Using a sail on a ship. Sail actions, sailing ship control, sail turns. Topic: “Physics of motion of a sailing yacht Sail operation in different winds

It is difficult to imagine how sailing ships can go “against the wind” - or, as sailors say, go “close-hauled”. True, a sailor will tell you that you cannot sail directly against the wind, but you can only move at an acute angle to the direction of the wind. But this angle is small - about a quarter of a right angle - and it seems, perhaps, equally incomprehensible: whether to sail directly against the wind or at an angle to it of 22°.

In reality, however, this is not indifferent, and we will now explain how it is possible to move towards it at a slight angle by the force of the wind. First, let's look at how the wind generally acts on the sail, that is, where it pushes the sail when it blows on it. You probably think that the wind always pushes the sail in the direction it blows. But this is not so: wherever the wind blows, it pushes the sail perpendicular to the plane of the sail. Indeed: let the wind blow in the direction indicated by the arrows in the figure below; line AB denotes a sail.

Since the wind presses evenly on the entire surface of the sail, we replace the wind pressure with a force R applied to the middle of the sail. Let's break this force down into two: force Q, perpendicular to the sail, and the force P directed along it (see figure above, right). The last force pushes the sail nowhere, since the friction of the wind on the canvas is insignificant. Strength remains Q, which pushes the sail at right angles to it.

Knowing this, we can easily understand how a sailing ship can sail at an acute angle towards the wind. Let the line QC depicts the keel line of the ship.

The wind blows at an acute angle to this line in the direction indicated by a series of arrows. Line AB depicts a sail; it is placed so that its plane bisects the angle between the direction of the keel and the direction of the wind. Follow the distribution of forces in the figure. We represent the force of the wind on the sail Q, which we know should be perpendicular to the sail. Let's break this force down into two: force R, perpendicular to the keel, and the force S, directed forward, along the keel line of the vessel. Since the ship's movement is in the direction R encounters strong water resistance (keel in sailing ships becomes very deep), then the strength R almost completely balanced by water resistance. Only strength remains S, which, as you can see, is directed forward and, therefore, moves the ship at an angle, as if towards the wind. [It can be proven that the force S receives the greatest value when the plane of the sail bisects the angle between the keel and wind directions.]. Typically this movement is performed in zigzags, as shown in the figure below. In the language of sailors, such a movement of the ship is called “tacking” in the strict sense of the word.

The movement of a sailing yacht in the wind is actually determined by the simple pressure of the wind on its sail, pushing the ship forward. However, wind tunnel research has shown that sailing upwind exposes the sail to a more complex set of forces.

When the incoming air flows around the concave rear surface of the sail, the air speed decreases, while when flowing around the convex front surface of the sail, this speed increases. As a result, an area of ​​high pressure is formed on the back surface of the sail, and a low pressure area on the front surface. The pressure difference on the two sides of the sail creates a pulling (pushing) force that moves the yacht forward at an angle to the wind.

A sailing yacht located approximately at right angles to the wind (in nautical terminology, the yacht is tacked) moves quickly forward. The sail is subject to pulling and lateral forces. If a sailing yacht sails at an acute angle to the wind, its speed slows down due to a decrease in the pulling force and an increase in the side force. The more the sail is turned towards the stern, the slower the yacht moves forward, in particular due to the large lateral force.

A sailing yacht cannot sail directly into the wind, but it can move forward by making a series of short zigzag movements at an angle to the wind, called tacks. If the wind blows to the left side (1), the yacht is said to be sailing on port tack; if it is blowing to starboard (2), it is said to be sailing on starboard tack. In order to cover the distance faster, the yachtsman tries to increase the speed of the yacht to the limit by adjusting the position of its sail, as shown in the figure below left. To minimize deviation to the side from a straight line, the yacht moves, changing course from starboard tack to port and vice versa. When the yacht changes course, the sail is thrown to the other side, and when its plane coincides with the wind line, it flutters for some time, i.e. is inactive (middle picture below the text). The yacht finds itself in the so-called dead zone, losing speed until the wind again inflates the sail from the opposite direction.

No less important than the resistance of the hull is the traction force developed by the sails. To more clearly imagine the work of sails, let's get acquainted with the basic concepts of sail theory.

