commit 560b206cd9a4c424449fe6795266d4d234c61695
parent a35ba4e888faa06e5a3087061057db9fc63389c5
Author: Ivan Gankevich <igankevich@ya.ru>
Date: Sun, 31 Mar 2019 15:25:42 +0300
Re-read.
Diffstat:
| main.tex | | | 135 | +++++++++++++++++++++++++++++++++++++++++-------------------------------------- |
| references.bib | | | 8 | +------- |
2 files changed, 71 insertions(+), 72 deletions(-)
diff --git a/main.tex b/main.tex
@@ -30,22 +30,26 @@ Ivan Petriakov
\email{st016177@student.spbu.ru},\\
\email{v.khramushin@spbu.ru},\\
\email{st049350@student.spbu.ru}\\
-\url{https://spbu.ru/,https://www.shipdesign.ru/}}
+\url{https://www.shipdesign.ru/}}
\maketitle
\begin{abstract}
-Initially, digital ship hull form geometric model is assumed to maintain
+Initially, digital geometric model of a ship hull is assumed to maintain
continuity in solving traditional ship theory problems, ship hydromechanics and
-seaworthiness in severe storm waves conditions. In the research reported here
-we consider using a table of plaza ordinates (transversal projection of frames)
-supplemented with description of sterns as a means of describing digital
-geometric model. This description allows for later addition of compartments,
-appendages and superstructures. These more complicated ship structures and
-their characteristics (e.g. ship compartments and superstructures are
-characterised by template-based modelling) are added to initial ship hull model
-in separate files from the working directory of a particular experiment.
+seakeeping in severe storm waves. In the research reported here we consider
+using a table of plaza ordinates (transversal projection of frames)
+supplemented with a description of sterns as a means of describing digital
+geometric model. This description, which we call Vessel (VSL) format, allows
+for later addition of compartments, appendages and superstructures. These more
+complicated ship structures and their characteristics (e.g. ship compartments
+and superstructures are characterised by template-based modelling) are added to
+initial ship hull model in separate files from the working directory of a
+particular experiment. We show how this model is converted into
+three-dimensional triangular mesh suitable for ship motion simulations. VSL
+format is generally more efficient than industry standard IGES format and
+is distinguished by the simplicity and capability of editing by hand.
\keywords{%
Ship lines \and
@@ -65,18 +69,19 @@ IGES.
\section{Introduction}
-\subsection{Digital models of ship lines and ship hull forms}
+%\subsection{Digital models of ship lines and ship hull forms}
Initial geometric model of a ship hull is very close to traditional hull
blueprints which are naturally rendered as a table of plaza ordinates in ship
-theory. Such digital ship hull model quite reliably characterises ship lines
-and above-water hull parts, while preserving continuity in hydrostatic and
+theory. Such a model quite reliably characterises ship hull lines and
+above-water ship hull parts, while preserving continuity in hydrostatic and
hydrodynamic calculations in ship theory and hydromechanics. This is important
for verification of newly created numerical experiments with a multitude of
historical series of ship calculations, model basin experiments and sea trials.
Obvious advantage of this digital format is that it is relatively simple and
-has compact data layout, and the data is prepared and refined as plain text
-strings representing stern and frame coordinate sequences.
+has compact data layout, with the data prepared and refined as plain text
+strings representing stern and frame coordinate sequences. We call this format
+Vessel (or VSL for short).
Numerous variants of ship hulls were systematically collected in VSL format in
Saint Petersburg State University in Vessel database~\cite{vessel2015}. The
@@ -89,7 +94,7 @@ hydrostatic characteristics.
