KR20100004150A - A methodology of hull-form generation by mathematical definition using analytic equations on waterlines of ship - Google Patents

Abstract

PURPOSE: A method for generating a ship shape by waterline sectional shape formation definition is provided to obtain smooth curvature of a waterline sectional shape, thereby obtaining a ship shape which reduce entire resistance. CONSTITUTION: A smooth curve shape is calculated using a coordinate of a distinguish point and the first and second differential values of the coordinate. The error between a coordinate value of each calculated distinguish point and an original design input value is reduced. A waterline sections which are not dimensioned are dimensioned. A ship shape is realized by combining the waterline sections.

Description

A methodology of hull-form generation by mathematical definition using analytic equations on waterlines of ship}

The present invention relates to a design method of the side surface and the water section of the hull in the appearance of the ship, in particular to express the shape of the water section (plan) of the ship in a dimensionless formula, and then expressed in coordinates at each point of the coordinate The present invention relates to a method of generating a curve from a slope input value and a method of generating a linear shape by defining a shape of a waterline section of a ship that generates a line by combining the generated curve and a boundary curve defined by a formula.

In general, there are two ways to design the alignment using conventional manual work and computer programs (a kind of CAD). Conventional manual work has been performed by expressing linearity using curved rulers and the like directly on drawings at the normal scale of 1/100 of ocean nautical vessels. Recently, as commercial computer programs have been developed, they have not been used in conventional design work. . Commercial programs almost always apply the principles of conventional manual methods. The method of creating flexible curves represented by curves or thinner splines has been replaced by the Bezier curve principle called B-Spline, followed by NUBBS (Non-Uniform) which is the principle of curves and curves. Rational B-spline), and all of the leading CAD programs support NUBBS curve representation. However, while the NUBBS curve has the advantage of expressing a complex curve freely and flexibly, it is relatively complicated because it requires more data than the present invention using a formula, and it is reproduced when it is not helped by a commercial program. Becomes difficult.

The smoothness of the curve is typically judged based on the change of curvature, such as sudden change or bending of curvature is ultimately directly related to the increase of the resistance of the ship, and the NUBBS curve guarantees the smoothness of the curve made from the given points. On the other hand, the NUBBS curve is not automatically given smoothness because the curvature pattern varies depending on the arrangement between the given points or the curve generation conditions.

In the linear generation process, the ship is usually divided into section curves, waterline curves and boundary curves. Since the longitudinal distribution of the ship's cross-sectional curve shape is relatively complicated compared to the distribution of the water-cross section, it shows systematic change compared to the shape of the water-cross section. As such, they prefer to adjust or adjust the volume by fine-tuning the longitudinal position of the cross-sections, and commercial programs offer features that meet these needs.

However, this convenient function has a problem such that the length of the curved portion starting from both ends of the central parallel portion becomes longer than necessary in the shape of the cross section. Judging from the cross-sectional shape, it will be a good linearity, but from the water-rectangular cross-sectional shape, it will be a malformed shape such that the length around the maximum width of the curve is kept too long and gentle. Of course, the designer is modifying the existing points to maximize the flexibility of the curvature by referring to the curvature distribution of the cross section shape, but the overall curvature of the cross section curve in the situation where the outline of the cross section shape is already defined. Artificially adjusting the distribution becomes virtually impossible.

The reason is that in a commercial linear design program, adjusting the side tangent curve position, which is the starting point of the curve, is too wide a wavelength across the linear line, which requires a lot of effort to modify the side tangent curve. This is because it is avoided if possible.

In addition to the side tangent curves described above, there is a practice that does not change the boundary profile (side profile), which is another boundary curve, at the initial stage of the design. Although these boundary curves will have a very large impact on the ship's resistance performance, it is difficult to understand such practices, but the same situation remains to this day, with the long-running practice of linear design, where the functionality of commercial programs is quite advanced.

In addition, since the shape of the cross section is derived from the repair section, the shape of the repair section and the cross section is present in a double, there is a problem that must be cross-correction of both cross-sections when modifying any cross-section.

The present invention devised to solve the above problems is designed a curve to have a smooth curvature in each repair cross section by a simple formula connection method, and in the cross-sectional configuration in the combination of each repair to modify the shape of the cross section and the desired cross-sectional shape It is an object of the present invention to provide a method of acquiring the distribution and deriving a linear result in which the resistance is reduced as a whole in order to secure a smooth curvature in the shape of the cross section.

To this end, the present invention is a method of determining the smoothness of the cross-section created by a combination of the above design, by designing the repair section curve in a dimensionless state, and smoothly adjusted based on the curvature calculated from the actual size. In order to solve the problem of the conventional cross-correction method, it is possible to modify the cross section only by modifying the repair section.

