Dept. of Communications and Information Engineering
University of Murcia
© English Translation by Scott Trotter
© English HTML Version by Fiona Sinclair
© Spanish Version by Humberto Martínez Barberá and
Germán Villalba Madrid
Document version 1.0, Revision January 17th, 2000
SDN is a software tool for the design and analysis of models with the intention of providing the facility to obtain the shapes of a model, as well as to give the best benefits in navigation. To do so, SDN makes use of NURBS surfaces, which posses an excellent ability to represent certain types of shapes. It allows different possibilities to create the forms of the model, among them, to digitize an already existing model for his mod NACA and Kárman-Trefftz. It also includes a module for hydrostatic calculations, for stability and for velocity prediction (VPP). All these calculations, graphs and information may be printed so much in PostScript as directly in the printer.
SDN attempts to be a simple tool usable by beginners in naval design, but also sufficiently powerful as to be used by engineers of naval design.
SDN is an experimental platform of investigation developed jointly by the Departments of Computer Science and Systems (now Dept. of Computer Science, Artificial Intelligence and Electronics) and Applied Engineering at the University of Murcia, grant PCOM- 02/96 TEC from Programa Séneca of Comunidad Autónoma de la Región de Murcia
A three-dimensional object is made up of curves and surfaces. Common methods of representing curves and surfaces are the implicit method and the parametric method. The implicit method utilizes a mathematical function which depends on the variables of the axes, and is even to zero. It describes a relation between the different variables from the axes. For example, the function:
f(x, y) = x2 + y2 - 1 = 0
In the parametric method, each variable is a function of an independent parameter. Here, curves could be defined with the independent variable such as
C(u) = [x(u), y(u)] for a <= u <= b
In order to represent the first quadrant of a circle in parametric form, we can write in several forms, for example
C(u) = [cos(u), sin(u) ] for 0 <= u <= PI/2
or as
C(u) = [ (1-t2 ) / (1+t2), 2t / (1+t2) ] for 0 <= t <= 1
That is to say, the representation of a curve in parametric form is not unique.
A parametrical class of curves and surfaces are Non-Uniform Rational B-Spline (NURBS). NURBS are desirable for computational reasons, because of the ease of processing by a computer, stability with regard to floating front errors, their requirement of little memory, and their ability to represent a wide variety of curves and surfaces. NURBS are the generalization of nonrational B-Splines, which are based on the Bezier rational curves. These in turn are a generalization of Bezeir curves. The important characteristics of Bezier curves are:
The problem with Bezier curves is that they are not able to represent conical cambers (curves originating from the cut of a cone with a plane). Conical cambers can however be represented using a rational functions, defined as the quotient between two polynomials according to
x(u) = X(u) / W(u), y(u) = Y(u) / W(u), z(u) = Z(u) / W(u)
The w (i) may be interpreted as scalable weights. When the weights are varied, control points may attract/repulse the curve. A curve formed by a single segment of a rational Bezier curve is often inadequate. A single segment requires a high degree to define a complex form, which is inefficient to process, and numerically unstable.
Curves using single segments have limitations in making local forms. This is solved by defining the curve in pieces. A Bezier curve or a B-Spline when formed by pieces is constructed with several curves united at "points of rupture" with continuity of alignment between them.
To create points of rupture in B-Splines one inserts knots in them. A sequence of knots form a vector of knots, and is defined by U = u (0) ,...u (m) , which must fulfill that it is a sequence of nondecreasing numbers; that is to say, u (i) <= u (i+1) for all i = 0,...,m. The knots are, therefore, where the curve parts connect.
In Figure 1, one may observe the knots of the curve (u (0) , u (1) , u (2) , u (3)), the parts into which curve is divided (C (1, u), C (2, u), C (3, u)), the control points (open circles at the ends of the curves) and control polygons (formed by the straight lines joining the control points).
We are introducing now the minimum parameters needed to work with this kind of surfaces. The working surfaces are NURBS, although the program at the moment does not allow modification of the distribution of knots; these are redistributed nonuniformly when control points are inserted or eliminated. NURBS curves have four fundamental elements in their definition: control points, weights, knot vectors, and degree (in general, one only speaks of the degree of functions with orders greater than one)
It is important to note that modifying the position of a control point produces a local modification of the surface. The area affected by this modification is given by the degree of the surface and the location of other control points, if the vector knots stay unchanged. That is, it is possible to modify an area by inserting rows and columns of control points in the area, and later, moving the points as necessary. When inserting new control points, the curve remains invariant; nevertheless, eliminating control points causes variations in the curve, allowing a resulting curve very different from the initial curve.
