Figure. 5 - Schematic of reference angles for yacht 5.3 NAVIGATOR
This represents the core of the control system and, as in real-life sailing, issues decisions that
Secondly, it detects when the weather affect both the
steering and sail trimming. Firstly, it checks the yacht position at each time-step of the simulation, detecting as an example when a layline is hit or a mark has to be rounded.
conditions change and can issue strategic decisions
accordingly (e.g. to tack on a windshift). The navigator sub-system also deals with manoeuvres: for instance, it issues the decision of tacking and detects when the boat has recovered from a tack (attainment of surge speed target value) and the next one can take place. In spite of the basic set of strategic rules implemented so far, broad spaces for simulating human behaviour are present. One example is provided below:
Windshifts: when sailing in shifty wind conditions on upwind or dead-downwind legs, considerable advantage can be obtained by sailing on the ‘lifted’ tack (i.e. the one that yields the higher boat speed towards the mark). The decision of tacking when a boat is hit by a windshift is not
trivial: the shift should be sufficiently large and
stable to be worth the time loss of a tack. 6.
UPWIND SAILING AND GAMBLING: A CASE STUDY
A common decision making problem arising while sailing upwind is considered in the present section. A yacht is supposed to be headed by a 10° windshift, which generates a strategic dilemma: tacking immediately, delaying the tack or waiting for further changes in the true wind direction. The situation described above is investigated in terms of a decision making problem with three alternatives (actions taken by the crew) and four outcomes (possible
developments in the weather
scenario). Purpose of the study is to quantify gains and losses following given strategic choices. Furthermore, possible decision-making strategies are suggested, in order to choose among alternatives in a context characterized by uncertainty.
6.1 GENERALITIES
A yacht is supposed to sail on port tack, in a Northerly breeze, in equilibrium conditions and towards the upwind mark. At time t0 = 200s, the True Wind direction is supposed to shift towards East by 10° (+10° header). The alternatives available are then three (m=3 in Tab.1): tacking immediately onto starboard, delaying the tack by 60 seconds or not to tack until further windshifts occur. The navigation stops at tend = 800s.
Four possible weather scenarios or ‘outcomes’ are set (n=4 in Tab.1):
B-16 ©2008: Royal Institution of Naval Architects
True Wind Speed and True Wind Angle constant from t0 = 200s onwards; True Wind shifts further right (additional +10° header) at t1 = 320s; True Wind shifts back North (-10° lift) at t1 =320s; True Wind shifts back North (-10° lift), at t1 =320s, then further left by extra -10° at t2 =440s;
Choices’ payoffs Ci,j are calculated according to Eqn.6 below, where DMGi,j is the distance sailed towards the mark (equal to zero if the yacht sailed at right angles to the mark itself) when considering the i-th strategical alternative and j-th weather scenario. DMG* is the reference distance sailed in 10 minutes at the initial surge speed u0 = u(t=0). This yields payoffs within the range [0;1], where higher payoffs correspond to higher levels of ‘utility’.
Cij ,
DMG
(100 *
DMG DMGij *
, )*100 (6)
After t0, when the decision is made, the yacht is always sailed according to a unique set of strategic principles: as an example, the navigator would always call for a tack on 10° headers or more. This propagates
to the whole
navigation the positive/negative effect of the decision made at t0.
6.2 DECISION TABLES
In order to investigate the sensitivity to simulation parameters, two factors are considered: awaref and tws. Each of them is varied at two levels, yielding four factor combinations: these are due to a 2 (awaref, 25° and 30°) by 2 (tws, 4m/s and 6m/s) factorial.
Payoffs are
calculated according to Eqn.6, where DMGs were estimated by means of the sailing simulator described in the previous Sections. The case awaref = 25° and tws = 4m/s is summarized in Tab.3 below; readers are referred to Appendix A for the whole set of payoff matrices.
Table 3 - payoff matrix for awaref = 25° and tws = 4m/s S1
S2 A1 - tack
A2 - don’t tack
A3 - delay tack by 60 secs
62.4 7
34,6 9
59,8 8
72,9 4
66,6 7
69,7 1
S3
51,7 7
47,2 9
48,4 3
S4
58,7 7
55,8 0
55,4 5
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