In addition, the present invention is to determine the shape of the vessel by a method of defining and expressing the linear form with simple equations, to enable a simple linear definition to escape from the conventional complex linear configuration method, thereby simplifying a few compared to the conventional The goal is to be able to determine the alignment using only the arguments.

The present invention for achieving the above object, (A) dimensioning the coordinates of any point in the repair section; (B) dividing the repair section into at least two parts by selecting at least one break point on the dimensionless repair section; (C) calculating a smooth curve shape using the coordinates of the cut point and the first and second derivatives at the coordinates; (D) reducing the error between the coordinate value and the original design input value at each calculated point; (E) dimensioning the dimensionless repair section; And (F) combining the plurality of repair cross sections calculated through the steps A to E to express the alignment.

Preferably, in the step (A), when the starting point of the curve that meets the side tangent is a non-dimensionalized coordinate (1,1), and the end point that meets the outline is converted to correspond to the coordinate (0,0), the curve If the longitudinal start of X _ST , the end point of X _E , the maximum width of the curve is Y _max , and the minimum width is Y _min , then at the bow or stern where any point on the curve is dimensionless (x, y),

player:

Stern:

It can be represented by the above equation.

Further, in the step (C), the repair section divided by the break point is a section expressed by the n-th order power of the horizontal axis variable (x), a section expressed by the fifth order polynomial, a 멱 function or an elliptical 멱 It may include at least one of the intervals expressed in the form of a function.

As described above, according to the present invention, a simple linear definition is possible, deviating from the conventional complicated linear configuration method, and thus, the linearity can be determined using only a few factors simplified compared to the conventional method.

In addition, it is easy to change to a linear having a new size based on the linear generated in the above manner, and by changing all the boundary curves constituting the linear by the formula, it is easy to change in connection with the non-dimensionalized curve portion have.

In addition, the method of expressing linearity by connection of appropriate equations is a smooth change characteristic of curvature, which is basically a linear expression of the effect of reducing drag applied to the hull under the water surface during sea navigation. From the basic stage of can be secured.

That is, in the present invention, the boundary curves can also be connected in accordance with the formula, so that the shape can be easily changed. It has a feature that changes automatically, making it easier to convert linear.

In addition, by designing the cross-sectional shape by applying the formula that can be obtained an analytical solution through the present invention, and designing the alignment through a combination of these, the non-dimensionalized curve when the size of the linear changes Since it can be easily extended (= dimensionalized) by using the formula of Equation, the time required for design is shortened compared to the existing method. Designed to smooth the curvature of the cross section shape, it is more likely that the resistance applied to the surface will be lower than that of the existing linear line in flight, and it is possible to change freely and easily in the representation of the linear line. There is also an advantage to development.

In order to fully understand the present invention, the advantages of the operability of the present invention, and the objects achieved by the practice of the present invention, reference should be made to the accompanying drawings which illustrate preferred embodiments of the present invention and the contents described in the accompanying drawings.

Hereinafter, exemplary embodiments of the present invention will be described in detail with reference to the accompanying drawings. Like reference numerals in the drawings denote like elements.

In order to achieve the above object, the present invention includes a process of deriving the solution by the construction and analytical method of the formula required to define the repair shape.

1 is a conceptual diagram of dimensionless the length- (half) width relationship in any waterline section (plane) shape of a ship.

Referring to FIG. 1, the linear repair section in the present invention has a characteristic curve and parallel portion as shown in FIG. The central parallel part is determined before the initial stage of the linear design because it is the maximum half-width value that is predetermined in the vertical direction. The point where the curve starts from the maximum width is different for each water cross section, and the side profile connecting the starting points of each curve in the water cross section from the bottom to the top of the ship, and the side showing the maximum width boundary of the ship specification. You need to define a side tangent curve.

When the starting point of the curve that meets the side tangent is a dimensionless coordinate (1,1), and the end point that meets the outline is converted to the coordinate (0,0) as shown in FIG. 1, the longitudinal point of the curve is X _ST. Given that the end point is X _E , the maximum width of the curve is Y _max , and the minimum width is Y _min , the following mathematics at the fore or the stern is that any point A (X, Y) on the curve is dimensionless (x, y) It will be represented by Equation 1.

player:

Stern:

FIG. 2 is a graph showing input parameters and a curve segmentation method in expressions to approximate the dimensionless curve of FIG. 1.

Referring to FIG. 2, an input factor necessary for defining a curve divided into three parts is illustrated. To design the dimensionless curves above, any two points (coordinates) between (0,0) and (1,1) should be similar to P (x ₁ , y ₁ ) and Q ( x ₂ , y ₂ ) and the slope of the two points as P 'and Q' of FIG. 2, which is the proper position and the slope of the curve at that position so that the linear designer is close to the desired shape. If the desired curve is not derived, you need to change the position and slope values of the points.

