4.4. The action of the wind on the sail
The boat under sail is affected by two media: the air flow acting on the sail and the surface of the boat, and the water acting on the underwater part of the boat.Thanks to the shape of the sail, even with the most unfavorable wind (badewind), the boat can move forward. The sail resembles a wing, the largest deflection of which is 1/3-1/4 of the sail width away from the luff and has a value of 8-10% of the sail width (Fig. 44).
If the wind, which has direction B (Fig. 45, a), meets a sail on the way, it goes around it from two sides. On the windward side of the sail, the pressure is higher (+) than on the lee side (-). The resultant of the pressure forces forms a force P directed perpendicular to the plane of the sail or the chord passing through the front and rear luffs and applied to the center of the windage of the CPU (Fig. 45, b).
Rice. 44. Sail profile:
B - the width of the sail along the chord
Rice. 45. Forces acting on the sail and the hull of the boat:
a - the effect of the wind on the sail; b - the effect of wind on the sail and water on the hull of the boat
Rice. 46. The correct position of the sail in different wind directions: a - close-hauled; b - gulfwind; in - jibe
The force P is decomposed into a thrust force T, directed parallel to the center plane (DP) of the boat, forcing the boat to move forward, and a drift force D, directed perpendicular to the DP, causing drift and roll of the boat.
The force P depends on the speed and direction of the wind relative to the sail. The more
If
The effect of water on the boat largely depends on the contours of its underwater part.
Despite the fact that with the wind, the drift force D exceeds the thrust force T, the boat moves forward. Here the lateral resistance R 1 of the underwater part of the hull affects, which is many times greater than the frontal resistance R.
Rice. 47. Pennant wind:
V I - true wind; В Ш - wind from the movement of the boat; B B - pennant wind
Force D, despite the opposition of the hull, nevertheless blows the boat off the course line. Compiled by DP and the direction of the true movement of the IP boat
Thus, the greatest thrust and the least drift of the boat can be obtained by choosing the most favorable position of the center plane of the boat and the plane of the sail relative to the wind. It is established that the angle between the DP of the boat and the plane of the sail should be equal to half
When choosing the position of the sail relative to the DP and the wind, the foreman of the boat is guided not by the true, but by the pennant (apparent) wind, the direction of which is determined by the resultant of the speed of the boat and the speed of the true wind (Fig. 47).
The jib, located in front of the forefoot, plays the role of a slat. The air flow passing between the jib and the foresail reduces the pressure on the lee side of the foresail and therefore increases its propulsive force. This happens only under the condition that the angle between the jib and the DP of the boat is slightly larger than the angle between the fore and DP (Fig. 48, a).
The impact of the wind on the 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 the wind within the heading angles of 0-110 ° causes a loss of speed, and at large heading angles and wind strength not more than 3-4 points - some of its increment.
Wind action within 30-120° is accompanied by drift and wind heel.
A moving ship is affected by a relative (apparent) wind, which is related to the true 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-angle of ship drift, deg.
Yk - apparent wind angle;
Yi is the angle of true wind.
The specific wind pressure on the ship in kgf / m is calculated by the formula
Where W - wind speed, m/s.
Rice. 7.1. Dependence of true and apparent wind
Rice. 7.2. heeling moment action
Thus, during a hurricane, when the wind speed reaches 40-50 m/s, the magnitude of 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 value 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 sail center, m;
T is the average draft of the ship, m.
The roughness of the sea has the most significant effect on the ship. It is accompanied by the action on the hull of significant dynamic loads and the pitching of the ship. When sailing in waves, the resistance of the ship's hull increases and the conditions for the joint operation of propellers, hull and main engines worsen.
Rice. 7.3. Wave elements
As a result, the speed decreases, the load on the main machines increases, fuel consumption increases and the cruising range of the ship 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 soles;
Wave period t is the time interval 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.
By 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 - developing, it is under the direct influence of the wind, in contrast to the 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 side is steeper than its windward side. At the tops of wind waves, ridges are formed, the tops of which collapse under the action of the wind, forming foam (lambs), and break 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 sizes of wind waves depend on the wind speed and the duration of its impact, the length of the path of wind flows over the water surface and the depth of the given area (Table 7.1).
TABLE 7.1. MAXIMUM VALUES OF WAVE ELEMENTS FOR THE DEEP SEA (H/Λ > 1/2)
The most intense wave growth is observed at the ratio C/W< 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 a steady ocean wave, the following formulas are used:
With wind up to 5 points
With winds over 5
Where B is the wind force in points on the Beaufort scale (§ 23.3).