We have already talked about the main forces acting on the sails of a yacht sailing with a tailwind (jibed course) and a headwind (behind wind course). We found out that the force acting on the sails can be decomposed into the force that causes the yacht to roll and drift downwind, the drift force and the traction force (see Fig. 2 and 3).

Now let's see how the total force of wind pressure on the sails is determined and what the thrust and drift forces depend on.

To imagine the operation of a sail on sharp courses, it is convenient to first consider a flat sail (Fig. 94), which experiences wind pressure at a certain angle of attack. In this case, vortices are formed behind the sail, pressure forces arise on the windward side, and rarefaction forces arise on the leeward side. Their resulting R is directed approximately perpendicular to the plane of the sail. To properly understand the operation of a sail, it is convenient to imagine it as the resultant of two component forces: X-directed parallel to the air flow (wind) and Y-directed perpendicular to it.

The force X directed parallel to the air flow is called the drag force; It is created, in addition to the sail, also by the hull, rigging, spars and crew of the yacht.

The force Y directed perpendicular to the air flow is called lift in aerodynamics. It is this that creates thrust in the direction of movement of the yacht on sharp courses.

If at the same drag of the sails X (Fig. 95) lift increases, for example, to the value Y1, then, as shown in the figure, the resultant of lift and drag will change by R and, accordingly, the thrust force T will increase to T1.

Such a construction makes it easy to verify that with an increase in drag X (at the same lift force), the thrust T decreases.

Thus, there are two ways to increase the traction force, and therefore the speed on sharp courses: increasing the lifting force of the sail and reducing the drag of the sail and the yacht.

In modern sailing, the lifting force of the sail is increased by giving it a concave shape with some “potbelliness” (Fig. 96): the size from the mast to the most deep place The "belly" is usually 0.3-0.4 of the sail's width, and the depth of the "belly" is about 6-10% of the width. The lifting force of such a sail is 20-25% greater than that of a completely flat sail with almost the same drag. True, a yacht with flat sails sails a little steeper into the wind. However, with potbellied sails, the speed of progress into the tack is greater due to the greater thrust.

Rice. 96. Sail profile

Note that with potbellied sails, not only the thrust increases, but also the drift force, which means that the roll and drift of yachts with potbellied sails is greater than with relatively flat ones. Therefore, a sail “bulge” of more than 6-7% in strong winds is unprofitable, since an increase in heel and drift leads to a significant increase in hull resistance and a decrease in the efficiency of the sails, which “eat up” the effect of increasing thrust. In weak winds, sails with a “belly” of 9-10% pull better, since due to the low total wind pressure on the sail, the heel is small.

Any sail at angles of attack greater than 15-20°, that is, when the yacht is heading 40-50° to the wind or more, can reduce lift and increase drag, since significant turbulence is formed on the leeward side. And since the main part of the lifting force is created by a smooth, turbulent-free flow around the leeward side of the sail, the destruction of these vortices should have a great effect.

The turbulence that forms behind the mainsail is destroyed by setting the jib (Fig. 97). The air flow entering the gap between the mainsail and the jib increases its speed (the so-called nozzle effect) and, when the jib is adjusted correctly, “licks” the vortices from the mainsail.

Rice. 97. Jib work

The profile of a soft sail is difficult to maintain constant at different angles of attack. Previously, dinghies had through battens running through the entire sail - they were made thinner within the “belly” and thicker towards the luff, where the sail is much flatter. Nowadays, through battens are installed mainly on ice boats and catamarans, where it is especially important to maintain the profile and stiffness of the sail at low angles of attack, when a regular sail is already lashing along the luff.

If the source of lift is only the sail, then drag is created by everything that ends up in the air flow flowing around the yacht. Therefore, improving the traction properties of the sail can also be achieved by reducing the drag of the yacht's hull, mast, rigging and crew. For this purpose, various types of fairings are used on the spar and rigging.

The amount of drag on a sail depends on its shape. According to the laws of aerodynamics, the drag of an aircraft wing is lower, the narrower and longer it is for the same area. That is why they try to make the sail (essentially the same wing, but placed vertically) high and narrow. This also allows you to use the upper wind.

