Plotting outwards from a vertical axis, distances corresponding to the areas of a section up to each waterline, a curve known as a Bonjean curve is obtained. Thus, the distance outwards at the LWL is proportional to the area of the section up to the LWL, the distance outwards at 1WL is proportional to the area of section up to 1WL and so on.
Clearly, a Bonjean curve can be drawn for each section and a set produced. For convenience of calculation, it is the addition of the volumes of the main body and append- ages such as the slices at the keel, abaft the AP, rudder, bilge keels, propellers, etc. It varies from about 0. Its value usually exceeds 0. Expected values generally exceed 0. Practice in this respect varies a good deal. Because y is rarely, with ship shapes, a precise mathematical function of x the integration must be carried out by an approximate method which will presently be deduced.
Some tools 15 Fig. The second moments of area or moments of inertia about the two axes for the waterplane shown in Fig. This is one convenient way to represent the three-dimensional shape of the main underwater form less appendages.
Its projection in plan may then be referred to as the transverse centre of buoyancy TCB. Had z been taken as the distance below the waterline, the second expression would, of course, represent the pos- ition of the VCB below the waterline. The weight of a body is the total of the weights of all of its constituent parts. Projections of the centre of gravity of a ship in plan and in section are known as the longitudinal centre of gravity LCG and vertical centre of gravity VCG and transverse centre of gravity TCG.
The centre of buoyancy for this new immersed shape is at B1. Lines through B and B1 Fig. The metacentre is the point of intersection of the normal to a slightly inclined waterplane of a body, rotated without change of displacement, through the centre of buoyancy pertaining to that waterplane and the vertical plane through the centre of buoyancy pertaining to the upright condition.
The term metacentre is reserved for small inclinations from an upright condition. If the body is rotated without change of displacement, the volume of the immersed wedge must be equal to the volume of the emerged wedge.
A mean value of this factor is found for each ordinate. It is now necessary to apply to each ordinate a mean plating thickness which must be found by examining the plating thicknesses or weights per unit area, sometimes called poundages along the girth at each ordinate Fig. Each section is divided by trial and error, into four lengths of equal weight.
The mid-points of two adjacent sections are joined and the mid-points of these lines are joined. An allowance for the additional weight of laps, if the plating is raised and sunken or clinker, can be made; an addition can be made for rivet heads. It is unwise to apply any general rule and these factors must be calculated for each case. Various international bodies attempt to promote this and the symbols used in this book, listed at the beginning, follow the general agreements.
The symbols and units associated with hydrodynamics are those agreed by the International Towing Tank Conference. It is not necessary to be familiar with the R integral calculus, however, beyond understanding that the elongated S sign, , means the sum of all such typical parts that follow the sign over the extent of whatever follows d. It is now necessary to adoptRvarious rules for calculating these integrals.
Clearly, this soon becomes laborious and other means of determining the value of an integral must be found. Clearly, the more numerous the ordinates,Rthe more accurate will be the answer. Expressions can be deduced for moments, but these are not as convenient to use as those that follow. Let us deduce a rule for integrat- ing a curve y over the extent of x. It will be convenient to choose the origin to be in the middle of the base 2h long, having ordinates y1 , y2 and y3.
The rule is one for evaluating an integral. While it has been deduced using area as an example, it is equally applicable to any integration R using Cartesian or polar co-ordinates. Some tools 27 All of these operations are best performed in a methodical fashion as shown in the following example and more fully in worked examples later in the chapter.
Students should develop a facility in the use of Simpson's rules by practice. The values of P at equal intervals of v are as follows: v 7 9 11 13 15 P 9 27 36 39 37 Solution: The common interval, i. To apply the trapezoidal rule to a curvilinear shape, we had to assume that the relationship between successive ordinates was linear.
Where there is known to be a rapid change of form, it is wise to put in an intermediate ordinate and the rule can be adapted to do this. Suppose that the rapid change is known to be between ordinates 3 and 4 Fig. It is suitable for 4, 7, 10, 13, 16, etc. Another particular Simpson's rule which will be useful is that which gives the area between two ordinates when three are known.
