounding difference, it is a third of the speed. Everything plotted on an open-water chart is indexed by the advance ratio J = Va/(nD), with n the rate of rotation in revolutions per second and D the diameter in metres, and the next lesson takes that number apart. Put the ship's speed in by mistake and she lands at J = 0.735 instead of 0.500, a point far up the chart where the same propeller makes barely a quarter of the thrust it is really making. The wrong speed does not give a slightly wrong answer. It gives a correct answer about a different operating condition.

There is a second and sharper reason to keep the two apart. The wake fraction is not measured directly: it is recovered by asking which advance ratio on the open-water curve reproduces the thrust a self-propulsion test actually made. The curve is logically prior to the wake fraction, and without it w has nothing to be measured against.

What the curve is a property of

An open-water curve is a property of three things and of nothing else.

The first is the blade geometry, all of it. The ship's propeller is quoted as four blades, pitch ratio 0.715 at 0.7R and expanded area ratio 0.55, which are the three numbers a published series is indexed on. They are not the propeller. This one also carries 18 degrees of total skew, 4 degrees of rake, a hub ratio of 0.180 and NACA 66 sections on an a = 0.8 mean line. Two wheels sharing the headline numbers and differing in section shape have different curves: a B4-55 is a family with one fixed shape, not a propeller.

The second is Reynolds number. Section drag falls as it rises, so torque falls, thrust rises a little and measured efficiency rises with them. A blade on a 250 mm model runs roughly two orders of magnitude below the ship's, and the curve it produces is not the ship's curve; lesson 5 sizes that gap and closes it. The working rule meanwhile is blunt: a curve arriving without a scale and a Reynolds number attached is not a curve you can use.

The third is that the blades are not cavitating. Once inception starts, one curve becomes a family indexed on cavitation number, and thrust breaks down at the low advance ratios where the blades work hardest.

What the curve is not a property of is the longer and more useful list: not the ship, not her draught, not the wake, not the engine, not the trial day, not the sea state. That independence is the entire value of it.

Five quantities, two curves, three free choices

An open-water operating point is fixed by four measured quantities: the rate of rotation n, the speed of advance Va, the thrust T and the torque Q. Two constants sit behind them, the diameter D and the blade geometry, both frozen the moment the propeller is cast.

The chart supplies exactly two relations, one for thrust and one for torque, each a coefficient against advance ratio. In dimensional terms they connect five quantities: n, Va, T, Q and D, and two equations among five unknowns leave three free. Give any three of n, Va, T, Q and D and the remaining two follow from the chart.

That one sentence is the working method of the whole subject. The ship enters through the door marked D = 7.00 m, Va = 4.897 m/s and n = 1.400 rev/s, and the chart returns T = 704 kN and Q = 726 kN·m. A designer sizing a new wheel enters with the thrust required, the speed of advance and the largest diameter the stern will take, and comes out with a shaft speed and a torque. Same chart, different door, and lesson 6 builds the constructions that open each one.

It is worth seeing what that buys. Her open-water efficiency here is 0.540, thrust power out over shaft power in with the ship stripped away; her quasi-propulsive coefficient, effective power over delivered power, is 0.658. The propeller alone is the smaller number, and the difference is interaction rather than propulsion. Keeping the two apart is the habit this course exists to install.

Monday morning

Open one ship's file and write her speed of advance on the front of it: design speed off the trial report, wake fraction out of the model-basin summary, one multiplication. Every propeller number you are handed this year is indexed on that speed, and none of them on ship speed. While the file is open, check whether the propeller data block gives skew and rake as well as pitch ratio and area ratio, because the curve belongs to all four and a series prediction knows only two. The next lesson turns n, Va, T and Q into the four dimensionless numbers the chart is actually drawn in.