Elements of initial lateral stability. Lateral stability of the vessel Lateral stability of the vessel
Vessel performance
The most characteristic operational qualities of a small vessel are: passenger capacity,load capacity, displacement and speed.
Passenger capacity is an indicator equal to the number of equipped places to accommodate people on the ship. Passenger capacity depends on the carrying capacity:
P = G/100, people (with luggage), or P =G/75 people (without luggage)
In this case, the result is rounded to a smaller integer. On a small vessel, the availability of equipped seats must correspond to the passenger capacity established for the vessel.
Passenger capacity can be approximately calculated using the formula:
N=Lnb Bnb/K, people,
Where TO - empirical coefficient taken equal to: for motor and rowing boats - 1.60; for boats - 2.15.
Load capacity— the payload of the ship, including the mass of people and luggage according to passenger capacity. A distinction is made between deadweight and net tonnage.
Deadweight - this is the difference between the displacement when fully loaded and when unladen.
Net load capacity - This is the mass of only the payload that the ship can take.
For large vessels, the unit of change in carrying capacity is ton, for small vessels - kg. Load capacity C can be calculated using formulas, or can be determined experimentally. To do this, when the vessel is empty, but with supplies and a reserve of fuel, cargo is sequentially placed until the vessel reaches the waterline corresponding to the minimum freeboard height. The mass of the placed cargo corresponds to the carrying capacity of the vessel.
Displacement . There are two types of displacement - mass (weight) and volumetric.
Mass (weight) displacement - this is the mass of the ship afloat, equal to the mass of the water displaced by the ship. The unit of measurement is ton.
Volumetric displacement V - this is the volume of the underwater part of the vessel in m3. The calculation is made through the main measurements:
V = SL VT,
where S is the coefficient of complete displacement, equal to 0.35 - 0.6 for small vessels, and a lower value of the coefficient is typical for small vessels with sharp contours. For displacement boats S = 0.4 - 0.55, planing boats S = 0.45 - 0.6, motor boats 5 - 0.35 - 0.5, for sailing ships this coefficient ranges from 0.15 to 0.4.
Speed.
Speed is the distance traveled by a ship per unit time. On seagoing vessels, speed is measured in knots (miles per hour), and on inland vessels - in kilometers per hour (km/h). The navigator of a small vessel is recommended to know three speeds: the highest (maximum) that the vessel develops at maximum engine power; the smallest (minimum) at which the ship obeys the rudder; medium - the most economical for relatively large transitions. The speed depends on the engine power, the size and shape of the hull, the loading of the vessel and various external factors: waves, wind, currents, etc.
Seaworthiness of the vessel
The ability of a vessel to stay afloat, interact with water, and not capsize or sink when flooded is characterized by its seaworthiness. These include: buoyancy, stability and unsinkability.
Buoyancy. Buoyancy is the ability of a ship to float on the surface of the water, having a given draft. The more weight you place on the boat, the deeper it will sink into the water, but will not lose buoyancy until water begins to flow into the hull.
In the event of a leak in the hull or a hole, as well as water entering the vessel during stormy weather, its weight increases. Therefore, the ship must have a reserve of buoyancy.
Buoyancy reserve - This is the water-tight volume of the ship's hull, located between the load waterline and the upper edge of the side. If there is no reserve of buoyancy, the ship will sink if even a small amount of water gets inside the hull.
The reserve of buoyancy necessary for safe navigation of a vessel is ensured by giving the vessel a sufficient freeboard height, as well as the presence of waterproof closures and bulkheads between compartments and buoyancy blocks - structural elements inside the hull of a small vessel in the form of a solid block of material (for example, polystyrene) having a density of less than one . In the absence of such bulkheads and buoyancy blocks, any hole in the underwater part of the hull leads to a complete loss of buoyancy reserve and the death of the vessel.
The reserve of buoyancy depends on the height of the freeboard - the higher the freeboard, the greater the reserve of buoyancy. This reserve is standardized by the minimum freeboard height, depending on the value of which the safe navigation area and permissible distance from the shore are established for a particular small vessel. However, the freeboard height cannot be abused, as this affects another equally important quality - stability
Stability. Stability is the ability of a ship to withstand the forces that cause it to tilt, and after the cessation of these forces (wind, wave, movement of passengers, etc.) to return to its original equilibrium position. The same vessel may have good stability if the cargo is located close to the bottom and may partially or completely lose stability if the cargo or people are placed slightly higher
There are two types of stability: transverse and longitudinal. Transverse stability manifests itself when the ship rolls, i.e. when tilting it on board. During navigation, two forces act on the ship: gravity and support. The resultant D (Fig. 1, a) of the vessel's gravity force, directed downwards, will be conditionally applied at point G, called the center of gravity (CG), and the resultant A of the support forces, directed upwards, will be conditionally applied at the center of gravity C of the part immersed in water vessel, called the center of magnitude (CV). When the ship has no trim and roll, the CG and CV will be located in the centerline plane of the ship (DP).
Fig 1 Location is equal active forces gravity and support relative to each other at different positions of the vessel
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The ho value characterizes the stability of the vessel at low inclinations. The position of point M under these conditions is almost independent of the roll angle f.
The force D and the equal supporting force A form a pair of forces with the shoulder /, which creates a restoring moment MB=Dl. This moment tends to return the ship to its original position. Note that the CG is below point M.
Now imagine that an additional load is placed on the deck of the same ship (Fig. 1, c). As a result, the CG will be located significantly higher, and during a roll, point M will be below it. The resulting pair of forces will no longer create a restoring moment, but an overturning moment Mopr. Consequently, the ship will be unstable and capsize.
The lateral stability of the vessel is greatly influenced by the width of the hull: the wider the hull, the more stable the vessel, and, conversely, the narrower and taller the hull, the worse the stability.
