It is not the wind, but the sail that determines the direction. Topic: “Physics of motion of a sailing yacht

Before looking at how a sail works, there are two short but important points to consider:
1. Determine what kind of wind affects the sails.
2.Talk about specific marine terminology associated with courses relative to the wind.

True and apparent winds in yachting.

The wind that acts on a moving ship and everything on it is different from the one that acts on any stationary object.
Actually, the wind as an atmospheric phenomenon blowing relative to land or water is what we call true wind.
In yachting, the wind relative to a moving yacht is called apparent wind and is the sum of the true wind and the oncoming air flow caused by the movement of the vessel.
The apparent wind always blows at a sharper angle to the boat than the true wind.
The apparent wind speed can be greater (if the true wind is headwind or sidewind), or less than the true wind (if it is from a tailwind).

Directions relative to the wind.

In the wind means from the direction from which the wind blows.
Downwind- from the direction the wind blows.
These terms, as well as derivatives from them, such as “windward”, “leeward”, are used very widely, and not only in yachting.
When these terms are applied to a ship, it is customary to also talk about the windward and leeward sides.
If the wind blows from the starboard side of the yacht, then this side is called windward, left side - leeward respectively.
Port and starboard tack are two terms directly related to the previous ones: if the wind blows to the starboard side of the ship, then they say that it is sailing on the starboard tack, if it is on the left, then on the left.
In English nautical terminology, what is associated with starboard and port is different from the usual Right and Left. They say Starboard about the starboard side and everything related to it, and Port about the left side.

Courses relative to the wind.

Courses relative to the wind vary depending on the angle between the direction of the apparent wind and the direction the vessel is moving. They can be divided into acute and full.

Close-hauled is a sharp course relative to the wind. when the wind blows at an angle of less than 80°. There can be a steep close-hauled wind (up to 50°) or a full close-hauled wind (from 50 to 80°).
Full courses relative to the wind are courses when the wind blows at an angle of 90° or more to the direction the yacht is moving.
These courses include:
Gulfwind - the wind blows at an angle of 80 to 100°.
Backstay - the wind blows at an angle from 100 to 150° (steep backstay) and from 150 to 170° (full backstay).
Fordewind - the wind blows astern at an angle of more than 170°.
Leftist - the wind is strictly headwind or close to it. Since a sailing ship cannot move against such a wind, it is more often called not a course, but a position relative to the wind.

Maneuvers relative to the wind.

When a yacht under sail changes its course so that the angle between the wind and the direction of motion decreases, then the ship is said to be is given. In other words, to flatten means to go at a sharper angle to the wind.
If the reverse process occurs, i.e. the yacht changes course towards increasing the angle between it and the wind, the vessel falls away .
Let us clarify that the terms (“lead” and “fall”) are used when the boat changes course relative to the wind within the same tack.
If the ship changes tack, then (and only then!) such a maneuver in yachting is called a turn.
There are two different ways to change tack and, accordingly, two turns: tack And jibe .
A tack is a turn into the wind. The vessel is driven, the bow of the boat crosses the wind line, at some point the vessel passes through the left-hand position, after which it lies on the other tack.
Yachting when jibes occurs in the opposite way: the ship falls away, the stern crosses the wind line, the sails are transferred to the other side, the yacht lies on a different tack. Most often this is a turn from one full course to another.

Sail operation during yachting.

One of the main challenges for a sailor when working with sails is to orient the sail at the optimal angle relative to the wind to best propel the sail forward. To do this, you need to understand how the sail interacts with the wind.
The work of a sail is in many ways similar to the work of an airplane wing and occurs according to the laws of aerodynamics. For particularly curious yachtsmen, you can learn more about the aerodynamics of a sail as a wing in a series of articles:. But it’s better to do this after reading this article, gradually moving from easy to more complex material. Although, who am I telling this to? Real yachtsmen are not afraid of difficulties. And you can do everything exactly the opposite.

The main difference between a sail and an aircraft wing is that for an aerodynamic force to appear on the sail, a certain non-zero angle is needed between it and the wind; this angle is called the angle of attack. The airplane wing has an asymmetrical profile and can operate normally at zero angle of attack, but the sail does not.
As the wind flows around the sail, an aerodynamic force arises, which ultimately moves the yacht forward.
Let's consider the operation of a sail in yachting at different courses relative to the wind. First, for simplicity, let's imagine that a mast with one sail is dug into the ground and we can direct the wind at different angles to the sail.

