could be to express sail lift and drag as a function of sail incidence angle () instead of apparent wind angle (awa): as a full set of data is not available on this, an estimate had to be made for sail coefficients between =, or dead downwind trim, and =2, when apparent wind hits the sail leech first, then flows towards the luff. This approximation, which is deemed reasonable for the purposes of the present paper, is shown in Figs. 1 and 2. Figure. 2 - Drag coefficient CD as a function of incidence angle ()
3.2 SIMULATIONS AND VISUALIZATION OF RESULTS
While a simulation is running, a stepwise solution of the four simultaneous equations of motion has to be calculated; a standard fourth order Runge-Kutta solver is used for this purpose. The CPU time required to simulate a one-mile upwind leg in an arbitrary true wind pattern is approximately 60 seconds on a conventional PC.
At every time-step, the time-histories of state variables (velocities, accelerations, leeway, yacht heading, apparent wind speed and angle), hydrodynamic and aerodynamic forces, rudder angle and sail trim parameters are recorded. This set of data can be supplied to the visualization routine, programmed within Simulink and using the features of MATLAB Virtual Reality Toolbox in order to generate ‘offline’ animations. Within this context, the use of
Virtual Reality Modelling
Language (VRML) allowed both the modelling and animation of the yacht motion within a 3D world. From a physical standpoint, this allows the yacht accelerations and
heel, rudder movements, and sail trim to be
visualized and compared with actual (recorded) values. In addition, positives and negative aspects of the race strategy implemented by the automatic crew can be highlighted as the simulation proceeds on. With this purpose, a one-design
fleet implementing different
strategies can sail the same course simultaneously (as in Fig. 3): in this case no mutual interactions occur, so that races can only be won thanks to better technical skills (i.e. driving style, sail trim) and a successful race strategy.
4.
HUMAN FACTOR ISSUES IN SALING 4.1 SOURCES OF UNCERTAINTY
As in most outdoor sports, sailing is a discipline rich in uncertainty
due to ever-changing environmental
conditions. One of the keys to winning races is indeed the ability to predict and to ‘play’ effectively all weather changes, namely speed and direction of wind and tide.
An extensive analysis on predicting the outcome of match races under weather uncertainty is due to Philpott and Mason [9]: speed and direction of true wind are considered as independent stochastic variables, whose values vary over time and over the racecourse. Changes in wind conditions are supposed
to propagate
downstream according to Taylor’s hypothesis of wind engineering: wind eddies travel down the flow field at a given mean wind speed. The model is based on wind measurements on Hauraki Gulf, New Zealand and can model large shifts in wind direction occurring at random intervals.
Other than weather conditions, many more non-
deterministic factors affect the outcome of sail races: insight on opponents behaviour, sailors’ self-confidence and personal attitude towards risk (risk-averse or risk- taking), knowledge of racing rules being just a few examples. These factors influence both racing strategy and tactics which, in turns, affect the way a yacht is sailed. Other than technical skills, a wide range of additional abilities are therefore required to win races: assess risks connected to decisions, estimate gain/loss probabilities, predict changes to present race scenario, and react to unforeseen events. Personal experience, training and recalling similar situations from the past are therefore key skills to winning races.
4.2 SAILORS AS DECISION MAKERS
The factors highlighted above and the role they play in winning or losing races are difficult to quantify and subsequently model within the framework of an ‘automatic’ yacht crew. However, it is felt that modelling them in general terms can still provide insight to the following questions:
What drives novices and expert athletes’ decisions? How do athletes assess the risk of their decisions? What gains/losses follow sailors’ choices? To what extent can athletes predict changes to racing conditions?
Can good technical skills (boat speed) compensate poor decisions and vice-versa?
Behavioural sciences are underpinning many disciplines such as football, cricket
and Figure.3 - A screenshot of the animation racquet sports and
interesting conclusions can be drawn. Regrettably, only a few behavioural investigations on competitive sailing contexts are available.
©2008: Royal Institution of Naval Architects B-13
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