Waterline area. Ships with a small waterline area: why does the fleet need them? Initial stability and emergency landing

Waterline is the line of contact between the calm surface of the water and the hull of a floating vessel.

The following waterlines are distinguished:

structural waterline (KWL)- waterline, taken as the basis for constructing a theoretical drawing and corresponding to the total displacement of the vessel and the normal displacement of the ship obtained by preliminary calculation;

load water line (GWL)- waterline when the ship is sailing with a full load. For sea transport ships, the water and air flow lines, as a rule, are the same;

design waterline- waterline corresponding to the vessel’s draft, for which its design characteristics are determined. When determining the design characteristics, the following is taken as the design waterline: for ships - the waterline corresponding to the normal displacement; for ships - the waterline corresponding to the draft at the center of the load line circle; (design characteristics are determined for all).

current waterline- current (at a given load and conditions);

theoretical waterlines- a set of sections at equal distances, forming one of the types of theoretical drawing: plan;

current waterline determined by the shape of the vessel, its average density, as well as the degree of agitation of the water in a given pool. The waterline area is used to calculate the hull fullness factor. The shape of the waterline area, or more precisely its moment of inertia, is a factor that determines the stability of the shape. Obviously, depending on the load conditions,

Waterline

Waterline marked on the ship's hull (in black)

Waterline(Dutch waterlinie) - the line of contact between the calm surface of the water and the hull of a floating vessel. Also, in the theory of a ship, there is an element of a theoretical drawing: a section of the hull by a horizontal plane.

The following waterlines are distinguished:

structural waterline (KVL) - that is, calculated, determined for the full load of the vessel;
load waterline - calculated for a predetermined load and sailing conditions;
current waterline - current, under a given load and conditions;
theoretical waterlines - a set of sections at equal distances, forming one of the types of theoretical drawing: plan.

The effective waterline is determined by the shape of the vessel, its average density, as well as the degree of roughness of the water in a given pool. The waterline area is used to calculate the hull fullness factor. The shape of the waterline area, or rather its moment of inertia, is a factor that determines shape stability. Obviously, depending on the load conditions, heel and trim, the shape of the waterline area, and with it stability, can change.

The waterline length serves as a characteristic linear dimension in determining the Froude number for displacement vessels, and, accordingly, their theoretical speed.

Load line

Load line (Plimsoll line)

All commercial vessels must have a mark on board entitled load line(English) load line, Plimsoll line). This mark determines the level to which the ship can be safely loaded, i.e. load waterline. When loading the vessel, it sits deeper in the water and the mark drops closer to the surface of the water.

Before this mark became mandatory, many ships were lost due to overloading. Sometimes the reason for overloading is the desire to obtain additional profit from transportation, and sometimes the difference in the density of water - depending on its temperature and the salinity of the vessel's sediment can vary significantly.

British politician Samuel Plimsol proposed a system of universal ship marking, which made it possible to determine the maximum load of a ship depending on the time of year and region.

The letters on the load line mean:

Storms are frequent in winter. A high wave can rock the ship or flood the deck, so additional buoyancy is required. The North Atlantic is a particularly stormy area, plus the danger of icing - the reserve of buoyancy there should be even greater. Tropical waters, on the contrary, are quiet, where you can safely load the ship.

The remaining two grades - F and TF - correspond to S and T, recalculated to the density of fresh water.

Literature

// Encyclopedic Dictionary of Brockhaus and Efron: In 86 volumes (82 volumes and 4 additional ones). - St. Petersburg. , 1890-1907.

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Synonyms

See what “Waterline” is in other dictionaries: Waterline...

Spelling dictionary-reference book - (Gol. and English. water, and Lat. linea line). The line at which a ship with luggage can be immersed in water. Dictionary of foreign words included in the Russian language. Chudinov A.N., 1910. WATERLINE from English. water, water, and lat. linea, line. Damn...

