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planform but in aircraft the resulting tip chord is so small that, for various reasons, that we cannot, due to space considera- tions, go into here – the tip would be very prone to stalling. Thus in aircraft the plan- form is more or less triangular but with the small tip cut off and these days, more often than not, replaced with a winglet. The bird can cope with this tendency to tip stall as it can readily adjust the angle of attack of its tip feathers to prevent this happening. But we digress. The beauty of an ellip - tical planform is that it produces the same Cl at all spanwise locations; ie the angle of attack is the same all along the wing and all parts of the wing contribute equally, in proportion to the local chord, to the required lift so that a smaller-area wing will do the same work as a larger wing where the Cl varies along its span. Any deviation from an elliptical planform will produce this uneven lift along the span. Building in washout or wash-in (twist) on such a wing can even this out but only at one Cl. At all other Cls it will be wrong. This is great for an aircraft designed to work well at a particular design point but our foil needs to be efficient over a wide range of conditions – the elliptical wing achieves this with the minimum of area. Straight tapered wings are popular in aircraft because they are easier to con- struct, but the use of CNC machines to produce accurate tooling makes this a non- issue for our purposes. It takes just as long to machine a mould for an elliptical wing as for a straight tapered wing.


The classic elliptical wing, as on the Spitfire or P47 Thunderbolt, was built around the quarter chord line. The reason- ing, I guess, was that lift is considered to work through the quarter chord line and having this line straight and building the ellipse around it must have seemed to make sense and gave you that classical Spitfire wing shape.


However, more recent research suggests that induced drag can be further reduced to below that of a classic ellipse, by shear- ing the wing such that the tip is moved rearwards. Van Dam noted that birds that travel large distances where speed is of some essence, and fast swimming fish, both had sheared wings or fins; noting also that nature is rarely wrong, he conducted some experiments to examine why. Essentially he designed four wings, one having a straight leading edge around which the ellipse was built, one having a straight quarter chord line as in the classical wing, one having the elliptical shape built around a straight trailing edge and, finally, one built around an aft curved trailing edge where the tip was half a root chord behind where a straight trailing edge would have been, much like a swallow’s wing. Surprise surprise, nature was right and it appeared that the further aft you moved the tip the lower the induced drag. Unfortunately, we are constrained in other ways and in a flapped foil we obviously have to have a straight flap line


54 SEAHORSE


Above: Glen Truswell and Sam Pascoe won back-to back Int14 world titles and two European titles in 2014-16 on their Hollom Departure – the same design went unbeaten in the Int14 POW Cup from 2014 to 2018 and over two years never lost a major regatta


to allow articulation; plus if you have gone to the trouble of designing a foil to work best when the flap hinge line is in a partic- ular chordwise position you will get the best results if that chordwise flap hinge position is maintained all along the span. This requires that the ellipse is con- structed around this flap hinge line which results in the tip being a lot further aft than on a classical ellipse but not as far aft as one would like. But that is a necessary compromise. Also, you must have some finite thickness on this hinge line at the tip, and on a perfect ellipse built around the hinge line the hinge line at the tip has zero thickness. Most aircraft solve this problem by finishing the flap inboard of the tip. Our solution was to clip the tip slightly so that the flap runs the full span but has adequate thickness at the tip.


We aimed to improve the flow around the hinge by having a flexible Kevlar hinge on the top surface and a radiused lower leading edge to the flap so that, in theory, through the range of flap movement, there was no gap on the bottom surface. Also, the large triangular gap in the vertical foil necessary to allow the upward movement of the flap appeared to be very draggy, so we designed a fairing that is attached to the flap and runs up inside the vertical fin and thus closes this gap. The horizontal rudder foil, which would be the tailplane on an aircraft and which serves a similar purpose on a Moth, uses a slightly de-cambered version of the section we use for the lift foil on our Int14 (it is producing less lift than on a 14 so needs less camber and will, on occasion, be asked to produce negative lift or downforce, so it’s useful to have the low-drag bucket dip below the zero lift line the reduced camber achieves). Again the planform is elliptical and, as there is no flap, none of the com- promises that had to be adopted for the main foil are necessary and the ellipse is built around a straight trailing edge.


A small amount of anhedral has been adopted for the tailplane as it allows the craft to fly higher before the tips break the surface. Flying higher, of course, by reduc- ing the immersed area, reduces the drag of the vertical foils. It does, however, come with some downside as the anhedral intro- duces some unwanted steering input. The handling of the junction between the vertical and horizontal foils is impor- tant. At any junction you get interference or junction drag. It is caused by the flow around one object interfering with the flow around another. Where two flows join, the combined velocity of both flows is greater than the velocity of the individual flows and so frictional drag rises. But also, because local velocity is higher, pressure is lower and because pressure is lower the pressure gradient that the flow must over- come to get back to free stream pressure at the trailing edge is steeper – thus any sepa- ration is greater so pressure drag rises. A number of factors influence junction drag. The larger the included angle between the two objects the less each of the flows will interfere with each other and the lower the drag will be. In this respect the anhedral on the tailplane helps. Junction length affects junction drag. The longer the junction the greater will be the area that this accelerated flow will be working on and the higher will be the drag. Pragmatically, we can say that junction drag will vary linearly with junction length, so one might think short junctions reduce interference drag. However, thickness chord ratio (T/C) also affects this drag. The thinner the foils the smaller the rise in velocity so that frictional drag is less and, because of the lower velocities, the adverse pressure gradient that the flow must navi- gate to get to the trailing edge is less steep so pressure drag reduces. (Because viscous drag is V2


increase varies approximately linearly with T/C ratio, junction drag varies as T/C2


dependent and the velocity .)


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