The drag of a sail depends to a very large extent on the condition of its leading edge. The luffs of all sails should be covered tightly to prevent the possibility of vibration.

It is necessary to mention one more very important circumstance - the so-called centering of the sails.

It is known from mechanics that any force is determined by its magnitude, direction and point of application. So far we have only talked about the magnitude and direction of the forces applied to the sail. As we will see later, knowledge of the application points is of great importance for understanding the operation of sails.

Wind pressure is distributed unevenly over the surface of the sail (its front part experiences more pressure), however, to simplify comparative calculations, it is assumed that it is distributed evenly. For approximate calculations, the resultant force of wind pressure on the sails is assumed to be applied to one point; the center of gravity of the surface of the sails is taken as it when they are placed in the center plane of the yacht. This point is called the center of sail (CS).

Let's focus on the simplest graphical method for determining the position of the CPU (Fig. 98). Draw the sail area of ​​the yacht on the required scale. Then, at the intersection of medians - lines connecting the vertices of the triangle with the midpoints of opposite sides - the center of each sail is found. Having thus obtained in the drawing the centers O and O1 of the two triangles that make up the mainsail and the jib, draw two parallel lines OA and O1B through these centers and lay on them in opposite directions in any but the same scale as many linear units as square meters in the triangle; the area of ​​the jib is plotted from the center of the mainsail, and the area of ​​the mainsail is plotted from the center of the jib. End points A and B are connected by straight line AB. Another straight line - O1O connects the centers of the triangles. At the intersection of straight lines A B and O1O there will be a common center.

Rice. 98. Graphical method of finding the center of sail

As we have already said, the drift force (we will consider it applied in the center of the sail) is counteracted by the lateral resistance force of the yacht’s hull. The lateral resistance force is considered to be applied at the center of lateral resistance (CLR). The center of lateral resistance is the center of gravity of the projection of the underwater part of the yacht onto the center plane.

The center of lateral resistance can be found by cutting out the outline of the underwater part of the yacht from thick paper and placing this model on a knife blade. When the model is balanced, lightly press it, then rotate it 90° and balance it again. The intersection of these lines gives us the center of lateral resistance.

When the yacht sails without heeling, the CP should lie on the same vertical straight line with the CB (Fig. 99). If the CP lies in front of the central station (Fig. 99, b), then the drift force, shifted forward relative to the force of lateral resistance, turns the bow of the vessel into the wind - the yacht falls away. If the CPU is behind the central station, the yacht will turn its bow to the wind, or be driven (Fig. 99, c).

Rice. 99. Yacht alignment

Both excessive adjustment to the wind, and especially stalling (improper centering) are harmful to the sailing of the yacht, as they force the helmsman to constantly work the helm to maintain straightness, and this increases hull resistance and reduces the speed of the vessel. In addition, incorrect alignment leads to deterioration in controllability, and in some cases, to its complete loss.

If we center the yacht as shown in Fig. 99, and, that is, the CPU and the central control system will be on the same vertical, then the ship will be driven very strongly and it will become very difficult to control it. What's the matter? There are two main reasons here. Firstly, the true location of the CPU and central nervous system does not coincide with the theoretical one (both centers are shifted forward, but not equally).

Secondly, and this is the main thing, when heeling, the traction force of the sails and the longitudinal resistance force of the hull turn out to lie in different vertical planes (Fig. 100), it turns out like a lever that forces the yacht to be driven. The greater the roll, the more inclined the vessel is to pitch.

To eliminate such adduction, the CP is placed in front of the central nervous system. The moment of traction and longitudinal resistance that arises with the roll, forcing the yacht to be driven, is compensated by the trapping moment of the drift forces and lateral resistance when the CP is located at the front. For good centering, the CP must be placed in front of the CB at a distance equal to 10-18% of the length of the yacht along the waterline. The less stable the yacht is and the higher the CPU is raised above the central station, the more it needs to be moved to the bow.

