Vessel completeness factor. The main dimensions of the vessel and its completeness coefficients. The ratio of the main dimensions of the vessel

Stability and metacentric height. A ship or yacht is subject to forces and moments of force that tend to tilt them in the transverse and longitudinal directions. The ability of a ship to withstand these forces and return to an upright position after their action ceases is called stability. The most important thing for a yacht is lateral stability.

When the ship floats without heeling, the forces of gravity and buoyancy, applied respectively in the CG and CV, act along the same vertical. If during a roll the crew or other components of the mass load do not move, then with any deviation the CG retains its original position in the DP point G in the figure, rotating with the ship.

At the same time, due to the changed shape of the underwater part of the hull, the CV shifts from point Co towards the heeled side to position C1. Due to this, a moment of a pair of forces D and gV arises with a shoulder l equal to the horizontal distance between the CG and the new CG of the yacht. This moment tends to return the yacht to an upright position and is therefore called restoring.

During a roll, the CV moves along a curved trajectory C0C1, the radius of curvature r of which is called the transverse metacentric radius, r the corresponding center of curvature M is the transverse metacenter. The value of the radius r and, accordingly, the shape of the C0C1 curve depend on the contours of the body. In general, as the heel increases, the metacentric radius decreases, since its value is proportional to the fourth power of the waterline width.

It is obvious that the arm of the righting moment depends on the distance - the elevation of the metacenter above the center of gravity: the smaller it is, the correspondingly smaller the arm l during roll. At the very initial stage of inclination, the value of GM or h is considered by shipbuilders as a measure of the vessel's stability and is called the initial transverse metacentric height. The greater h, the greater the heeling force required to tilt the yacht to any specific angle of heel, the more stable the vessel. On cruising and racing yachts, the metacentric height is usually 0.75-1.2 m; on cruising dinghies - 0.6-0.8 m.

Using the GMN triangle, it is easy to determine that the restoring shoulder is.

The restoring moment, taking into account the equality of gV and D, is equal to:

Thus, despite the fact that the metacentric height varies within rather narrow limits for yachts of different sizes, the magnitude of the righting moment is directly proportional to the displacement of the yacht, therefore, a heavier vessel is able to withstand a larger heeling moment.

The righting shoulder can be represented as the difference between two distances:

lf - shape stability shoulder and lv - weight stability shoulder. It is not difficult to establish the physical meaning of these quantities, since lв is determined by the deviation during roll of the line of action of the weight force from the initial position exactly above C0, and lв is determined by the displacement to the leeward side of the center of the value of the immersed volume of the hull. Considering the action of forces D and gV relative to Co, one can notice that the weight force D tends to heel the yacht even more, and the force gV, on the contrary, tends to straighten the vessel.

Using the triangle CoGK, you can find that, where CoC is the elevation of the CG above the CB in the upright position of the yacht. Thus, in order to reduce the negative effect of weight forces, it is necessary to lower the CG of the yacht if possible. In an ideal case, the CG should be located below the CV, then the weight stability arm becomes positive and the mass of the yacht helps it resist the action of the heeling moment.

However, only a few yachts have this characteristic: the deepening of the CG below the CV is associated with the use of very heavy ballast, exceeding 60% of the yacht’s displacement, and excessive lightening of the hull, spars and rigging. An effect similar to a decrease in CG is achieved by moving the crew to the windward side. If we are talking about a light dinghy, then the crew manages to shift the overall CG so much that the line of action of the force D intersects with the DP significantly below the CG and the weight stability arm turns out to be positive.

In a keelboat, thanks to the heavy ballast keel, the center of gravity is quite low (most often below the waterline or slightly above it). The yacht's stability is always positive and reaches its maximum at a heel of about 90°, when the yacht lies with its sails on the water. Of course, such a list can only be achieved on a yacht with securely closed openings in the deck and a self-draining cockpit. A yacht with an open cockpit can be flooded with water at a much lower angle of heel (a Dragon class yacht, for example, at 52°) and go to the bottom without having time to straighten out.

