Topic: “Physics of motion of a sailing yacht. Using a sail on a boat
Courses relative to the wind. Modern yachts and sailing boats in most cases equipped oblique sails. Their distinctive feature is that the main part of the sail or all of it is located behind the mast or forestay. Due to the fact that the leading edge of the sail is pulled tightly along the mast (or by itself), the sail flows around the air flow without flushing when it is positioned at a fairly acute angle to the wind. Thanks to this (and with appropriate hull contours), the ship acquires the ability to move at an acute angle to the direction of the wind.
In Fig. 190 shows the position of the sailboat at different courses relative to the wind. An ordinary sailboat cannot sail directly against the wind - the sail in this case does not create a traction force capable of overcoming the resistance of water and air. The best racing yachts in medium winds can sail close-hauled at an angle of 35-40° to the wind direction; Usually this angle is not less than 45°. Therefore, the sailboat is forced to get to a target located directly against the wind. tacking- alternately starboard and port tack. The angle between the ship's courses on one tack and the other is called tacking angle, and the position of the vessel with its bow directly against the wind is leftist. The ability of a ship to tack and move at maximum speed directly into the wind is one of the main qualities of a sailboat.
Courses from close-hauled to halfwind, when the wind blows at 90° to the ship's port, are called sharp; from gulfwind to jibe (the wind blows directly astern) - full. Distinguish steep(course relative to the wind 90-135°) and full(135-180°) backstays, as well as close-hauled (40-60° and 60-80° to the wind, respectively).
Rice. 190. Courses of a sailing ship relative to the wind.
1 - steep close-hauled; 2 - full close-hauled; 3 - gulfwind; 4 - backstay; 5 - jibe; 6 - leftist.
Apparent wind. The air flow that flows around the sails of the yacht does not coincide with the direction true wind(relative to sushi). If the ship is moving, then a counter flow of air appears, the speed of which is equal to the speed of the ship. When there is wind, its direction relative to the ship is deviated in a certain way due to the oncoming air flow; the magnitude of the speed also changes. Thus, the total flow, called apparent wind. Its direction and speed can be obtained by adding the vectors of the true wind and the oncoming flow (Fig. 191).
Rice. 191. Apparent wind at various courses of the yacht relative to the wind.
1 - close-hauled; 2 - gulfwind; 3 - backstay; 4 - jibe.
v- speed of the yacht; v and - true wind speed; v in - apparent wind speed.
It is obvious that on a close-hauled course the apparent wind speed is the greatest, and on a gybe it is the smallest, since in the latter case the speeds of both flows are directed in exactly opposite directions.
The sails on a yacht are always set in the direction of the apparent wind. Note that the speed of the yacht does not grow in direct proportion to the wind speed, but much more slowly. Therefore, when the wind increases, the angle between the direction of the true and apparent wind decreases, and in weak winds, the speed and direction of the apparent wind differs more noticeably from the true one.
Since the forces acting on a sail as on a wing increase in proportion to the square of the speed of the flow, sailboats with minimal resistance to movement may experience a “self-acceleration” phenomenon, in which their speed exceeds the speed of the wind. These types of sailboats include ice yachts - ice boats, hydrofoil yachts, wheeled (beach) yachts and proa - narrow single-hull vessels with an outrigger float. Some of these types of vessels have recorded speeds up to three times the wind speed. So, our national iceboat speed record is 140 km/h, and it was set in a wind whose speed did not exceed 50 km/h. We note in passing that absolute record sailing speeds on water are significantly lower: it was installed in 1981 on a specially built two-masted catamaran “Crossbau-II” and is equal to 67.3 km/h.
Conventional sailing ships, unless they are designed for planing, rarely exceed the displacement speed limit of v = 5.6 √L km/h (see Chapter I).
Forces acting on a sailing ship. There is a fundamental difference between the system of external forces acting on a sailing vessel and a vessel driven by a mechanical engine. On a motorized vessel, the thrust of the propeller - the propeller or water jet - and the force of water resistance to its movement act in the underwater part, located in the center plane and at a small distance from each other vertically.
