
\documentclass[11pt,a4paper,oneside]{report}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\usepackage{amsmath}
\usepackage{suthesis-2e}
\usepackage[a4paper]{geometry}

\setcounter{MaxMatrixCols}{10}
%TCIDATA{OutputFilter=LATEX.DLL}
%TCIDATA{Version=4.00.0.2321}
%TCIDATA{LastRevised=Friday, January 31, 2003 18:03:37}
%TCIDATA{<META NAME="GraphicsSave" CONTENT="32">}
%TCIDATA{Language=American English}
%TCIDATA{CSTFile=report.cst}

\input{tcilatex}
\onehalfspacing
\geometry{left=20mm,right=15mm,top=15mm,bottom=15mm} 

\begin{document}

\title{Application of Computational Fluid Dynamics\ to Downwind Sail Flows}
\author{Stephen Collie}

\chapter{Introduction to Sailing, Sails and Sail Flows }

\label{Chapter intro sails}

\section{Introduction}

The purpose of this Chapter is to give the reader a solid background in sail
flows and some insight into sailing and the America's Cup. In particular the
challenges\ involved with sail performance analysis and computer modelling
are highlighted. Whilst the discussion is primarily amied at IACC\ yachts
and America's Cup racing, much of the work is relevant to sailing yachts in
general.

\section{The America's Cup}

\subsection{The history of the Cup}

\FRAME{fhFU}{1.6845in}{2.4292in}{0pt}{\Qcb{The America's Cup.}}{}{thecup.jpg%
}{\special{language "Scientific Word";type "GRAPHIC";maintain-aspect-ratio
TRUE;display "USEDEF";valid_file "F";width 1.6845in;height 2.4292in;depth
0pt;original-width 2.7596in;original-height 4in;cropleft "0";croptop
"1";cropright "1";cropbottom "0";filename
'figures/thecup.jpg';file-properties "XNPEU";}}The America's Cup was built
in 1848 and is the worlds oldest sporting trophy. The Cup was originally
refered to as the 100 Guinea Cup and was presented to the Royal Yacht
Squadron as a prize for the club's annual regatta. In 1951 the Squadron put
up the Cup for a contest between the 101-foot New York Yacht Club schooner
America and a fleet of Royal Yacht Squadron vessels in a race clockwise
around the Isle of Wight. America was formidable opponent for the brittish.
The schooner was was by designed by a George Steers, a leading marine
designer, with the objective to create a "yacht that would be the fastest
afloat". Whether or not this objective was met, America was certainly fast
enough to lead the fifteen British yachts around the Isle of Wight to claim
the 100 Guinea Cup for the United States.America's victory had more
significance\ than the prestige of winning the world's first international
regatta, it illustrated the emergence of the United States of America as a
technological power. Ever since the America's Cup has been as much about
technology as it has been about sailing. \FRAME{fhFU}{3.2287in}{2.582in}{0pt%
}{\Qcb{The schooner America, the winner of the first race for the Americas
Cup (then known as the 100 Guinea Cup).}}{}{america.jpg}{\special{language
"Scientific Word";type "GRAPHIC";maintain-aspect-ratio TRUE;display
"USEDEF";valid_file "F";width 3.2287in;height 2.582in;depth
0pt;original-width 4in;original-height 3.1913in;cropleft "0";croptop
"1";cropright "1";cropbottom "0";filename
'figures/america.jpg';file-properties "XNPEU";}}

Back in New York the 100 Guinea Cup was narrowly saved from being melting
down into medals and instead was donated to the New York Yacht Club and
subsequently was renamed after the famous schooner as the Americas Cup. The
donation of the Cup came with a list of racing conditions detailed under
"the deed of gift" which is still the seminary document that governs the
Americas Cup. The deed was designed to set up the Americas Cup "as a
perpetual Challenge Cup for friendly competition between foreign countries". 

Between 1870 and 1983 the New York Yacht Club had the longest wining streak
in sailing history, successfully defending the cup 24 times before it first
left American shores after victory by the Austrailian Challenge in 1983.
Dennis Conner won back the Cup for the U.S.A. in 1987, and it stayed in San
Diego untill it was won by Team New Zealand in 1995. In the year 2000 Team
New Zealand became the first team to successfully defend the Americas Cup
outside the USA.

\subsection{The Americas Cup Rule}

The International Americas Cup Class (IACC) was developed in 1989 by a group
of the world's top yacht designers and sailing administrators. 

\subsection{The Americas Cup Course}

\section{Upwind Sailing}

\section{Downwind sailing}

In a downwind leg of an Americas Cup match race the objective is a mark 3
nautical miles directly downwind of the top mark. If a course directly
downwind is taken then the velocity of the yacht is limited to being less
than the true wind speed, since the apparent wind speed reduces as the boat
speed in increased. For IACC\ yachts it is advantageous to sail a "zigzag"
course downwind to enable the yachts to potentially sail faster than the
wind by generating lift from the sails.