In seaworthy yachts, a position of unstable equilibrium occurs at a list of about 130°, when the mast is already under water, being directed downward at an angle of 40° to the surface. With a further increase in the roll, the stability arm becomes negative, the capsizing moment helps to achieve the second position of unstable equilibrium with a roll of 180° (keel up), when the center of gravity turns out to be located high above the center of gravity of a small enough wave so that the ship again takes a normal position - keel down. There are many cases where yachts made a full 360° rotation and retained their seaworthiness.

Combat lines along frames and waterlines. To characterize the distribution of displacement forces along the length of the vessel, a special diagram is constructed, called a frame diagram. To construct this diagram, a horizontal line, expressed in the accepted scale as the theoretical length of the vessel, is divided into n equal parts equal to the number of spacing on the theoretical drawing of the vessel.

On the perpendiculars restored at the division points, the area values ​​of the immersed parts of the corresponding frames are plotted on a certain scale and the ends of these segments are connected by a smooth line. The building area along the frames is equal to the volume of the vessel's displacement.

In the absence of a theoretical drawing, the volumetric displacement of the vessel can be approximately determined by its main dimensions:

V= k*L*B*T,
where L, B, T are the length, width and draft of the vessel, respectively; k is the coefficient of displacement completeness or the overall coefficient of completeness. The values ​​of the completeness coefficient k for various types of vessels are taken from reference data.

Construction on frames.

Since the center of the vessel’s size is located in the center of gravity of the underwater part of the vessel, and the formation area expresses the volume of the underwater part, the abscissa of the center of gravity of the formation along the frames is equal to the abscissa of the center of the vessel’s size.

A similar diagram characterizing the distribution of displacement forces along the height of the vessel is called a waterline diagram.

Construction along the waterline.

The formation area along the waterline is also equal to the volumetric displacement of the vessel, and the ordinate of its center of gravity determines the position of the center of the vessel's size according to its height.

If we take into account the properties of the formation along the frames and waterlines, then determining the location of the center of the vessel's size will be reduced to calculating the abscissa of the center of gravity of the formation along the frames and the ordinate of the center of gravity of the formation along the waterlines.

Calculation of the area of ​​the immersed part of the frame using the trapezoid method. To calculate roll and trim, it is necessary, in addition to the mass and position of the ship's center of gravity, to know its volumetric displacement and the position of the center of magnitude, center of gravity, which is the center of gravity of the volume of water displaced by the ship's hull. The simplest way to calculate these quantities is to plot combatant on frames.

The DP line at half-latitude of the theoretical drawing serves as the basis for constructing this curve, and the lines of the theoretical frames are extended downward. On each of these lines, on a certain scale, the immersed area of ​​the corresponding frame should be plotted. For sharp-cheeked, flat-bottomed or deadrise vessels, calculating the area of ​​the boat is not difficult: it is enough to divide it into simple geometric shapes: rectangles, triangles, trapezoids.

The same principle can be applied to calculate the areas of the frames of round bilge hulls, but a more accurate result gives trapezoid method. Its essence is as follows. If a figure bounded by a curved line is divided by equally spaced straight lines into a sufficiently large number of equal parts, then the area of ​​each part can be calculated as for a trapezoid:

By then summing the areas of all trapezoids, we can obtain the area of ​​the entire figure as the sum of the areas of all trapezoids:

Thus, to calculate the area of ​​the frame, it is necessary to find the sum of all ordinates yi along the waterlines minus half the sum of the ordinates of the extreme waterlines - at OP and KVL, and multiply the result by the distance DT between the waterlines and by 2, since the calculation was carried out for half of the frame. A similar principle can be used to calculate the area of ​​any waterline, which is divided by theoretical frames into sections DL of equal length.