\subsection{Vessel format}
Formalised description of ship hull geometric form is done using plain text
-data which include ship name, hull dimensions, and subsequent description of
+data which include ship name, hull dimensions, and successive description of
aft, main (table of plaza ordinates) and bow sections. When digital ship hull
model is first added to Vessel database the following design characteristics
are specified in the comments: displacement, wetted surface area, hull volume
@@ -102,29 +107,29 @@ is presented in tab.~\ref{tab:format}.
\begin{tabular}{p{1cm}p{1cm}p{9cm}}
\toprule
\multicolumn{3}{l}{1. Technical vessel description (lines starting
- with \texttt{//} or \texttt{;} are comments)} \\
+ with \texttt{//} or \texttt{;} are comments).} \\
\multicolumn{3}{l}{2. Format magic number (30) and hull model name in
angle brackets \texttt{<...>}.} \\
\multicolumn{3}{l}{3. The number of frames and middle frame number.} \\
\multicolumn{3}{l}{4. Hull dimensions (length, beam, draft).} \\
- \addlinespace
+ \cmidrule(lr){1-3}
\multirow{5}{*}{\rotatebox[origin=c]{90}{\parbox[t]{2.9cm}{\centering{}The
number of points on a curve}}} & \multicolumn{2}{l}{5. \(X(z)\)~---
sternpost contour abscissas as a function of applicates.} \\
& \multicolumn{2}{l}{6. \(Y(z)\)~--- transom width ordinates as a
function of applicates.} \\
- \addlinespace
+ \cmidrule(lr){2-3}
& \rotatebox[origin=c]{90}{\parbox[t]{1.4cm}{\centering{}Frame
abscissas}} & 7. \(Y(z)\)~--- frame curves as functions of
applicates of general hull line. \\
- \addlinespace
+ \cmidrule(lr){2-3}
& \multicolumn{2}{l}{8. \(Y(z)\)~--- bulbous bow width ordinates as a
function of applicates.} \\
& \multicolumn{2}{l}{9. \(X(z)\)~--- stern contour abscissas as a
function of applicates.} \\
- \addlinespace
+ \cmidrule(lr){1-3}
\multicolumn{3}{l}{10. Design characteristics (displacement, wetted
- surface, volume ratio).} \\
+ surface, volume ratio coefficient).} \\
\bottomrule
\end{tabular}
\end{table}
@@ -146,10 +151,10 @@ is presented in tab.~\ref{tab:format}.
In accordance with initial purpose of a digital ship hull model, Hull programme
-makes basic calculations of certain characteristics of a ship hull, blueprint
-curved elements and ship stability diagrams by fixing centre of gravity with
-respect to general line, centre of buoyancy, metacentre or current waterline.
-The programme also performs wave resistance calculations for arbitrary travel
+makes basic calculations of certain characteristics of a ship hull, curved
+elements and ship stability diagrams by fixing centre of gravity with respect
+to general line, centre of buoyancy, metacentre or current waterline. The
+programme also performs wave resistance calculations for arbitrary travel
speeds taking into account radiation intensity and interference of ship waves
with respect to waterline as a function of Froude number.
@@ -170,8 +175,8 @@ In the original programme~\cite{hull2010} that visualises ship lines and
calculates hydrostatic characteristics, ship hull is described by a collection
of curves; however, for a programme that simulates ship dynamics in rough sea
this description is not convenient. A better representation would be a
-collection of triangles (a \emph{triangular mesh}) that approximate
-analytically given ship hull geometry. At the centre of each triangle pressure
+collection of triangles (a \emph{triangular mesh}) that approximates
+analytic ship hull geometry. At the centre of each triangle pressure
force induced by ocean waves is applied, and then these forces are used to
calculate ship motion. Triangles is a better representation because they
\begin{itemize}
@@ -182,7 +187,7 @@ calculate ship motion. Triangles is a better representation because they
that visualise simulation frames.
\end{itemize}
In the following paragraphs we describe how analytically given ship hull is
-transformed into a fully-connected collection of triangles.
+transformed into a fully connected collection of triangles.
In Vessel database each ship hull is divided into three sections
(fig.~\ref{fig:sections}): aft, main and bow sections. Main section consists of
@@ -197,7 +202,7 @@ frames and defines intermediate points between endpoints of subsequent frames.