Incidentally, applying the 5,8 minus one rule backwards, the unshaded area of Fig. Rules can be combined one with another just as the unit for each rule is combined in series to deal with many ordinates. It is important that any discon- tinuity in a curve falls at the end of a unit, e.
Let us deduce a rule for six ordinates Fig. Multipliers are always symmetrical and are indicated by dots. Some tools 31 These few Simpson's rules, applied in a repetitive manner, have been found satisfactory for hand computation for many years.
The rule could have been forced to take many forms, most of them inconvenient. Similar rules can be deduced for 2, 3, 4, 5, 6, 7 and 9 ordinates when spacings become as shown in Table 2. A third set of rules, the Gauss rules, uses unequal spacing of ordinates and unequal multipliers as shown in Table 2. Table 2. Multiplier 2 Spacing 0. By using Gauss rules, the naval architect can either obtain greater accuracy by using the same number of ordinates or obtain the same accuracy with fewer ordinates and in less time.
As such it is as much a tool for the naval architect to use, as the slide rule, or the rule for calculating areas and volumes. It is, of course, much more powerful but that makes it even more important to under- stand. It is not necessary to know in detail how it works but its basic char- acteristics, strengths and weaknesses, should be understood. The system includes input units which accept information in a suitably coded form CD-rom or disk readers, keyboards, optical readers or light pens ; storage or memory units for holding instructions; a calculation unit by which data is manipulated; a control unit which calls up data and programs from storage in the correct sequence for use by the calculation unit and then passes the results to output units; output units for presenting results visual display units, printers, or plotters ; and a power unit.
The immediate output may be a magnetic tape or disk which can be decoded later on separate print-out devices. Sometimes the output is used directly to control a machine tool or automatic draughting equipment. Input and output units may be remote from the computer itself, providing a number of out- stations with access to a large central computer, or providing a network with the ability to interact with other users.
As with any other form of communication, that between the designer and the computer must be conducted in a language understood by both. Input systems are usually interactive, enabling a designer to engage in a dialogue with the computer or, more accurately, with the software in the computer.
Software is of two main types; that which controls the general activities within the computer e. The computer may prompt the operator by asking for more data or for a decision between possible options it presents to him. The software can include decision aids, i. If the operator makes, or appears to make, a mistake the machine can challenge the input. Displays can be in colour and present data in graphical form. Red can be used to highlight hazardous situations because humans associate red with danger.
However, for some applications monochrome is superior. Shades of one colour can more readily indicate the relative magnitude of a single para- meter, e. Thus a plot of points which should lie on smooth curves will quickly highlight a rogue reading. The computer can cause the display to rotate so that a complex shape, a ship's hull for instance, can be viewed from a number of directions. The designer can view a space or equipment from any chosen position.
In this way checks can be made, as the design progresses, on the acceptability of various sight lines. Can operators see all the displays in, say, the Operations Room they need to in order to carry out their tasks? Equally, maintainers can check that there is adequate space around an equipment for opening it up and working on it.
Taking this one stage further, the computer can generate what is termed virtual reality VR. Typically a helmet, or headset, is worn which has a stereoscopic screen for each eye.
Colours, surface textures and lighting can all be represented. Such methods are capable of replacing the traditional mock-ups and the 3-D and 2-D line outs used during construction.
All this can be done before any steel is cut. To enhance the sense of realism gloves, or suits, with force feed back devices can be worn to provide a sense of touch. It does not follow that because a computer can be used to provide a service it should be so used.
It can be expensive both in money and time. In such systems the designer uses a terminal to access data and a complete suite of design programs. Several systems have been developed for ship design, some concentrating on the initial design phase and others on the detailed design process and its interaction with production.
This clearly reduces the chance of errors. Again, once the structure has been designed the computer can be programmed to generate a materials ordering list. Then given suitable inputs it can keep track of the material through the stores and workshops. The complexity of a ship, and the many inter-relationships between its component elements, are such that it is an ideal candidate for computerization. The challenge lies in establishing all the interactions. Provided that the factors governing a real life situation are understood, it may be possible to represent it by a set of mathematical relationships.
Consider tankers arriving at a terminal. The economics of such a procedure is also conducive to this type of modelling. Expert systems and decision aiding. Humans can reason and learn from previous experience. It has been possible to program them to carry out fairly complex tasks such as playing chess. The computer uses its high speed to consider all possible options and their consequences and to develop a winning strategy.