On a sailboat, the driving force is applied high above the surface of the water and, therefore, above the line of action of the drag force. If the ship moves at an angle to the direction of the wind - close-hauled, then its sails operate according to the principle of an aerodynamic wing, discussed in Chapter II. When air flows around a sail, a vacuum is created on its leeward (convex) side, and increased pressure is created on the windward side. The sum of these pressures can be reduced to the resulting aerodynamic force A(see Fig. 192), directed approximately perpendicular to the chord of the sail profile and applied at the center of sail (CS) high above the surface of the water.
Rice. 192. Forces acting on the hull and sails.
According to the third law of mechanics, during steady motion of a body in a straight line, each force applied to the body (in this case, to the sails connected to the hull of the yacht through the mast, standing rigging and sheets) must be counteracted by a force equal in magnitude and oppositely directed. On a sailboat this force is the resultant hydrodynamic force H, attached to the underwater part of the hull (Fig. 192). Thus, between the forces A And H there is a known distance - the shoulder, as a result of which a moment of a pair of forces is formed, tending to rotate the ship relative to an axis oriented in a certain way in space.
To simplify the phenomena that arise during the movement of sailing ships, hydro- and aerodynamic forces and their moments are decomposed into components parallel to the main coordinate axes. Guided by Newton's third law, we can write out in pairs all the components of these forces and moments:
| A | - aerodynamic resultant force; |
| T | - the thrust force of the sails moving the ship forward: |
| D | - heeling force or drift force; |
| A v | - vertical (trimming to the nose) force; |
| P | - mass force (displacement) of the vessel; |
| M d | - trimming moment; |
| M cr | - heeling moment; |
| M P | - the moment leading to the wind; |
| H | - hydrodynamic resultant force; |
| R | - the force of water resistance to the movement of the vessel; |
| R d | - lateral force or resistance to drift; |
| H v | - vertical hydrodynamic force; |
| γ· V | - buoyancy force; |
| M l | - moment of resistance to trim; |
| M V | - restoring moment; |
| M at | - sinking moment. |
In order for the ship to move steadily along its course, each pair of forces and each pair of moments must be equal to each other. For example, the drift force D and drift resistance force R d create a heeling moment M kr, which must be balanced by the restoring moment M in or moment of lateral stability. This moment is formed due to the action of mass forces P and buoyancy of the vessel γ· V, acting on the shoulder l. The same forces form the moment of resistance to trim or the moment of longitudinal stability M l, equal in magnitude and opposing the trimming moment M d. The terms of the latter are the moments of pairs of forces T - R And A v - H v .
Thus, the movement of a sailing ship on an oblique course to the wind is associated with roll and trim, and the lateral force D, in addition to roll, also causes drift - lateral drift, so any sailing ship does not move strictly in the direction of the DP, like a ship with a mechanical engine, but with a small drift angle β. The hull of a sailboat, its keel and rudder become a hydrofoil, onto which an oncoming flow of water flows at an angle of attack equal to the angle of drift. It is this circumstance that determines the formation of a drift resistance force on the keel of the yacht R d, which is a component of the lift force.
Stability of movement and centering of a sailing vessel. Due to heel, the thrust force of the sails T and resistance force R appear to be active in different vertical planes. They form a pair of forces that bring the ship towards the wind - knocking it off the straight course it is following. This is prevented by the moment of the second pair of forces - heeling D and drift resistance forces R d, as well as a small force N on the steering wheel, which must be applied in order to correct the yacht’s movement along the course.
It is obvious that the vessel’s reaction to the action of all these forces depends both on their magnitude and on the ratio of the arms a And b on which they act. With increasing roll, the arm of the drive pair b also increases, and the leverage of the falling pair a depends on the relative position center of sail(CP - points of application of the resulting aerodynamic forces to the sails) and center of lateral resistance(CBS - points of application of the resulting hydrodynamic forces to the yacht hull).