- (Water line) a curve obtained when the surface of the ship’s hull intersects a horizontal plane parallel to the water level. See theoretical drawing of the vessel. Samoilov K.I. Marine dictionary. M.L.: State Naval Publishing House... ... Marine Dictionary

- (from Dutch water and lijn line) the line of contact between the calm surface of the water and the hull of a floating vessel. The load waterline, marked by the load line, coincides with the surface of the water when the vessel is fully loaded and corresponds to... ... Big Encyclopedic Dictionary

A line along the side of a ship defining the maximum draft of a ship when fully loaded. Dictionary of business terms. Akademik.ru. 2001 ... Dictionary of business terms

WATERLINE, waterline, female (Dutch. waterlinie) (marine). The line along the side to which the ship is immersed in water. Ushakov's explanatory dictionary. D.N. Ushakov. 1935 1940 ... Ushakov's Explanatory Dictionary

- [te], and, female. (specialist.). Line along the side, before the ship is immersed in water at normal draft. Freight in. (coinciding with the surface of the water when the vessel is fully loaded). Ozhegov's explanatory dictionary. S.I. Ozhegov, N.Yu. Shvedova. 1949 1992 … Ozhegov's Explanatory Dictionary

Female, marine the line on the hull of the vessel along which it sits in the water; load, load, draft. This feature is calculated in advance by the builder and indicated on the drawing of the vessel. Men's spirit level, Dutch. projectile showing the plane in level, how it stands... ... Dahl's Explanatory Dictionary

To study the navigational qualities of a vessel, it is necessary to know the quantities on which they depend. These values include a group of indicators that characterize the geometry of the ship’s hull and are called - elements of theoretical drawing; the latter are also called - hydrostatic indicators of the vessel.

The elements of the theoretical drawing include:

V	–	volumetric displacement, m3;
z With	–	applicate of the center of gravity of the immersed volume of the body (applicate of the center of magnitude - CV), m;
X With	–	abscissa CV, m;
x f	–	abscissa of the center of gravity of the waterline area, m;
S	–	waterline area, m2;
w	–	immersed area of the frame, m 2 ;
d,a,b	–	completeness coefficients: displacement, waterline area and immersed frame area, respectively;
I x	–	moment of inertia of the waterline area relative to the longitudinal axis 0X, m 4;
I f	–	moment of inertia of the waterline area relative to the transverse axis passing through its center of gravity, m 4 ;
r	–	small (transverse) metacentric radius, m;
R	–	large (longitudinal) metacentric radius, m.

The elements of a theoretical drawing are usually divided into two groups: buoyancy elements ( V, S, w, z With , X c , x f , a, d, b) and elements of initial stability ( I x , I f , r, R). The use of buoyancy elements is shown in the “Buoyancy” section of this manual.

The main parameter characterizing the landing of the vessel (the position of the vessel relative to the water) is its depth ( z). In the absence of roll and trim (landing straight and on an even keel), depth is the only landing parameter, and in the case of an arbitrary landing, it is the main parameter. Taking into account what has been noted, the values of the elements of a theoretical drawing are usually presented in the form of dependencies (curves) on immersion (Fig. 1.10).

In Fig. 1.10 does not show the dependence of the change in the immersed area of the frames ( w). As a basis (argument) for representing a change w the length of the waterline is taken ( L) at some value of immersion ( z). The graph of such a dependence (Fig. 1.11) is called a drill by frames.

General expressions for buoyancy elements. To calculate the volumetric displacement, coordinates of the center of magnitude and other elements of buoyancy, a theoretical drawing is used.

Let us select from the underwater volume of the hull two planes of frames, separated by an infinitely small amount dx element of this volume (Fig. 1.12, A). The volume of such an element will be w · dx, and the loaded volume of the vessel is determined by integrating this expression over the length of the vessel

Rice. 1.11. Construction on frames

To determine the abscissa of the center of a quantity (X c) we use the theorem that the static moment of volume ( V) relative to the midsection is equal to the total moment of its elements, i.e.

The applicate of the center of magnitude is determined, similarly to (1.6), through the static moment of the volume relative to the main plane

Static moment of an elementary platform (see Fig. 1.14) relative to axis 0 U equal to ; and for the entire area of the waterline we will have

Similarly, if in formula (1.7) the area of the waterline is replaced by expression (1.10), we will have

(1.15)

General expressions for determining completeness coefficients a, b, d, related to the elements of buoyancy, are represented by formulas (1.1) (1.2) and (1.3); the use of the latter is possible with known values ( S, V And w).

The general expressions presented above for determining the elements of buoyancy contain a definite integral, which can have an exact solution if the function is specified analytically.

The dependencies describing the theoretical surface of the ship's hull are specified in the form of a drawing, i.e. in graphical form. In this case, the definite integral is calculated using approximate formulas (quadrature formulas). In calculations based on ship theory, quadrature formulas are called rules. In the practice of shipbuilding calculations, three rules have become widespread: the trapezoidal rule, Simpson’s rule and Chebyshev’s rule. . The advantage of the trapezoidal rule is its simplicity and clarity; it is widely used in practice.