When starting SDN, the user initially sees the interface and the working tools. The three-dimensional workspace is divided into quadrants by means of the orthogonal surfaces X=0.0, Y=0.0, Z=0.0, sharing the origin common. The projection of these surfaces on the screen are displayed as two perpendicular straight red lines, initially centered in the work area. These may be moved by means of the windows' horizontal and vertical scroll bars, located at its lower and right edges, respectively. In the lower left area is an icon visually indicating which axes are visible in the present View, designating the positive direction of each one. Upon changing the active View, this icon is updated.
The work area is composed of four parts, including:
The Files menu options include:
The Edit menu includes the following options:
In the Modules menu , options (also present in the toolbar) are available including: Add or Modify a surface, Add weights, Sails, Stations, Appendages, 3d View, Hydrostatic Calculations, Plans digitizer, and Plan Drawing. These functions are described in section 3.2.
The Tools menu opens the scaling options window: Scaling may be accomplished by percentage, increasing or reducing the dimensions of the model by some amount greater or smaller of 100; or by absolute value, in which given a 1- meter model with the x-axis scaled to 12, a model of 12 meters length is obtained. This utility is, after introduction of digitized data, is able to correct the scale easily. In addition, scaling can be in all dimensions or in one individual dimension. Figure 2 shows the Scaling Options window, which is activated from the Tools menu .
a) The tool bar, as described in part 3.2.
b) The control area (as seen in Figure 3) indicates cursor coordinates, zoom control, level, and present View. To the left is the value of coordinates x, y and z of the cursor in real units. Because the View in the drawing area is two-dimensional, only two of the coordinates may change. The cursor remains stationary with respect to the third inalterable dimension perpendicular to the current view. The Zoom slider allows the user to move the view away from or toward the model. Its use, together with the horizontal and vertical scroll bars, allows one to work on details of any part of design. In order to facilitate work with models in which one dimension is much greater than the other two, the zoom is independent for each View so that, when changing from one View to another it is not necessary to readjust it to the dimensional maximums of the View. The window combined of level the frontal View indicates this is the column of points of active control when visualizing, with which the work with this column of control points in this View is facilitated. The level control does not function in the side and plan view. Normally, level zero corresponds to the stern, with the smaller value of X, and the highest level corresponds to the column of points at the bow. In the combined View window, one of the three possible views can be selected (front, side or upper). In addition, an icon indicates the current view axis.
c) The drawing or work area. It is the largest area of the window, where the design is viewed. In it, red horizontal and vertical lines indicate the straight cutting lines of the surfaces defining the workspace. An icon in the lower left indicates the directions of the main X, Y and Z axes depending on the present view. This way, when in the plan view, the icon indicates the directions X and Y; in the front view indicates Y and Z; and in the side view the X and Z. When the cursor coincides with the point (0.0,0.0) in the current view, it changes to a cyan color, visually indicating the location of the cursor. In the lower and right area of the window is a grab allowing free resizing of the window. In the upper-right corner of the window is a grow-button, which expands the window to fill the available screen area.
Objective: to understand the main working surroundings, the procedure for the definition of surfaces, basic work options (including units) and the possibilities of structuring and visualization of surfaces.
Define three surfaces: a hull, rudder, and a keel. The hull dimensions 10 meters length and 2 meters of height. The rudder size of dimensions 0.5 meters of length and 1.5 meters of depth. The keel to be of 0.75 meters by 2.5 meters.
First, enter the Edit menu, and chose Preferences. Select like units of centimeters and kilograms. Section 3.3 explains in detail the available Preferences options.
SDN allows the user to work with independent surfaces, such as appendages or a sail, separately from the hull surface. Choose the Add or Modify a Surface option from the Modules menu. Press the New (surface) button in the active window. Under the Attributes tab, by default, the new surface is named "unnamed", located in the layer "hull", and of green color.