Accurately determining the position of these points is a rather difficult task, especially when you consider that it changes depending on many factors: the ship's course relative to the wind, the cut and tuning of the sails, the list and trim of the yacht, the shape and profile of the keel and rudder, etc.
When designing and re-equipping yachts, they operate with conventional CPs and CBs, considering them located in the centers of gravity of flat figures, which represent sails set in the DP, and the outlines of the underwater part of the DP with a keel, fins and rudder (Fig. 193). The center of gravity of a triangular sail, for example, is located at the intersection of two medians, and the common center of gravity of the two sails is located on a straight line segment connecting the CP of both sails, and divides this segment in inverse proportion to their area. If the sail has a quadrangular shape, then its area is divided diagonally into two triangles and the CP is obtained as the common center of these triangles.
Rice. 193. Determination of the conditional center of sail of a yacht.
The position of the central center can be determined by balancing a template of the underwater profile of the DP, cut out of thin cardboard, on the tip of a needle. When the template is positioned horizontally, the needle will be at the conditional center point. However, this method is more or less applicable for ships with a large area of the underwater part of the wing - for traditional yachts with a long keel line, ship's boats, etc. On modern yachts, the contours of which are designed based on wing theory, the main role in creating the drag force drift is facilitated by a fin keel and a rudder, which is usually installed separately from the keel. The centers of hydrodynamic pressures on their profiles can be found quite accurately. For example, for profiles with a relative thickness δ/ b about 8% this point is at a distance of about 26% of the chord b from the incoming edge.
However, the hull of the yacht in a certain way influences the nature of the flow around the keel and rudder, and this influence varies depending on the roll, trim and speed of the vessel. In most cases, on sharp courses into the wind, the true center of gravity moves forward with respect to the center of pressure determined for the keel and rudder as for isolated profiles. Due to the uncertainty in calculating the position of the CP and the central center, when developing a design for sailing ships, designers place the CP at a certain distance a- ahead - ahead of the Central Bank. The amount of advance is determined statistically, from a comparison with well-proven yachts that have underwater contours, stability and sailing rigs close to the design. The lead is usually set as a percentage of the length of the vessel at the waterline and is 15-18% for a vessel equipped with a Bermuda sloop. L. The less stability of the yacht, the more roll it will receive under the influence of the wind and the greater the advance of the CPU in front of the central steering system is necessary.
Precise adjustment of the relative position of the CP and CB is possible when testing the yacht while underway. If the ship tends to fall into the wind, especially in medium and fresh winds, then this is a major alignment defect. The fact is that the keel deflects the flow of water flowing from it closer to the vessel’s DP. Therefore, if the rudder is straight, then its profile operates with a noticeably lower angle of attack than the keel. If, in order to compensate for the tendency of the yacht to sink, the rudder has to be shifted to the wind, then the lifting force generated on it turns out to be directed in the leeward direction - in the same direction as the drift force D on sails. Consequently, the ship will have increased drift.
Another thing is the easy tendency of the yacht to be driven. The rudder, shifted 3-4° to the leeward side, operates with the same or slightly greater angle of attack as the keel, and effectively participates in resistance to drift. Lateral force H, which occurs on the rudder, causes a significant shift of the general center of gravity towards the stern while simultaneously reducing the drift angle. However, if in order to keep the yacht on a close-hauled course you have to constantly shift the rudder to the leeward side at an angle greater than 2-3°, it is necessary to move the CPU forward or move the central steering system back, which is more difficult.
On a completed yacht, you can move the CPU forward by tilting the mast forward, moving it forward (if the step design allows), shortening the mainsail along the luff, and increasing the area of the main jib. To move the central steering wheel backwards, you need to install a fin in front of the steering wheel or increase the size of the steering blade.
To eliminate the yacht's tendency to sink, it is necessary to apply opposite measures: move the CPU back or move the central center forward.
The role of aerodynamic force components in the creation of thrust and drift. The modern theory of the operation of an oblique sail is based on the provisions of the aerodynamics of the wing, the elements of which were discussed in Chapter II. When an air flow flows around a sail set at an angle of attack α to the apparent wind, an aerodynamic force is created on it A, which can be represented in the form of two components: lift Y, directed perpendicular to the air flow (apparent wind), and drag X- force projections A on the direction of air flow. These forces are used when considering the characteristics of the sail and everything sailing equipment generally.