If it does not go between some frames, then there are no intermediate points
between them. Curves are not closed and define only left part of the ship hull,
the full ship hull model is created by mirroring each point of the curve with
-respect to longitudinal axis and connection corresponding curve endpoints by
+respect to longitudinal axis and connect corresponding curve endpoints by
straight lines.
\begin{figure}
@@ -210,18 +215,18 @@ straight lines.
Ship hull is transformed from analytic to discrete form by using
\emph{intermediate representation} in a form of two-dimensional rectangular
array of points, which makes it easy to obtain triangular mesh. Each ship hull
-section is transformed to such an array, then arrays are concatenated. Each row
-of the resulting array represents a frame, and each frame is an array of points
-of this frame. Since the array have to be rectangular, the number of points
-equal the maximum number of points across original frames in VSL file. After
-that, endpoints are added to make curves closed, and the whole array is
-mirrored with respect to longitudinal axis. Then each rectangular patch of the
-resulting array is divided into two triangles to obtain triangular mesh.
-Duplicate vertices and faces, that may have been introduced by mirroring or
-making curves closed, are removed from the mesh. So, intermediate
-representation is easy to transform to a triangular mesh, but all frame have to
-have the same number of points in order to transform them to such a
-representation.
+section is transformed to such an array, and then these arrays are
+concatenated. Each row of the resulting array represents a frame, and each
+frame is an array of points of this frame. Since the array have to be
+rectangular, the number of points equal the maximum number of points among all
+original frames in VSL file. After that, endpoints are added to make curves
+closed, and the whole array is mirrored with respect to longitudinal axis. Then
+each rectangular patch of the resulting array is divided into two triangles to
+obtain triangular mesh. Duplicate vertices and faces, that may have been
+introduced by mirroring or making curves closed, are removed from the mesh. So,
+intermediate representation is easy to transform to a triangular mesh, but all
+frames have to have the same number of points in order to transform them to such
+a representation.
It is straightforward to transform main section to a rectangular array of
points in one stage. First, we determine the maximum number of points in a
@@ -267,25 +272,25 @@ between four curves \(c_0(u)\), \(c_1(u)\), \(d_0(v)\), \(d_1(v)\):
\quad c_0(1) = d_1(0), \quad c_1(0) = d_0(1),
\quad c_1(1) = d_1(1).
\end{align*}
-Here \(C_1\) is linear interpolation between points \(c_0(u)\) and \(c_1(u)\),
-\(C_2\) is linear interpolation between points \(d_0(v)\) and \(d_1(v)\), and
+Here \(C_1\) is linear interpolation between points \(c_0\) and \(c_1\),
+\(C_2\) is linear interpolation between points \(d_0\) and \(d_1\), and
\(C_3\) is bilinear interpolation between corner points of the patch. \(C_1\)
-and \(C_2\) are ruled surfaces~--- surfaces between two curves, that generated
-by interpolating corresponding curve points. Bicubic interpolation can be used
-instead of bilinear to get the same derivative when joining multiple Coons
-patches together, but for a grid of interior points linear interpolation is
-enough.
+and \(C_2\) are ruled surfaces~--- surfaces between two curves, that are
+generated by interpolating corresponding curve points. Bicubic interpolation
+can be used instead of bilinear to get the same derivative when joining
+multiple Coons patches together, but for a grid of interior points linear
+interpolation is enough.
Using these formulae we generate a grid of interior points between curves of
-each bow/aft patch during the second stage. Our first approach was use one
+each bow/aft patch during the second stage. Our first approach was to use one
Coons patch for each subsequent pair of frames, but we have found that some
ship hulls have horizontal curves with large curvatures which cause linear
interpolation to produce cusps on the resulting surface (fig.~\ref{fig:cusp}).
-We solved this problem by using multiple vertically arranged Coons patches for
-each subsequent pair of frames. This approach removes the cusps, but the
-vertical size of the patch have to be small enough to reduce effect of large
-curvature of the horizontal curve. We concatenate grids of subsequent frames'
-grids to obtain rectangular array for bow/aft sections.