For small high-speed vessels (especially when moving on high speed during rough seas) the problem of maintaining longitudinal stability is not always solved.
For small keel vessels, the initial metacentric height is, as a rule, 0.3 - 0.6 m. The stability of the vessel depends on the loading of the vessel, the movement of cargo, passengers and other reasons. The greater the metacentric height, the greater the righting moment and the more stable the vessel, however, with high stability the vessel has a sharp roll. Stability is improved by the low position of the engine, fuel tank, seats and appropriate placement of cargo and people.
In heavy winds, a strong wave hitting the side, and in some other cases, the ship's roll increases quickly and a dynamic heeling moment occurs. In this case, the ship's roll will increase even after the heeling and righting moments are equal. This occurs due to the action of inertial force. Typically, such a roll is twice as large as the roll from the static action of the same heeling moment. Therefore, sailing in stormy weather, especially for small vessels, is very dangerous.
Longitudinal stability acts when the ship is tilted to the bow or stern, i.e. during pitching. The navigator should take this stability into account when moving at high speeds during waves, because Having buried its nose in the water, a boat or motorboat may not restore its original position and sink, and sometimes even capsize.
Factors affecting ship stability:
a) The stability of a vessel is most significantly affected by its width: the greater it is in relation to its length, side height and draft, the higher the stability.
b) The stability of a small vessel increases if the shape of the submerged part of the hull is changed at large angles of heel. This statement, for example, is the basis for the action of side boules and foam fenders, which, when immersed in water, create an additional righting moment.
c) Stability deteriorates if the ship has fuel tanks with a surface mirror from side to side, so these tanks must have internal partitions
d) Stability is most strongly influenced by the placement of passengers and cargo on the ship; they should be located as low as possible. On a small vessel, people should not be allowed to sit on board or move around arbitrarily while it is moving. Cargoes must be securely fastened to prevent their unexpected displacement from their stowage locations e) In strong winds and waves, the effect of heeling moment is very dangerous for the vessel, therefore, with deterioration weather conditions it is necessary to take the ship to shelter and wait out the bad weather. If this is impossible to do due to the considerable distance to the shore, then in stormy conditions you should try to keep the ship “head to the wind”, throwing out the sea anchor and running the engine at low speed.
Unsinkable. Unsinkability is the ability of a ship to remain buoyant after part of the ship has been flooded.
Unsinkability is ensured structurally - by dividing the hull into waterproof compartments, equipping the vessel with buoyancy blocks and drainage means.
The non-flooded volumes of the hull are most often made of foam blocks. Its required quantity and location are calculated to ensure an emergency reserve of buoyancy and maintain the emergency vessel in the “even keel” position.
Of course, in conditions of strong excitement, not everyone who received a hole powerboat and the boat will ensure that these requirements are met.
Maneuverability of a small vessel
The main maneuvering qualities of a vessel include: controllability, circulation, propulsion and inertia
Controllability. Controllability is the ability of a vessel to maintain a given direction of movement while moving with a constant rudder position (heading stability) and to change the direction of its movement while moving under the influence of the rudder (agility).
Course stability is the property of a vessel to maintain a straight direction of motion. If the ship, with the rudder in a straight position, deviates from the course, then this phenomenon is usually called the yaw of the ship.
If the ship, with the rudder in a straight position, deviates from the course, then this phenomenon is usually called the yaw of the ship.
The causes of yaw can be permanent or temporary. Constant reasons include those related to the design features of the vessel: blunt bow contours of the hull, discrepancy between the length of the vessel and its width, insufficient rudder blade area, the influence of propeller rotation
Temporary yaw can be caused by improper loading of the vessel, wind, shallow water, uneven currents, etc.
The concepts of “course stability” and “agility” are contradictory, but these qualities are inherent in almost all ships and characterize their controllability.
Controllability is influenced by many factors and reasons, the main ones being the action of the steering wheel, the operation of the propeller and their interaction.
Agility- the property of a ship to change the direction of movement under the influence of the rudder. This quality primarily depends on the correct ratio of the length and width of the hull, the shape of its contours, as well as the area of the rudder blade.
Features of vessel controllability when moving from forward to reverse
When carrying out mooring operations or the need to urgently stop the vessel (risk of collision, preventing grounding, assisting a person overboard, etc.), it is necessary to switch from forward to reverse. In these cases, the navigator must take into account that in the first seconds, when changing the operation of the right-hand rotation propeller from forward to reverse, the stern will rapidly roll to the left, and with a left-hand rotation propeller - to the right.
Reasons affecting controllability
In addition to the rudder and the rotating propeller, the stability and agility of the vessel are influenced by other factors, as well as a number of design features of the vessel: the ratio of the main dimensions, the shape of the hull contours, the parameters of the rudder and propeller. Controllability also depends on sailing conditions: the nature of the vessel’s loading, hydrometeorological factors.
Circulation If you move the rudder to any side while the ship is moving, the ship will begin to turn and describe a curved line on the water. This curve, described by the vessel’s center of gravity during a turn, is called the circulation line (Fig. 2), and the distance between the centerline plane of the ship on the forward course and its centerline plane after turning on the return course (180) is the tactical circulation diameter. The less tactical diameter circulation, the better the maneuverability of the vessel is considered. This curve is close to a circle, and its diameter serves as a measure of the maneuverability of the ship
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The circulation diameter is usually measured in meters. For small motor vessels, the size of the tactical circulation diameter in most cases is equal to 2-3 ship lengths. Every driver needs to know the circulation diameter of the vessel he has to control, since correct and safe maneuvering largely depends on this. The speed of the vessel during circulation is reduced to 30%. We should never forget that when moving along a curve, a centrifugal force acts on the ship (Fig. 3), directed from the center of curvature to the outer side and applied to the center of gravity of the ship. |
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Fig 2 Circulation /—circulation line, 2—tactical circulation diameter, 3—steady circulation diameter |
The drift of the vessel arising from the centrifugal force is prevented by the force of water resistance - lateral resistance, the point of application of which is located below the center of gravity. As a result, a pair of forces arises that creates a roll on board, opposite to the direction of rotation. Roll increases as the vessel's center of gravity increases above the center of lateral resistance and as the metacentric height decreases. |
An increase in turning speed and a decrease in the circulation diameter significantly increase the roll, which can lead to the vessel capsizing. Therefore, never make sharp turns when the boat is moving at high speed.
