Laws of similitude

Similitude of the scale models

Froude’s law, associated with the other physical laws that govern the magnitudes involved during ship movements, are explained in the appendix (photo: Port Revel). They are summarised below.

• Shape: all the dimensions of the real ship and the scale model are in the same ratio — the scale factor — which is 1:25 on the Port Revel model ships. So the scale model has exactly the same shape as the ship that it represents. The angles and the block coefficient(*) are the same. Of course, the surface areas and volumes are at ratios proportional to the square and the cube of the scale factor respectively.
(*) The block coefficient is the ratio of the immersed volume of the ship to the (theoretical) volume of the rectangular parallelepiped enclosing the immersed part of the ship (product of length by waterline width by moulded draught). It could be described as a "filling coefficient".

• Mass and displacement: these magnitudes follow the same law as the volumes (lake water and sea water have similar densities). The same applies for forces.

• Time: since Froude’s law induces that the time scale is the square root of the length scale, everything happens five times faster! So the students must react five times faster at the helm of their scale model than on the bridge of the real ship. Students must pay attention during the first "practical session" on the lake ... and be even more proactive. On the other hand, acceleration is identical. Lastly, the angular velocity variation is five times faster.. (photo Port Revel)

• • Power: the coefficient has been shown (cf. appendix) to be 1/78 125. Taking the example of the EUROPE (255 000 dwt), her propulsion power is 29 550 kW. Her scale model (19 dwt) only requires a 0.30 kW engine which, to use a "landlubber’s" image, is equivalent to running a 20 t truck on a moped engine!

Wind is obviously the only parameter that cannot be modelled... but the lake was chosen in order to minimise uncontrollable effects (region not subject to strong winds, lake surrounded by a "protective" forest). However, students must bear in mind the fact that a 10 kn puff of wind on the lake corresponds to a 50 kn gale!

To conclude, the scale models at Port Revel are 25 times smaller than the real ships, with five times slower speeds but, since the distances are 25 times shorter, time is five times faster. But the advantage is that 35 hrs of manoeuvres at Port Revel are equivalent to 175 hrs of real manoeuvres!

Similitude of manœuvres

Manœuvres on the scale models are the same as in reality, except that the captain sends his orders to the helmsman five times faster!

	Click on the diagram opposite to enlarge it (photo. Port Revel)
	The captain is in position at his raised post at the stern, with a 360° view. His field of vision is exactly the same as from the bridge of the real ship. He gives orders to the helmsman who, positioned below and in front of him, operates helm and engine. The students take turns to occupy the two posts.

The captain controls the transverse thrusters (a similar effect to tug assistance).

Although the instrument panels look simple, they give all the usual information: wheel with rudder angle indicator, telegraph to the helm with propeller RPM indicator, ship heading, electronic log, wind speed and direction, remote control of windlasses and anchors. It is important to note that indications are given in values that correspond to the real ship and not to the scale model, to make the students “forget” that they are handling large scale models.

First practical session...

On to the first practical session and ... no mistakes allowed as all ship movements are tracked to within a centimetre by Port Revel’s DGPS⁽¹⁾! This facility, fitted in 2000 and linked to the American and Russian satellite systems, has an accuracy of 25 cm in reality (i.e. 1 cm on the lake). Positions of ships and their main parameters (rudder angle, RPM, ship speed, wind speed and direction, etc.) are continuously recorded and sent to a central computer at the port for processing. The evening debriefing is the moment of truth ... the trajectory maps don’t miss a thing! This is a highly valuable teaching tool.
(1) DGPS : Differential Global Positioning System.