Trapezoid rule. The essence of this rule and its application to the calculation of buoyancy elements is presented below.

If it is necessary to calculate a definite integral of the form , and the integrand function y=f(x) is given in the form of a curve (Fig. 1.15), then the geometric expression of the integral will be the area ( A), limited by a given curve, x-axis and end ordinates. To approximately calculate the area, it is divided into a number of trapezoids with the same height; in this case, the calculation of the integral is reduced to determining the area bounded by the broken line, i.e. to calculating the sum of the areas of trapezoids whose bases are ordinates at 0 , y 1 , … y n:

where is the height of the trapezoid; n– number of intervals.

Since half of each ordinate, except the extreme ones, enters the resulting expression twice, the formula can be transformed to the form

and the half-sum of the extreme ordinates, called the correction to the sum, as

The trapezoidal rule can be applied to evaluate any definite integrals, and the integrand function y = f(x) can have any geometric or physical meaning.

Calculation of frame area. The frame is specified by its outline on the “hull” projection of the theoretical drawing (see Fig. 1.13). according to the trapezoidal rule, the frame area is determined as the sum of the areas of trapezoids with the same height , i.e.

(1.20)

After transformations and notations (1.16) – (1.18) adopted according to the trapezoidal rule, expression (1.20) can be represented in the form

waterline

and. Morsk. the line on the hull of the vessel along which it sits in the water; load, load, draft. This feature is calculated in advance by the builder and indicated on the drawing of the vessel. Spirit level m. Holland. a projectile showing the level of the plane, how the surface of the water stands; level. Walk or level the place according to the spirit level, walk along the level or at sight. The projectile is anti-pol. level, plumb; but placed on a ruler, it combines both projectiles, which is why the level of this device is called a plumb line. The simplest level: a plumb line above a lying ruler; more precisely, a glass tube with liquid into which an air bubble is inserted; When the tube is positioned according to the level, it stands on the mark, in the middle. Spirit level, related to the level; horizontal, level, straight, without slope, suspended, water-direct. Water hose m. morsk. canvas or leather sleeve, intestine to filler pumps; also for filling barrels with water. Water stay m. Morsk. one of the thick tarred riggings holding the bowsprit to the cutwater. Water backstay m. Morsk. a similar tackle that strengthens the bowsprit from the sides. Watervuling m. Morsk. a tarred rope that pulls the bowsprit with many turns to the stem, to the bow riser of the ship. Waterways m. Morsk. timber lying right next to ship's side, on beams, crossbars above the deck. Water-tali w. pl. Morsk. large hoists (running, pulling), with which barrels of water and other weights are lifted onto the ship. The water closet is a latrine, according to the English design, with water inlet.

Explanatory dictionary of the Russian language. D.N. Ushakov

waterline

waterline, g. (Gol. waterlinie) (Marine). The line along the side, before the cut of the ship is immersed in the water.

Explanatory dictionary of the Russian language. S.I.Ozhegov, N.Yu.Shvedova.

waterline

[te], -i, f. (specialist.). The line along the side until the ship is immersed in water at normal draft. Freight in. (coinciding with the surface of the water when the vessel is fully loaded).

New explanatory dictionary of the Russian language, T. F. Efremova.

waterline

and. A line along the hull of a vessel (usually marked with paint) that coincides with the surface of the water at its maximum permissible load.

Encyclopedic Dictionary, 1998

waterline

WATERLINE (from Dutch water - water and lijn - line) the line of contact between the calm surface of the water and the hull of a floating vessel. The load waterline, marked by the load line, coincides with the surface of the water when the vessel is fully loaded and corresponds to the maximum draft allowed in operation. The shape of the waterline and the size of the area outlined by it affect the characteristics of the propulsion and stability of the vessel.

Waterline

(Dutch water-lijn, from water ≈ water and lijn ≈ line), the line of contact of the water surface with the hull of a floating vessel. The cargo water level coincides with the calm surface of the water when the ship is fully loaded and corresponds to the maximum draft allowed in operation; The position of the cargo V. is marked with a load line. Theoretical dimensions depicted on a theoretical drawing of a ship are obtained by cutting the surface of the ship's hull with horizontal planes. The shape of the vessel and the size of the area outlined by it influence the characteristics of the propulsion and stability of the vessel.