Under conditions of developed waves, there is interference of individual waves (up to 2% of the total number or more), which reach their 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 most intensively occurs when the wind direction changes, frequent alternation of storm winds and before the front of tropical cyclones (4).
The energy of the developed waves is extremely high. For a ship lying in a drift, 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.
So, for wave periods of about 6-10 s, the value of P can reach impressive values (3.6-10 t/m²).
When the ship moves against the wave, the dynamic effect of the waves will increase in proportion to the square of the ship's speed, expressed in meters per second.
Wavelength in meters, speed in meters per second and period in seconds are related by the following relationships:
A practically moving ship meets not the true, but the relative (apparent) period of the wave 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 located relative to the reduced wavelength λ ":
The nature of the ship's roll has a complex relationship between the elements of the waves (h, λ, τ and C) and the elements of the ship (L, D, T1,2 and δ).
The safety of a ship in terms of stability is determined not only by its design and distribution of cargo, but also by its course and speed. Under conditions of developed waves, the shape of the operating waterline is continuously changing. Accordingly, the shape of the immersed part of the hull, the shape stability arms and restoring moments change.
The stay of the ship at the bottom of the wave is accompanied by an increase in restoring 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 the resonant roll, in which the period of the ship's natural oscillations T1,2 is equal to the visible (observed) period of the wave?" The nature of the onboard resonant roll is shown in Fig. 7.4.< T1 /τ" < 1,3
Resonant pitching is especially dangerous when the ship is positioned with a lag to the wave.
When the ship follows the course against the wave, the speed losses increase significantly, the extremities are exposed and the revolutions abruptly jump. Wave impacts in the bottom of the bow (the phenomenon of "slemming") can lead to deformation of the hull and disruption 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 “saddled” the wave) leads to a sharp loss of lateral stability due to a change in the shape and area of the active waterline, and this leads to the emergence of a gyroscopic moment, which acts in the plane of the waterline and significantly impairs the controllability of the ship.
Rice. 7.4. resonant roll
The most dangerous is the navigation of a small ship on a fair sea, when λ=L of the ship, and VK=C.
Yu.V. Remeza
The universal roll diagram determines the dependence of the observed elements of waves on changes in the elements of the ship's motion.
The diagram is calculated by 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 built with respect to the prevailing wave system, which can be distinguished in any wave and has the most significant effect on the ship's rolling (§ 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 tasks:
- determine the course and speed at which the ship can get into the position of resonant rolling (keel and side);
Determine the wavelength in the navigation 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 state of the most dangerous 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 associated with the earth, and the apparent wind with the ship.
(3) In practice, the movement of water particles of wind waves occurs in orbits close in shape to a circle or an ellipse. Only the wave profile moves.
(4) The nature of wave formation and its relationship with wind elements are discussed in detail in the course of oceanography.
I think that many of us would take the chance to dive into the abyss of the sea on some kind of underwater vehicle, but still, most would prefer a sea voyage on a sailboat. When there were no planes or trains, there were only sailboats. Without them, the world was not the same.
Sailboats with straight sails brought Europeans to America. Their stable decks and capacious holds brought men and supplies for the construction of the New World. But these ancient ships also had their limitations. They were moving slowly and in almost the same direction downwind. A lot has changed since then. Today, completely different principles of controlling the force of wind and waves are used. So if you want to ride a modern one, you will have to learn physics.
Modern sailing is not just moving with the wind, it is something that affects the sail and makes it fly like a wing. And this invisible "something" is called lifting force, which scientists call lateral force.
An attentive observer could not fail to notice that no matter which way the wind blows, a sailing yacht always moves where the captain needs - even when the wind is headwind. What is the secret of such an amazing combination of stubbornness and obedience.
Many do not even realize that a sail is a wing, and the principle of operation of a wing and a sail is the same. It is based on the lifting force, only if the lifting force of the wing of the aircraft, using a headwind, pushes the aircraft up, then a vertically located sail directs the sailboat forward. To explain this from a scientific point of view, it is necessary to go back to the basics - how a sail works.
Look at the simulated process, which shows how air acts on the plane of the sail. Here you can see that the air currents under the model, which have a greater curvature, bend to go around it. In this case, the flow has to speed up a little. As a result, an area of low pressure arises - this generates lift. Low pressure on the underside pulls the sail down.
In other words, the high pressure area is trying to move towards the low pressure area by putting pressure on the sail. There is a difference in pressure, which generates lift. Due to the shape of the sail, on the inner windward side, the wind speed is less than on the leeward side. On the outside, a vacuum is formed. Air is literally sucked into the sail, which pushes the sailing yacht forward.