Unlike conventional displacement vessels, vessels with planing contours on the circulation turn to the inside (Fig. 4). This occurs from the additional lifting force that occurs on the hull during lateral displacement due to planing contours. At the same time, sliding occurs under the influence of centrifugal force to the outside, which is why planing ships have a slightly greater circulation compared to displacement ships.
In addition to the circulation diameter, you should also know its time, i.e. the time it takes the ship to make a 360° turn.
The named circulation elements depend on the displacement of the vessel and the nature of the placement of cargo along its length, as well as on the speed. At low speed the circulation diameter is smaller.
Mobility. Propulsion is the ability of a vessel to move at a certain speed with a given engine power, while overcoming the forces of resistance to movement.
The movement of the vessel is possible only if there is a certain force that can overcome the resistance of the water - the thrust. At a constant speed, the amount of stop is equal to the amount of water resistance. Vessel speed and thrust are related following dependency:
R. V=ho-N.Where: V - ship speed; K - water resistance; N - engine power; ho -Efficiency=0.5.
This equation shows that as speed increases, water resistance also increases. However, this dependence has a different physical meaning and character for displacement vessels and planing vessels.
For example, at a speed of a displacement vessel up to a value equal to V = 2 ÖL, km/h (L is the length of the vessel, m), the water resistance K consists of the friction resistance of water on the hull skin and the shape resistance, which is created by the turbulence of the water. When the speed of this vessel exceeds the specified value, waves begin to form and a third resistance is added to the two resistances - wave resistance. Wave drag increases sharply with increasing speed.
For planing vessels, the nature of water resistance is the same as for displacement vessels and the speed value is V = 8 ÖL km/h. However, with a further increase in speed, the ship receives a significant trim to the stern and its bow rises. This mode of movement is called transitional (from displacement to planing). A characteristic sign of the beginning of planing is a spontaneous increase in the speed of the vessel. This phenomenon is caused by the fact that after the bow rises, the overall resistance of the water to the vessel decreases, it seems to “float up” and increase speed while maintaining constant power.
When planing, another type of water resistance arises - splash resistance, and the wave resistance and shape resistance are sharply reduced and their values are practically reduced to zero.
Thus, four types of resistance affect the propulsion of the vessel:
friction resistance- depends on the area of the wetted surface of the vessel, on the quality of its processing and the degree of fouling (algae, mollusks, etc.);
shape resistance- depends on the streamlining of the vessel’s hull, which in turn is better, the sharper the stern end and the greater the length of the vessel compared to the width;
characteristic impedance- depends on the shape of the bow and the length of the vessel, the longer the vessel, the less wave formation;
splash resistance- depends on the ratio of the width of the body to its length.
Conclusion: 1. Displacement vessels with a narrow hull, round bilge lines and pointed bow and stern ends experience the least water resistance.
2. For planing vessels, in the absence of waves, a wide flat-bottomed hull with a transom stern provides the least water resistance with the greatest hydrodynamic lift.
More seaworthy planing vessels with a keeled or semi-keeled hull. Increasing the speed of these vessels is achieved by longitudinal steps and bilge splash guards.
Inertia. A very important maneuvering quality of a vessel is its inertia. It is usually estimated by the lengths of the braking distance, coasting and acceleration paths, as well as their duration. The distance that a ship travels during the period of time from the moment the engine switches from full forward to reverse until the ship finally stops is called braking distance. This distance is usually expressed in meters, less often in ship lengths. The distance covered by the vessel during the period of time from the moment the engine is stopped running in forward motion until the vessel comes to a complete stop under the influence of water resistance is called coasting. The distance that the ship travels from the moment the engine is switched on to forward speed until full speed is acquired at a given engine operating mode is called the acceleration path. Accurate knowledge by the driver of the above qualities of his vessel greatly ensures the safety of maneuvering in narrow areas and roadsteads with cramped navigation conditions. Remember! Motorized boats do not have brakes, so they often require significantly more distance and time to absorb inertia than, say, a car.
Stability is the ability of a ship tilted from a position of equilibrium by the action of external forces to return to a state of equilibrium after the action of these forces ceases.
The tilting of the vessel can occur under the influence of such external forces as the movement, reception or discharge of cargo, wind pressure, wave action, tension in the towing rope, etc.
The stability that a ship has during longitudinal inclinations, measured by trim angles, is called longitudinal. It is usually quite large, so there is never any danger of the vessel capsizing through the bow or stern. But studying it is necessary to determine the trim of the vessel under the influence of external forces. The stability that a ship has during transverse inclinations, measured by roll angles 6, is called transverse.
Lateral stability is the most important characteristic of a vessel, determining its seaworthiness and degree of navigation safety. When studying lateral stability, a distinction is made between initial stability (at small inclinations of the vessel) and stability at large angles of roll. Initial stability. When the ship rolls at a small angle under the influence of any of the above-mentioned external forces, the central point moves due to the movement of the underwater volume (Fig. 149). The magnitude of the restoring moment generated in this case depends on the size of the shoulder l= GK between forces
weight and support of a tilted vessel. As can be seen from the figure, the restoring moment Mv= Dl = Dh sinθ, where h- point elevation M above the ship's CG G, called transverse metacentric height of the vessel. Dot M is called the transverse metacenter of the vessel.