Angle of attack 0°. The wind blows along the sail, the sail flutters like a flag. There is no aerodynamic force on the sail, there is only drag force.
Angle of attack 7°. An aerodynamic force begins to appear. It is directed perpendicular to the sail and is still small in size.
The angle of attack is about 20°. The aerodynamic force has reached its maximum value and is directed perpendicular to the sail.
Angle of attack 90°. Compared to the previous case, the aerodynamic force did not change significantly either in magnitude or direction.
Thus, we see that the aerodynamic force is always directed perpendicular to the sail and its magnitude practically does not change in the angle range from 20 to 90°.
Angles of attack greater than 90° do not make sense to consider, since the sails on a yacht are usually not set at such angles relative to the wind.

The above dependences of the aerodynamic force on the angle of attack are largely simplified and averaged.
In fact, these properties vary markedly depending on the shape of the sail. For example, a long, narrow and fairly flat mainsail of racing yachts will have a maximum aerodynamic force at an angle of attack of about 15°; at higher angles the force will be slightly less. If the sail is more potbellied and does not have a very large aspect ratio, then the aerodynamic force on it can be maximum at an angle of attack of about 25-30°.

Now let's look at how a sail works on a yacht.

For simplicity, let's imagine that there is only one sail on the yacht. Let it be a grotto.
First, it’s worth looking at how the yacht + sail system behaves when moving on the sharpest courses relative to the wind, since this usually raises the most questions.

Let’s say the yacht is affected by wind at an angle of 30-35° to the hull. By orienting the sail on course at an angle of approximately 20° to the wind, we obtain a sufficient aerodynamic force A on it.
Since this force acts at right angles to the sail, we see that it pulls the yacht strongly to the side. By decomposing the force A into two components, you can see that the forward thrust force T is several times less than the force pushing the boat sideways (D, drift force).
What causes the yacht to move forward in this case?
The fact is that the design of the underwater part of the hull is such that the resistance of the hull to movement to the side (the so-called lateral resistance) is also several times greater than the resistance to movement forward. This is facilitated by the keel (or centreboard), rudder and the very shape of the hull.
However, lateral resistance occurs when there is something to resist, i.e., for it to start working, some sideways displacement of the body, the so-called wind drift, is required.

This displacement naturally occurs under the action of the lateral component of the aerodynamic force, and as a response, a lateral drag force S immediately arises, directed in the opposite direction. As a rule, they balance each other at a drift angle of about 10-15°.
So, it is obvious that the lateral component of the aerodynamic force, most pronounced on sharp courses relative to the wind, causes two undesirable phenomena: wind drift and roll.

Wind drift means that the yacht's trajectory does not coincide with its centreline (diameter plane, or DP, is a smart term for the bow-stern line). There is a constant shift of the yacht to the wind, moving as if a little sideways.
It is known that when yachting on a close-hauled course under average weather conditions, the wind drift as the angle between the DP and the actual trajectory is approximately 10-15°.

Advance against the wind. Tacking.

Since yachting under sails is not possible strictly against the wind, and you can only move at a certain angle, it would be good to have an idea of ​​how sharply the yacht can move in degrees to the wind. And what, accordingly, is that slow sector of courses relative to the wind, in which movement against the wind is impossible.
Experience shows that a regular cruising yacht (not a racing yacht) can effectively sail at an angle of 50-55° to the true wind.

Thus, if the goal that needs to be achieved is located strictly against the wind, then yachting to it will not take place in a straight line, but in a zigzag, first on one tack, then on the other. In this case, on each tack, naturally, you will need to try to sail as sharply as possible into the wind. This process is called tacking.

The angle between the trajectories of yachts on two adjacent tacks when tacking is called tacking. Obviously, with a sharpness of movement to the wind of 50-55°, the tacking angle will be 100-110°.

The magnitude of the tacking angle shows us how effectively we can move towards the target if it is strictly against the wind. For an angle of 110°, for example, the path to the target increases by 1.75 times compared to moving in a straight line.

Sail operation on other courses relative to the wind

It is obvious that already on a gulfwind course the thrust force T significantly exceeds the drift force D, so the drift and roll will be small.

With the backstay, as we see, not much has changed compared to the gulfwind course. The mainsail is placed in a position almost perpendicular to the DP, and this position is extreme for most yachts; it is technically impossible to deploy it even further.

The position of the mainsail on the gybe course is no different from the position on the backstay course.
Here, for simplicity, when considering the physics of the process in yachting, we take into account only one sail - the mainsail. Typically, a yacht has two sails - a mainsail and a staysail (headsail). So, on a gybe course, the jib (if it is located on the same side as the mainsail) is in the wind shadow of the mainsail and practically does not work. This is one of several reasons why jibes are not a favorite among boaters.

The winds that are in the southern part Pacific Ocean blowing in a westerly direction. That is why our route was designed so that sailing yacht"Juliet" move from east to west, that is, with the wind blowing at your 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 we 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 long ago well and simply in his second book from the series “Entertaining Physics”. I present this piece here verbatim with pictures.

"Sailing against the wind

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; the line AB represents the sail.