Having found the immersed areas of each frame Wi on the hull projection, they are laid down from the DP on a certain scale, then a smooth curve is drawn. It is not difficult to figure out that if, for example, we add up the ordinates of the areas w. 5 and 6 and multiplied by the distance between the frames DI, you get the volume of the hull part as a truncated pyramid, having bases in the form of parts 5 and 6 immersed in water. Consequently, placing the line along the frames, you can calculate the displacement using the same principle of trapezoids,

Here all quantities must be expressed in m and m2. Using the trapezoidal rule, you can also find the position of the center of magnitude - CV, since it must coincide with the position of the center of gravity of the drill line along the waterline relative to the midsection. To do this, the static moment of the area limited by the front frames is calculated, relative to the midsection - frame, and the abscissas of the bow frames are taken with a plus sign, and the stern frames with a minus sign. With ten theoretical frames:

The abscissa of the CV from the midsection is:

Calculations to determine the coordinates of the vessel’s center of gravity. Calculations to determine coordinates ship's center of gravity It is convenient to keep in tabular form, which is called a weight journal. This log records the weights of all elements of the vessel itself and all cargo on it.
If we take into account the properties of the formation along the frames and waterlines, then determining the location of the center of the vessel's size will be reduced to calculating the abscissa of the center of gravity of the formation along the frames and the ordinate of the center of gravity of the formation along the waterlines.
Using the definition known from statics for the static moment of area, we can write formulas to determine the coordinates of the center of the vessel:

where wi and wi* are the areas of combat units enclosed between two adjacent frames or waterlines; Xi, Yi, Zi are the coordinates of the centers of gravity of the corresponding areas.
At approximate calculations You can use approximate formulas to determine the location of the center of gravity, the center of magnitude and the metacenter along the height of the vessel.
The ordinate of the vessel's center of gravity is determined by the expression:

Where:
k is a practical coefficient, the value of which, for example, for boats lies in the range of 0.68 - 0.73
h is the height of the ship's side.

Ordinates of the magnitude center. To calculate the ordinate of the center of a quantity, the formula of Academician V.L. Pozdyunin is recommended:

Zс = T/(1-b/a).

where T is the draft
b(betta) - displacement completeness coefficient
a(alpha) coefficient of fullness of the load waterline.

Static stability diagram. Static stability diagram. Obviously, a complete characteristic of a yacht’s stability can be a curve of changes in the righting moment Mv depending on the heel angle or a static stability diagram. The diagram clearly distinguishes the moments of maximum stability (W) and the maximum angle of heel at which the ship, left to its own devices, capsizes (3-sunset angle of the static stability diagram). Using the diagram, the captain of the vessel has the opportunity to assess, for example, the ability of the yacht to carry or other windage in a wind of a certain strength. To do this, curves of changes in the heeling moment Mkr depending on the roll angle are plotted on the stability diagram. Point B of the intersection of both curves indicates the angle of heel that the yacht will receive under static wind action with a smooth increase. In the figure, the yacht will receive a roll corresponding to point D - about 29°. For vessels with clearly defined downward branches of the stability diagram (dinghies, compromises and catamarans), navigation can only be allowed at heel angles not exceeding the maximum point on the stability diagram.

Comparison of the contours of various ships. When comparing the contours of various ships and performing calculations of their seaworthiness, dimensionless coefficients of completeness, volume and area are often used. These include:

— displacement coefficient or general completeness — δ , connecting the linear dimensions of the body with its immersed volume. This coefficient is defined as the ratio of the volumetric displacement V along the vertical line to the volume of a parallelepiped having sides equal to L, B and T;

The lower the coefficient , the more sharp the contours of the ship and, on the other hand, the smaller the useful volume of the hull below the waterline;

— coefficient of completeness of the waterline area — α and - β midsection - frame; the first is the ratio of the area of ​​the waterline S to a rectangle with sides L and B;

The main dimensions of a vessel are length, width, draft and side height (Fig. 2).

Rice. 2. Main dimensions of the vessel: a - vessels without permanently protruding parts; b - vessels with permanently protruding parts; c - vessels with transom stern; d - main dimensions in the cross sections of the body; d - examples of determining theoretical lines and nasal perpendicular

Vessel length L. There are:

• length along the design waterline L KVL- the distance between the points of intersection of the bow and stern parts of the structural waterline with the centerline plane of the vessel. The length for any design waterline is determined similarly L VL;
• length between perpendiculars L PP. Behind nasal perpendicular(NP) take the line of intersection of the DP with the vertical transverse plane passing through the extreme bow point of the design waterline of the vessel. Behind stern perpendicular(CP) take the line of intersection of the vessel's DP with a vertical transverse plane passing through the point of intersection of the stock axis with the plane of the structural waterline. In the absence of a stock, the stern perpendicular of the vessel is taken to be the line of intersection of the vessel's DP with a vertical transverse plane passing at a distance of 97% of the length along the vertical line from the bow perpendicular;
• longest length L NB- the distance measured in the horizontal plane between the extreme points of the theoretical surface of the ship’s hull (excluding the outer plating) at the bow and stern ends;
• overall length L GB- the distance measured in the horizontal plane between the extreme points of the bow and stern ends of the vessel, taking into account permanently protruding parts.