Rice. 149. The action of forces when the ship rolls
Metacentric height is the most important stability characteristic. It is defined by the expression
h = z c + r - z g,
Where z c- elevation of the CV above the OL; r- transverse metacentric radius, i.e. the elevation of the metacenter above the central point; z g- elevation of the ship’s CG above the OL.
Meaning z g determined when calculating the mass load. Approximately possible
accept (for a ship with a full load) z g = (0,654-0,68) N, Where N- side height at midships.
Meaning z c And r determined from a theoretical drawing or (for rough calculations) using approximate formulas, for example:
Where IN- width of the vessel, m; T- draft, m; α - waterline completeness coefficient; δ - coefficient of overall completeness; TO- a coefficient that depends on the shape of the waterline and its completeness and varies within the range of 0.086 - 0.089.
From the above formulas it is clear that the lateral stability of the vessel increases with increasing B and α; with decreasing T and δ; with increasing CV z c; With
lowering the central heating z g. Thus, wide ships, as well as ships with a low CG location, are more stable. When the CG decreases, i.e. when heavier loads - machinery and equipment - are located as low as possible and at
By lightening high-lying structures (superstructures, masts, pipes, which are sometimes made of light alloys for this purpose), the metacentric height increases. And vice versa, when heavy loads are received on deck, icing occurs on the surface of the hull, superstructures, masts, etc., while the vessel is sailing in winter conditions, the stability of the vessel decreases.
Inclining experience. On a constructed vessel, the initial metacentric height is determined (using the metacentric stability formula) experimentally - by tilting the vessel, which is carried out at an angle of 1.5-2 by transferring a pre-weighed load from side to side. The diagram of the inclining experiment is shown in Fig. 150.
Rice. 150. Scheme of inclining experiment.
1 - rack with divisions; 2 - weight and lionfish; 3 - bath with water or oil; 4 - weight thread; 5 - portable securing weight
Heeling moment M cr caused by load transfer R to a distance at: M cr = Ru. According to the metacentric stability formula h = M KP /Dθ (sin θ is replaced by the value θ due to the small roll angle θ). But θ = d/l, That's why h = Pyl/Dd.
The values of all quantities included in this formula are determined during the inclination experiment. The displacement is determined by calculation based on precipitation measured along the marks of the depression.
On small ships, carrying cargo (pig iron, sandbags, etc.) is sometimes replaced by running people with a total mass of about 0.2-0.5% of the displacement of an empty ship. The roll angle θ is measured with scales dipped in oil baths. Recently, weights have been replaced with special devices that make it possible to accurately measure the angle of heel during an inclining experiment (taking into account the rocking of the vessel that occurs when carrying a load), the so-called inclinographs.
Based on the initial metacentric height found using the inclination experiment, the position of the CG of the constructed vessel is calculated using the above formulas.
The following are approximate transverse metacentric heights for different types of fully laden vessels:
Large passenger ships …………………………… 0,3-1,5
Medium and small passenger ships. . . ……………… 0.6-0.8
Large dry cargo ships…………………………….. 0.7-1.0
Average…………………………………………………………….. 0.5-0.8
Large tankers ………………………………… 2.0-4.0
Average……………………………………………………………... 0.7-1.6
River passenger ships…………………………….... 3.0-5.0
Barges………………………………………………………2.0-10.0
Icebreakers……………………………………………………………1.5-4.0
Tugs…………………………………………………… 0.5-0.8
Fishing vessels …………………………………. 0.7-1.0
Stability at high roll angles. As the angle of roll of the vessel increases, the righting moment first increases (Fig. 151, a-c), then decreases, becomes equal to zero and no longer prevents, but, on the contrary, promotes further tilting of the vessel (Fig. 151, d).
Rice. 151. The action of forces when the ship heels at large angles
Since the displacement D for a given load condition remains constant, then the restoring torque M in changes proportionally to the change in leverage l lateral stability. This change in the stability arm depending on the roll angle 8 can be calculated and depicted graphically in the form static stability diagrams(Fig. 152), which is built for the most typical and dangerous ship loading cases with respect to stability.
The static stability diagram is an important document characterizing the stability of the vessel. With its help, it is possible, knowing the magnitude of the heeling moment acting on the ship, for example, from wind pressure determined on the Beaufort scale (Table 8), or from the transfer of cargo on board, from the asymmetrically accepted DP of ballast water or fuel reserves, etc. , - find the value of the resulting roll angle if this angle is large (more than 10°). The small roll angle is calculated without constructing a diagram using the above metacentric formula.
Rice. 152. Static stability diagram
Using the static stability diagram, you can determine the initial metacentric height of the vessel, which is equal to the segment between the horizontal axis and the point of intersection of the tangent to the curve of the stability arms at the origin with the vertical drawn at a heel angle equal to one radian (57.3°). Naturally, the steeper the curve at the origin, the greater the initial metacentric height.
The static stability diagram is especially useful when you need to find out the angle of heel of the ship due to the action of a suddenly applied force - with the so-called dynamic action of force.
If any statically, i.e. smoothly, without jerking, applied force acts on the ship, then the heeling moment generated by it creates a roll angle, which is determined from the static stability diagram (constructed in the form of a curve of changes in righting moments D(from the roll angle) at the point of intersection with the curve of a horizontal straight line drawn parallel to the horizontal axis at a distance equal to the value of the heeling moment (Fig. 153, a). At this point (point A) heeling moment from the action of static
Characteristics of wind and sea waves
force is equal to the restoring moment that occurs when the ship heels and tends to return the heeled ship to its original, straight position. The roll angle at which the heeling and righting moments are equal is the desired roll angle from the statically applied force.
If the heeling force acts on the ship dynamically, that is, suddenly (gust of wind, jerk of the towing cable, etc.), then the angle of heel it causes is determined from the static stability diagram in a different way.