At the same time force A can be represented in the form of two other components: traction force T, directed along the axis of motion of the yacht, and the drift force perpendicular to it D. Let us recall that the direction of movement of the sailboat (or path) differs from its course by the value of the drift angle β, however, in further analysis this angle can be neglected.
If on a close-hauled course it is possible to increase the lifting force on the sail to the value Y 1, and the frontal resistance remains unchanged, then the forces Y 1 and X, added according to the rule of vector addition, form a new aerodynamic force A 1 (Fig. 194, A). Considering its new components T 1 and D 1, it can be noted that in this case, with an increase in lift, both the thrust force and the drift force increase.
Rice. 194. The role of lift and drag in creating driving force.
With a similar construction, one can be convinced that with an increase in drag on a close-hauled course, the thrust force decreases and the drift force increases. Thus, when sailing close-hauled, the lifting force of the sail plays a decisive role in creating sail thrust; drag should be minimal.
Note that on a close-hauled course the apparent wind has the highest speed, so both components of the aerodynamic force Y And X are quite large.
On a Gulfwind course (Fig. 194, b) lift is the traction force, and drag is the drift force. An increase in the drag of the sail does not affect the amount of traction force: only the drift force increases. However, since the apparent wind speed in the gulfwind is reduced compared to the close-hauled wind, drift affects the ship's performance to a lesser extent.
Backstay on course (Fig. 194, V) the sail operates at high angles of attack, at which the lifting force is significantly less than the drag. If you increase the drag, the thrust and drift force will also increase. As the lifting force increases, the thrust increases and the drift force decreases (Fig. 194, G). Consequently, on the backstay course, an increase in both lift and (or) drag increases thrust.
During a gybe course, the angle of attack of the sail is close to 90°, so the lifting force on the sail is zero, and the drag is directed along the axis of motion of the vessel and is the traction force. The drift force is zero. Therefore, on a gybe course, to increase the thrust of the sails, it is advisable to increase their drag. On racing yachts this is done by setting additional sails- spinnaker and blooper, having a large area and poorly streamlined shape. Note that on a gybe course, the yacht's sails are affected by the apparent wind of minimum speed, which causes relatively moderate forces on the sails.
Drift resistance. As shown above, the force of drift depends on the yacht's course relative to the wind. When sailing close-hauled, it is approximately three times the thrust force T, moving the ship forward; on gulfwind both forces are approximately equal; on a steep backstay, the sail thrust turns out to be 2-3 times greater than the drift force, and on a pure gybe there is no drift force at all. Consequently, in order for a sailboat to successfully move forward on courses from close-hauled to gulfwind (at an angle of 40-90° to the wind), it must have sufficient lateral resistance to drift, much greater than the resistance of the water to the movement of the yacht along the course.
The function of creating resistance to drift on modern sailing ships is mainly performed by fin keels or centerboards and rudders. The mechanics of the generation of lift on a wing with a symmetrical profile, such as keels, centerboards and rudders, was discussed in Chapter II (see page 67). Note that the drift angle of modern yachts - the angle of attack of the keel or centerboard profile - rarely exceeds 5°, therefore, when designing a keel or centerboard, it is necessary to select its optimal dimensions, shape and cross-sectional profile in order to obtain maximum lifting force with minimal drag. at low angles of attack.
Tests of aerodynamic symmetrical airfoils have shown that thicker airfoils (with a larger cross-sectional thickness ratio t to his chord b) provide greater lifting force than thin ones. However, at low speeds such profiles have higher drag. Optimal results on sailing yachts can be achieved with keel thickness t/b= 0.09÷0.12, since the lifting force on such profiles depends little on the speed of the vessel.
The maximum thickness of the profile should be located at a distance of 30 to 40% of the chord from the leading edge of the keel profile. The NACA 664‑0 profile also has good qualities with a maximum thickness located at a distance of 50% of the chord from the nose (Fig. 195).