In fact, this principle is quite simple to understand, just look at any sailing vessel. The trick here is that the sail, no matter how it is located, transmits the wind energy to the vessel, and even if it visually seems that the sail should slow down the yacht, the center of application of forces is closer to the bow of the sailboat, and the wind force provides translational motion.
But this is theory, but in practice everything is a little different. In fact, a sailing yacht cannot go against the wind - it moves at a certain angle to it, the so-called tacks.
The sailboat moves due to the balance of forces. The sails act like wings. Most of the lift they produce is directed to the side, and only a small amount is directed forward. However, the secret is in this wonderful phenomenon in the so-called "invisible" sail, which is located under the bottom of the yacht. This is a keel or in the sea language - a centerboard. The lift of the centerboard also produces lift, which is also directed mainly to the side. The keel resists roll and the opposite force acting on the sail.
In addition to the lifting force, there is also a roll - a phenomenon that is harmful to moving forward and dangerous to the crew of the vessel. But for that, there is a team on the yacht to serve as a living counterbalance to the inexorable physical laws.
In a modern sailboat, both the keel and the sail work together to guide the sailboat forward. But as any novice sailor will confirm, in practice everything is much more complicated than in theory. An experienced sailor knows that the slightest change in the camber of the sail makes it possible to obtain more lift and control its direction. By varying the bow of the sail, a skilled sailor controls the size and location of the area that produces lift. A deep forward bend can create a large pressure zone, but if the bend is too large or the leading edge is too steep, the air molecules will no longer follow the bend. In other words, if the object has sharp corners, the particles of the flow cannot make a turn - the impulse of movement is too strong, this phenomenon is called the "separated flow". The result of this effect is that the sail will "wash", losing the wind.
And here are some more practical tips for using wind energy. Optimal heading into the wind (racing close-hauled). Sailors call it "going against the wind." The apparent wind, which has a speed of 17 knots, is noticeably faster than the true wind, which creates a wave system. The difference in their directions is 12°. The course to the apparent wind is 33°, to the true wind - 45°.
WIND DRIVING FORCE
Very interesting materials have been published on the NASA website 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). Going through the "upper", leeward side of the sail, the air flow travels a longer path and, in accordance with the principle of the continuity of the flow, moves faster than from the windward, "lower" side. The result is less pressure on the lee side of the sail than on the windward side.
When gybeing, with the sail set perpendicular to the direction of the wind, the pressure increase on the windward side is greater than the pressure decrease on the lee side, in other words, the wind pushes the yacht more than it pulls. As the boat turns sharper into the wind, this ratio will change. So, if the wind is blowing perpendicular to the boat's course, an increase in sail pressure to windward has less effect on speed than a decrease in pressure to leeward. 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. The analysis of this interaction leads to unexpected, for many beginners, results. It turns out that the maximum speed is achieved, not at all when the wind blows exactly behind, but the wish for a “tailwind” carries a completely unexpected meaning.
Both the sail and the keel, when interacting with the flow, respectively, of air or water, create a lifting force, therefore, to optimize their work, wing theory can be applied.
WIND DRIVING FORCE
The air flow has kinetic energy and, interacting with the sails, is able to move the yacht. The work of both the sail and the wing of an aircraft is described by Bernoulli's law, according to which an increase in the flow velocity leads to a decrease in pressure. When moving in the air, the wing separates the flow. Part of it bypasses the wing from above, part from below. An aircraft wing is designed so that the airflow over the top of the wing moves faster than the airflow under the underside of the wing. The result is that the pressure above the wing is much lower than below. The pressure difference is the lift force of the wing (Fig. 1a). Due to the complex shape, the wing is able to generate lift even when it cuts through the flow, which moves parallel to the plane of the wing.
The sail can only move the yacht if it is at a certain angle to the flow and deflects it. The question remains as to which part of the lifting force is associated with the Bernoulli effect, and which is the result of flow deflection. According to the classical theory of the wing, the lift force arises solely as a result of the difference in flow speeds above and below the asymmetric wing. At the same time, it is well known that a symmetrical wing is also capable of creating lift if it is installed at a certain angle to the flow (Fig. 1b). In both cases, the angle between the line connecting the anterior and posterior points of the wing and the direction of the airflow is called the angle of attack.
The lift force increases with the angle of attack, however, this dependence works only for small values of this angle. As soon as the angle of attack exceeds a certain critical level and the flow stall occurs, numerous vortices are formed on the upper surface of the wing, and the lift force sharply decreases (Fig. 1c).