Vessel width B. Distinguish:

• width according to KVL V KVL- the distance measured in the widest part of the vessel at the level of the vertical line perpendicular to the DP without taking into account the outer plating. Similarly, the width along the waterline is determined for any design waterline In VL;
• width at midship frame B- the distance measured at the midship frame at the level of the waterline or design waterline without taking into account the outer hull plating;
• greatest width in NB- the distance measured in the widest part perpendicular to the DP between the extreme points of the body without taking into account the outer skin;
• overall width in GB- the distance measured in the widest part perpendicular to the DP between the extreme points of the body, taking into account the protruding parts.

Vessel draft T- vertical distance measured in the plane of the midship frame from the main plane to the plane of the design waterline (T VL) or to the plane of the water line (G KVL).

Control over the landing of the vessel (average draft, trim and roll) during operation of the vessel is carried out according to recess brands. Recess marks are applied in Arabic numerals on both sides, the stem, in the midship-frame area and on the sternpost and indicate the recess in decimeters (Fig. 3).

Rice. 3. Recess marks.

Vessel side height N- vertical distance measured in the plane of the midship frame from the main plane to the side line of the upper deck of the ship. Under side line refers to the line of intersection of the side surface (without taking into account the plating) and the upper deck (without taking into account the thickness of the flooring).

Freeboard F- is the difference between the height of the side and the draft F=H - T.

Main dimensions L, V, H And T determine only the dimensions of the vessel, and their ratios L/B, H/T, H/T, L/H And B/H to a certain extent characterize the shape of the ship’s hull and influence its seaworthiness and strength characteristics. For example, increase L/B contributes to the speed of the vessel, the more B/T the more stable it is.

Rice. 4. To determine the coefficients of completeness: a - waterline area; b - midsection frame area; in - displacement.

An additional idea of ​​the shape of a ship’s hull is provided by dimensionless values ​​called ship fullness coefficients.

Waterline completeness coefficient α- the ratio of the area of ​​the waterline S to the area of ​​the rectangle with sides circumscribed around it L And IN(Fig. 4):

Midship frame completeness coefficient β is the ratio of the immersed part of the midsection to the area of ​​the rectangle with sides circumscribed around it IN And T:

Displacement completeness coefficient δ is the ratio of volumetric displacement V to the volume of a parallelepiped with sides L, B And T:

Longitudinal completeness coefficient φ V to the volume of a prism having the base area of ​​the midship frame and the height L:

Vertical completeness coefficient χ- volumetric displacement ratio V to the volume of a prism whose base is the area of ​​the structural waterline S and the height T:

Like the ratios of the main dimensions, the coefficients of completeness affect the seaworthiness of the vessel. Decrease δ, α And φ contributes to the speed of the vessel, and an increase α increases its stability.

The vessel is characterized by volumetric and mass indicators, which include: volumetric displacement V, m 3, - the volume of the underwater part of the vessel, and displacement D, t, - weight of the vessel: D = ρV, Where ρ - density of water, t/m3.

Each vessel draft corresponds to a certain volumetric displacement and weight of the vessel (displacement). The displacement of a fully built ship, but without stores, consumables, cargo or people is called displacement of an empty vessel. The displacement of a ship loaded to the load line is called displacement of the vessel with full cargo

Assortment completeness factor

Completeness of assortment is the ability of a set of goods of a homogeneous group to satisfy the same needs. A relative indicator of assortment completeness is the completeness coefficient, which is calculated based on a separate attribute of the selected product /14, p.57/.

Electric motor power was chosen as a fundamental feature when calculating the completeness coefficient.

