Physics of sailing yacht motion. Topic: “Physics of motion of a sailing yacht Sail operation in different winds

20.04.2020

Apparent wind

Let's try to understand due to what forces, and on the basis of what principles, the movement of a sailing ship occurs under the influence of the wind. Let's consider only oblique sails, as they are the most common at present. The Bermuda-type oblique sail rig is the main rig of most modern single-mast and two-mast vessels. All sport and cruising single-mast yachts are also armed with a Bermuda sloop.

This rig provides maximum opportunities for choosing a course relative to the direction of the wind and requires a significantly smaller crew to control the sails and does not require such a high level of training as in the case of using direct sailing rigs.

A remarkable feature of an oblique sail is its ability to create traction on courses up to 30-40 degrees to the wind direction.

It must be taken into account that the sailing vessel is moving relative to the apparent or apparent wind, and not relative to the true or meteorological wind.

When any object moves in the air, a flow of incoming air arises, the speed of which is determined by the speed of the object. Accordingly, even in the complete absence of wind (calm), an observer on the ship will feel a wind equal to the speed of the ship - a heading wind, which will be equal in magnitude to the speed of the ship, and in the direction opposite to the direction of movement of the ship. Thus, a sailing ship, when moving, experiences the action of two air flows:

The action of a flow caused by the presence of a true wind;

The action of the flow caused by the movement of the vessel - directional wind.

To determine the resulting air flow felt by an observer located on a moving object, it is necessary to perform a vector addition of the flows. The resulting vector will be the speed and direction of the felt or apparent wind, which is called the apparent wind. This wind will be considered as the wind acting on the sails of the ship as it moves (Fig. 1).

This wind is the only wind with which the sails interact, and its decomposition into true wind and directional wind is the result of an analysis of the original air flows.

Apparent wind is a variable value even when the true wind is stable in speed and direction, since its speed and direction depend on the speed and direction of the ship's movement. For simplicity of reasoning, let us consider the case in which Fig. 1.

the true wind is directed at right angles to the direction of movement of the vessel and the speed of the true wind is equal to the speed of the vessel (Fig. 2). The figure shows that when moving at an angle of 90 degrees to the true wind, the ship is moving at an angle of 45 degrees to the apparent wind.

true In accordance with the above, you can

wind apparent wind assert that two vessels moving at the same

him and the same course, with the same wind conditions

conditions, but with different speeds relative to the water, they will move at different angles to the apparent wind. A vessel moving at a higher speed will sail sharper into the apparent wind while maintaining the same heading angle relative to the true wind. At the same time, wind indicators will be located on the masts of these ships.

the directional wind is at different angles to the ship's DP, fixing the direction

rice. 2 the apparent wind of each vessel (Fig. 3).

ship 1 ship 2

It can be seen from the figure that a ship traveling at a higher speed moves at a smaller angle to the apparent wind. From this we can conclude that as the speed of the vessel increases, the apparent wind sets in (the angle between the direction of the vessel’s movement and the apparent wind decreases). With a further increase in the speed of the vessel (better lines, less friction, sails work more efficiently, a different design of the vessel's hull), the angle between the direction of the vessel's movement and the apparent wind will become less than the minimum tacking angle (the minimum angle between the direction of the vessel's movement and the apparent wind, at which the possibility of effective sail operation). After this, the vessel, which has a high speed, will be forced to fall off (increase the angle between the direction of the vessel's movement and the direction of the apparent wind) until the minimum tacking angle is restored. This explains the different windward angles (the angle between the direction of the true wind and the direction the ship is moving). At the same time, the speed of approaching the wind (the speed of approaching the point of arrival located in the wind) can be greater for a vessel with a large angle of approach to the wind, but also a higher speed. As an example, consider the speed at which a keel yacht, a sports dinghy and a catamaran go out to wind (Fig. 4).