Rice. 195. Profiled keel-fin of a yacht.
| Distance from spout x, % b | ||||||
| 2,5 | 5 | 10 | 20 | 30 | 40 | |
| Ordinates y, % b | ||||||
| NACA-66; δ = 0.05 | 2,18 | 2,96 | 3,90 | 4,78 | 5,00 | 4,83 |
| 2,00 | 2,60 | 3,50 | 4,20 | 4,40 | 4,26 | |
| - | 3,40 | 5,23 | 8,72 | 10,74 | 11,85 | |
| Profile; relative thickness δ | Distance from spout x, % b | |||||
| 50 | 60 | 70 | 80 | 90 | 100 | |
| Ordinates y, % b | ||||||
| NACA-66; δ = 0.05 | 4,41 | 3,80 | 3,05 | 2,19 | 1,21 | 0,11 |
| Profile for centerboards; δ = 0.04 | 3,88 | 3,34 | 2,68 | 1,92 | 1,06 | 0,10 |
| Keel of yacht NACA 664-0; δ = 0.12 | 12,00 | 10,94 | 8,35 | 4,99 | 2,59 | 0 |
For lightweight racing dinghies capable of planing and reaching high speeds, centerboards and rudders with a thinner profile are used ( t/b= 0.044÷0.05) and geometric elongation (deepening ratio d to the middle chord b Wed) to 4.
The elongation of the keels of modern keel yachts ranges from 1 to 3, the rudders - up to 4. Most often, the keel has the form of a trapezoid with an inclined leading edge, and the angle of inclination has a certain effect on the amount of lift and drag of the keel. When extending the keel around λ = 0.6, an inclination of the leading edge of up to 50° can be allowed; at λ = 1 - about 20°; for λ > 1.5, a keel with a vertical leading edge is optimal.
The total area of the keel and rudder to effectively counteract drift is usually taken to be from 1/25 to 1/17 of the area of the main sails.
The winds that are in the southern part Pacific Ocean blowing in a westerly direction. That is why our route was designed so that on the sailing yacht “Juliet” we move from east to west, that is, so that the wind blows at our 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 receives the highest great importance 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."
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.
How does a sailing ship move? Obviously, the cause of movement is the wind pressure on the sail. But, surprisingly, a sailing ship can move not only in the direction the wind is blowing, but also in the opposite direction (well, almost in the opposite direction, at an acute angle, changing tacks, but nevertheless moving against the wind). What are the physical principles of a ship moving against the wind?
Let's consider the forces acting on a yacht sailing at an acute angle to the wind. 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 figure). 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 performance of a sail on sharp courses, it is convenient to first consider a flat sail that 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. On sharp courses it creates thrust in the direction of the yacht's movement.
If, with the same drag of the sail X, the lift force increases, for example, to a value of Y1, then, as shown in the figure, the resultant of the lift force and drag will change by R and, accordingly, the thrust force T will increase to T1.
Dependence of thrust and drift forces on the lifting force and drag of the sail
From this drawing it can be seen that with increasing drag X (at the same lift force), 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 a sail is increased by giving it a concave shape with some “belliness”: 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. 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, the “potbelliness” of the sail is more than 6-7% when strong wind unprofitable, since an increase in roll and drift leads to a significant increase in hull resistance and a decrease in the efficiency of 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.
§ 61. Use of a sail.
In the practice of operating small motorized vessels on the sea and river, there are many examples where even the most primitive sail, made from the “improvised” means available on the vessel, allowed a small self-propelled vessel, which had lost the ability to move independently, to successfully complete a voyage without outside help.
A hobby boater needs to have a good understanding of how a sail works and how to make simple sailing equipment in case the boat's mechanical engine fails, runs out of fuel, or the outboard motor falls overboard, as well as in case the propeller is damaged or lost.
The combination of sailing equipment with a motor increases the tourist capabilities of the vessel. With the help of a sail, the emergency vessel can be brought to the base or to the nearest populated area.