Wikipedia

Waterline

effective waterline depending on draft The effective waterline is determined by the shape of the vessel, its average density, as well as the degree of roughness of the water in a given pool. The waterline area is used to calculate the hull fullness factor. The shape of the waterline area, more precisely its moment of inertia, is a factor that determines the stability of the shape. Obviously, depending on the load conditions, heel and trim, the shape of the waterline area, and with it the stability, can change.

The length along the waterline serves as a characteristic linear dimension in determining the Froude number for displacement ships, and accordingly, their theoretical speed.

Examples of the use of the word waterline in literature.

Ruiz drove slowly around the sides of the submarine, noticing that rust was oozing from the holes, that the anti-corrosion paint was cracked along the waterline, other signs of careless handling did not escape him.

Sat next to a bandit and murderer, dressed in an elegant two-decker suit, fitted lower waterline.

Having opened the hatch and overcoming the pressure of the air flow, I grabbed the support with my hand and released the entire clip along one of the boats, stitching it along waterline.

At the same time, it is absolutely clear that water has already penetrated into some compartments of the subsoil, because the waterline.

In each new option, the chancellor refused any privilege for himself, but the discarded ballast was so insignificant that the sunken ship of his dreams could not rise to waterline.

Roscoe Bunyan's acquaintances often said that, even loaded with money, waterline, he will not be too lazy to walk ten miles in tight shoes to pick up a copper dropped by someone.

Too much water has been absorbed by the papyrus bundles above waterline, and all these tons of invisible ballast jokingly outweighed two or three hundred kilograms of provisions and drinking water who migrated to the other side.

The straight, sheer stem, like a hellish cleaver, entered the side of the other ship during the collision, piercing it in the same way as above waterline, and below the water level.

This means that the bow of the ship is lower waterline is torn off or has a hole in it.

In the bow of the hull, on the starboard side, much lower waterline, a significant hole.

This room is located six meters below waterline, in front is the gun magazine of the second turret, behind is the bow boiler room, below is an unprotected bottom, an excellent - it’s better not to think of it - target for acoustic mines and torpedoes.

Almost to the very waterline the side of the cruiser seemed to be ripped open by a giant can opener.

Previously, similar operations were carried out only after the actual determination waterline on the water.

This idea did not find application immediately: it took time for classification societies to issue a rule according to which the length of the vessel is higher waterline was not taken into account during register measurements.

The sides of the steamer were already glowing cherry blossoms, along its entire waterline Steam rose from the water.

Modern approaches to shipbuilding require a continuous search for original technical solutions to gain superiority over potential opponents in the world's oceans. And increasingly, designers are turning to projects of multi-hull watercraft - catamarans and trimarans. Suffice it to recall the littoral ships of the US Navy "Independence" type or the latest Russian development "Rusich-1". Doctor of Technical Sciences Viktor Dubrovsky tells how else you can improve specifications multihulls due to an original solution - reducing the waterline area.

Introduction

Objects with a small waterline area include semi-submersible (usually drilling) platforms and small water-plane area ships.

In Fig. 1 shows the diagram appearance semi-submersible platform. In the working position, the waterline is located approximately at the middle of the height of the racks (columns) connecting the pontoons with the upper structure; in the stowed position, it is slightly below the upper decks of the pontoons.

Semi-submersible platforms have been used in the world since the 50s; since that time, more than 300 such objects of fairly large displacement have been built. Practice has shown that they can constantly be in the harshest seas of the planet and work most time, including during very intense excitement. In Fig. Figure 2 shows a double-hulled ship with a small waterline area (SMWA).

Research, design and construction of SMPV began in the 60s, since then more than 70 such vessels have been built in the world, mostly of small displacement, often used as experimental ones.

Already these illustrations reveal the main difference between objects with a small waterline area: a decrease in displacement volumes near the waterline with compensation for these volumes due to parts of the vessel more submerged below the surface.

Currently, displacement volumes crossing the free surface are usually called “pillars” (for ships) or “columns” (for platforms). Underwater volumes today do not have an established name: they talk about “pontoons” for platforms and ships, “underwater hulls”, “underwater volumes”, etc. for ships.

In the author's publications since 1978, the following terminology has been used for ships: each hull consists of a surface platform - rack (racks) - nacelle (the latter term was borrowed from aviation). The same terminology is used below.

In addition, to characterize the location of the hulls relative to each other and relative to the water surface, the following terms are used: transverse clearance (usually the distance between the diametrical planes of the hulls); vertical clearance (distance of the platform bottom from the design waterline); longitudinal clearance (the distance between the midships of the hulls, if they are shifted in the longitudinal direction).