In order that it be named correctly, the surface type (Hull) is entered by default in the Layer name field; if desired, change the name of the surface and press the Modify button (if the Modify button is not pressed, the options in this dialog is not updated). The Type tab accesses the default surface definition. Increase the number of control points in the U direction to 7, by entering the value into the corresponding field, and press the Modify button. Observe that the length in the U direction has not been modified. The degree of the surfaces will not be changed, but we are going to modify the length longitudinally. As the length and depth of the hull are known ahead of time, in this case 1000cm and 200cm, enter the values in the fields for the U and V directions, respectively. It is possible to modify these values at any time in the surface generation procedure. Press the Modify button to update changes. Confirm that the button indicating symmetry with respect to x-axis is active, to facilitate the creation of a symmetric model (as it is in this case). Press the Exit button. The surface that we have created -the hull- is now visible in the working area. It may be necessary to use the zoom slider to see the entire surface.
In order to define the surface of the Rudder, it is necessary to create a new surface. Choose the Add or Modify a Surface option from the Modules menu. Press the New button. The attributes dialog will appear, with the default values. Enter the name "rudder", select the appendages layer, and the color yellow. Press the Modify button. Under the Type tab, leave the order and number of control points as established by default in the parametric dimension fields. The dimensions in U and V should be of 50.0 cm and 150.0 cm, respectively. Press the Modify button to save the values. Again, symmetry with respect to x-axis must be active. Press the Exit button.
The steps in the definition of the Keel are similar to those for the other surfaces, but for the color (use magenta) and the corresponding dimensions. It may be observed that the three surfaces appear superimposed at the origin. Note that the different colors permit easy recognition. Finally, save the file with Files/Save. Open the Forms folder, rename the file YATE01.SHP, and press the Save button.
Figure 4 shows the buttons bar. These are divided in two groups: those that operate on control points, and those that operate on surfaces.
With the five buttons of the leftmost group, the following actions can be taken (from left to right):
Objective: to work with surfaces, columns and rows of control points.
Using file YATE01.SHP saved from example No.1, move the surfaces to the following positions: locate the rudder 0.5 meters off the stern, against the lower surface of the hull, and the keel to 4.0 meters off the stern, against the lower part of the hull.
Load the file YATE01.SHP using File/Load. Activate the select button (the leftmost), and click on the yellow surface (the rudder). When it is selected, its control points will become visible. Press the Move Surface button. Locate the cursor on a control point, and drag the surface with the mouse to the new position. Next, select the surface corresponding to the keel and, using the same procedure, locating the keel in the desired position. Activate the Side view by selecting the pull-down View option. Adjust the screen-size of the model by means of the zoom lens control at the top of the screen. Note that when moving the mouse, its coordinates are updated in the control bar. In the side View, selecting a different zoom does not affect the other views.
Change to the Front view. Begin at the zero level (the stern station; the levels increase towards the bow). Observe that although all the structure is visible in the current view, only the control points corresponding to level zero are highlighted and active. They may only be moved in the Y and Z directions, perpendicular to the view. Select the surface corresponding to the hull (green color) by activating the select button then clicking on the surface with the mouse. Activate the front View. Select an intermediate level between the stern and bow, noting how the control points corresponding to the level to become visible. Activate the Move Control Points button, and drag the points so that they take on the approximate form of a hull section.
Normally, the user will wish to make modifications in a particular area without affecting the rest of the surface. To accomplish this, it is necessary to add rows or columns of control points around the area to be modified, so that upon moving the control points, the surface is not modified except in the area of interest. Changes in the surface are according to the relation between this modification and the degree of the surface. With the View set to Front, activate level 5. We are going to add five rows of control points. To do this, we press the Add Row of Control Points button, and select two consecutive points between which we want to make the insertion We repeat the process four times more, using the new column and one of the two previously inserted curves. Now, of the new control points, we will move the one that has remained trim between the two initial columns (when inserting rows or columns of control points, the surface is invariant, but the control points can be put under an automatic replacement). Using the mouse, move several of the control points to new positions. Note that the modifications affect only the local form. Once modifications have been made, it will sometimes be necessary (or convenient) to delete columns or rows of control points. This is dependant on the form of the model - eliminating control points can produce a modification in the surface. For that reason the user may or may not be able to take this action successfully. In order to illustrate this, activate the Erase Column of Control Points button, locate the cursor on a control point, and press the mouse button. If the action can be made without producing great modifications in the model, the action will be carried out. Otherwise, the control points will not be eliminated.
