Left: the AC40 one design foils are direct descendants of those seen on Team New Zealand’s Cup-winning AC75 in Auckland, but with longer more conservative foils reflecting the more ‘flexible’ use of these 40-footers as well as the relative lack of foiling experience of some of the crews. Above: Team NZ continue to develop the theme of ‘smaller foils-sail better’ with the odd left-field diversion to check in (right)
thickness halves its strength. As the strength of a solid foil varies as the square of its thickness the foil would have to be thicker by the square root of its required extra strength so that would be 20.5 = 1.4142 times its original thickness; so if the original T/C was 10% it would become (0.1/0.5)*1.4142=0.28284 or 28.284% T/C ratio. Which is a huge increase. However, even a relatively modest
reduction of 25% in chord results in an increase of T/C from 10% to 15.396% to maintain the strength of the foil. Thus reducing the span has the advan-
tage of reducing profile drag at a greater rate than reducing the chord. However, because the span will have reduced, induced drag will have increased which will compromise the boat’s ability to get aloft. On the other hand, reducing the chord, even though the reduction of profile drag is not as great, has the advantage that induced drag does not increase so take-off will not be overly compromised. To digress for a moment, there is a
popular misconception that if you reduce the chord of a wing while keeping the span constant, because the aspect ratio has increased, induced drag will be reduced. This is actually not true and induced drag will remain unaltered. Induced drag is determined by the span,
lift and velocity, and not by aspect ratio. Induced drag does vary directly with aspect ratio but only if the wing area remains the same. Aspect ratio is a useful tool for doing various aerodynamic calculations but it is span that ultimately determines induced drag provided the lift, velocity and wing planform remain the same. As a matter of interest some professors
of aerodynamics use this as a trick question to a new class. They will ask students what would happen to induced drag if an air- craft wing was halved in chord while maintaining the span, thus doubling the aspect ratio, and the weight of the aircraft and its speed remained the same? Usually about 80 per cent of the class get it wrong saying that induced drag is halved. It will
50 SEAHORSE
of course remain constant. This reduction in span has been the way forward to faster speeds in the Moth class, but things are a little different in the AC75 class. Firstly, in the Moth class there is no
span limit other than the overall beam limit, which is way greater than what appear to be optimum spans. Secondly, again in the Moth class, crew weights vary wildly and, while a light crew may get foil borne more easily, heavy crew weight is king once you are up and flying. Thirdly, race committees will usually not
start until a large proportion of the com- petitors are up on the foils. Because the really good guys can get on the foils sooner they can go out on small-span foils with the confidence that, by the time a sufficient number of boats crewed by mere mortals with long-span foils are foil borne, they will be foil borne too on their smaller foils. And from then on the advantage is all theirs. However, Moth racing is fleet racing and
the America’s Cup is match racing and therein lies one big difference. Also, you can change the foils on a Moth, sometimes even between races, whereas you have to race the whole series with the same or very similar foils in the America’s Cup with very little variation in foil shape allowed. So, whereas in the Moth you can have very specialist foils, optimised for a particular condition and which you can sometimes change at the drop of a hat, time allowing, and thus without too much of a performance risk, in the America’s Cup you are very much more restricted; the foils you build must cover a wide range of conditions. As one of those conditions is to be able
to take off at the same or lower windspeed than the competition, and because, as already mentioned, getting foil borne is very much a factor of span, you are less likely to sacrifice span; thus to reduce foil area in an attempt to improve high-speed performance you are really restricted to reducing the chord with all the structural problems already discussed, which require (fatter) foils of greater T/C ratio. Earlier I mentioned that thick foils also
have other ramifications besides increasing foil profile drag. A condition of high-speed sailing on foils, sometimes encountered at the upper end of the speed envelope, is cavitation. Cavitation is caused when the pressure becomes so low that the water boils. According to Bernoulli increases in the speed of flow lower the fluid pressure while reductions in the speed of flow increase the fluid pressure. As the flow has to accelerate to a higher velocity to pass a thick foil than it does to pass a thin foil, the thicker the foil the greater the local velocity around it, the lower the pressure and the more prone it will be to cavitation. Thus the designer, wanting to retain maxi- mum span for a low take-off speed, but also wanting to reduce the area of his foil to reduce profile drag at sub-cavitation speeds, has a problem. As discussed, to maintain strength he
has to use a fatter section and that fatter section, because it speeds the flow up to a greater extent than a thinner foil, lowers the boat speed at which cavitation will occur. However, there is a solution that reduces the problem… In previous articles I have stated that
minimum induced drag for a given span occurs with an elliptical spanwise lift distribution which, in the absence of any wing twist, is achieved by having a span- wise elliptical area distribution. This is only true, of course, if span is the control- ling factor. As, on the other hand, we are trying to reduce the wing-bending moment to reduce the wing thickness, the bending moment becomes the driving factor, which requires an altogether different planform. A triangular planform with a pointed
tip gives minimum induced drag for a given wing-bending moment… if span is unlimited. Put another way, a triangular wing planform with a pointed tip gives minimum wing-bending moment for a given span, but induced drag will be higher than an elliptical planform of the same span; but that elliptical planform will have a higher wing-bending moment and will thus have to be thicker!
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