The noted feature of the contours affects all technical and operational qualities of ships. In addition, like all multi-hull objects, SMPVs are distinguished by an increased deck area relative to their volumetric displacement. Therefore, like all multihulls, SMPVs are effective for transporting light payloads that require large deck areas or large volumes for their placement, i.e. "light" cargo. These include passengers in cabins, rolling equipment, light containers, research laboratories, weapons systems, primarily aviation ones. Therefore, in particular, it is most rational to design an SMPV based on the initially required deck area.

Dimension ratios and types of SMPV

The specific distribution of displacement volumes also determines the specificity of the ratios of SMPV dimensions.

To make it easier to use the internal volumes of the nacelles and improve the manufacturability of their assembly, it is advisable to ensure continuous flow around the ends: choose a semi-elliptical shape for the bow and a cone-shaped shape for the stern. The remaining length is a cylinder. As a result, the fullness coefficient of the nacelle and the body as a whole becomes dependent on the extension of the nacelle L/D, where L is the length, D is the diameter of the nacelle.

The reduced waterline area requires increased hull spacing to provide the required initial lateral stability. These and other features of the architectural and structural type described below determine the ratios of the main dimensions that are not typical for single-hull ships and multi-hull ships with traditional lines. The most probable values of these ratios are given below when considering the characteristics of the deck area and the initial stability of various SMPVs.

Until now, several types of SMPVs have been studied to one degree or another, although only double-hulled ones are in practical use (most of the more than 70 SMPVs built in recent years are duplexes, in the terminology described above). In Fig. Figure 3 shows the types of SMPV studied.

It should be noted that the terminology shown, proposed by the author in 1978, is not generally accepted. For example, in Japan, all double-hulled ships are called catamarans, regardless of the shape of the lines. It seems that distinguishing two types of double-body SMPV makes the classification more accurate. The SMPV with one long post in each hull was first built in Holland; the name of this first vessel was proposed by the author as a common one for ships of this architecture. The term "trisec" was proposed by the authors of the first two-hull SMPV with two short racks in the composition of each hull built in the USA: "THREE SECTIONS", i.e. platform and two underwater volumes.

In addition, in the English-language literature, all three-hulled vessels are called trimarans, regardless of the shape and size ratios. On the contrary, in Russian practice Since the 70s (research on the performance of high-speed river vessels by A.G. Lyakhovitsky), the name “trimaran” has been applied to three-hulled vessels with identical hulls of conventional contours. Therefore, a separate name for three-hull SMPVs with identical bodies seems appropriate.

SMPV have both general features, distinguishing them from single-hull ships and from multi-hull ships with conventional contours, and specific to each type. Below these features are discussed in more detail. It should be noted that almost every feature of a particular type of vessel can be favorable, unfavorable or neutral for a particular application. All these issues are briefly discussed below.

Here, a single-hull object of equal displacement is conventionally used as a basis for comparison, although in practice, when choosing vessel options at the very beginning of its design, it is also necessary to consider comparable types of multi-hull vessels with traditional lines.

It should be especially noted that each SMPV can be designed so that at full displacement the vessel will have a draft at the top of the nacelles, which expands the possibilities of using shallow water areas and ports. At the same time, to improve seaworthiness in rough seas, it is necessary to provide for the intake of water ballast. It is clear that the volume of this ballast corresponds to the volume of the immersed part of the racks, i.e. relatively small in relation to the total displacement of the vessel.

However, the strong influence of relatively small volumes of ballast on the landing of the SMPV is a significant inconvenience of its operation. If not foreseen in advance, the simple consumption of fuel during navigation will lead to unacceptable changes in landing, primarily in roll and trim. Therefore, for example, one of the world's first SMPVs, a Japanese passenger ferry, had automatic system ballasting to maintain the required limits of fit changes during operation.

How it works

1. Deck area

Although the redistribution of volumes most affects hydrostatics and hydrodynamics, from a design point of view it is more convenient to start by considering the relative area of decks. This consideration is based on the above-mentioned system of the most probable dimensional ratios, which determine the specifics of this type of vessel.

The main results of such assessments are shown in Table 1.

