c Allerton Press, Inc., 2012. ISSN 0027-1330, Moscow University Mechanics Bulletin, 2012, Vol. 67, No. 3, pp. 62–65.  c V.G. Chikarenko, 2012, published in Vestnik Moskovskogo Universiteta, Matematika. Mekhanika, 2012, Original Russian Text  Vol. 67, No. 3, pp. 32–35.

Comparing the Efficiency of Rectangular and Triangular Submarine Sails V. G. Chikarenko Moscow State University, Faculty of Mechanics and Mathematics, Leninskie Gory, Moscow, 119899, Russia Received June 01, 2011; in final form, March 02, 2012 Abstract—A number of pollution-free sea wave converters installed on ship models are considered. The operation of the wave generator used in the hydraulic channel of Moscow University Institute of Mechanics is described. The performance evaluation of rectangular and triangular submarine sails is discussed.

DOI: 10.3103/S0027133012030028 The energy source problem is one of the most important in modern science and technology. On the Earth, the amount of organic fuel burnt per day is equal to that synthesized in the nature over a period of 1000 years. At the same time, about 2/3rds of the Earth’s surface is covered by seas and oceans whose wave energy considerably exceeds the energy of mineral resources. The wave intensity magnitude about 3 or 4 characterizes the mean state of seas and oceans. Thousands of ships are crossing the seas and oceans using the organic fuel, but ignoring the huge amount of wave energy. From the time of sail ships, the wind pressure force acting on sails is used, whereas the forces induced by waves on ships remain unused in spite of the fact that the sea wave energy significantly exceeds the wind energy, since the water density is greater than the air density by a factor of 800. In the case of choppy water, the ship’s speed loss may reach 50%, whereas the doubling of speed may require the increase of the ship’s engine power by a factor of 3. The sea wave energy N can be estimated as [1] Vs + Vw N = ρga2 B, 2 where ρ is the density of water, g is the gravitational acceleration, a is the wave amplitude, B is the width of the ship, Vs is the velocity of the ship, and Vw is the wave velocity. A ship moving across the waves acquires this amount of energy per unit time. Hence, the use of wave energy is a promising technique of speed enhancing for ships. It remains to solve the engineering problem of obtaining the energy from sea waves. To accomplish this, various technical devices can be used. Presently, a number of pollution-free sea wave converters installed on model ships are tested at the Moscow University Institute of Mechanics. This new direction of shipbuilding is attracted considerable attention. Before performing experiments in reality, it is necessary to conduct numerous model tests in channels and pools to determine the optimal size of wave propulsion devices and their speed and traction characteristics. A wave generator is installed in the hydraulic channel of Moscow University Institute of Mechanics to perform experimental studies of ship models equipped with wave propulsion devices. This wave generator is installed in the hydraulic channel of cross section 1.5 × 1.5 m; the length of its working section is equal to 48 m (Fig. 1). The wave formation device 1 is a wedge-shaped body whose wedge angle is 20◦ . The width of this body is equal to 1480 mm; its height is equal to 600 mm. The body is fixed on the guides capable of moving along a stationary platform with the aid of rollers. The operation of the wave formation device is based on the back-and-forth motion of the wedge-shaped body that generates the waves of given amplitude and frequency. The body’s displacement ranges from 100 to 300 mm, which corresponds to the mean range of sea waves when modeling them in hydraulic channels. The wave generator is driven by a three-phase asynchronous motor whose power is equal to 2.2 kW and whose number of revolutions per minute is equal to 1440. A reducer and a mechanical transformer of rotary motion to the back-and-forth motion are used. An IS-5-RUS electronic frequency converter is used to control the motor (i.e., to change its number of revolutions). This converter is useful to regulate the frequency of revolutions of the asynchronous motor in a wide range without a significant loss of energy. The wave initiated by the wave formation device travels between the viewing windows marked by 2 in Fig. 1. The video filming 62

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of wave profiles is performed through these windows; they are also used to observe the operation of wave propulsion devices installed on the model ships. The waves are damped by the wave absorbers marked by 3 in Fig. 1; they are installed at the end of the working section of the channel.

Fig. 1. Location of the wave generator in the hydraulic channel.

A SONY DCR-T RV 900E digital video camera is used. A Pentium-4-1 computer (8 GHz) is used to process the video data with the aid of the VIRTUAL DUB software package capable of data processing with the use of frame numbers in the real-time mode with an accuracy of 1 s. The waves transfer their energy to a ship whose motion causes the interaction between the water flow and the wave propulsion device. Because of incident waves, a ship performs oscillations (Fig. 2). The wave effects are observed on the free wave surface. The complexity of the problem becomes obvious in the case of storm winds. As shown in Fig. 2, a ship may move with the following six degrees of freedom: ξ1 , ξ2 , and ξ3 are the longitudinal, transverse, and vertical oscillations; ξ4 is the roll; ξ5 is the pitch; and ξ6 is the yaw. For a ship, thus, the equations of free oscillations are as follows [2]: in the case of roll, we have Fig. 2. Position of a ship in the case of choppy water.