A keel yacht, which has the lowest speed of all these vessels, moves sharper into the wind. Behind it comes a sports dinghy and the sports catamaran, which is least sensitive to the true wind. Each of these ships sails at the same angle to the apparent wind, but at different angles to the true wind. But at the same time, a sports catamaran will have the highest speed when going into the wind. From considering the speed triangle, it becomes clear that it is possible to reduce gusts of wind to true wind (short-term wind acceleration). In a gust, the speed of the true wind increases, but the speed of the ship remains, for some time, the same. The apparent wind moves away and it becomes possible to settle down and restore the tacking angle relative to the apparent wind (Fig. 5)

rice. 4

Keel yacht

dinghy

Catamaran

After some time, the ship's speed will increase, and it will be forced to fall back to its previous course relative to the true wind, maintaining an angle relative to the apparent wind. However, an increase in the speed of the vessel is possible until the speed limit for the movement of the vessel in displacement mode is reached (the speed of the vessel in displacement mode, expressed in knots, cannot exceed the length of the vessel, expressed in meters). Consequently, with a further increase in wind speed, the ship's speed will not increase and the ship's course relative to the true wind may be sharper.

The presence of currents in the area where the vessel is sailing is very important from the point of view of the behavior of the apparent wind. When sailing in a current, the speed of the vessel is vectorially added to the speed of the current. As a result, the absolute speed of the vessel changes and the speed and direction of the apparent wind changes. When moving with a tailwind, the apparent wind enters, and when moving with a countercurrent, it moves away. Consequently, with a tailwind, the tacking angle increases, and with a headwind, it decreases. At the same time, the speed of the yacht going into the wind remains almost unchanged. When the current is directed in the direction or against the direction of the true wind, a change in the speed of the true wind occurs. When the wind and current are unidirectional, the apparent wind enters, and when it is multidirectional, it moves away due to an increase in the speed of the true wind. The interaction of wind and current will change the ship's tacking angles relative to the true wind.

Modern navigation equipment makes it possible to obtain information not only about the direction and strength of the apparent wind, but also about the strength and direction of the true wind, by recalculating the speed triangle (Fig. 1). GPS provides information about the speed and direction of the vessel's movement, and an anemometer provides information about the speed and direction of the apparent wind. By recalculating the speed triangle, the system obtains information about the speed and direction of the true wind.

Understanding the behavior of apparent wind is key to planning a ship's route, given the known direction and speed of the true wind and the actual speed of the sailing vessel.

However, for slow-moving ships, the angle between the direction of the true and apparent wind is insignificant and it can be stated, with a certain degree of accuracy, that this angle is within 10-20 degrees.

As an introduction. This article was born with the encouragement and moral support of my long-time communication colleagues on the site’s forum “Shipyard on the Table.” Its purpose was to cover, within the limited framework of the site, an extensive section of nautical practice associated with changing the sail of a ship in proportion to the strength and direction of the wind. That is why only the process of taking the reefs and cleaning the sails is described. The publication is intended for people familiar with the basic concepts and terms from the practice of arming sailing ships. In order not to repeat myself, I deliberately miss and shorten everything that has already been published on this site and related to this topic, and I will try to summarize what, in my opinion, may seem interesting to an inquisitive reader in the works published for the most part in Russia in the second half of the 19th century.

So, first about the wind. Yes, yes about him, because, without going into theory and detailed calculations, it is he who is the driving force of a sailing ship. In the heyday of sailing shipbuilding, sailors characterized the strength of the wind depending on the sails that could be carried while sailing close-hauled. This was explained by the fact that when taking a close-hauled course, ships are forced to carry less windage. The main reasons are that, firstly, the lateral, most dangerous from the point of view of loss of spar, effect of the sails through the covered yards on the masts and topmasts, supported by the shrouds and foreduns more from the rear than from the sides, turns out to be greater than with other courses; secondly, the lateral stability of the ship is significantly less than the longitudinal one; and thirdly, the force of the wind acting on the ship as well as other moving object depends on the direction of its movement, that is, in close-hauled conditions it increases, and with a tailwind it decreases. Therefore, with the same wind, close-hauled it was necessary to take reefs from the topsails, while the topsails could also be carried in the jibe. Based on the above, they talked about wind with top-topsails, top-topsails, topsails, reef-topsails and under-sail, when lying close-hauled you can raise the top-topsails, or go under the top-topsails, or only under the topsails or under reefed topsails, or carry only the lower topsails sail. To more accurately characterize the wind, they said, for example, the topsail wind is quiet, the topsail wind is strong, the topsail wind is gusty, etc. By calm we meant complete calm, and by storm we meant wind, in which we kept under a tightly reefed main topsail or only under the trysails. Later they moved to a more accurate determination of wind strength in points according to the Beaufort system (Table 1).