Such programs are called expert systems. These know- ledge-based expert systems have been used as decision aids. An early application of such techniques was in medicine. The SBA would examine a sick crew member, taking temperature and other readings to feed into a computer program containing contributions from distinguished doctors.
The computer then analyzed the data it received, decided what might be wrong with the patient and asked for additional facts to narrow down the possibilities. The end result was a print out of the most likely complaints and their probability.
This enabled the command to decide whether, or not, to abort the mission. In the same way, the naval architect can develop decision aids for problems where a number of options are available and experience is useful. The applied forces may arise from the deliberate action of those on board in moving a control surface such as a rudder or from some external agency such as the seaway in which the ship is operating.
The same form of equation can be represented by a suitably contrived electrical circuit. By extending the circuitry, more variables can be studied such as the angle of heel, drift angle and advance. This is the fundamental principle of the analogue computer.
The correct values of the electrical components can be computed by theoret- ical means, or measured in model experiments or full scale trials. Having set up the circuit correctly it will represent faithfully the response of the ship. It can be made to do this in real time.
The realism can be heightened by mounting the set-up on a enclosed platform which turns and tilts in response to the output signals. Furthermore, the input can be derived from a steering wheel turned by an operator who then gains the impression of actually being on a ship. The complete system is called a simu- lator and such devices are used to train personnel in the operation of ships and aircraft.
They are particularly valuable for training people to deal with emer- gency situations which can arise in service but which are potentially too dangerous to reproduce deliberately in the vehicle itself. Simulators for pilotage in crowded and restricted waters are an example. The degree of realism can be varied to suit the need, the most comprehensive involving virtual reality tech- niques.
If desired, components of a real shipboard system can be incorporated into the electrical system. The operator can be presented with a variety of displays to see which is easiest to understand and act upon. Research of this type was done in the early days of one-man control systems for sub- marines. Computer graphics allow the external environment to be represented pictorially in a realistic manner.
Thus in a pilotage simulator the changing external view, as the ship progresses through a harbour, can be projected on to screens reprodu- cing what a navigator would see from the bridge if negotiating that particular harbour. Other vessels can be represented, entering or leaving port. Changed visibility under night time or foggy conditions can be included. Any audio cues, such as fog sirens or bells on buoys, can be injected for added realism.
Another useful simulator is one representing the motions of a ship in varying sea conditions. Some subjects can be cured of seasickness by a course of treatment in a simulator. Apart from physical symptoms, such as nausea or loss of balance, the mental processes of the operator may be degraded. Optimum orientation of displays to the axes of motion can be developed. Some tools 39 Approximate formulae and rules Approximate formulae and rules grew up with the craftsman approach to naval architecture and were encouraged by the secrecy that surrounded it.
Many were bad and most have now been discarded. There remains a need, however, for coarse approximations during the early, iterative processes of ship design. It gives the distance of the centre of buoyancy of a ship-like form below the waterline. This is not because the subject itself has changed but rather that the necessary mathematical methods have been developed to the stage where they can be applied to the subject.
Again, in the study of ship motions the extreme amplitudes of motion used in calculations must be associated with the probability of their occurrence and probabilities of exceeding lesser amplitudes are also of consid- erable importance. It is not appropriate in a book of this nature to develop in detail the statistical approach to the various aspects of naval architecture.
Students should refer to a textbook on statistics for detailed study. However, use is made in several chapters of certain general concepts of which the following are important.
The prob- ability that R will not occur is 1 p. If an event is impossible its probability is zero. If an event is a certainty its probability is unity. Some tools 41 Consider the following example of experimental data. Successive amplitudes of pitch to the nearest half degree recorded during a trial are: 4, 2, 3 12, 2 12, 3, 2, 3 12, 1 12, 3, 1, 3 12, 12, 2, 1, 1 12, 1, 2, 1 12, 1 12, 4, 2 12, 3 12, 3, 2 12, 2, 2 12, 2 12, 3, 2, 1 It is m long.