Boaters know that gybe is not the fastest course. If the wind of the same strength is blowing at a 90 degree angle to the course, the boat is moving much faster. On a jibe, the force with which the wind pushes against the sail depends on the speed of the yacht. With maximum force, the wind presses on the sail of a yacht standing still (Fig. 2a). As the speed increases, the pressure on the sail drops and becomes minimal when the yacht reaches its maximum speed (Fig. 2b). The maximum speed on a jibe is always less than the wind speed. There are several reasons for this: firstly, friction, in any movement, some 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 the gybe is equal to the difference between the speed of the true wind and the speed of the yacht.
On a gulfwind course (at 90º to the wind), sailing yachts are able to move faster than the wind. Within the framework of this article, we will not discuss the features of the pennant wind, we will only note that on the 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 the increase in speed is friction. Therefore, sailboats with little drag can reach speeds much faster than the wind, but not on a gybe. For example, a buer, due to the fact that skates have negligible slip resistance, can accelerate 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
Winds that blow westward in the South Pacific. That is why our route was drawn up so that on the sailing yacht "Juliet" we move from east to west, that is, so that the wind blows in the back.
However, if you look at our route, you will notice that often, for example when moving from south to north from Samoa to Tokelau, we had to move perpendicular to the wind. And sometimes the direction of the wind changed completely and you had to go against the wind.
Juliet's route
What to do in this case?
Sailing ships have long been able to sail against the wind. The classic Yakov Perelman wrote about this for a long time well and simply in his Second book from the Entertaining Physics series. This piece I quote here verbatim with pictures.
"Sailing against the wind
It is hard to imagine how sailing ships can go "against the wind" - or, in the words of the sailors, go "hauled". True, a sailor will tell you that you cannot sail directly into 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 of 22 ° to it.
In fact, 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. Let us first consider how the wind acts on the sail in general, 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 is blowing. 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; the line AB represents the sail.
The wind pushes the sail always at right angles to its plane.
Since the wind pushes evenly over the entire surface of the sail, we replace the wind pressure with the force R applied to the middle of the sail. We decompose this force into two: the force Q, perpendicular to the sail, and the force P, directed along it (see the figure above, on the right). The last force pushes the sail nowhere, since the friction of the wind on the canvas is negligible. There remains a force Q that pushes the sail at right angles to it.
Knowing this, we can easily understand how a sailing ship can go at an acute angle into the wind. Let the KK line represent the keel line of the ship.
How can you sail against the wind.
The wind blows at an acute angle to this line in the direction indicated by the row of arrows. The line AB represents the 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 diagram for the distribution of forces. We represent the pressure of the wind on the sail by the force Q, which, we know, should be perpendicular to the sail. We decompose this force into two: the force R, perpendicular to the keel, and the force S, directed forward along the keel line of the vessel. Since the movement of the vessel in the direction R meets strong water resistance (the keel in sailing ships is very deep), the force R is almost completely balanced by the water resistance. There remains only the force S, which, as you see, is directed forward and, therefore, moves the ship at an angle, as if towards the wind. [It can be shown that the force S is greatest when the plane of the sail bisects the angle between the directions of the keel and the wind.]. Usually this movement is performed in zigzags, as shown in the figure below. In the language of sailors, such a movement of the vessel is called "tacking" in the narrow sense of the word.
Let's now consider all possible wind directions relative to the boat's course.
A diagram of the ship's courses relative to the wind, that is, the angle between the direction of the wind and the vector from stern to bow (course). 
When the wind blows in the face (head wind), the sails dangle from side to side and it is impossible to move with the sail. Of course, you can always lower the sails and turn on the engine, but this is no longer relevant to sailing.
When the wind blows exactly at the back (jibe, tailwind), the dispersed air molecules put pressure on the sail from one side and the boat moves. In this case, the ship can only move slower than the wind speed. The analogy of riding a bicycle in the wind works here - the wind blows in the back and it is easier to pedal.
When moving against the wind (hauled), the sail moves not because of the pressure of air molecules on the sail from behind, as in the case of a jibe, but because of the lift that is created due to different air speeds on both sides along the sail. At the same time, because of the keel, the boat does not move in a direction perpendicular to the course of the boat, but only forward. That is, the sail in this case is not an umbrella, as in the case of a badewind, but an airplane wing.
During our passages, we mostly sailed with backstays and gulfwinds at an average speed of 7-8 knots with a wind speed of 15 knots. Sometimes we went against the wind, half-wind and close-hauled. And when the wind died down, they turned on the engine.
In general, a boat with a sail going against the wind is not a miracle, but a reality.
The most interesting thing is that boats can go not only against the wind, but even faster than the wind. This happens when the boat goes backstay, creating its own wind.