Rice. 153. Determination of the roll angle from the action statically ( A) and dynamically ( b) applied force
The horizontal line of the heeling moment, for example from the action of the wind during a squall, is continued to the right from point A (Fig. 153, b) until the area ABC cut off by it inside the diagram becomes equal to the area AOD outside of it; in this case, the roll angle (point E) corresponding to the position of the straight line Sun, is the desired roll angle from the action of a dynamically applied force. Physically, this corresponds to the roll angle at which the work of the heeling moment (graphically represented by the area of the rectangle ODCE) turns out to be equal to the work of the restoring moment (area of the figure BOTH).
If the area limited by the curve of righting moments turns out to be insufficient to equal the area of the figure limited by the heeling moment outside it, then the ship will capsize. Therefore, one of the main characteristics of the diagram, indicating the stability of the vessel, is its area limited by the curve and the horizontal axis. In Fig. 154 shows the curves of the static stability arms of two ships: with high initial stability, but with a small diagram area ( 1 ) and with a smaller initial metacentric height, but with larger area diagrams (2). The latter vessel can withstand stronger winds and is more stable. Typically, the diagram area is larger for a vessel with a high freeboard and smaller for a vessel with a low freeboard.
Rice. 154. Static stability curves of a vessel with high (1) and low (2) freeboard
The stability of seagoing vessels must comply with the Stability Standards of the USSR Register, which stipulate the following condition as the main criterion (called the “weather criterion”): capsizing moment M def, i.e. the minimum dynamically applied moment, which, under the simultaneous influence of rolling motion and the worst loading, causes the vessel to capsize, should not be less than the dynamically applied heeling moment to the vessel M cr on wind pressure, i.e. K = M def/M cr≥ l.00.
In this case, the value of the overturning moment is found from the static stability diagram according to a special scheme, and the value (in kN∙m) of the heeling moment compared with it (Fig. 155) according to the formula M cr = 0.001P in S p z n, Where R in- wind pressure, MPa or kgf/m 2 (determined according to the Beaufort scale in the “in a squall” column or according to the USSR Register table); S n- sail area (area of the lateral projection of the surface of the vessel), m 2 ; z n- elevation of the center of sail above the waterline, m.
When studying the static stability diagram, the angle at which the curve intersects the horizontal axis is of interest - the so-called sunset angle. According to the Register Rules, for seagoing vessels this angle should not be less than 60°. The same Rules require that the maximum values of righting moments on the diagram be achieved at a heel angle of at least 30°, and the maximum stability arm should be at least 0.25 m for ships up to 80 m in length and at least 0.20 m for ships with a length of more than 105 m.
Rice. 155. To determine the heeling moment from the action of wind force
in a squall (the sail area is shaded)
Effect of liquid cargo on stability. The liquid cargo in the tanks, when the tanks are incompletely filled, in the event of the vessel tilting, moves in the direction of the tilt. Because of this, the ship’s CG moves in the same direction (from the point G 0 exactly G), which leads to a decrease in the restoring moment arm. In Fig. 156 shows how the stability arm l 0 when taking into account the displacement of the liquid load, it decreases to l. Moreover, the wider the tank or compartment having a free liquid surface, the greater the movement of the CG and, consequently, the greater the decrease in lateral stability. Therefore, to reduce the influence of liquid cargo, they strive to reduce the width of the tank, and during operation, to limit the number of tanks in which free levels are formed, i.e., to consume supplies not from several tanks at once, but one by one.
The influence of bulk cargo on stability. Bulk cargo includes grain of all types, coal, cement, ore, ore concentrates, etc.
The free surface of liquid cargo always remains horizontal.
In contrast, bulk cargo is characterized by an angle of repose, i.e., the largest angle between the surface of the cargo and the horizontal plane, at which the cargo is still at rest and, when exceeded, spillage begins. For most bulk cargo this angle is within 25-35°.
Bulk cargo loaded onto a ship is also characterized by porosity, or porosity, i.e., the ratio of the volumes occupied directly by cargo particles and the voids between them. This characteristic, depending both on the properties of the cargo itself and on the method of loading it into the hold, determines the degree of its shrinkage (compaction) during transportation.
Rice. 156. To determine the influence of the free surface of a liquid load
for stability
When transporting bulk cargo (especially grain), as a result of the formation of voids as they shrink due to shaking and vibration of the hull during the voyage, during sudden or large inclinations of the vessel under the influence of a squall (exceeding the angle of repose), they spill onto one side and are no longer returned completely to the starting position after straightening the vessel.
The amount of cargo (grain) spilled in this way gradually increases and causes a list, which can lead to the capsizing of the vessel. To avoid this, special measures are taken - they place bags of grain on top of the grain poured into the hold (cargo bagging) or install additional temporary longitudinal bulkheads in the holds - shifting boards (see Fig. 154). If these measures are not followed, serious accidents and even the loss of ships occur. Statistics show that more than half of the ships lost due to capsizing were carrying bulk cargo.
A particular danger arises when transporting ore concentrates, which, when their humidity changes during the voyage, for example when thawing or sweating, become highly mobile and easily move to the side. This little-studied property of ore concentrates has caused a number of serious ship accidents.
LECTURE No. 4
General provisions of stability. Stability at low inclinations. Metacenter, metacentric radius, metacentric height. Metacentric formulas of stability. Determination of landing parameters and stability when moving cargo on a ship. Influence on the stability of loose and liquid cargo.
Inclining experience.
Stability is the ability of a ship, removed from a position of normal equilibrium by any external forces, to return to its original position after the cessation of the action of these forces. External forces that can displace a ship from a position of normal equilibrium include: wind, waves, movement of cargo and people, as well as centrifugal forces and moments that arise when the ship turns. The navigator is obliged to know the characteristics of his vessel and correctly assess the factors affecting its stability.
A distinction is made between transverse and longitudinal stability. The lateral stability of a vessel is characterized by the relative position of the center of gravity G and center of magnitude WITH. Let's consider lateral stability.