When calculating the assortment completeness coefficient based on the power of the electric motor, it is necessary to determine the actual completeness and the basic completeness. As a result of research at three retail outlets, it turned out that each seller can present to the consumer electric drills with the following electric motor powers (W): 400, 450, 500, 550, 600, 650, 700, 850, 900, 1000, i.e. actual completeness is 10. In addition, the main competitors of the retail outlet under study were found to have electric drills with electric motor powers of 800 W and 950 W. Based on the above data, it follows that the basic completeness is 12.

To determine the completeness coefficient, the formula is used:

Kp = (Pd: Pb), (2)

where Kp is the completeness coefficient;

Pb - basic completeness;

Pd - real completeness,

Let's calculate the fullness index of trouser suits:

Kp = (10:12) = 0.83

As a result of calculations, the completeness coefficient of electric drills was 0.83. This coefficient shows that the range of electric drills with different motor powers in the retail outlet under study is presented quite fully, in comparison with the available number of electric drills with the same motor powers from the main competitors. Since this indicator is quite high, it means that there is a high probability that consumer demand for electric drills is satisfied.

Assortment novelty coefficient

Novelty (updating) of the assortment is the ability of a set of goods to satisfy changing needs through new goods /7, p.14/. The reasons for updating the assortment are:

Replacement of obsolete goods that are not in demand;

Development of new products of improved quality;

Creating competitive advantages of the organization;

Satisfying the needs of a wide range of consumers.

Consumers of new products are “innovators”. New products satisfy not so much the physiological as the psychological and social needs of this group of people.

The novelty of the assortment is characterized by the novelty coefficient, which is defined as the ratio of the number of new products in the general list of products presented (N) to the actual breadth of the assortment (Wd).

Thus, the novelty coefficient is calculated using the following formula:

Kn = (N: Shd) , (3)

where Kn is the coefficient of novelty;

N - the number of new models of electric drills that went on sale over a certain period of time;

Шд - actual breadth of assortment.

This indicator is necessarily calculated for a certain period of time and shows the number of new products that went on sale in the department for the selected period of time.

By interviewing the seller of the Amursnabsbyt store under study, it was found that over the past 3 months, 10 new models of electric drills have appeared.

Let's calculate the novelty coefficient:

Kn=(10:43)=0.23

The novelty coefficient for this outlet was 0.23. This fact indicates a gradual updating of the range of electric drills. The Amursnabsbyt store pays great attention to updating its own assortment, offering new models in moderate quantities, minimizing the risk of incurring losses due to low demand for the new models of electric drills presented.

There are structural, design, largest and overall dimensions of the ship's hull. The constructive dimensions, which are understood as the main dimensions, include:

H - bow perpendicular, K - stern perpendicular, L - length of the vessel, B - width of the vessel, H - side height, F - freeboard height, d - draft.

- ship length(L) - the distance along the vertical line between the extreme points of its intersection with the DP. –

vessel width(B) - the largest width of the vertical line.

- board height(H) - the distance measured in the plane of the midship frame from the main plane to the deck line at the side.

- ship's draft(d) - the distance between the KBL and main planes, measured in the section where the mid-frame and diametral planes intersect.

The dimensions corresponding to the vessel's immersion along the design waterline are called calculated. The largest dimensions correspond to the maximum dimensions of the body without protruding parts (stems, outer plating, etc.). And the overall dimensions correspond to the maximum dimensions of the case, taking into account protruding parts.

The shape of the body is determined by the ratios of the main dimensions and the coefficients of completeness. The most important characteristics are the relationships:

L/B- largely determining the vessel’s propulsion: the higher the vessel’s speed, the greater this ratio;

V/d- characterizing the stability and propulsion of the vessel;

N/d- determining the stability and unsinkability of the vessel;

L/H- on which the strength of the ship’s hull depends to a certain extent.

To characterize the shape of the hull contours of various ships, the so-called completeness coefficients. They do not give a complete picture of the shape of the hull, but they allow a numerical assessment of its main features. The main dimensionless coefficients of the completeness of the shape of the underwater volume of the ship’s hull are:

- displacement coefficient(general completeness) δ - this is the ratio of the volume of the hull immersed in water, called volumetric displacement V, to the volume of a parallelepiped with sides L, B, d:

Completeness factor midship frame area β- the ratio of the area of ​​the midsection frame ω Ф to the area of ​​the rectangle with sides B, d;

Coefficient vertical completeness χ - the ratio of the volumetric displacement V to the volume of the prism, the base of which is the waterline area S, and the height is the vessel’s draft d:

χ = V/(S×d)=δ/α

The above fullness factors are usually determined for the vessel sitting at the load line. However, they can also be attributed to other drafts, and the linear dimensions, areas and volumes included in them are taken in this case for the current waterline of the vessel.