In order for the yacht to have a good move, it must be centered, that is, put the CP and CB in a position in which the vessel on a close-hauled course in a light wind was completely balanced by the sails, in other words, it was stable on the course with the rudder thrown or fixed in the DP (allowed slight tendency to float in very light winds), and in stronger winds had a tendency to float. Every helmsman must be able to center the yacht correctly. On most yachts, the tendency to roll increases if the rear sails are overhauled and the front sails are loose. If the front sails are overhauled and the rear sails are damaged, the ship will sink. With an increase in the “belliness” of the mainsail, as well as poorly positioned sails, the yacht tends to be driven to a greater extent.

Rice. 100. The influence of heel on bringing the yacht into the wind

The effect of wind on a ship is determined by its direction and strength, the shape and size of the ship's sail area, the location of the center of sail, the values ​​of draft, roll and trim.

The action of wind within the heading angles of 0-110° causes a loss of speed, and at large heading angles and wind strength not exceeding 3-4 points - a slight increase in speed.

The action of wind within 30-120° is accompanied by drift and wind roll.

A moving ship is affected by a relative (apparent) wind, which is related to the true one in the following relationships (Fig. 7.1)(2):

Where Vi is the true wind speed, m/s;

VK-apparent wind speed, m/s;

V0 - ship speed, m/s;

βo-ship drift angle, degrees.

Yk - apparent wind angle;

Yi is the true wind angle.

The specific wind pressure on the ship in kgf/m is calculated using the formula

Where W is wind speed, m/s.

Rice. 7.1. Relationship between true and apparent wind

Rice. 7.2. Heeling moment effect

So, during a hurricane, when the wind speed reaches 40-50 m/s, the wind load reaches 130-200 kgf/m2.

The total wind pressure on the ship is determined from the expression P = pΩ, where is the sail area of ​​the ship.

The magnitude of the heeling moment Mkr (Fig. 7.2) in kgf m for the case of steady motion and the action of the wind pressure force P, perpendicular to the ship's DP, is determined from the expression

Where zn is the ordinate of the center of sail, m;

T - average draft of the ship, m.

Rough seas have the most significant effect on a ship. It is accompanied by the action of significant dynamic loads on the hull and the rolling of the ship. When sailing in rough seas, the resistance of the ship's hull increases and the conditions for the joint operation of the propellers, hull and main engines worsen.

Rice. 7.3. Wave elements

As a result, the speed decreases, the load on the main engines increases, fuel consumption increases and the ship's cruising range decreases. The shape and size of the waves are characterized by the following elements (Fig. 7.3):

Wave height h - vertical distance from the top to the bottom of the wave;

Wavelength λ is the horizontal distance between two adjacent crests or troughs;

Wave period t - the period of time during which the wave travels a distance equal to its length (3);

Wave speed C is the distance traveled by the wave per unit time.

Based on their origin, waves are divided into wind, tidal, anemobaric, earthquake (tsunami) and ship waves. The most common are wind waves. There are three types of waves: wind, swell and mixed. Wind waves are developing, they are under the direct influence of the wind, in contrast to swell, which is an inertial wave, or a wave caused by a storm wind blowing in a remote area. The wind wave profile is not symmetrical. Its leeward slope is steeper than its windward one. At the tops of wind waves, ridges are formed, the tops of which collapse under the influence of the wind, forming foam (lambs), and are torn off in strong winds. The direction of the wind and the direction of wind waves in the open sea, as a rule, coincide or differ by 30-40°. The size of wind waves depends on the wind speed and duration of its influence, the length of the path of wind flows over the water surface and the depth of the area (Table 7.1).

TABLE 7.1. MAXIMUM VALUES OF WAVE ELEMENTS FOR THE DEEP SEA (Н/Λ > 1/2)

The most intense wave growth is observed at the C/W ratio< 0,4-0,5. Дальнейшее увеличение этого отношения сопровождается уменьшением роста волн. По­этому волны опасны не в момент наибольшего ветра, а при последующем его ослаблении.

For approximate calculations of the average wave height of steady ocean waves, the following formulas are used:

With winds up to 5 points

When the wind is over 5 points

Where B is the wind force in points on the Beaufort scale (§ 23.3).

In conditions of developed waves, there is interference of individual waves (up to 2% of the total number or more), which reach maximum development and exceed the average wave height by two to three times. Such waves are especially dangerous.

