Type a line (pitch 4.2 m 105 r/min 14 kn log; engine 750 r/min gear 4.2 pitch 3.1 m 15 kn) or fill in the fields: the line and the fields stay in step.
Enter the propeller pitch, the shaft speed and the ship speed by log or by GPS, and the calculator gives the theoretical speed of the propeller in knots and m/s and the apparent slip, and the true slip with a wake fraction of your own. It also works the other way round: the ship speed for a given slip, the pitch for a speed and a slip, or the shaft speed. The shaft speed can come from the engine speed and the gear ratio, the pitch from the P/D and the diameter; the working is shown with your numbers, the two speeds are drawn to scale, and the result is a line you can copy or add to a request.
The slip arithmetic, nothing more: no normal or recommended slip figures, no typical wake fractions, no propeller selection and no verdict on the condition of a propeller. Compare the result with the sea-trial and with the records of the vessel at the same shaft speed, loading and kind of speed.
At each turn the propeller would move ahead by its pitch if the water did not give way, so the propeller speed is the pitch times the shaft speed: 4.2 m x 105 r/min x 60 = 26 460 m/h = 14.29 kn (1 kn = 1852 m/h). The apparent slip is (propeller speed - ship speed) / propeller speed x 100 %: 2.0 % at 14 kn by log.
A log speed is through the water, a GPS speed over the ground, so a slip by GPS includes the current along the track: a head current makes it larger, a following current smaller and can make it negative. With a negative slip by log, check the log reading, the pitch entered and the shaft speed. Compare slips worked out from the same kind of speed.
The water near the stern moves along with the hull, and the propeller meets it at Va = Vs x (1 - w), with w the wake fraction. The true slip is (propeller speed - Va) / propeller speed, larger than the apparent slip. The wake fraction is used only as typed: there is no default value; enter a wake fraction from the data of the vessel.
| Shaft speed | Per 1 m of pitch, kn | Per 1 m of pitch, m/s | Per 1 ft of pitch, kn |
|---|---|---|---|
| 60 r/min | 1.944 kn | 1.000 m/s | 0.592 kn |
| 80 r/min | 2.592 kn | 1.333 m/s | 0.790 kn |
| 100 r/min | 3.240 kn | 1.667 m/s | 0.987 kn |
| 120 r/min | 3.888 kn | 2.000 m/s | 1.185 kn |
| 140 r/min | 4.536 kn | 2.333 m/s | 1.382 kn |
| 160 r/min | 5.184 kn | 2.667 m/s | 1.580 kn |
| 180 r/min | 5.832 kn | 3.000 m/s | 1.777 kn |
| 200 r/min | 6.479 kn | 3.333 m/s | 1.975 kn |
For another pitch, multiply the figure in the table by the pitch in metres or feet: a 4.2 m pitch at 100 r/min gives 4.2 x 3.240 = 13.61 kn. The slip follows from comparing this speed with the ship speed.
The theoretical speed of a propeller (the pitch times the revolutions) and the apparent slip as the share of that speed the ship does not make follow two independent references and are checked against three more: a marine technology encyclopedia, a ship propulsion handbook from an engine designer, a description of a method for measuring the apparent slip, marine engineering study notes and a training article for deck officers. That a slip by the speed over the ground includes the current, and can be negative with a following current, is stated by the encyclopedia and the study notes; that hull fouling, wind and sea raise it, by the propulsion handbook and a training article for marine engineers. Va = Vs x (1 - w) follows the definitions of the wake fraction in the encyclopedia and the handbook; the true slip as (propeller speed - Va) / propeller speed, and that it is larger than the apparent slip, follow the handbook and the study notes. The gear ratio as engine turns over shaft turns, and the pitch ratio P/D as the pitch over the diameter, each follow two independent references. The factors are exact: 1 nautical mile = 1852 m, 1 ft = 0.3048 m (the unit definitions).
The propeller would move ahead by its pitch at each turn if the water did not give way, so its theoretical speed is the pitch times the shaft speed: 4.2 m x 105 r/min x 60 = 26 460 m/h, which over 1852 m to the nautical mile is 14.29 kn, or 7.35 m/s. The apparent slip is the share of that speed the ship does not make: at 14 kn by log, (14.29 - 14) / 14.29 x 100 = 2.0 %. The calculator shows each step with your figures.
The log gives the speed through the water (STW), GPS the speed over the ground (SOG). A slip worked out from the GPS speed includes the current along the track: a head current makes it larger, a following current smaller, and a strong following current can make it negative, because the ship then makes more over the ground than the propeller pitch alone would give. Say which speed you entered (log, STW, GPS or SOG); with both, the calculator gives both slips, and the difference between the two speeds is the current along the track, together with any error of the log.
The water near the stern moves along with the hull, so the propeller meets it at the speed of advance, Va = Vs x (1 - w), lower than the ship speed; w is the wake fraction. The true (real) slip is (propeller speed - Va) / propeller speed, larger than the apparent slip. The calculator uses a wake fraction only when you type one (wake 0.25): there is no default value; enter a wake fraction from the data of the vessel.
With a gearbox, enter the engine speed and the gear ratio, engine turns over shaft turns: engine 750 r/min gear 4.2 gives a shaft speed of 750 / 4.2 = 178.6 r/min; a ratio written 4.2:1 reads the same. With a controllable pitch propeller the pitch changes with the setting, so enter the pitch at the current setting, or the pitch ratio with the diameter: P/D 0.8 diameter 5.5 m gives a pitch of 0.8 x 5.5 = 4.4 m.
The calculator gives no figure for a normal slip. The references read do not agree on one range, and the slip of the same ship changes with hull fouling, wind and sea, and the current. Compare the result with the sea-trial figures and with the records of the vessel at the same shaft speed and loading, and use the same kind of speed, log or GPS, each time.
With the pitch, the shaft speed and a slip it gives the ship speed (P/D 0.8 diameter 5.5 m 95 r/min slip 8 %); with the shaft speed, the ship speed and a slip, the pitch; with the pitch, the ship speed and a slip, the shaft speed. The pitch and the diameter in m, mm or ft (1 ft = 0.3048 m exactly); the shaft and engine speed in r/min, also written as rpm, 1/min or min-1; the ship speed in kn (1 kn = 1852 m/h exactly) or m/s.
The calculator works out the slip only. When a propeller part, a pitch control part, a stern tube seal or a shaft line part is needed, send the line from the calculator with the propeller and vessel details, and Vessel Core checks the details before an offer goes back.