If the ship is tilted on one side at a small angle (5-10°) (Fig. 1), the central point will move from point C to point . Accordingly, the supporting force acting perpendicular to the surface will intersect the center plane (DP) at the point M.
The point of intersection of the vessel's DP with the continuation of the direction of the supporting force during a roll is called initial metacenter M. Distance from the point of application of the supporting force WITH to the initial metacenter is called metacentric radius .
Fig.1 – C static forces acting on the ship at low heels
Distance from initial metacenter M to the center of gravity G called initial metacentric height
.
The initial metacentric height characterizes the stability at small inclinations of the vessel, is measured in meters and is a criterion for the initial stability of the vessel. As a rule, the initial metacentric height of motor boats and speedboats is considered good if it is greater than 0.5 m, for some ships it is permissible less, but not less than 0.35 m.
A sharp tilt causes the ship to roll and the period of free rolling is measured with a stopwatch, that is, the time of full swing from one extreme position to the other and back. The transverse metacentric height of the vessel is determined by the formula:
,
m
Where IN- width of the vessel, m; T- rolling period, sec.
To evaluate the results obtained, use the curve in Fig. 2, built according to data 
dacha designed boats.
Ri.2 – W Dependence of the initial metacentric height on the length of the vessel
If the initial metacentric height 
, determined by the above formula, will be below the shaded line, which means that the ship will have a smooth roll, but insufficient initial stability, and sailing on it can be dangerous. If the metacenter is located above the shaded strip, the vessel will be characterized by rapid (sharp) rolling, but increased stability, and therefore, such a vessel is more seaworthy, but its habitability is unsatisfactory. The optimal values will be those that fall within the shaded band area.
The roll of the ship on one side is measured by the angle 
between the new inclined position of the center plane with the vertical line.
The heeled side will displace more water than the opposite side, and the center of gravity will shift towards the heel. Then the resultant forces of support and weight will be unbalanced, forming a pair of forces with a shoulder equal to
.
The repeated action of weight and support forces is measured by the righting moment:
.
Where D- buoyancy force equal to the weight of the vessel; l- stability arm.
This formula is called the metacentric stability formula and is valid only for small roll angles, at which the metacenter can be considered constant. At large roll angles, the metacenter is not constant, as a result of which the linear relationship between the righting moment and roll angles is violated.
Small ( 
) and big ( 
) metacentric radii can be calculated using the formulas of Professor A.P. Fan der Fleet:
;
.
By the relative position of the cargo on the ship, the navigator can always find the most favorable value of the metacentric height, at which the ship will be sufficiently stable and less subject to pitching.
The heeling moment is the product of the weight of the cargo moved across the vessel by a shoulder equal to the distance of movement. If a person weighs 75 kg, sitting on a bank will move across the ship by 0.5 m, then the heeling moment will be equal to 75 * 0.5 = 37.5 kg/m.
To change the moment that heels the ship by 10°, it is necessary to load the ship to full displacement completely symmetrically relative to the center plane. The vessel's loading should be checked by drafts measured on both sides. The inclinometer is installed strictly perpendicular to the DP so that it shows 0°.
After this, you need to move loads (for example, people) at pre-marked distances until the inclinometer shows 10°. The test experiment should be carried out as follows: tilt the ship on one side and then on the other side. Knowing the fastening moments of a ship heeling at various (up to the greatest possible) angles, it is possible to construct a static stability diagram (Fig. 3), which will allow assessing the stability of the ship.
Fig.3 – Static stability diagram
Stability can be increased by increasing the width of the vessel, lowering the center of gravity, and installing stern bulges.
If the CG of the vessel is located below the CV, then the vessel is considered to be very stable, since the supporting force during a roll does not change in magnitude and direction, but the point of its application shifts towards the tilt of the vessel (Fig. 4, a). Therefore, when heeling, a pair of forces is formed with a positive restoring moment, tending to return the ship to its normal vertical position on a straight keel. It is easy to verify that h>0, with a metacentric height of 0. This is typical for yachts with a heavy keel and is not typical for larger vessels with a conventional hull design.
If the CG is located above the CV, then three cases of stability are possible, which the navigator should be well aware of.
1st case of stability
Metacentric height h>0. If the center of gravity is located above the center of magnitude, then when the vessel is in an inclined position, the line of action of the supporting force intersects the center plane above the center of gravity (Fig. 4, b).
Fig. 4 – Case of a stable vessel
In this case, a couple of forces with a positive restoring moment is also formed. This is typical for most conventionally shaped boats. Stability in this case depends on the hull and the position of the center of gravity in height. When heeling, the heeling side enters the water and creates additional buoyancy, tending to level the ship. However, when a ship rolls with liquid and bulk cargo that can move towards the roll, the center of gravity will also shift towards the roll. If the center of gravity during a roll moves beyond the plumb line connecting the center of magnitude with the metacenter, then the ship will capsize.
2nd case of an unstable vessel in indifferent equilibrium
Metacentric height h= 0. If the CG lies above the CG, then during a roll the line of action of the support force passes through the CG MG = 0 (Fig. 5).
Fig. 5 – Case of an unstable vessel in indifferent equilibrium
In this case, the CV is always located on the same vertical with the CG, so there is no recovering pair of forces. Without the influence of external forces, the ship cannot return to an upright position. In this case, it is especially dangerous and completely unacceptable to transport liquid and bulk cargo on a ship: with the slightest rocking, the ship will capsize. This is typical for boats with a round frame.
3rd case of an unstable ship with unstable equilibrium
Metacentric height h<0. ЦТ расположен выше ЦВ, а в наклонном положении судна линия действия силы поддержания пересекает след диаметральной плоскости ниже ЦТ (рис. 6). Сила тяжести и сила поддержания при малейшем крене образуют пару сил с отрицательным восстанавливающим моментом и судно опрокидывается.