1. Action of the sail.
The pressure of the air flow on the surface of the sail moves the ship. The direction of this movement depends on the position of the sail relative to the direction of the wind. The point of application of the resultant of all wind pressure forces on the sail is called the center of sail - CPU.
Rice. 137. Forces acting on the sail and ship when the wind comes from the bow angles
If the sail were extended along the centerline of the ship, then the force of wind pressure A(Fig. 137) would tilt the ship, but would not move it forward. But if the plane of the sail is set at a certain angle to the direction of the wind, then the force A can be decomposed into two components B And IN. The first “works”, and the second “slides” along the sail (see Fig. 137, a and 138, A).
Every vessel has the ability to resist lateral shear in water - it has the so-called lateral resistance and its center - CBS- is usually located close to the amidships of the ship in its underwater part and approximately on the same vertical line with CPU(Fig. 139). Transferring force B V CBS, neglecting the roll and counting CBS fixed point, can be expanded B into two components T And D. The first pulls the ship forward along the center plane, and the second tends to move the ship to the side, creating a drift for it (see Fig. 137, b). The amount of drift depends on the shape of the underwater part of the vessel and the angle between the directions of the center plane DP ship and wind. This can be verified by constructing a diagram of forces for several positions. The smaller the angle between DP and the direction of the wind, the greater the force A and less strength T(see Fig. 138, A and b).
Rice. 138. Forces acting on the sail and the ship in the wind from the stern angles
If the vessel has highly developed longitudinal planes under water (sides, angular chines, keel, rudder), then the displacement of the vessel to the side is insignificant. If the vessel is flat-bottomed, unloaded and wide, then it BS insignificant and the drift is great. Therefore, vessels of the first type, for example, yachts or keelboats, are capable of moving forward at an angle of up to 40-30° to the wind direction, counting from the bow, and flat-bottomed boats and boats only when the wind is from the stern, i.e. at wind angles of at least 120° to the center plane.
Rice. 139. Position of the center of sail relative to the center of lateral resistance
The most advantageous position of the sail in any wind direction is one in which the plane of the sail bisects the angle between DP and wind (see Fig. 137, A, 138, a). In practice, the sail should be set so that angle I is slightly less than angle II.
If CPU vertically coincides with CBS, then the ship moves forward without the help of a rudder. However, on the go CBS shifts slightly to the bow or stern, and therefore the ship while moving will always deviate from the course with its bow to the wind or downwind. It is usually believed that a sailing ship, under the influence of a squall or without steering, must itself, under the influence of the sail, “yaw” or “come to the wind,” that is, turn its bow against it. Then the heeling effect of the wind will naturally stop. Therefore, the mast and sail on the ship are placed so that CPU was always somewhat aft (vertically) from CBS. This is achieved by calculation on a drawing or experimentally on water (see Fig. 139). However, for ships capable of sailing only with favorable winds, CPU should be located in the nose from CBS. Then, during a squall, the ship will move away from it on its own, that is, it will tend to “fall into the wind.” This is safer and makes it easier to quickly retract the sail in case of increased wind, even if the rudder control is abandoned to do this.
2. Basic terms.
Depending on the wind direction relative to DP and the sides of the vessel, the following terms are accepted for the rules of sailing a vessel.
The side facing the wind is called windward. The side facing away from the wind is called leeward. Walking with the wind blowing in starboard, called starboard tack, to port - port tack. The straight section of sailing is called a tack.
To move towards a windward target, located on the side from which the wind is blowing, means to rise; move towards a leeward goal - descend; a sailing ship cannot sail directly against the wind, it must go in zigzags, lying either on the right or on the left tack. This movement is called tacking.
The wind blowing from the bow heading angles in the 0-85° sector is called close-hauled; they say: “The ship is close-hauled” (starboard or port tack). The wind blowing on board (85-95°) is called gulfwind; they say: “The ship is sailing at gulfwind or at half wind” (starboard or port tack). The wind blowing from the stern heading angles (95-170°) is called the backstay; they say: “The ship is heading into the backstay” (starboard or port tack). The wind blowing directly astern (175° port side - 175° starboard side) is called gybe; They say: “The ship is gybeing.” Tack is not noted. The greater the angle between the wind direction and DP, the more wind becomes “fuller”; the less, the wind and course are “steeper”.