Lever Func. The total of the f y column must be multiplied by 23 times 22, the common interval, to complete the integration and by 2, for both sides of the waterplane. We have also chosen Oy as number 6, the mid-ordinate as being somewhere near the centre of area, to ease the arithmetic; it may well transpire that number 7 ordinate would have been closer. The waterlines are 0.
What are the volume of displacement and the position of the VCB? All of these examples are worked out by slide rule. The number of digits worked to in any number should be pruned to be compatible with this level of accuracy. Solution: WL Offset, y Trap. Calculate the volume of the appendage and the longitudinal position of its centre of buoyancy. Solution: Ord. Area, A S. The areas and distances of the centres of areas from the axis of rotation of the immersed half water planes have been calculated at 5 degree intervals as follows: Angle of inclination deg 0 5 10 15 20 Area m2 Centre of area from axis m 3.
Solution: The Theorem of Pappus Guldinus states that the volume of a solid of revolution is given by the area of the plane of revolution multiplied by the distance moved by its centre of area. A ship, m between perpendiculars, has a beam of 22 m and a draught of 7 m. The length, beam and mean draught of a ship are respectively , Two similar right circular cones are joined at their bases. Each cone has a height equal to the diameter of its base.
A curve has the following ordinates, spaced m apart: What is the ratio of the two solutions? The half ordinates of the load waterplane of a vessel are 1. What is its area? Calculate the volume of the plating. The half ordinates of a vessel, m between perpendiculars, are given below.
In addition, there is an appendage, m long, abaft the AP, whose half ordinates are: 7. Find the area and position of the centre of area of the complete waterplane.
The bulkhead is m deep. Calculate the total load on the bulkhead and the position of the centre of pressure 7. The sections forward, in the middle and at the after end are all triangular, apex down and the widths of the triangles at the tank top are respectively 15, 12 and 8 m. Draw the calibration curve for the tank in tonnes of fuel against depth and state the capacity when the depth of oil is m. Areas of waterplanes, m apart, of a tanker are given below. Calculate the volume of displacement and the position of the VCB.
Area m 2 The waterline of a ship is 70 m long. Its half ordinates, which are equally spaced, are given below. Calculate the least second moment of area about each of the two principal axes in the waterplane. The half ordinates of the waterplane of a ship, m between perpendicu- lars, are given below.
There is, in addition, an appendage abaft the AP with a half area of 90 m2 whose centre of area is 8 m from the AP; the moment of inertia of the appendage about its own centre of area is negligible. Calculate the least longitudinal moment of inertia of the waterplane. The half breadths of the 16 m waterline of a ship which displaces 18, tonnef in salt water are given below.
In addition, there is an appendage abaft the AP, 30 m long, approximately rectangular with a half breadth of m. The length BP is m. Calculate the transverse BM and the approximate value of KM. Breadth m Each of the two hulls of a catamaran has the following dimensions. The length and volume of displacement of each hull are respectively 18 m and m3.
The hull centre lines are 6 m apart. Calculate the transverse BM of the boat. The distance between ordinates is 10 m. Express the error from the true position of the VCB as a percentage of the draught. Deduce a trapezoidal rule for calculating longitudinal moments of area. A quadrant of 16 m radius is divided by means of ordinates parallel to one radius and at the following distances: 4, 8, 10, 12, 13, 14 and 15 m. The lengths of these ordinates are respectively: Find: 7. From strains recorded in a ship during a passage, the following table was deduced for the occurrence of stress maxima due to ship motion.
Calculate for this data a the mean value, b the standard deviation. Occurrences 42 Construct a probability curve from the following data of maximum roll angle from the vertical which occurred in a ship crossing the Atlantic. What are a the mean value, b the variance, c the probability of exceeding a roll of 11 degrees 7. That is to say, any movement can be resolved into movements related to three orthogonal axes, three translations and three rotations. With a knowledge of each of these six movements, any combination movement of the ship can be assessed.
Generally, it is the change from one static condition to another that will be of interest and so it is convenient to imagine any movement occurring very slowly. Dynamic behaviour, involving time, motion and momentum will be dealt with in later chapters. Since they vary with pressure and temperature, the values must be related to a standard condition of pressure and temperature.