Of the curve it is also passed from the coordinates (1, 1) on the _{2 Q (x 2, y 2} ) passing through the first curve and the coordinates _{Q (x 2, y 2)} P up to (x _1, y ₁₎ The second curve is divided by the third curve up to (0,0) after the coordinate P (x ₁ , y ₁ ). If the coordinates P (x ₁ , y ₁ ) and Q (x ₂ , y ₂ ) coincide, the second curve interval does not exist, and the coordinates P (x ₁ , y ₁ ) and Q (x ₂ , y ₂₎ If additional R (x ₃ , y ₃ ) is given between), the curve is divided into four parts.

There will be a number of methods for designing a curve as shown in FIG. 2, but in the present invention, arbitrary coordinates for the purpose of shape representation in the plane between the dimensionless coordinates (0,0) and (1,1) where the waterline section curve part is replaced With 1 to 3 slope values at each point, smooth curves are calculated through the following mathematical principle.

First, in order to express the first curve as an equation, the y value is expressed in the form of n-th order power of the horizontal axis variable x having the coordinate (1, 1) as the origin, and is defined as in Equation 2 below.

이 되고, x₂에서의 y₂를 지나는 것과 기울기 조건인

를 대입하면, 수학식 2의 미계수인

와

를 구할 수 있다.A ₁ and n ₁ in Equation 2 are obtained from a coordinate Q (x ₂ , y ₂ ) condition and a slope condition, respectively. Differentiating Equation 2 representing the first curve

This is, as the slope condition in by the y ₂ at x ₂

If we substitute, we are the non-coefficient of Equation 2

Wow

Can be obtained.

가 되고, 이 값은 제2곡선을 정의하는 조건으로 사용된다.The second derivative at x ₂ passing through the first curve is

This value is used as a condition for defining the second curve.

The second curved portion of FIG. 2 is defined as a fifth order polynomial, and may be expressed as Equation 3 below.

Since Equation 3 has six coefficients, y ₂ 'corresponding to the second derivative at the coordinates of the point P, in addition to the four conditions obtained by the coordinates of the points P and Q and the slope at the point. A condition in which the value 'coincides with the second derivative value of Equation 3 forming the second curve, and any variation value represented by y ₁ ''were added. By arranging the above conditions, the following six equations to obtain six non-coefficients a, b, c, d, e, f can be summarized.

In the six conditional expressions above, y ₁ '' is an unknown number or an analytic solution for a, b, c, d, e, and f can be determined by a known coefficient. It is possible to obtain an equation from the non-coefficient a and serially to f. The method of solving multi-order equations (Gaussian elimination, etc.) is generally well known even if it is not through an analytical method, so the detailed description thereof is omitted.

Set the initial value of y ₁ '' to about 1.0, solve the fifth-order equation to obtain a, b, c, d, e, f, and use Equation 3 to find the y ₁ value that corresponds to the x ₁ value at point P. When calculated, it is out of the original design input value y ₁ . Set to y ₁ '' so that the computed value close to y ₁ increment (or decrement) value compared after continuously performing the computation, and go out by reducing the increment size gradually. The finally calculated values to obtain a result that substantially matches the y _1, the incremental value of the y ₁ '' to be calculated until it is approximately 0.00001.

식에 대입하여 구해지며, 초기에 입력된 설계 값과는 약간의 차이를 보이게 되나, y₁ 값과는 일치하고, y₁' 에 근접하는 값을 얻은 것이므로 문제가 되지 않는다.If the final values of a, b, c, d, e, and f are obtained with respect to the second curve, the slope of the P point on the second curve is

Is obtained by substituting the formula, but with a design value input initially show some difference, and the value y ₁ is because matched, and obtained a value approximate to y ₁ 'is not a problem.

To define the third curve, we pass the point P and use the condition that the slope is changed y ₁ '. The third curve uses two types of equations as shown in Equations 5 and 6 according to the characteristics of the shape to be designed, where Equation 5 is the power function form and 6 is the elliptic power function (tentative name). Defined in form.

Unknowns a ₃ and n ₃ of Equation 5 are obtained by applying the above two conditions using Equation 3 above.

In the case where the equation is defined as in Equation 6, the inclination condition at the point P may be applied to a negative value. A and n _x are additionally designed and input as appropriate values, and the unknown B and n _y values are calculated and obtained under the same conditions as the above-described solution in relation to Equation 5.

FIG. 3 is a diagram illustrating input of the values of the factors as in FIG. 2 and a dimensionless state of the coefficients calculated by the equation constituting the analytical solution and the entire curve calculated therefrom.