3. Setting the sails and controlling the sailing vessel.
The setting of the sails should be consistent with the direction of the wind. As a rule, oblique sails are raised by placing the vessel with its bow against the wind (“towards the wind”, “towards the wind”). A straight sail is raised, placing the ship in the wind. If the wind prevents setting the sail near the shore, you should turn the ship around or move away from the shore. The mainsail is set first, loosening the sheet. When the halyard is pulled out to its destination, they tighten the sheet and begin to steer the rudder, setting it on the desired course. After this, the jib is set and its leeward sheet is tightened.
The mainsail and staysail, under the influence of the wind, press on the corresponding tip of the vessel. If these forces are unequal, then the ship tends to rotate around its CBS, scurrying or falling off. When sailing on a straight course with a crosswind, it is necessary to adjust both sails by tensioning the sheets so that the ship sails straight with a straight rudder. If there is still a desire to fall off or dive, it is necessary to level the ship on course with the rudder. It is, however, possible to achieve a balanced action of the sails by moving cargo or people along the boat. If the bow goes into the wind, load the bow; if it goes into the wind, load the stern.
You cannot stand in the boat while sailing. Everyone should sit on the seats on the windward side, or in strong winds, on the bottom facing the sail (i.e., on the windward side). When sailing, an amateur navigator must maintain discipline on the ship, and only at his command is it allowed to move on the ship or perform this or that work. Tackle should not be scattered in disarray inside the vessel; it should be placed in coves. The sheets must be straightened cleanly; the main sheet and jib sheet should be held by hand; It is forbidden to wrap them overlapping on ducks.
As a last resort, make one or two turns and hold the running end in your hands.
Loads, tools and other things must be stowed so that when the ship rolls, they cannot move and do not interfere with sail operations, forward observation and pumping out water. The halyards must be wrapped so that in the event of a strong squall they can be released instantly.
If the ship is heeling strongly in the wind, then when there is wind from the side or from the bow, the sheets should be loosened, and then “brought to the wind”, for which the helm of the ship should be placed almost against the wind, with the jib sheets pulled apart. When sailing with a tailwind, “leading to the wind” in a strong squall is dangerous, so it is better to remove the mainsail and continue sailing under the jib. When sailing close-hauled, it is useful to load the bow somewhat, in this case the vessel listens better to the rudder and sails. If you need to keep it steeper to the wind, then you should pick up the main sheet and slightly lower the jib sheet, but you should not allow the sails to “sweep” (flap) in the wind.
As already mentioned, the angle between the wind and DP The sail must be divided in half. Having set the ship on course and positioned the sail accordingly, you should then slightly adjust the main sheet so that its luff begins to tremble slightly. This means the sail is working well. Excessive sheeting only upsets the vessel, reducing speed and increasing drift (drift to wind). The steeper the ship goes to the wind, the less the speed and the greater the drift. There is practically no drift when backstaying, and it is completely absent when gybeing.
Steering the steering wheel while gybeing is the most difficult. The ship tends to turn sideways to the wind, and it can throw itself on any tack. The sail stands across the ship and its outer luff always runs the risk of being blown downwind, that is, from the bow, when the wind subsides after a gust. Then the sail can quickly be thrown from one side to the other with a sharp blow, the shrouds and sheet can be torn, or the ship can be capsized.
Therefore, when going to gybe, you should load more stern, and in order to avoid throwing the mainsail onto another tack, it is useful to spread the clew of the sail with a thin pole (hook, oar). To do this, the thin end of the pole is inserted into the clew of the sail, and the thick end is rested against something inside the vessel - against the side, the keelson. A person should sit at the spreader pole and hold it with their hands.