Since it is the basic reference for all such materials, the weight properties of pure distilled water are reproduced in Fig. Corrections are applied for variations of reciprocal weight density from this value. Table 3. This upthrust is called the buoyancy of the object. This leads to a corollary of Archimedes' principle known as the Law of Flotation. The buoyancy is the resultant of all of the forces due to hydrostatic pressure on elements of the underwater portion Fig.
The body is supported by the summation of all the pressure forces acting on small elements of the surface area of the body. The same is not quite true for the study of dynamic behaviour of a vessel which depends upon mass rather than weight. The tonnef is the force due to gravity acting on a mass of one tonne. The watertight volume of a ship above the water line is called the reserve of buoyancy.
It must be made clear that when the ship is still, the weight and buoyancy forces must act in the same straight line BG, otherwise a couple would act upon the ship, causing it to change its attitude. What happens when a small weight is placed on the vertical line through BG? The ship undergoes a parallel sinkage having a buoyancy W and the centre of buoyancy B moves towards the addition by an amount BB0.
It has been assumed that there is no trim; when there is, Fig. In the same way, the ship has a new centre of gravity.
Taking moments about G see Fig. Note the similarity of the expressions. Equation 1 involves a knowledge of the position of b, the centre of buoy- ancy of the added layer of buoyancy. Frequently, however, additions are small in comparison with the total displacement and b can be taken half way up a slice assumed to have parallel sides. This latter has the merit of retaining a long established set of initials.
When TPI is used in this book it has this meaning. Of course, arguments are completely reversed if weights are removed and there is a parallel rise. It will sink deeper because the water is less buoyant. The weight and buoyancy have not changed because nothing has been added to the body or taken away. There are occasions when a greater accuracy is needed. What is the relationship between the change in displacement and TPI? It will be remembered from Chapter 2 Fig. Displacement of a ship is calculated with some accuracy during its early design to a series of equally spaced waterlines.
For example, suppose Fig. The displacement at say 6. Worked example 4, illustrates this. An excess draught aft is called trim by the stern, while an excess forward is called trim by the bow. It is important to know the places at which the draughts are measured and trim, unless it is obvious, is usually referred to between perpendiculars or between Fig.
Used as a verb, trim refers to the act of angular rotation about the Oy-axis, from one angular position to another. There is also another important use of the word trim which must be excluded for the time being; in relation to submarines, trim is also the relationship between weight and buoyancy. This can be shown by writing down the condition that there shall be no change in displacement, i. Practitioners will also find it to be an invaluable reference book.
Basic Ship Theory. Get Books. Rawson and Tupper's Basic Ship Theory, first published in , is widely known as the standard introductory text for naval architecture students, as well as being a useful reference for the more experienced designer. The fifth edition continues to provide a balance between theory and practice.
Volume 1 discusses ship. Eric Charles , Rawson, E. Contents: v. Hydrostatics and strength v. Ship dynamics and design. Includes bibliographicalreferences and index. ISBN v. Naval architecture I. Tupper, E. R37 Symbols and nomenclature The sea Answers to problems ForewordtotheftheditionOver the last quarter of the last century there were many changes inthemaritime scene.
Ships maynowbe muchlarger; their speeds are generallyhigher; thecrews havebecomedrasticallyreduced; therearemanydierenttypes includinghovercraft, multi-hull designsandsoon ; muchquickerandmoreaccurateassessments of stability, strength, manoeuvring, motions andpoweringarepossibleusingcomplexcomputerprograms;on-boardcomputersystemshelptheoperators; ferriescarrymanymorevehiclesandpassengers;andsothelistgoeson.
However,thefundamentalconceptsofnavalarchitec-ture, whichtheauthorsset out whenBasicShipTheorywasrst published,remainas valid as ever. As with many other branches of engineering, quite rapid advances have beenmadeinshipdesign, productionandoperation.
Manyadvancesrelatetotheeectiveness in terms of money, manpower and time with which older proced-ures or methods can be accomplished. Send your feedback through Order form too. Help Desk. Rawson and Tupper's "Basic Ship Theory", first published in , is an introductory text for naval architecture students, and a reference for the more experienced designer. Blog Archive Blog Archive January Oferty i praca w Zarabiaj.
0コメント