In the Files menu, choose the Save As option and name the file YATE02.SHP.
The Preferences allow the activation or deactivation of the following options:
Project development may be divided into three phases: in the first the form of the model is developed; in the second, the physical weights are located on the model (motor, tankage, etc.); in the third, technical calculations are made.
The first phase begins with the definition of the stations of the model, either manually or by digitalization. It is recommended to include the data of the project, as they are name of the project, date, and data of the engineer before beginning the design, so that this information is stored from the beginning, with the model. This first phase can make use of 3D visualization to observe possible irregularities of the model. Once the hull stations are developed, the next step is to move to design of the appendages.
In the second phase, the physical weights of the important elements are included in the system. These weights are used in determining the results in the third phase. In the third phase the calculation are completed, including those of hydrostatics, stability and speed prediction. If the results of these technical calculation do not fulfill the required specifications, or they do not correspond with the desired results, it will then be necessary to make the opportune modifications on the model by returning to the first phase, modifying the forms as necessary, back to calculations, and so on.
The creation of stations is a method used to generate the desired model. Whether there is a pattern model or not, this is done either manually or by digitalization of the surfaces. In manual modification, the designer has some idea of the geometry of the model to be developed, but no previous model. It is necessary then to begin with a flat surface, and to modify this surface to obtain the desired forms. This method uses the procedures outlined in examples 1 and 2. When digitizing surfaces, part of the model is formed by curves which have been previously determined. This way the designer does not start from scratch, but from a previous model that, by applying the necessary transformations, will be the base of the desired model.
When there is no previous model to serve as a basis for development, stations creation and modification is carried out manually. Starting with a flat surface, the Stations Creator module works similarly to the main work window, and is activated by pressing the corresponding button in the tool bar. As in the main work window, there are three views (front, side and upper). These views zoom independently, facilitating the interaction of one view with another. It is necessary to work in this window when it is desired to make modifications in X- direction. When working with the other two coordinates (Y, Z), it is more efficient to use the Stations creator. In it, besides allowing one to manipulate the control points, it is also possible to save stations in a separate file, so as to be able to use these stations in later developments, as well as being able to use a frame previously stored to obtain a particular form. These are stored with an .STA extension (more details are available in Appendix A: Files Extensions).
Figure 5 shows the tool bar for the Frame Editor. In addition to the options of Select a Surface, Add/Remove Columns/Rows of Control Points, and Move Control Points, it is possible to save the selected column of control points to a file, to load a column of control points from a file, to format a column of control points with the form stored in memory, and to print the stations window. In order to accelerate of the system, when making a modification in the control points, actions in the stations window are not automatically recorded. For this reason, it is necessary to press the Modify button (at the right).
Objective: to learn to create a model by means of manual modification of station forms.
Design a model using the manual modification of stations. The characteristics of the model are 22.5 meters of length, 5 meters of beam, 3 meters of depth and 25 tons of displacement. Make use of the stored master frame in file Master.sta.
In the Edit menu, select Preferences, click on the Units tab, and select meters and kilograms. In the Print menu, input the data for the project. Close the Preferences dialog by clicking on the close-button at the upper-left hand corner of the window. Choose Add or Modify a Surface from the Modules menu. Name the surface, press New, and define the parameters (length, width, number of control points; 10 in the U-direction, and 5 in V). When the data has been entered, press the "Modify" button. Once the new surface has been obtained, enter the stations creator by clicking the fifth button from the right. Figure 6 shows the stations creator window. This has three view panes. The window to the left is the front View. In the right upper window, the column of control points just loaded into memory. In the lower-right, the stations window. Begin by pressing the button to load a frame from file.
Find and open the Master.sta file. In the right upper window, note the station to be used as a section in our design. The next step is to activate level 4 to give a suitable format. Activate the Format Column of Control Points button, and with the cursor click on one of the control points of level 4. In this window, the control points at level 4 are automatically distributed to obtain the form loaded from the Master.sta file. The front view is shown in Figure 7.