The superposition of one wave system on another occurs most intensely when the wind direction changes, there is a frequent alternation of storm winds, and before the front of tropical cyclones (4).

The energy of waves of developed waves is exceptionally high. For a ship drifting, the dynamic effect of waves can be determined from the expression p=0.1 τ² where τ is the true period of the wave, s.

Thus, for wave periods of about 6-10 s, the P value can reach impressive values ​​(3.6-10 t/m²).

When a ship moves against a wave, the dynamic effect of the waves will increase in proportion to the square of the ship's speed, expressed in meters per second.

The wavelength in meters, speed in meters per second and period in seconds are related to each other by the following relationships:

A practically moving ship encounters not the true, but the relative (apparent) wave period τ", which is determined from the expression

Where a is the heading angle of the wave crest front, measured along any side.

Plus refers to the case of movement against the wave, minus - along the wave.

When changing course, the ship is positioned relative to the reduced wavelength λ":

The nature of the ship's rolling has a complex relationship between the wave elements (h, λ, τ and C) and the ship elements (L, D, T1,2 and δ).

The safety of a ship in terms of stability is determined not only by its design and load distribution, but also by its course and speed. In conditions of developed waves, the shape of the existing waterline continuously changes. Accordingly, the shape of the immersed part of the hull, the shape stability arms and the restoring moments change.

The stay of the ship at the bottom of the wave is accompanied by an increase in righting moments. Staying a ship (especially for a long time) on the crest of a wave is dangerous and can lead to capsizing. The most dangerous is resonant rolling, at which the period of the ship's own oscillations T1,2 is equal to the visible (observed) period of the wave?" The nature of the onboard resonant rolling is shown in Fig. 7.4. As follows from the figure, the resonance phenomenon is observed at a ratio of 0.7< T1 /τ" < 1,3

Resonant rocking is especially dangerous when the ship is positioned with the lag facing the wave.
When a ship follows a course against the wave, losses in speed increase significantly, exposing the ends and sudden surges in speed occur. Wave impacts at the bottom of the bow (slamming phenomenon) can lead to deformation of the hull and tearing of individual mechanisms and devices from the foundations.

When following a wave, the ship is less susceptible to wave impacts. However, following it along the wave at a speed close to the wave speed VK = (0.6--1.4) C (the ship “rided” the wave) leads to a sharp loss lateral stability due to a change in the shape and area of ​​the acting waterline, and this leads to the emergence of a gyroscopic moment acting in the plane of the waterline and significantly worsening the controllability of the ship.

Rice. 7.4. Resonant pitching

The most dangerous navigation of a small ship is in favorable seas, when λ=L of the ship, and VK=C.

Universal pitching diagram Yu.V. Remeza

The universal rolling diagram determines the dependence of the observed wave elements on changes in the elements of the ship's motion.

The diagram is calculated using the formula

Where V is the speed of the ship, knots.

The diagram determines the relationship between X and V sin a for various values ​​of m. It is constructed relative to the prevailing wave system, which can be identified at any sea level and has the most significant effect on the ship's motion (§ 23.4). The universal diagram can only be used in areas with sufficiently large depths (more than 0.4X waves).

The use of a universal pitching diagram allows you to solve the following main problems:
- determine the course and speed at which the ship can get into a position of resonant pitching (pitching and side);

Determine the wavelength in the sailing area;

Determine the course sectors and speed ranges at which the ship will experience strong rolling, close to resonant;

Determine the courses and speeds at which the ship will be in the most dangerous state of reduced lateral stability;

Determine the courses and speeds at which the ship will experience the “slamming” phenomenon.

(1) Further increase in wind is accompanied by wind waves, which reduce the speed of the ship.
(2) The coordinates of the true wind are related to the earth, and the apparent wind to the ship.
(3) In practice, the movement of water particles in wind waves occurs in orbits close in shape to a circle or ellipse. Only the wave profile moves.
(4) The nature of wave formation and its connection with wind elements are discussed in detail in the oceanography course.

WIND DRIVING FORCE

The NASA website has published very interesting materials about various factors influencing the formation of lift by an aircraft wing. There are also interactive graphical models that demonstrate that lift can also be generated by a symmetrical wing due to flow deflection.