+We solved this problem by using multiple smaller vertically arranged Coons
+patches for each subsequent pair of frames. This approach removes the cusps,
+but the vertical size of the patch have to be small enough to reduce effect of
+large curvature of the horizontal curve. We concatenate grids of subsequent
+frames to obtain rectangular array for bow/aft sections.
\begin{figure}
\centering
@@ -312,7 +317,7 @@ ship hulls}
As an illustrative example of simulating seakeeping ship characteristics we
consider ship stability diagrams for contemporary and historical ships, and for
-a ship that is purposely optimised for improved storm seakeeping.
+a ship that is purposely optimised for improved seakeeping in storm waves.
\begin{figure}
\centering
@@ -328,7 +333,7 @@ Fig.~\ref{fig:stability} shows that Aurora cruiser ship hull has excellent
seakeeping characteristics in severe storm waves conditions, which guarantee
safe small oscillations and smoothness of roll by reducing metacentric height~---
initial ship hull stability. Additional positive stability appears for
-large roll angles and arbitrary changes in heave.
+large roll angles and arbitrary heaving.
\begin{figure}
\centering
@@ -374,7 +379,7 @@ in tab.~\ref{tab:performance}.
\end{table}
We chose MICW (a hull with reduced moments of inertia for the current
-waterline) and Aurora ship hulls in VSL format and tanker (KVLCC2),
+waterline) and Aurora cruiser ship hulls in VSL format and tanker (KVLCC2),
container ship (KCS) and combat ship (5415) in IGES format that are freely
available on the Internet\footnote{\url{https://simman2014.dk/ship-data/}}.
VSL format showed higher performance in comparison to IGES format considering
@@ -417,7 +422,7 @@ used to legacy blueprints to reason about ship hull characteristics.
\subsection{Disadvantages}
The main disadvantage of VSL format is that triangular mesh generated from it
-approximates ship hull surface only to a certain precision, but cannot
+approximates ship hull surface only with a certain accuracy, but cannot
represent it exactly. This is due to the fact that we choose the same number of
points for each frame to be able to create rectangular array of all points and
convert it to a mesh. Obvious solution to this problem is to use
@@ -427,22 +432,22 @@ intermediate points for smaller patches, and it would be more difficult to make
the resulting surface as smooth as the original, especially at intersections of
frames with different number of points.
-A simpler approach is to use rectangular array as original ship hull
+A simpler approach is to use rectangular array as the original ship hull
representation, not an intermediate one. In that case each array element
-represent a geometrical vertex and in addition the type of spline surface that
+represents a geometrical vertex and in addition the type of spline surface that
represents ship hull surface \emph{exactly} is specified in the file. That way
-it is easy to create triangular mesh that would be exact representation of the
+it is easy to create triangular mesh that would be an exact representation of the
original analytic surface when the number of grid points tends to infinity, and
-the resulting surface would as smooth as the original one with all derivatives
+the resulting surface would be as smooth as the original one with all derivatives
and surface normals computed using analytic representation. Similar approach is
-followed by FastShip~\cite{fastship} in which ship hull is defined by B-spline
+followed by FastShip~\cite{fastship} in which ship hull is defined by a B-spline
surface, that in turn is defined by control points, allowing ship hull designer
and ship motion simulation programmes to use exactly the same ship hull
representation.
\section{Conclusion}
-In computation experiments we used theoretical blueprints of Aurora cruiser
+In computational experiments we used theoretical blueprints of Aurora cruiser
which has excellent seakeeping characteristics and for which there can be no
dangerous situations in severe storm waves. We presented the more complicated
geometric ship hull form which is optimised for storm seakeeping. This ship
diff --git a/references.bib b/references.bib
@@ -36,13 +36,7 @@
}
@Book{ khram2018,
- title = {Поисковые исследования
- штормовой мореходности корабля},
- subtitle = {История эволюционного развития
- инженерно-технических решений об
- обводах и архитектуре корабля, о
- единении морских наук и хорошей
- морской практики},
+ title = {Search studies of ship seakeeping in storm waves (in Russian)},
publisher = {Lambert Academic Publishing},
edition = {3},
isbn = {978-613-8-23643-6},