The wind always pushes the sail at right angles to its plane.

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. We will split this force into two: force Q, perpendicular to the sail, and 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. The force Q remains, 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 line KK 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 a series of arrows. Line AB represents 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 wind pressure on the sail by force Q, which, we know, must be perpendicular to the sail. Let us divide this force into two: force R, perpendicular to the keel, and force S, directed forward along the keel line of the ship. Since the movement of the vessel in the direction R encounters strong resistance from the water (keel in sailing ships becomes very deep), then the force R is almost completely balanced by the resistance of the water. There remains only one 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 proven that the force S is greatest 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."

Let's now consider all possible wind directions relative to the boat's heading.

Diagram of the ship's course relative to the wind, that is, the angle between the wind direction and the vector from stern to bow (course).

When the wind blows in your face (leventik), 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 no longer has anything to do with sailing.

When the wind blows directly behind you (jibe, tailwind), the accelerated air molecules put pressure on the sail on 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 at your back and it is easier to turn the pedals.

When moving against the wind (close-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 lifting force that is created due to different air velocities on both sides along the sail. Moreover, 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 close-hauled sail, but an airplane wing.

During our passages, we mainly sailed with backstays and gulfwinds at an average speed of 7-8 knots with a wind speed of 15 knots. Sometimes we sailed against the wind, halfwind 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 sail not only against the wind, but even faster than the wind. This happens when the boat backstays, creating its own wind.

A boat under sail is influenced by two environments: the air flow acting on the sail and the above-water part of the boat, and the water acting on the underwater part of the boat.

Thanks to the shape of the sail, even in the most unfavorable wind (close-hauled), the boat can move forward.

The sail resembles a wing, the greatest 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. 18).

Rice. 18. Sail profile: B - the width of the sail along the chord (according to I.I. Khomyakov, 1976).

If the wind has a direction IN(Fig. 19, a), meets a sail on the way, it goes around it on both sides. The windward side of the sail creates a higher pressure (+) than the leeward side (-). The resultant of pressure forces forms a force R, directed perpendicular to the plane of the sail or chord passing through the luff and luff and applied to the center of the sail CPU(Figure 19, b).

Rice. 19 Forces acting on the sail and hull of the boat (according to I.I. Khomyakov, 1976):

a is the effect of wind on the sail; b - the effect of wind on the sail and water on the boat hull.

Force R decomposes into traction force T, directed parallel to the diametrical plane ( DP) of the boat, causing the boat to move forward, and the drift force D, directed perpendicularly DP, causing the boat to drift and roll.

Force R depends on the speed and direction of the wind relative to the sail. The more Ðb between wind direction IN and the plane of the sail PP, the greater the power R. If Ðb=90°, force R reaches its maximum value.

Powers T And D depends on Ðg between DP boat and the plane of the sail. With increase Ðg force T increases and strength D decreases.

The effect of water on a boat largely depends on the contours of its underwater part.

Fig. 20. Correct position of the sail in different wind directions (according to I.I. Khomyakov, 1976): a - close-hauled; b - gulfwind, c - jibe.

Despite the fact that in close-hauled winds the drift force D exceeds the traction force T, the boat moves forward. This is where lateral resistance comes into play. R 1 underwater part of the hull, which is many times greater than the drag R.

Force D, despite the resistance of the hull, still blows the boat off the course line. Compiled DP and the direction of the true movement of the boat IPÐ a called the drift angle. The sharper the angle between DP and the direction of the wind, the greater the drift angle, since at acute angles the traction force T is insignificant and the boat, not having sufficient forward movement, is blown into the wind. In a close-hauled wind steeper than 40-45°, the boat cannot move forward.

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 has been established that the angle between DP boat and the plane of the sail should be equal to half Ð A between the center plane and the wind direction. Figure 20 shows the correct position of the sail in close-hauled (a), half-wind (b) and gybe (c) winds.

When choosing the position of the sail relative to DP and wind, the boat foreman is guided not by the true, but by the apparent (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. 21).

Figure 21. Apparent wind.

b and - true wind; V w - wind from the movement of the boat;

In in - apparent wind.

Rice. 22. Installation of the jib relative to the foresail (according to I.I. Khomyakov, 1976):

a - correct; b - incorrect.

The jib, located in front of the foresail, acts as a slat. The air flow passing between the jib and the foresail reduces the pressure on the leeward side of the foresail and, therefore, increases its bollard force. This only happens if the angle between the jibs and DP boats are slightly larger than the angle between the foresail and DP(Figure 22, a). If the jib is pressed to DP, then the air flow will hit the leeward side of the foresail, worsen its shape and reduce the traction force (Figure 22, b). The same effect is produced by a jib that is too curved.

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.

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 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 is 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 average height waves 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 phenomenon of resonance 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.