Ship architecture.

Ship architecture is the general arrangement of hull elements, equipment, devices, and the layout of ship premises, which must be carried out in the most rational way, in compliance with safety requirements.

The main architectural elements of any vessel are: the hull of the vessel with its decks, platforms, strong transverse and longitudinal bulkheads, superstructures and deckhouses.

Deck is called a continuous floor on a ship, running in a horizontal direction. A deck that does not extend along the entire length or width of the ship, but only on part of it, is called platform. The internal space of the hull is divided in height by decks and platforms into inter-deck space, which are called twin decks(minimum height 2.25m).

Upper deck(or design) is the deck that makes up the upper cross-sectional zone of the strong part of the ship's hull. The name of the remaining decks is given from the upper deck, counting down, depending on their location (second, third, etc.). A deck extending above the bottom over some part of the length of the vessel and structurally connected to it is called second bottom. The decks located up from the upper deck are named according to their purpose (promenade, boat, etc.), the deck above the wheelhouse is called the upper bridge.

The ship's hull is divided along the length strong transverse watertight bulkheads, forming waterproof spaces called compartments.

The premises located above the second bottom, and intended for placing dry cargo in them, are called holds.

The compartments in which the main power plants are located are called engine room.

Any container formed by the hull structures and intended to contain liquid cargo is called tank. A container for liquid cargo located outside the second bottom is called deep tank.

Tanks are called compartments on tankers designed for the transport of liquid cargo.

Some compartments have special names:

Terminal - the first compartment from the stem is called forepeak, and the first transverse watertight bulkhead is called forepeak or ram

· End – the last compartment before the afterpeak is called afterpeak, and the bulkhead is called the afterpeak.

Narrow compartments separating tanks from other rooms are called rubber dams. They must be empty, well ventilated and convenient for inspection of the bulkheads forming them.

To divide the ship's hull along the width, in some cases, strong waterproof longitudinal bulkheads

Fences On ships, all sorts of light watertight bulkheads separating rooms are called.

Mines- are called compartments limited by vertical bulkheads, passing through several decks, and not having horizontal ceilings.

Superstructure is a closed structure on the upper deck, extending from one side to the other, and not reaching the side at a distance not exceeding 0.04 of the width of the ship. The space on the upper deck from the stem to the bow bulkhead of the bow superstructure is called tank. The space on the upper deck from the aft bulkhead of the aft superstructure to the sternpost is called Utah. The space on the upper deck between the bow and stern superstructures is called waist.

Chopping refers to any kind of enclosed space on the upper or higher decks of superstructures, the longitudinal external bulkheads of which do not reach the sides of the main hull at a distance of more than 0.04 of the width of the ship's hull.

By the bridge called a narrow transverse platform that runs across the ship from one side to the other. The part of the bridge protruding beyond the outer longitudinal bulkheads of the deckhouse located below it is called wing of the bridge.

False side is called a continuous fencing of an open deck made of sheet material. At the upper end edge the bulwark is trimmed with a horizontal strip called gunwale. The bulwark sheathing is supported to the hull by oblique struts called buttresses. Holes are made along the length of the bulwark to quickly drain water that gets on the deck, which are called storm porticoes. The space at the bulwark running along the side of the upper deck around the entire perimeter, serving for water drainage, is called waterway gutter(waterweiss). The hole with a tube used to drain water from the waterway gutter is called scupper.

Spar are called round wooden or steel tubular parts of the weapons of ships located on the open deck and are designed to carry signals, structures of communication devices, serving as supports for cargo devices. Spars include masts, topmasts, booms, yards, gaffs, etc.

Rigging – the name of all the cables that make up the armament of individual masts. The rigging serves to hold and permanently secure the spar in the proper position is called standing rigging. All other rigging that can move on blocks is called running.