If, nevertheless, the sail has thrown to the other side, then you should pick up the slack of the sheet with your hands as quickly as possible, and press the tiller with your body and bring the ship onto the backstay course of the tack on which the sail has thrown. Otherwise, the transfer may happen again. This means that if, for example, the sail was on the port tack (it was thrown to the starboard side) and it was thrown onto the starboard tack, then when the sail moves to the port side, the ship should be brought to the full backstay of the starboard tack (take it more to the right) and so steer.
If, when gybeing in a strong wind, waves begin to fill the vessel from the stern, and for some reason it is impossible to change the course, then the stern should not be loaded to improve controllability; instead, it should be released from the stern on a strong end 5-8 long m drag (drag). A dredge can be a tied strong basket, loaded so that it barely floats, as well as a bunch of any objects that have minimal buoyancy and provide significant resistance. In a shallow place, you can lower a small smooth ballast from the stern, dragging along the ground behind the ship.
A straight sail, as already mentioned, is unsuitable for tacking, but can still work in cross winds. By general rules with guys and sheets it is turned to the required position and the rudder is used to keep the ship on the desired course or as close as possible to it. In these cases, the windward sheet and yard guy are brought forward, and the leeward ones - aft.
4. Turns.
Under sails, two types of turns are made to change tack: a tack is made by bringing the ship to the wind and moving the bow through the wind line; A gybe turn is made by pushing the bow of the vessel into the wind and crossing the wind line with the stern.
Figure 140. Tack
A tack turn (Fig. 140) is more convenient and safer than a jibe, since the ship does not accelerate, but, on the contrary, almost stops, passing the wind line with its bow. Before the turn, they give the command: “Prepare to tack for the turn,” take it a little fuller to increase the speed, then pick up the main sheet, put the rudder to the wind and trim the jib sheet. The ship will go with its bow to the wind, the jib will flap. At the moment when the ship has turned its bow to the wind and has rinsed the mainsail, it is useful to pick up the main sheet again so that it helps to cross the wind line, for this they command: “Jib to the wind.” Then the main sheet is set, the jib sheet is moved to the new tack with the sheets, commanding: “The jib sheet is on the starboard (or left) side,” and under its action the vessel is allowed to fall to the wind on the new tack, after which the main sheet is selected and set on the desired course .
Rice. 141. Yibing
To make tacking easier, it is useful to place one or two people in the bow before starting the tack. It may happen that the ship, having come with its bow to the wind, stops and goes in reverse. You need to monitor this and immediately shift the steering wheel. Then, in reverse, the steering wheel can turn the stern in the desired direction and the turn will be successful. If the turn is not successful at all, then you should quickly get on the same tack and repeat the maneuver.
A gybe turn (Fig. 141) is made when required by the shape of the fairway or when the weather and terrain are favorable. This turn requires space, as the ship gets a lot of speed. To gybe, after a warning command, they begin to fall into the wind, gradually lowering the main sheet. Having arrived at the backstay, they gradually put the rudder even further into the wind, and at the same time quickly select the main sheet so that when the sail is thrown, it is selected and the sail is pulled out in the middle of the ship.
Then the transition of the mainsail to the other side will occur without a jerk. The ship will cross the wind line with its stern, the sails will switch to another tack and “take away” the wind. The jib sheet is trimmed so that it does not prevent the ship from sailing with its bow to the wind. As soon as the ship has arrived on a new tack, the main sheet and rudder are brought to the required course and steered by selecting the jib and main sheets accordingly.
In strong winds, a jibe is made by removing the mainsail or grabbing it to the mast.
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, with the same drag of the sail X (Fig. 95), the lift force increases, for example, to the value Y1, then, as shown in the figure, the resultant of the lift force 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 a sail is increased by giving it a concave shape with some “belliness” (Fig. 96): the size from the mast to the deepest part of the “belly” is usually 0.3-0.4 times the width of the sail, and the depth of the “belly” -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 rigidity 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 staysail, 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; From the center of the mainsail the area of the jib is laid off, and from the center of the jib - the area of the mainsail. 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 drag 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 prone 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, it is necessary to place the CP 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