(Jx + Δx)ξ4 + Drξ4 = 0; in the case of pitch, we have

(Jy + Δy)ξ5 + DRξ5 = 0; in the case of dipping, we have (D/g + Δz)ξ3 + Slwa ξ3 = 0. Here ξ4 is the trim angle, ξ5 is the angle of roll, r is the transverse metacentric height, R is the longitudinal metacentric height, D is the ship’s displacement, Jx is the ship mass moment of inertia with respect to the central longitudinal axis, Δx is the added mass moment of inertia with respect to the central longitudinal axis, Jy is the ship mass moment of inertia with respect to the central transverse axis, Δy is the added mass moment of inertia with respect to the central transverse axis, Δz is the added water mass in the case of dipping, and Slwa is the load waterline area. When a ship moves against sea waves, the incident wave is deformed by the bow of the ship. The energy of this wave decreases when it moves to the rear part of the ship. For this reason, the wave propulsion devices are installed in the fore part of a ship at a distance about 1–10% of the ship length. In our experiments, the interaction between a ship equipped with a wave propulsion device and the gravity wave proceeds in the channel of finite depth h < λ, where λ is the wave length. In such a case of shallow water, thebottom MOSCOW UNIVERSITY MECHANICS BULLETIN

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pressure is less than that in the case of deep water. When an immersed body moves in water, the complete description of the wave surface becomes a very complex problem. Because of this, some simplifications are made. Let us consider the behavior of a ship in the case of choppy water. Water is inviscid, gravitational, and incompressible. The elementary wave is twodimensional and sinusoidal; its circular Fig. 3. Operation scheme of a submarine sail. frequency is equal to ω = 2π/Tw , where Tw is its period. The phase velocity of the wave is denoted by Vw . Rigid wings and submarine sails can be employed as devices using the wave energy (see Fig. 3 and [2–10]). Since the water density is greater than the air density by a factor of 800, there is no need for a large area of sails: it is sufficient to use a submarine sail whose area Ssail is about one tenth of Slwa . When ship’s nose moves down, the water flow becomes accelerated over the convex part of the sail and becomes decelerated beneath this part of the sail. The water pressure measured on the lower surface of the sail is greater than that Fig. 4. A model ship equipped with submarine sails. measured on the upper surface of the sail. The resulting hydrodynamic force F can be decomposed into the following two components: the force N (it reduces the amplitude of rolling) and the traction force T (Fig. 3). When the wave phase oppositely changes, the convex part of the sail is directed down and the force N is also directed down, whereas the direction of the force T remains unchanged; as a result, the force T continues to set the ship in motion. Figures 4 and 5 illustrate a model ship equipped with wave propulsion sails.

Fig. 5. A model ship equipped with (a) triangular and (b) rectangular submarine sails.

Fig. 6.Dependence of the velocity V on the frequency F for (1) triangular and (2) rectangular submarine sails; the frequency of the wave generator is indicated in brackets.

The aim of our experimental studies is to compare the efficiency of rectangular and triangular submarine sails (Fig. 5). These sails were examined under the same conditions with H = 70 cm and A = 27 cm,where H MOSCOW UNIVERSITY MECHANICS BULLETIN

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is the water depth and A is the displacement of the wave generator. However, the area of the triangular sail was half the area of the rectangular sail. From Fig. 6 it follows that the triangular sail is more efficient. The model equipped with the triangular sail was faster. The maximum Froude number Fr obtained in our experiments was equal to 0.013. This situation can be explained by the following. In the case of a rigid wing, the force T is always directed in the direction of motion. In the case of a submarine sail, the force T is oppositely directed at the rear of this sail (Fig. 3). Hence, the ship’s speed increases if the area of this part of the sail is lesser. This fact was confirmed even in the case of a triangular sail whose area was significantly less. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

S. N. Blagoveshchenskii, Rolling of Ships (Sudpromgiz, Leningrad, 1954) [in Russian]. A. V. Boiko, V. V. Prokof’ev, and V. G. Chikarenko, Drift Anchor, RF Patent No. 2 326 018 (2008). V. A. Eroshin and V. A. Samsonov, Wave Propulsion Device, RF Patent No. 2 347 714 (2009). G. A. Konstantinov and Yu. L. Yakimov, “Calculation of the Thrust of a Wave-Powered Marine Propelling Device,” Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 3, 139–143 (1995) [Fluid Dyn. 30 (3), 453–456 (1995)]. J. N. Newman, Marine Hydrodynamics (MIT Press, Cambridge, 1977; Sudostroenie, Leningrad, 1985). G. E. Pavlenko, “Use of Wave Energy for the Motion of Ships,” Tr. Leningrad. Inst. Inzh. Vodn. Transp., No. 6, 394–401 (1936). L. I. Sedov, Plane Problems of Hydrodynamics and Aerodynamics (Nauka, Moscow, 1980; Interscience, New York, 1965). V. G. Chikarenko, The Bow of a Ship is a Wave Propulsion Device (Nauka, Moscow, 1980) [in Russian]. V. G. Chikarenko, Experimental Studies of Model Ships Equipped with Wave Propulsion Devices (Sputnik, Moscow, 2004) [in Russian]. L. A. Epshtein, Methods in the Theory of Dimension and Similarity (Sudostroenie, Leningrad, 1970) [in Russian].

Translated by O. Arushanyan

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