Vessel type	Relative length of one body	Probable dimensional relationships	Relative deck area
Single-hull		L/B=8;
A D ~0.8		Trisec or duplus	(*L SW =0.64L;** B OA =(0.3÷0.5)*L SW ;
0.19÷0.32		)*L 2 Low waterline hull and two outriggers	(*L M =0.8L;** B OA =(0.3÷0.5)*L SW ;
		L M /B M =8;	(*L A =(0.3÷0.4)L M ;** B OA =(0.3÷0.5)*L SW ;

B OA =(0.3÷0.4)*L M ;

0.13÷0.16

It is obvious that with an equal number of decks, the SMPV will have, to one degree or another, an increased deck area and internal volume of the surface part, compared to a single-hull high-speed vessel. That is why payload large volume is always located in the surface platform connecting the hulls.

2. Initial stability and emergency landing

The longitudinal stability of the SMPV is noticeably lower than that of a comparable traditional vessel. Therefore, in contrast to the current situation, when longitudinal stability is not standardized for any types of vessels, when designing an SMPV it is necessary to accept some approximate limits of the longitudinal metacentric height. Taking into account the ratio of overall dimensions in plan, it seems convenient to choose the longitudinal height of double-hull SMPVs 2 times greater than the transverse height, and 3 times greater for three-hull SMPVs.

The transverse stability of SMPV determines the ratio of their overall dimensions in plan, see Table 2, where examples of SMPV are considered various types with the same displacement. To explain the place of the SMPV in the general range of multihull vessels, the table also includes vessels with a traditional hull shape: a catamaran (double-hull), a trimaran (three identical hulls) and a vessel with outriggers (a large central and two small side hulls). For simplicity, the requirement to ensure the initial transverse stability of the SMPV is the same as that of the compared single-hull vessel.

Main dimensions and initial lateral stability of 1000-ton vessels of various types (outrigger dimensions in brackets):

Vessel type	Single-hull (high-speed)	Catamaran	Trimaran	Traditional center body + 2 outriggers	Center. Housing with MPV + 2 outriggers
Length of one body, m		65, 80		95 (30)	65 (35)
Overall length, m		65, 80
Width of one body, m		6, 4		7 (1)	7 (1.5)
Overall width, m		18, 16
Waterline area, kW m		2 x 310, 2 x 250
Design draft, m
Height of the center of magnitude, m
Side height, m
Center of mass height, m
Transverse metacenter.
.radius, m
Transverse metacentre. height, m
Longitudinal metacenter. radius, m

Longitudinal metacentre. height, m
* - up to the bulkhead deck.
Analysis of the data presented shows that the transverse size of the SMPV is selected according to a completely different principle than the same dimensions of multihull vessels with traditional lines. The overall width of the SMPV is determined by the requirement of a certain initial stability. On the contrary, the distance between traditionally shaped bodies is chosen to be minimally acceptable to reduce their hydrodynamic interaction, which is usually unfavorable, i.e. according to performance requirements. At the same time, the lateral stability of all vessels with traditional hulls, except outrigger ones, is much greater than that of the compared single-hull vessel. Moreover, the initial lateral stability of a catamaran, if necessary, can be equal to the longitudinal one, and even slightly exceed it. The stability of an outrigger vessel is comparable to the same characteristic of a monohull or slightly more, if necessary.

The longitudinal stability of the SMPV is significantly less than that of all other types of vessels, both single-hull and multi-hull. This circumstance greatly influences many characteristics of the SMPV.

First of all, we note that a decrease in stability leads to difficulties in limiting the angle of emergency roll (trim): flooding of the same volume leads to a significantly greater roll or trim of the SMPV than that of a single-hull vessel of comparable displacement. In this case, usually ensuring a minimum freeboard does not cause difficulties if the bulkhead deck is the upper deck connecting the superstructure hulls.

The lack of lateral stability of the SMPV can be partially compensated by the camber of the struts near the surface platform, which ensures an increase in the area of the stability diagram. But the main thing is that all multihulls have an impenetrable platform connecting the hulls. This volume sharply reduces the angles of heel and trim as soon as its sides or ends begin to enter the water. The likelihood of flooding in the event of an accident is also significantly reduced, since usually the cutouts in the platform are located quite far from the sides and ends.

Ensuring the emergency stability of the SMPV usually also does not cause problems as soon as the waterproof surface platform begins to enter the water.

As a significant design measure to ensure an emergency landing of the SMPV, it is possible to recommend filling the compartments (usually at the ends) with non-flammable floating blocks (or large granules in nets to simplify movements during repairs).

Typically, the sizes of outriggers are small and comparable to the sizes of statistically possible holes in accidents. This means that in the event of an accident, the outrigger is likely to be completely flooded, that is, a significant loss of waterline area and stability. In turn, this means that usually lateral stability must be provided by a single outrigger. However, filling the outriggers with floating materials makes it possible to reduce the size, self-drag and weight of the outriggers.