Calculated speed per second of time	Pressure in Russian pounds per foot	Points indicating the degree of wind strength	Name of winds according to Beaufort	Name of winds according to the Chapman system
10,4	0,28	1	Light air Very weak
20,8	1,11	2	Light wind Weak
31,2	2,49	3	light breeze
41,6	4,43	4	Moderate breeze Moderate	Bom-bramsel
51,9	6,92	5	Fresh breeze fresh	Bramselny
62,3	9,97	6	Strong breeze Very fresh	Marseille
72,7	13,57	7	Moderate gale Strong	Reef topsail
83,1	17,72	8	Fresch gale Very strong	Under Zeil
93,5	22,43	9	Strong gale Strong	Half-storm
103,9	27,69	10	Heavy gale Very strong	Total Storm
-	-	11	Storm Storm
124,7	39,88	12	Hurricane Hurricane

According to the gradually increasing wind force, the sail of the vessel was gradually reduced, usually in the following order:

The top staysails and boom topsails with boom jib were stowed;

They fastened the topsails or, leaving the last ones, took one reef from the topsails;

They took a second reef from the topsails, and usually attached topsails;

They took the third reef from the topsails and replaced the fore-topmast jib with a jib, while trying to hold the jib as long as possible;

We fastened the cruise, took the last reef from the fore and main topsails, took one reef from the mizzen;

The foretopsail was fastened and the last reef was taken from the mizzen (or a storm mizzen was installed), the foretopmastsail was replaced by the foresail staysail.

The lower sails were usually reefed in the following sequence: together with the fourth reef from the topsails, they took the first reef from the mainsail, then the second reef from the mainsail and the first from the foresail, then the second from the foresail and secured the mainsail or replaced it with a mainsail trysail, and, as a last resort, when the force of the wind and waves made it impossible to move and forced her to stay under the main topsail, the foresail was secured.

With fair winds, the procedure for gradually retracting the sails was assumed to be similar to that stated above, with the only difference being that to reduce yaw rate, the mizzen was removed from the backstay and the cruise was attached while taking the third reef from the other topsails.

Thus, storm sail close-hauled on ships with direct sailing equipment usually consisted of a dully reefed main topsail (a sail was said to be dully reefed if all four reefs were taken from it), a foresail staysail and a reefed mizzen. When jibed, these were usually fore-topmasts, jib, reefed main-topsail and foresail. The main topsail is needed as a sail from which the waves rising from behind do not take away much wind, the foresail moves the overall center of sail forward, and the fore topmast is a staysail to compensate for occasional strong yaw.
As an illustrative example, I cite a lithograph by T. G. Dutton. It (Fig. 1) shows the barque Constance running backstay in a reef-topsail wind under three sails: a fore-topmast with a staysail, a foresail and a main-topsail, taken on two reefs; the crew at this time removes the fore-topsail and mainsail. At the same time, the corresponding foils are raised above the yards to make room for laying the sails.

Rice. 1. Bark Constance, running backstay.

It should be mentioned that the number of sails installed depends not only on the strength of the wind and its direction relative to the course of the ship, but also on the size of the waves, personal experience captain, characteristics and properties of a particular ship and some other factors. A significant role is played by the timeliness of making a decision to change the sail when the wind force changes: a premature reduction in the sail leads to loss of speed, and overexposure can make cleaning the sails and taking reefs difficult and dangerous for the topsailers.

