Out on a limb
After examining foils in issue 485 Dave Hollom moves on to AC75 rigs. And (bravely) offers some hints of hull performance
Now that we have the righting moment and the side force that the rig must pro- duce for everything to remain in equilib- rium we can look at how this affects the rig. The area (jib and main) is about 230m2 and the rig height is about 26m so the geo- metric aspect ratio is about 3.0. However, as pointed out by Andy Claughton in a previous Seahorse article, the effective aspect ratio on these boats can be consider- ably different from the geometric aspect ratio. There are several conflicting factors, some tending to increase effective aspect ratio, some tending to reduce it. In theory minimum induced drag, for a
given span, is provided by a wing or rig planform that produces an elliptical span- wise lift distribution. In a uniform flow
56 SEAHORSE
an elliptical spanwise area distribution achieves this aim though there are other area distributions that achieve that ellip - tical loading by using wash in or wash out along the span. However, the flow in which our sails
work is anything but uniform. Due to shear, wind speed varies at different heights up the rig. Also, due to the forward motion of the boat the apparent wind angle also varies with height and then the water surface also interferes. The expression describing induced drag in coefficient form is: Cdi = Cl2/Pi*AR*k
where: Pi = 3.142, AR = aspect ratio (span2
/area) and k = efficiency factor. Aerodynamicists use the efficiency factor
k to allow for non-elliptical spanwise lift distributions and other factors that affect induced drag. An efficiency factor of one indicates an elliptical lift distribution in a uniform flow. A non-elliptical lift distribu- tion will have a k factor of less than one which will raise induced drag; factors like the surface of the sea which will increase effective AR and reduce induced drag will attract a k number greater than one. For example, if our sails went right
down to the surface of the sea we would have a perfect reflection plane and the k factor would be two, provided the rest of the sail produced a spanwise lift distribu- tion that minimised induced drag which, on sailboat rigs, because of the non- uniform flow, may or may not be elliptical.
To find out in which part of the horse-
shoe drag curve our sails are working and thus to see where best to reduce aerody- namic drag it is necessary to work out a drag curve for the rig. To do this we must calculate both the induced drag and the profile drag and, of course, any parasitic drag such as caused by the hull, rigging and the crew. Because the double-luff sails used by these AC75s are very efficient and produce an airfoil section enclosing the mast, the profile drag of the sails can be fairly easily worked out from various air- foil analysis programs. The viscous drag of the hull, rigging and crew is a bit more of a guess; finally, to work out the induced drag we need to determine how efficient our rig is and thus determine that k factor. Besides the proximity of the rig to the
water surface there is the probably less than perfect spanwise lift distribution. Proximity to the water surface will increase the effi- ciency number and the less than perfect lift distribution will reduce it. For conventional waterborne craft I find that a k factor of 1.2 works well in practice but waterborne craft don’t have a gap between hull and water surface as on the latest Cup class but, on the other hand, to operate the boat they require some gap between boom and deck which reduces endplate. For these ‘back of the envelope’ calculations we won’t be far out with the same k factor of 1.2. Using the methodology opposite we can calculate that the apparent windspeed at
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