Thus, the emergency landing and stability of the SMPV, like most multihull vessels, does not correspond much to the concepts underlying the rules previously created for single-hull vessels. As a result of the absence of specific stability rules, any SMPV turns out to be an experimental object, that is, all its characteristics are determined by calculations and agreed with the corresponding Register for each project separately.

3. Seaworthiness

The high seaworthiness of SMPVs is their main difference and greatest advantage. The differences in geometry and stability of the SMPV described above also determine the characteristics of seaworthiness.

It is known that natural rolling periods greatly affect seaworthiness. These periods are determined by the ratios of restoring and inertial forces and moments. For pitching, this is the ratio of longitudinal stability and the moment of inertia of masses (including the added mass of water) relative to the transverse axis.

When moving from a single-hull traditional object to a double-hull SMPV, stability drops more than the moment of inertia of the masses. As a result, the pitching period of a double-hull SMPV increases by approximately 2 times.

With regard to roll, the picture is the opposite: with approximately the same initial stability, the moment of inertia of the masses (including the attached one) relative to the longitudinal axis sharply increases. As a result, the self-rolling period of the SMPV is also approximately 2 times greater than that of a comparable single-hull object. These relationships are shown in Fig. 4.

It is clear that such significant differences greatly change the behavior of the SMPV in waves. So, if single-hull ships usually resonate with pitching in head waves, then SMPV - in tail seas and heading angles close to it. Sufficiently large SMPVs rarely resonate when moving lag-to-wave. The pitching amplitudes of SMPVs without stabilizers in resonant modes are greater than those of comparable vessels of other types, but the accelerations in this mode are very small.

In Fig. Figure 5 shows the pitching amplitudes of two 100-ton boats in head seas. These data were obtained from testing the duplex and catamaran models, however, the amplitudes of the second can be fairly accurately considered equal to the amplitudes of a single-hull vessel of the same length and displacement.

The dependence of the roll on the speed of the duplex in the oncoming sea, which is completely unusual for objects with traditional contours, is obvious: the amplitudes fall with increasing speed.

Unfortunately, the amplitudes of vertical accelerations of pitching depend on speed differently, see Fig. 6.

It is obvious that with the usual speed limit in oncoming waves by acceleration values, the duplus has a significant advantage in terms of achievable speed.

Already the first full-scale tests of the SMPV showed that in terms of seaworthiness such a vessel is comparable to a traditional single-hull with a displacement of 5-15 times greater (depending on the ratio of the relative areas of the waterline). In Fig. Figure 7 shows the heaving amplitudes of the semi-natural SMPV model in natural waves with working and non-working heave dampers.

In 1978, the author published and in 2000 detailed a method for “collapsing” all information about seaworthiness, allowing it to be characterized by one number. This “seaworthiness coefficient” represents the average annual probability of meeting specified seaworthiness standards by the vessel in question in a given water area.

These calculations show that the SMPV becomes practically “all-weather” with a displacement of about 5–6 thousand tons.

4. Speed in calm water

A separate SMPV body usually differs from the same traditional one in having an increased wetted surface and a reduced residual resistance coefficient. It must be remembered that these quantities are interdependent in the usual system for predicting the towing resistance of a full-scale object: if the wetted surface is artificially increased, then the coefficient of residual resistance, as a relative value, decreases - with a constant absolute value of this component of resistance.

Rice. 8 contains a comparison of the relative values of the wetted surface of two types of hulls: traditional and with a small waterline area.

In Fig. 9 shows the residual drag coefficients of conventional and small waterline area hulls.

Essentially, it is possible to compare the performance of different types of hulls only at the level of designed vessels for the same purpose. In this case, another side of the flow around two or three hulls that makes up a multihull vessel, including the SMPV, will be noticeable: the hydrodynamic interaction of the hulls, primarily the wave systems generated by them. The interaction features are varied and depend on the number, relative position, dimensions and shape of the cases.

It can be assumed that the maximum of the upper curve corresponds to a Froude number of about 0.5 along the length of the strut, of which there are two on the SMPV body of this type.

An interesting example of “longitudinal interaction is the option of replacing each duplus body with two shorter bodies of the same type. In this case, the Froude number along the length of one part of such a tandem will be 1.5 – 1.7 times greater than the original body. And if the original body moved at a relative speed of about 0.5, i.e. on the “hump” of wave resistance, then the shorter hulls in the tandem will move already in the behind-the-hump zone. Together with a decrease in the wetted surface with a decrease in the elongation, such a transition can be effective in reducing towing resistance.