Fig.6 - C beam of an unstable ship in unstable equilibrium
The analyzed cases show that the ship is stable if the metacenter is located above the ship's CG. The lower the CG goes, the more stable the ship is. In practice, this is achieved by placing cargo not on the deck, but in the lower rooms and holds.
Due to the influence of external forces on the ship, as well as as a result of insufficiently strong securing of the cargo, it is possible for it to move on the ship. Let us consider the influence of this factor on changes in the landing parameters of the vessel and its stability.
Vertical movement of cargo.
Fig. 1 – The influence of vertical movement of the load on the change in metacentric height
Let us determine the change in the landing and stability of the vessel caused by the movement of a small load 
in the vertical direction (Fig. 1) from the point 
exactly 
. Since the mass of the cargo does not change, the displacement of the vessel remains unchanged. Therefore, the first equilibrium condition is satisfied: 
. It is known from theoretical mechanics that when one of the bodies moves, the CG of the entire system moves in the same direction. Therefore, the ship's CG 
will move to a point 
, and the vertical itself will pass, as before, through the center of the quantity 
.
The second equilibrium condition will be met: 
.
Since in our case both equilibrium conditions are met, we can conclude: When the load moves vertically, the ship does not change its equilibrium position.
Let's consider the change in initial lateral stability. Since the shape of the volume of the ship’s hull immersed in water and the area of the waterline have not changed, the position of the center of the value 
and the transverse metacenter remains unchanged when the load moves vertically. Only the ship's CG moves, which will result in a decrease in metacentric height 
, and 
, where 
, Where 
- weight of the transported cargo, kN;
- the distance by which the CG of the load has moved in the vertical direction, m.
So the new meaning 
, where the (+) sign is used when moving the load up, and the (-) sign is used down.
From the formula it can be seen that the vertical movement of the load upward causes a decrease in the lateral stability of the vessel, and when moving downward, the lateral stability increases.
The change in stability is equal to the product 
. The change in lateral stability will be relatively less for a ship with a large displacement than for a ship with a small displacement, therefore, on ships with a large displacement, the movement of cargo is safer than on small ships.
Transverse horizontal movement of cargo.
Moving cargo 
from point 
exactly 
(Fig.2) at a distance 
will cause the ship to roll at an angle 
and displacement of its CG in a direction parallel to the line of movement of the load.
Fig. 2 – Occurrence of heeling moment during transverse movement of cargo
Leaning at an angle 
, the ship comes to a new equilibrium position, the ship's gravity 
, now applied at the point 
and maintaining power 
, applied at the point 
, act along one vertical perpendicular to the new waterline 
.
The movement of the load leads to the formation of a heeling moment:
,
Where 
- load moving shoulder, m.
Righting moment according to the metacentric stability formula
.
Since the ship is in equilibrium, then 
and , where is the roll angle during transverse movement of the load 
. Since the roll angle is small, then 
.
If the ship already has an initial heel angle, then after the horizontal movement of the load the heel angle will be 
.
The main characteristic of stability is righting moment, which must be sufficient for the vessel to withstand the static or dynamic (sudden) action of heeling and trim moments arising from the displacement of cargo, under the influence of wind, waves and other reasons.
The heeling (trimming) and righting moments act in opposite directions and are equal in the equilibrium position of the vessel.
Distinguish lateral stability, corresponding to the inclination of the vessel in the transverse plane (vessel roll), and longitudinal stability(ship trim).
The longitudinal stability of sea vessels is obviously ensured and its violation is practically impossible, while the placement and movement of cargo leads to changes in lateral stability.
When the ship tilts, its center of magnitude (CM) will move along a certain curve called the CM trajectory. With a small inclination of the vessel (no more than 12°), it is assumed that the trajectory of the central point coincides with a flat curve, which can be considered an arc of radius r with a center at point m.
The radius r is called transverse metacentric radius of the vessel, and its center m - initial metacenter of the ship.
Metacenter - the center of curvature of the trajectory along which the center of magnitude C moves during the process of tilting the ship. If the inclination occurs in the transverse plane (roll), the metacenter is called transverse, or small, while the inclination in the longitudinal plane (trim) is called longitudinal, or large.
Accordingly, transverse (small) r and longitudinal (large) R metacentric radii are distinguished, representing the radii of curvature of the trajectory C during roll and trim.
The distance between the initial metacenter t and the center of gravity of the vessel G is called initial metacentric height(or simply metacentric height) and are designated by the letter h. The initial metacentric height is a measure of the ship's stability.
h = zc + r - zg; h = zm ~ zc; h = r - a,
where a is the elevation of the center of gravity (CG) above the CV.
Metacentric height (m.h.) - the distance between the metacenter and the center of gravity of the vessel. M.v. is a measure of the initial stability of the vessel, determining the righting moments at small angles of roll or trim.
With increasing m.v. The stability of the vessel increases. For positive stability of the ship, it is necessary that the metacenter be above the center of gravity of the ship. If m.v. negative, i.e. the metacenter is located below the center of gravity of the ship, the forces acting on the ship form not a restoring moment, but a heeling moment, and the ship floats with an initial roll (negative stability), which is not allowed.
OG – elevation of the center of gravity above the keel; OM – elevation of the metacenter above the carina;
GM - metacentric height; CM – metacentric radius;
m – metacenter; G – center of gravity; C – center of magnitude
There are three possible cases of the location of the metacenter m relative to the center of gravity of the vessel G:
the metacenter m is located above the center of gravity of the vessel G (h > 0). With a low inclination, gravity and buoyancy forces create a pair of forces, the moment of which tends to return the ship to its original equilibrium position;
The ship's CG G is located above the metacenter m (h< 0). В этом случае момент пары сил веса и плавучести будет стремиться увеличить крен судна, что ведет к его опрокидыванию;
The ship's center of gravity G and the metacenter m coincide (h = 0). The ship will behave unstable, since the shoulder of the couple of forces is missing.