Note that no change has taken place in the Station Design window. Pressing the button to activate the Stations window updates it, with the masterful frame like unique modification.
Once form has been given to the master frame, generate stations manually by means of the Move Control Points option column of control points. The process consists of advancing from the bow to the stern, and later creating the stern and the bow. In Figure 8, the plan view can be seen showing the columns of control point sections from center to stern.
In Figure 9, progress has been made well towards the bow. In this figure, the side View is seen. The model is not finished (lacking the form of the stern and of the bow), but already has the basic structure of bow and stern defining what will ultimately be the hull.
In Figure 10, the updated stations window shows the unfinished model.
In order to finish giving form to the model, we make use of the Move Control Points button. As may be noted in Figure 9, the lines of the surface in the lengthwise direction (green) do not have continuity. Therefore, we will first modify the positive control points in the side View, so that they improve the appearance so that the effect of Figure 11 is obtained. Once made the step previous and made level the linear of cover, proceed to the creation of the stern and bow. For this, a column of control points between each pair of columns of the ends has been inserted. Finally, it is enough with moving the control points, with the intention of obtaining a form similar to the one of Figure 11
In Figures 11, 12 and 13, can be seen the three views of the finished model. In Figure 14, is the Stations window showing the finalized model.
In order to verify the finished form of the model, it is advisable to view it in 3d. For this, the 3D visualization button is pressed, and using the zoom and rotation sliders, to view the model from all the possible angles so as to detect faults in the surface. In Figure 15 shows the model in 3d, without rendering.
At this point the model would be finished, but for saving it as YATE02.shp, and for printing the surfaces of the complete model as seen in the Stations window.
If use becomes of a digitized model, whose file must have the extension .DIG, the window of stations is loaded digitized. From this window, it is possible to make technical calculation directly, or to create a different model by modifying a previous one. The other method consists of introducing coordinates of points in the table. For this, press the button of Digitalization of Stations.
This method is for use with previously digitized models. It is possible to achieve this process in three ways: keying in the coordinates in separate tables corresponding to each station; by means of a digitizer; or by a previously stored file. It is worthwhile to keep the digitized points, unmodified, so that they may serve for later developments. If a digitized model is available in a file, with extension .DIG, the stations table is loaded digitized. From this table, it is possible to make the technical calculations directly, or to create a new model through modification of the previous one.
The other method (illustrated in Example 4) consists of introducing coordinate points into the table. To accomplish this, the Plans Digitization procedure will be used. The buttons to each side serve to define the form of the bow and the stern. The button more to the right is for fitting the points.
Objectives: to obtain a model from a series of definition points. To model a surface from an assembly of points stored in the file araez-22.dig.
The first step is to create a new surface or to enter the Surface digitizer directly. For this example, we will enter the Digitizer by pressing the corresponding button in the main interface. This will bring up the window seen in Figure 16. Press the Load File button, and select areaz-22.dig.
Once the file with the digitized points is loaded, the stations are shown in the left upper window, as seen in Figure 17.
The combined Refinement panel allows us to specify as desired how the points are approached by the NURBS curves. In that a series of discreet points define the stations, it is necessary to obtain an approach by the NURBS so that the error (tolerance) is minimal, reducing to a minimum the control points necessary to define the surface. The user, by means of the following options in Refinement, can define this tolerance:
In our example, we will define the refinement to be of low tolerance. In the Front view, one can see the digitized points in blue, and the form of the mesh NURBS in black. The control points can be seen as a dense mesh. The greater the density of the mesh, the greater the number of control points.
As the file araez-22.dig contains the stations of the stern and bow, it will not be necessary to define them. However, should it be necessary to digitize the shapes manually using a list of x,z coordinates (it is possible to drawn with the cursor, or to introduce the coordinates) one may take the following steps:
Pressing the Stations Digitizer button, a screen is opened where manual modification of the coordinates of the points is undertaken (see Figure 18). This Module is used when the coordinates of the points of the stations are available, but not stored in a file.
The editing of stations is different from previous procedures. The button with the blue "X" is used to erase the columns previously selected. The button with a green arrow is the option of symmetry. This button may be used when a window of stations in a plane is present, and digitizes the stations of stern to section to the left, and the stations of section to bow to the right. As the program works with all the stations to the right (and > 0.0), pressing the symmetry button duplicate the stations from the left to the right. Of this form one goes of a standardized plane to the structure of work of this program. The units are the previously selected ones. Upon saving, each column creates a separate file of extension .DIG. Each must have a different x coordinate value.