A general idea of ​​the shape of the outer surface of the housing is given by a section of it with three mutually perpendicular planes (Figure 5.1).

The vertical plane running along the ship in the middle of its width and dividing the ship into two symmetrical halves (port and starboard) is called the center plane (DP). The surface of the water in a calm state, which intersects the outer hull of the vessel carrying all the loads required by the nature of its service, forms the plane of the load waterline (GWL). This plane separates the underwater part of the vessel from the surface part. The transverse plane cutting the ship in the middle of its length is called the midship plane.

Figure 5.1 Location of the main planes. 1-plane of the mid-frame; 2- diametrical plane; 3 - load waterline plane

A number of planes parallel to the DP form buttock lines on the surface of the vessel (Figure 5.2).

Figure 5.2 Lines of intersection of the outer surface of the vessel with planes parallel to the main planes: 1 - buttocks; 2 - stem; 3 - waterline; 4 - frames; 5 - sternpost.

The intersections of the outer skin with horizontal planes form intermediate waterlines, and with vertical transverse planes - frames. When all of the listed sections are combined on one drawing, a form of representation of the surface of the vessel that is usual for shipbuilders will be obtained - a theoretical drawing (Fig. 3).

A comprehensive idea of ​​the shape of the ship’s hull is given by its theoretical drawing (Figure 5.3). It consists of three projections, on each of which sections of the body are depicted by planes parallel to those discussed above - DP, pl. MS and OP. The theoretical drawing represents the theoretical surface of the hull without taking into account the outer plating and protruding parts.

Figure 5.3 Theoretical drawing of the vessel

The main overall dimensions of the body are usually called the main dimensions. This is L - the length of the ship; B -- width; H - side height; T—draft. The first three are unchanged and relate to the geometric characteristics of the hull as a whole, the last - draft - can vary within wide limits and determines the submerged (underwater volume) of the vessel. Usually, when talking about the main dimensions of a ship, they take the draft along the design, or design, waterline, corresponding to the design load of the ship.

The length must also be specified. The length between perpendiculars L is distinguished, according to the KVL Lkvl, the maximum Lmax. The first two are close to each other, the latter is dimensional. When studying the seaworthiness of a vessel, strictly speaking, one should operate with the length along the waterline, but often instead they take a uniquely defined value - Lхх.

The largest modern ships reach very impressive sizes: their length can exceed 400 m, width 60, and the loaded draft is about 30 m.

Generalized characteristics of the form. Along with the theoretical drawing, an idea of ​​the shape of the ship's hull is given by generalized dimensionless characteristics - the ratios of the main dimensions and the coefficients of completeness. Both the seaworthiness and other qualities of the vessel largely depend on these characteristics.

The basic relationships of the main dimensions are as follows: . The ratio, or, as it is sometimes called, the relative length, largely determines the performance: the larger it is, the relatively faster the vessel. For modern displacement ships this value fluctuates in a range. The lower limit is typical for some tugboats, the upper limit is typical for high-speed warships. Naturally, there are exceptions, for example, some rowing boats have > 25.

Attitude mainly affects stability and pitching. The larger it is, the better in terms of stability, although the rolling becomes more choppy. For modern marine vessels.

Attitude - affects handling: increasing it increases course stability and worsens agility.

The ratio determines the stability at large angles of inclination and the unsinkability of the vessel. Height has a beneficial effect on both of these qualities.

The ratio affects the strength of the hull; the higher the ratio, the more difficult it is to ensure the overall strength of the vessel.

There are three main independent completeness coefficients. This is the coefficient of completeness of the waterline area

where S is the area of ​​the water line;

midship frame completeness coefficient

where is the cross-sectional area of ​​the midsection frame below the overhead line

overall completeness ratio

where V is the volume of the underwater part of the hull or volumetric displacement.

As follows from (5.1) - (5.3), all coefficients of completeness are the ratio of the areas (volume) of the corresponding elements to the areas (volume) of the described rectangles (parallelepipeds). All these coefficients are less than one, their numerical values ​​for sea vessels lie within the limits: . Smaller values ​​are typical for faster ships; the upper boundaries correspond to slow-moving vessels with very full contours (formations).