The sail, being at an angle to the air flow, deflects it (Fig. 1d). Coming through the “upper”, leeward side of the sail, the air flow travels a longer path and, in accordance with the principle of flow continuity, moves faster than from the windward, “lower” side. The result is that the pressure on the leeward side of the sail is less than on the windward side.

When sailing on a jibe, when the sail is set perpendicular to the direction of the wind, the degree of increase in pressure on the windward side is greater than the degree of decrease in pressure on the leeward side, in other words, the wind pushes the yacht more than it pulls. As the yacht turns sharper into the wind, this ratio will change. Thus, if the wind is blowing perpendicular to the yacht's course, increasing the pressure on the sail on the windward side has less effect on speed than decreasing the pressure on the leeward side. In other words, the sail pulls the yacht more than it pushes.

The movement of the yacht occurs due to the fact that the wind interacts with the sail. Analysis of this interaction leads to unexpected results for many beginners. It turns out that the maximum speed is achieved not at all when the wind blows directly from behind, and the wish for a “fair wind” carries a completely unexpected meaning.

Both the sail and the keel, when interacting with the flow of air or water, respectively, create lift, therefore, to optimize their operation, wing theory can be applied.

WIND DRIVING FORCE

The air flow has kinetic energy and, interacting with the sails, is capable of moving the yacht. The work of both the sail and the airplane wing is described by Bernoulli's law, according to which an increase in flow speed leads to a decrease in pressure. When moving in the air, the wing divides the flow. Part of it goes around the wing from above, part from below. An airplane wing is designed so that the air flow over the top of the wing moves faster than the air flow under the bottom of the wing. The result is that the pressure above the wing is much lower than below. The pressure difference is the lifting force of the wing (Fig. 1a). Thanks to its complex shape, the wing is able to generate lift even when cutting through a flow that moves parallel to the plane of the wing.

The sail can move the yacht only if it is at a certain angle to the flow and deflects it. It remains debatable how much of the lift is due to the Bernoulli effect and how much is the result of flow deflection. According to classical wing theory, lift arises solely as a result of the difference in flow velocities above and below an asymmetrical wing. At the same time, it is well known that a symmetrical wing is capable of creating lift if installed at a certain angle to the flow (Fig. 1b). In both cases, the angle between the line connecting the front and rear points of the wing and the direction of flow is called the angle of attack.

Lift increases with increasing angle of attack, but this relationship only works at small values ​​of this angle. As soon as the angle of attack exceeds a certain critical level and the flow stalls, numerous vortices are formed on the upper surface of the wing, and the lift force decreases sharply (Fig. 1c).

Yachtsmen know that gybe is not the fastest course. If the wind of the same strength blows at an angle of 90 degrees to the heading, the yacht moves much faster. On a jibe course, the force with which the wind presses on the sail depends on the speed of the yacht. With maximum force, the wind presses on the sail of a yacht standing motionless (Fig. 2a). As speed increases, the pressure on the sail drops and becomes minimal when the yacht reaches maximum speed (Fig. 2b). Maximum speed On a jibe course, the wind speed is always less. There are several reasons for this: firstly, friction; during any movement, some part of the energy is spent on overcoming various forces that impede movement. But the main thing is that the force with which the wind presses on the sail is proportional to the square of the speed of the apparent wind, and the speed of the apparent wind on a gybe course is equal to the difference between the speed of the true wind and the speed of the yacht.

With a gulfwind course (at 90º to the wind), sailing yachts are able to move faster than the wind. In this article, we will not discuss the features of the apparent wind; we will only note that on a gulfwind course, the force with which the wind presses on the sails depends to a lesser extent on the speed of the yacht (Fig. 2c).

The main factor that prevents an increase in speed is friction. Therefore, sailboats with little resistance to movement are able to reach speeds much higher than the speed of the wind, but not on a gybe course. For example, a boat, due to the fact that skates have negligible sliding resistance, is capable of accelerating to a speed of 150 km/h with a wind speed of 50 km/h or even less.

The Physics of Sailing Explained: An Introduction

ISBN 1574091700, 9781574091700