In order to be able to take sails to reefs, during the rigging process, reef lines, reef lines and reef lines are threaded into the sails; Krengels and spruits are tied in, legs and collars are sewn on, benzels and bayonet bolts are threaded through. A more detailed consideration of this issue may undoubtedly be of interest from the point of view of making ship models.

Reef seasons usually consisted of five fish. They were hung over a pole and from the long ends they wove a braid long enough to form a double point, which was necessary so that the threaded reefs could not slip through the grommet of the sail (Fig. 2). Then the woven part was hung in the middle through the pole, one end was made around the pole to form a double point, both ends were connected and the sesen continued to be woven from the shkims of both halves. (Fig. 3). The ends of the seams were wrapped with a sailing thread and girded, stitched through. The length of the reef-sezny must correspond to the thickness of the yard, and since the reef was tied on the yard as high as possible, the rear halves of the sezny were usually made longer than the front ones, with the exception of the sezny of the fourth reef, in which, on the contrary, the front ends were made longer than the rear, due to the fact that the bayonet bolt The fourth reef was taken, as a rule, from behind the yardarm and the reef itself was fitted under the bottom of the yardarm. During the rigging process, the reef sails were threaded while sitting on the floor by two people, one on each side of the outstretched sail. Each, taking one half of the reef season, passed its end into the grommet, at the same time accepting the other end of the season from his colleague and passed it into the point of his half. Next, an ordinary pulley was put on the end of the sesen; people each grabbed their end with their hands, rested their feet on the pulleys and thus tightly pulled the sesen, securely fastening it in the grommet. When taking reefs, the canvas between the yard and the corresponding reef bow was rolled up and the resulting roll was tied with a straight reef bow (Fig. 4) or a reef knot (Fig. 5).

Rice. 2 - 5. Reef seasons.

In the second half of the 19th century, one or two reef ropes began to be inserted through the eyelets in the reef bow using one of the methods shown below (Fig. 6). To prevent the half-bayonets of the reefers from weakening, benzels made of skimushgar were placed on them.

Rice. 6 and 7. Reef line wiring.

Reef lines with brakes were secured on a rod rail used to tie the sail, or on a special rail mounted behind the sail line, or were carried around the yard (Fig. 8) (on topsail yard they were attached in pairs - one for 1st and 3rd -th reef, second for the 2nd and 4th). When taking such a reef, the canvas was picked up to the corresponding reef bow, the end of the reef rope was passed into the loop of the reef rope and closed on the brake (Fig. 9).

Rice. 8 and 9. Reef seasons.

When taking such a reef, the flesh was not touched, but was left hanging between the sail and the yard.

The reef lines of trysails and mizzens were cut out of white cable and sewn into the sail in a slightly different way. Here's one way: they made a hole in the sail where the reef thread was threaded, threaded it through and aligned the ends on both sides of the sail. Then the sesen was unwound close to the sail so that the strands unfurled and formed pegs in loops. These loops were sewn to the sail, and a little lower they quilted both parts of the canvas and the sails all the way through. The ends of the seams were wrapped with sailing thread and also quilted through for strength.

Reef pins, also called snakes, served to conveniently attract the sail to the yard when taking reefs. They were a thin rope, one end of which was molded to the luff grommet; the other end went down the front side of the sail and was grabbed onto the necks of the corresponding reef seasons up to the fourth reef (Fig. 7). The lower sails had from 6 to 8 snakes, the topsails had 6, (on small ships 4), the cruisers had 4.

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, so that the wind blows at 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 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 vessel. 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 walked by backstays and gulfwinds with average speed at 7-8 knots at 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.

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. 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.

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 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 meets strong water resistance (the keel in sailing ships is made very deep), then the force 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 directions of the keel and the wind.]. 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.

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 capable of generating 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 the 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