The user can leave gaps between stations (for example, between station 3 and station 5), and then, the program automatically compacts the data.
Once the digitized points are introduced, select the surface that will take this form. In this example there is no previous surfaces, so it will be created with the Add or Modify Surface module. Once it is created select it, and press the Modify a Surface button to the digitized points of the Surface digitizer. This surface will take the form of the digitized hull.
With the Save option, only the digitized points are filed.
In order to create appendages, it is first necessary to create a new surface corresponding to the appendage. Any new surface is created with the Add New Surface button or from the Modules menu. Locate this surface in the appendages layer, and add the identifier Keel to it. Press the Modify button, so that the changes are carried out, and press the Exit button. Select this surface and press the Edit Appendages button. The active window is shown in Figure 20. Of the four windows, three contain the side, front, and plan views. The fourth window (upper right) contains the profile.
As may be seen in Figure 19, the Appendages Creation tool bar can define four types of profiles: NACA-4, NACA-5, Karman-Trefftz and luff. These profiles are defined through their corresponding buttons, located to the right area of the tool bar. It is also possible to load a previously saved profile from a file.
Upon entering the appendage creator, the flat surface is displayed in its three views. The first step consists of selecting the type of profile desired, and to continue defining its parameters. In this example the Karman-Trefftz profile has been used.
Figure 21 illustrates the Karman-Trefftz profiles definition window. We can modify the position of camber, and the thickness, as well as studying the lift and drag of the defined profile.
Pressing the Lift/Drag button opens the window shown in Figure 22. In this window the lift generated by the defined profile for a given angle of given attack may be calculated. This value of this angle can be changed and, upon pressing the Recalculate button, the results for the new conditions obtained. By repeatedly modifying angle of attack, the behavior of the profile may be obtained.
If the profile fulfills the requirements of lift for the desired angles of attack, the next step is to give form to the surface using this profile. The method followed for the design of this keel has consisted of a Karman-Trefftz profile, reducing the thickness of the profile while increasing the depth. Note that changing the thickness changes the behavior of the profile, so that with less thickness there is less lift and less drag.
We begin at the upper waterline assigning the greatest thickness. In order to give form to the rows of control points, the button labeled with that name in the Appendage Creator is clicked. Clicking on the control point corresponding to the plane of upper waterline automatically forms of the control points in that row. The next is to return to enter the definition of Karman-Trefftz profiles, and to reduce the thickness. The procedure is applied to the next lowest waterline, successively to the bottom. Although it is not advisable to mix different profiles in the same appendage, this possibility exists, as it is possible to use any profile and indicating which waterline to which it should apply.
Once the profiles are complete, finish the profile by moving control points as necessary so that the lines of the surface are well distributed. At this time, complete the geometry the vertices of the appendix. The file QUILLA.shp contains the keel used in this example.
Figure 23 shows the completed keel viewed in 3D. In this image, as in the case of the hull, deformations or flaws in the appendage surface may be noted.
In order to store a design, select the Files menu, and then Save. The extension of the design is .SHP. If it is desired to save with a name different from the present one, use the Files/Save As option. In this case, it is also possible to change the target folder to save the file. If it is desired to recover a previously stored design, choose the Files/Open option. A dialog will open indicating files with the .SHP extension in the present folder. If the file to load is not there, we will have to open the folder that contains the file, and to continuation, to press the button to open. If the complete path is known, thus like the name of the file to load, it easily can be entered into the corresponding fields.
Files with the extension .STA store station forms. Access to this type of file must be within the Stations creator, with the stations to be modified selected. When saving files from the Stations creator, SDN requests the name of the file to save; the extension is added automatically by default. In order to load a stations file, press the Load Station button. A standard print dialog is opened, indicating the name of the file, and the folder where it is located.
DXF files are exported, so that they may be loaded by other graphic programs accepting this format. In order to export the model in DXF, select the File/Export option, suboption DXF (this feature might be unavailable in the current version).