The physical meaning of the metacenter is that this point serves as the limit to which the ship’s center of gravity can be raised without depriving the ship of positive initial stability.
- Depending on the plane of inclination there are lateral stability when heeling and longitudinal stability at trim. In relation to surface ships (vessels), due to the elongated shape of the ship's hull, its longitudinal stability is much higher than transverse stability, therefore, for navigation safety, it is most important to ensure proper lateral stability.
- Depending on the magnitude of the inclination, stability at small angles of inclination is distinguished ( initial stability) and stability at large inclination angles.
- Depending on the nature of the acting forces, static and dynamic stability are distinguished.
Initial lateral stability
During roll, stability is considered as initial at angles up to 10-15°. Within these limits, the righting force is proportional to the roll angle and can be determined using simple linear relationships.
In this case, the assumption is made that deviations from the equilibrium position are caused by external forces that do not change either the weight of the vessel or the position of its center of gravity (CG). Then the immersed volume does not change in size, but changes in shape. Equal-volume inclinations correspond to equal-volume waterlines, cutting off immersed volumes of the hull of equal magnitude. The line of intersection of the waterline planes is called the inclination axis, which, with equal volume inclinations, passes through the center of gravity of the waterline area. With transverse inclinations, it lies in the center plane.
Free surfaces
All the cases discussed above assume that the center of gravity of the vessel is stationary, that is, there are no loads that move when tilted. But when such loads exist, their influence on stability is much greater than others.
A typical case is liquid cargo (fuel, oil, ballast and boiler water) in tanks that are partially filled, that is, with free surfaces. Such loads can overflow when tilted. If the liquid cargo fills the tank completely, it is equivalent to a solid fixed cargo.
Effect of free surface on stability
If the liquid does not fill the tank completely, that is, it has a free surface that always occupies a horizontal position, then when the vessel is tilted at an angle θ the liquid flows towards the inclination. The free surface will take the same angle relative to the KVL.
Liquid cargo levels cut off equal volumes of tanks, that is, they are similar to equal-volume waterlines. Therefore, the moment caused by the overflow of liquid cargo during a roll δm θ, can be represented similarly to the moment of shape stability m f, only δm θ opposite m f by sign:
δm θ = − γ f i x θ,Where i x- moment of inertia of the free surface area of the liquid load relative to the longitudinal axis passing through the center of gravity of this area, γ f- specific gravity of liquid cargo
Then the restoring moment in the presence of a liquid load with a free surface:
m θ1 = m θ + δm θ = Phθ − γ f i x θ = P(h − γ f i x /γV)θ = Ph 1 θ,Where h- transverse metacentric height in the absence of transfusion, h 1 = h − γ f i x /γV- actual transverse metacentric height.
The effect of the iridescent weight gives a correction to the transverse metacentric height δ h = − γ f i x /γV
The densities of water and liquid cargo are relatively stable, that is, the main influence on the correction is exerted by the shape of the free surface, or rather its moment of inertia. This means that the lateral stability is mainly affected by the width, and the longitudinal length of the free surface.
The physical meaning of the negative correction value is that the presence of free surfaces is always reduces stability. Therefore, organizational and constructive measures are being taken to reduce them:
Dynamic stability of the vessel
In contrast to the static effect, the dynamic effect of forces and moments imparts significant angular velocities and accelerations to the vessel. Therefore, their influence is considered in energies, more precisely in the form of the work of forces and moments, and not in the efforts themselves. In this case, the kinetic energy theorem is used, according to which the increment in the kinetic energy of the vessel's inclination is equal to the work of the forces acting on it.
When a heeling moment is applied to the ship m cr, constant in magnitude, it receives a positive acceleration with which it begins to roll. As you tilt, the restoring moment increases, but at first, up to the angle θ st, at which m cr = m θ, it will be less heeling. Upon reaching the static equilibrium angle θ st, the kinetic energy of rotational motion will be maximum. Therefore, the ship will not remain in the equilibrium position, but due to kinetic energy it will roll further, but slowly, since the righting moment is greater than the heeling moment. The previously accumulated kinetic energy is extinguished by the excess work of the restoring torque. As soon as the magnitude of this work is sufficient to completely extinguish the kinetic energy, the angular velocity will become zero and the ship will stop heeling.
The greatest angle of inclination that a ship receives from a dynamic moment is called the dynamic angle of heel θ din. In contrast, the angle of roll with which the ship will float under the influence of the same moment (according to the condition m cr = m θ), is called the static roll angle θ st.
If we refer to the static stability diagram, the work is expressed by the area under the righting moment curve m in. Accordingly, the dynamic roll angle θ din can be determined from the equality of areas OAB And BCD, corresponding to the excess work of the restoring torque. Analytically the same work is calculated as:
,in the range from 0 to θ din.
Having reached the dynamic bank angle θ din, the ship does not come into equilibrium, but under the influence of an excess righting moment begins to accelerate to straighten. In the absence of water resistance, the ship would enter into undamped oscillations around the equilibrium position when heeling θ st / ed. Physical encyclopedia
Ship, the ability of a ship to resist external forces causing it to roll or trim, and to return to its original equilibrium position after their action ceases; one of the most important seaworthiness vessel. O. when heeling... ... Great Soviet Encyclopedia
The quality of a ship being in equilibrium in an upright position and, having been removed from it by the action of some force, returning to it again after its action ceases. This quality is one of the most important for navigation safety; there were many… … Encyclopedic Dictionary F.A. Brockhaus and I.A. Ephron
G. The ability of a vessel to float in an upright position and to straighten itself after tilting. Ephraim's explanatory dictionary. T. F. Efremova. 2000... Modern Dictionary Russian language Efremova
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