In some calculations of the ship theory, it is more convenient to use derivatives of the main ones, additional coefficients of longitudinal φ and vertical completeness, the physical interpretation of which is clear.

Example 5.1. We will illustrate some of the theoretical positions and conclusions under consideration with examples. We will assign most of them to one vessel, which we will give the name “Engineer”. The choice of the name is not accidental: firstly, the original meaning of the word engineer is an inventor, creator; secondly, an engineer is the main driving force of scientific and technological progress, the fruits of which are not yet as significant as desired; thirdly, the purpose of this book is to make a feasible contribution to the transformation of a student into a qualified engineer.

So, the multi-purpose dry cargo vessel “Engineer” is specified, the side view of which is shown in Figure 5.4, and the main characteristics are as follows:

L max = 181 m; V = 28700 m3;

L++ = 173 m; D = 29400 t;

B = 28.2 m; G = 288000 kN;

T = 9.5 m; S = 3700 m2;

H = 15.1 m; sch msh = 261m 2.

The vessel has a bow bulb, the engine room is shifted to the stern (intermediate position of the engine room MO). Combination system - the upper deck and double bottom are assembled according to the longitudinal system, the sides according to the transverse system

Let us find the ratios of the main dimensions and the coefficients of completeness of the vessel:

Overall completeness coefficient according to (5.3)

Overhead line area completeness coefficient according to (5.1)

Midship frame completeness coefficient according to (5.2)

Figure 5.4 Vessel “Engineer”

The values ​​of the overall completeness coefficient and the ratio give reason to believe that the “Engineer” has fairly sharp contours and belongs to the medium-speed transport vessels.

Elements of a theoretical drawing. Calculations based on ship theory include various characteristics of the hull shape. The main elements of a theoretical drawing include:

• -- volumetric displacement V;
• -- coordinates of the center of the quantity x c, z c ;
• -- waterline area S;
• - abscissa of the center of gravity of the overhead line area x F;
• -- central moments of inertia of the overhead line area I X and Iу;
• -- completeness coefficients b, c, d.

The center of magnitude is the center of gravity (center of mass) of the underwater volume of the hull (volume displacement).

Construction along the waterline is the dependence of the area of ​​the waterline on the draft; therefore, it also characterizes the distribution of volume as a function of the draft. Most modern transport ships have a flat bottom, in this case the dependence S(T) does not originate from the origin (Figure 5.5). It is obvious that the area limited by the formation along the overhead line and the ordinate axis is the volumetric displacement at a given draft T. The formation along the overhead line is widely used in solving problems of receiving and discharging small cargo.

Cargo size represents the relationship between displacement and draft. On this graph, in addition to the volumetric displacement V determined from the theoretical drawing, the displacement taking into account the plating and protruding parts V i is also plotted, as well as the mass displacement D (Figure 5.6). The cargo size, in particular, is used when solving problems of receiving and removing large loads.

Figure 5.5 Drilling along waterlines

Figure 5.6 Cargo size

The Bonjean scale represents the totality of the dependences of the areas of all theoretical frames on their immersion u(z). The values ​​of the indicated areas are determined: in the form

The Bonjean scale is constructed on the transformed contour of the body section by the diametrical plane. The transformation lies in the fact that for ease of use, the linear scales along the ox and oy axes are chosen different (Figure 5.7). From the vertical lines and traces of the corresponding theoretical frames, the values ​​of the frame areas u(z) brought to the height of the upper deck are laid off.

Using the Bonjean scale, you can determine the displacement along any waterline, including an inclined one (for a vessel sitting in trim). The Bonjean scale is used in calculations of unsinkability, longitudinal descent of a ship, as well as for other purposes. The structure along the frames characterizes the distribution of volumes along the length of the vessel and represents the dependence of the area of ​​the frame on its location along the x axis at a given draft (Figure 5.8).

Figure 5.7 Bonjean scale

Figure 5.8 Formation along frames

A line along the frames can be constructed using the Bonjean scale for any waterline. Obviously, the area enclosed between the front and the axis oh is the volumetric displacement. Construction by frames, in particular, is used when calculating the moments bending the ship.