The Print option of the File menu includes the option of printing in the Publisher of Frames, and saving a file in PostScript format. The user must indicate the name of the file, as well as the folder where it will be stored. The name of the project, that of the engineer and other printing data will be taken from their definitions under Preferences.
In the Hydrostatic Calculation module, the Report option prints a summary of the results obtained in the technical calculation. The name of the plan and the name of the engineer are obtained from the data introduced in Preferences. This information can be modified before printing. In this Module, when viewing graphics, it is easy to print them. Simply press the Print button, and the visible curves are printed, with the name of the plane associated with the curves.
Pressing the Hydrostatic Calculations button starts the Hydrostatic Calculations module. The technical calculations are divided into hydrostatics, stability, and speed prediction (VPP). In the Hydrostatic Calculations module it is possible, by means of selection buttons, to make the calculation for all or only one flotation, to calculate the VPP, or to use data from a previously saved VPP.
In the hydrostatic calculations module, before pressing the "Calculate" button, the user should indicate in the corresponding selection buttons if calculations should be made for all the flotations, if the calculations need stability, or solely to work with the speed prediction calculations.
Once it is determined which calculations are to be made, the Calculate button is pressed. In this window the wetted surface curve, the submerged volume curve, the careening position, and the center of gravity are displayed, as well as the longitudinal plane of flotation. In these curves, the coordinate origin is to the left.
In the lower right area, coefficients from the model are displayed, including the length, beam, prop, and geometric moments of inertia coefficients. In order to view the hydrostatic graphs, press Graphs button, and to choose the basic curves in the panel, as in Figure 24.
Moving the cursor on the curves indicates the value at that point, as indicated at the lower right.
The calculations of stability consist of two groups of graphics: KN and GZ. Visualization is accomplished by pressing the Graphics button in the Hydrostatics Calculation Module, and selecting the KN curves (Figure 26) or the GZ curves (Figure 27). KN Curves are of 5º to 90º of inclination, represented in different colors for each angle. Moving the cursor over the curves, one is shown the value of the KN and the displacement (in the work units), as seen in Figure 26. To the lower left, the correspondence between colors and angles is indicated.
Static and dynamic GZ curves are plotted for the defined flotation, between 0° and 180°. In the same graph the straight GMt line is also plotted. Each curve is represented in a different color. Moving the cursor on the curves, the value of the curve on the graph is indicated in the work units, as may be seen in Figure 28. In the left lower area is a table illustrating the correspondence of color with each curve.
Files generated during the speed prediction calculations are given the extension ".VPP". When the analysis is run, a file is automatically generated called sdn.tmp.vpp. The name of this file may be changed (if not renamed, when making subsequent calculations the previously stored data in the file is lost), with the purpose of keeping, to view and to compare results. The results are viewed, like the rest of the graphics, by pressing the Graph button, and selecting the Vpp desired. If it is desired to view a previously created VPP file, it is necessary only to press the VPP button, indicate the desired file to open, and press Graph to view. Figures 28 to 32 are graphs obtained from the VPP. In all of them the coordinates of the cursor are shown in the bottom-right, displaying the respective units of force, speed, or angle, depending on the selected VPP.
Figure 28 shows the speed prediction of a yacht as a function of real windspeed. For each real windspeed, a curve of a different color is generated according to the legend. In the lower-right are the coordinates translated in a prediction of speed of the yacht, and angle of the real wind, according to the location of the cursor in the graphic.
Figure 29 is the VPP of the force on the sail. The graphs are calculated for different apparent windspeeds, according to the colors indicated in the legend. It may be seen that when increasing the apparent wind speed, the value maximum is at an incidence of 120°, where the force is at its maximum. By moving the cursor on the screen, the force in Newtons and the apparent wind angle is indicated at the lower right.
Figure 30 shows the force generated by the sail. The concentric sectors indicate the force, increasing as the curve moves away of the center of semicircle. The sectors are divided according to its angle of incidence, divided into sectors of 30°. A curve is obtained according to the apparent windspeeds, each a different color for identification. As may be seen, as the wind speed approaches a maximum, the force in the sail does so also. By moving the cursor on the screen, the force in Newtons and the apparent wind angle is indicated at the lower right.
SDN works with files of different formats according to the type of information stored; each is identified by its extension. In the following table, the relation between the extension and the type of stored information is indicated:
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