In addition to the “longitudinal” interaction, there is also the interaction of two bodies located at a certain (stability) distance from each other.

IN in this case favorable interaction is observed in rather narrow ranges of relative speed (from 0.33 to 0.43 and 0.2 to 0.25); the entire rest of the studied range of relative velocities is characterized by unfavorable – to one degree or another – interaction of wave systems. At high speeds interaction tends to zero.

A variant of the “longitudinal” interaction is the influence of the longitudinal shift of the central body of a three-body object on the total value of its residual resistance coefficient.

The available test results of a large domestic series of SMPV models make it possible to evaluate all possible options for dimensions and relative positions of housings at the early stages of design.

The greatest influence on the residual resistance of an outrigger vessel is exerted by the longitudinal position of the outriggers.

As for propulsors, the same types can be used for SMPVs as for traditional ships and ships, most often placed one on each of the two hulls or one on the aft hulls of three-hulled objects, or one or two on the stern of the central hull vessels with outriggers. Since SMPVs can have an increased design draft, at least when moving at sufficient depths, the propellers of these objects usually have increased diameters, which has a positive effect on the propulsive coefficient. Another feature of the SMPV is a higher viscous associated flow and a reduced suction coefficient, which also means an increase in the propulsive coefficient.

A unique series of SMPV models, tested at the A.N. Krylov Central Research Institute in the 70s, makes it possible to predict the towing resistance of various types of ships at the early stages of design (without additional tests before the technical design stage).

5. Durability

The complete scheme of forces and moments acting on multihull vessels, including SMPV, is quite complex. However, in the early stages of design, the main external load is the transverse horizontal force and the transverse bending moment determined by it, Fig. 10.

The greatest lateral loads act when parking with a log facing waves, which is the design case for lateral strength.

The transverse bulkheads located along the entire height of the side of the SMPV most effectively counteract the general lateral loads, Fig. 11, and associated attached skin strips.

The arrangement of bulkheads providing transverse strength, each of which should be from side to side and from bottom to upper deck, must begin in the first stages of designing the general arrangement. If such a bulkhead is to be permeable, then the loss of its strength due to the cutouts must be compensated for by reinforcements.

For double-hull SMPVs, longitudinal strength is less important than for traditional vessels, mainly because the hulls are shorter for the same displacement. The longitudinal strength of three-hull and outrigger SMPVs plays a significant role and should be checked, as with traditional hulls. General difference is a decrease in the longitudinal bending moment of the SMPV with increasing speed - in traditional ships, the longitudinal bending moment increases with increasing speed in the oncoming wave. The most loaded section of the SMPV is usually the horizontal section of each rack at the point where its vertical camber begins. The design of the rack must be smooth - to prevent stress concentration in the most loaded section.

If we estimate the required thickness of the rack skin in the most loaded section and take this thickness as the average, and then determine dimensions of all parts of the structure, the mass of the SMPV hull structures can be estimated, see Fig. 12.

Typically, the mass of SMPV hull structures in relation to displacement is greater than that of comparable traditional vessels, but less in relation to deck area.

SMPVs with outriggers have the smallest relative mass.

7. Design

To take into account the features of SMPVs, the author proposed a special algorithm for their design. One of the main input data in this algorithm is the deck area required to perform the vessel’s tasks.

As a rule, the designed SMPV does not have prototypes, or access to relevant information is impossible. Therefore, dimensions are selected using a variant method when calculating the basic technical and operational qualities by direct calculations. The diagram of the corresponding algorithm is shown in Fig. 13.

The result of domestic research into the characteristics of SMPV since the late 60s has become the possibility of developing the early stages of projects for vessels for any purpose. During this time, the author proposed many options for SMPV and other multihull vessels, see Fig. 14.

1. The main advantage of ships with a small waterline area is their high seaworthiness, comparable to the seaworthiness of traditional ships with 5-15 times greater displacement.

2. Available domestic materials for testing, calculations and methodological developments make it possible to carry out the early stages of projects of such vessels without additional tests and calculations.

The widespread use of vessels with a small waterline area is recommended in all cases where high seaworthiness increases the efficiency of fleet use. To demonstrate the effectiveness of the use of such vessels, it is recommended to use a method for comparing seaworthiness, which “collapses” all information into one figure, the “seaworthiness coefficient”.

Victor Dubrovsky