If R (x ₃ , y ₃ ) is additionally given between the coordinates P and Q, then the coefficients of the fifth-order polynomial are determined using six conditions in a similar manner between P and R, and then between R and P It is possible to express the curve of as 5th or 4th polynomial. The three-point input method may be used when the curvature is to be defined perfectly smoothly in all sections, or when a more complicated curve is expressed than the curve obtained by the two-point input method.

The above method is necessary to define the curve for one repair section, and to express all the alignments, it is necessary to combine the curves in about 15 to 20 repair sections, and the non-dimensionalization is defined as one of the bow or the stern. Because of this characteristic, the athlete and the stern must be designed separately.

In general, even if the three-dimensional shape can be imagined by designing the shape of the water surface, there is a feature that is difficult to know the exact shape. Therefore, it is a necessary process to draw the shape of the cross section. In case of designing by the above-mentioned method of dimensionless cross section curve, side profile of bow and stern should be defined, and side tangent curve representing the maximum width boundary of ship specification is needed. In the present invention, it is possible to implement a shape very similar to the current design result by combining the formulas in the design of the boundary curve, the formulas are represented as a function of Z and X, the inverse calculation (calculate the X value from Z, Calculate Z from X values) has the limitation of expression. Since the formula of the boundary curve is a field outside the scope of the present invention, a detailed description of the configuration of the formula is omitted.

식으로 계산되는데, 이 과정을 요약하면 X를 무차원화하여 x로 표현하고, x를 이용하여 계산된 계수를 사용하여 y 값을 계산하며, 다시 y 값을 차원화하여 Y로 표현하게 된다.Since the curve at the cross section represents the shape at a given z, first we can calculate the values of x _E and x _ST corresponding to z from the designed profile and side tangent curves, The dimension value x is calculated, the y at x is calculated using the coefficients of the curves obtained through the above method implemented in r in the present invention, and the dimensioned Y value is simply

In summary, this process is summarized as a non-dimensionalized X to be expressed as x, using a coefficient calculated using x to calculate the y value, and again to dimension the y value as Y.

4 is a view showing the result of calculating the shape in the stern cross section, which is the second half of the ship using the curves defined in the plurality of water cross section.

Referring to FIG. 4, the cross-sectional shape as shown in FIG. 4 is derived, and the designer performs a task of modifying the input value of each repair section curve and comparing the results until the desired shape is derived. The design results of the bow shape, the first half of the ship and the stern shape, the second half of the ship.

Although the present invention has been described with reference to one embodiment shown in the drawings, this is merely exemplary, and those skilled in the art will understand that various modifications and equivalent other embodiments are possible therefrom. . Therefore, the true technical protection scope of the present invention will be defined by the technical spirit of the appended claims.

1 is a conceptual diagram of dimensionless the length- (half) width relationship in an arbitrary cross-sectional (planar) shape of a ship.

FIG. 2 is a graph illustrating input parameters and a curve segmentation method in terms of equations to approximate the dimensionless curve of FIG. 1; FIG.

FIG. 3 shows the coefficients calculated by the equations constituting the analytical solution and the entire curve calculated therefrom in a non-dimensionalized state by inputting values of the factors as in FIG. 2 actually;

4 is a view showing the result of calculating the shape in the stern cross section, which is the second half of the ship, using the curves defined in the plurality of water cross sections.

Claims (3)

(A) dimensionless the coordinates of any point in the repair section; (B) dividing the repair section into at least two parts by selecting at least one break point on the dimensionless repair section; (C) calculating a smooth curve shape using the coordinates of the cut point and the first and second derivatives at the coordinates; (D) reducing the error between the coordinate value and the original design input value at each calculated point; (E) dimensioning the dimensionless repair section; And (F) a linear generation method according to the definition of the water-shape cross-sectional formula of the ship comprising the step of expressing a linear by combining a plurality of water-cross section calculated through the steps A to E. The method of claim 1, In the step (A), the starting point of the curve meeting the side tangent is a non-dimensionalized coordinate (1,1), and when the end point meeting the outline is converted to correspond to the coordinate (0,0), the longitudinal starting point of the curve Where X _ST , the end point is X _E , the maximum width of the curve is Y _max , and the minimum width is Y _min , at the bow or stern where any point on the curve is dimensionless (x, y),

player:

Stern:

Linear generation method by defining the longitudinal cross-sectional shape of the ship represented by the equation. The method of claim 1, In the step (C), the repair section divided by the break point is a section expressed by the n-th order power of the horizontal axis variable (x), a section expressed by the fifth order polynomial, a power function or an elliptic power function form. Linear generation method according to the definition of the longitudinal section shape of the ship including at least one of the intervals represented by.

Images