The prudence of determining the best windward and running courses for sailing yachts can be seen from Fig. 1 in which the heart shaped curve represents a polar diagram of yacht performance with respect to the true wind direction. It is a diagram of yacht velocity V and the angle α between the yacht's track and the true wind direction. The gap in the curve dead to windward is an area over which no performance is possible, whereas any destination lying outside this zone can be reached directly; there is only one sailing angle at which a destination lying between X and Y can be reached the quickest. A similar situation occurs on the running point of sailing where the curve may have an inflexion, i.e. there is profit in tacking a course downwind.