\subsection{Flow structure for two dimensional downwind sail sections}

A schematic of the flow structure of the flow past a two dimensional
downwind sail near maximum lift is illustrated in Figure \ref{sailflow}. For
a typical sail design maximum lift occurs at approximately 20$%
%TCIMACRO{\U{b0}}%
%BeginExpansion
{{}^\circ}%
%EndExpansion
$. The forward stagnation point rests on the pressure (windward) side of the
sail just back from the leading edge (luff). If the flow stagnates on the
leading edge or on the leeward surface of the sail then the luff of the sail
will collapse (for non-rigid sails) due to the pressure difference across
the sail. Real sails are trimmed so that the sail is only just supported at
the luff with the flow stagnating on the pressure (weather) side of the
sail, as close as possible to the leading edge. A leading edge bubble is
created on the leeward surface of the sail as the flow separates as it
rounds the sail's sharp leading edge. Near the leading edge the separated
shear layer rapidly undergoes transition and begins to curve back towards
the surface of the sail due to the growth of the shear layer and suction
near the leading edge. The shear layer reattaches between 0.05-0.1$x/c$ and
downstream of reattachment a turbulent boundary layer forms. Further
downstream a adverse pressure gradient forms and forces the boundary layer
to separate, this generally occurs in close proximity to the position of
maximum draft.\FRAME{ftbpFU}{4.6778in}{1.9501in}{0pt}{\Qcb{A two-dimenaional
downwind sail flow.}}{\Qlb{sailflow}}{sail_flow.jpg}{\special{language
"Scientific Word";type "GRAPHIC";maintain-aspect-ratio TRUE;display
"USEDEF";valid_file "F";width 4.6778in;height 1.9501in;depth
0pt;original-width 20.8333in;original-height 16.8232in;cropleft "0";croptop
"1";cropright "1";cropbottom "0";filename
'figures/sail_flow.jpg';file-properties "XNPEU";}}

The separted region that extends over the aft half of the sail is unsteady
and periodic with counter rotating vortices being shed alternately from the
windward and leeward surfaces of the sail. This unsteady process has a
dramatic effect on the loading of the sail with the forces oscillating in a
semi-sinusoidal fashion. Since the sail's circulation is changing the degree
of incidence to the leading edge also oscillates, hense the positions of
stagnation, reattachment and separation points must also osillate in a
semi-sinusiodal manner.

\subsection{Flow structure for three dimensional downwind sails}

Real sail flows are intrinsically three-dimensional. Through smoke
visualisation streams have been observed to pass a gennaker to weather
approximately a third of the height up the luff, then drop dramatically and
exit approximately midway along the foot. To leeward the opposite occurs;
smoke streams passing the luff near the foot leave the sail well up the
leech. Even near mid height there is considerable cross flow. A schematic of
the flow past a gennaker is provided in Figure \ref{3D_Sailflow}
illustrating cross flow on the sail surface and the development of tip
vortices around the head and foot.\FRAME{ftbpFU}{4.4105in}{2.3013in}{0pt}{%
\Qcb{Schematic of the flow past a gennaker, ------ Leeward streamlines, - -
- Windward streamlines.}}{\Qlb{3D_Sailflow}}{3d_sailflow.jpg}{\special%
{language "Scientific Word";type "GRAPHIC";maintain-aspect-ratio
TRUE;display "USEDEF";valid_file "F";width 4.4105in;height 2.3013in;depth
0pt;original-width 20.8333in;original-height 11.3645in;cropleft
"-0.024331";croptop "1";cropright "1.027669";cropbottom "0";filename
'figures/3D_Sailflow.jpg';file-properties "XNPEU";}}

The three-dimensionality of downwind sail flows has a large influence on
performance. Downwash due to the tip vorticies is considerable and the
sectional pressure distributions for a real sail have different
characteristics than two-dimensional sails. \ \ \ typically real sails are
trimmed approximately 10$%
%TCIMACRO{\U{b0}}%
%BeginExpansion
{{}^\circ}%
%EndExpansion
$ higher than

\bigskip

\bigskip

Despite the fact that real sail flows are strongly three-dimensional,
two-dimensional sail flow solutions are still valuable. They provide a
useful tool for a designer to explore the influence of design parameters
such as camber and draft position. This type of analysis is valuable both as
a tool to provide force output and performance analysis but also to
visualise the consequences of design changes.

Two-dimensional simulations are also valuable for validation of
three-dimensional simulations. From a turbulence modelling perspective the
two-dimensional simulations present many of the same difficulties as the
three-dimensional problem: leading edge separation, reattachment, boundary
layer recovery, separation and the formation of an unsteady wake. The only
additional complexity in the three-dimensional case is the development of
tip vortices that involve large streamline curvature. However for validation
of the ability of turbulence models to predict separation and the resulting
unsteady wake, two-dimensional sail flows provide a good test case.

\bigskip 
\bibliographystyle{PHREPORT}
\bibliography{PLATE}

\bigskip

\end{document}
