Sometimes an incident occurs at sea which proves in a trice the value of practical experience over theory. Such an occasion came for the 1930s German Navy when their Schnellboot, later to be dubbed the 'E-Boat' by the Allies, was undergoing its sea trials. A prototype, S2, was being driven flat out at over 30 knots when the order was given to put the helm hard over. Possibly too eager to please, the helmsman slammed it over instantly as far and as fast as it would go. Not only did the boat continue on course without any deviation, it also picked up speed. I'll leave you to consider the puzzle before returning to it later, in the hope that this cheap trick will make you read on.

As I read Roy Downes's comments on the rôle of foils when manoeuvring performance dinghies in rough weather (B186, page 25), I was reminded that good foil design is also beneficial on boats which are not, by any criteria, 'high-performance'. When I was a lad, my friends and I would opine sagely that motor-racing was A Good Thing for the Average Driver because the latest developments in racing cars would always feed down into production models for the road. Whatever the truth of that idealistic adolescent whimsy, it came back to me as I read Roy's piece. Sophisticated foil design pioneered on racing craft does have relevance for those of us who like simply to potter about in more modest boats, as poorly-shaped foils can stall at low angles in a variety of sea conditions and boat speeds – especially slow speeds.

No doubt these brief notes on foils will be superfluous for veteran DCA members, well-versed in fluid phenomena and Daniel Bernoulli's Theorem as they are, as they drop off to sleep each night dreaming happily of Reynolds numbers by the million; but just in case there are one or two less grizzled faces out there that went blank when Roy referred to a 'NACA 0010 section for maximum coefficient of lift' – here goes.

The initials NACA stand for the National Advisory Committee for Aeronautics, a committee which investigated and tested a great number of diverse foil shapes and sections and recorded the results. It was superseded eventually by NASA. It is clearly sensible for designers to make use of catalogued data such as theirs rather than start experimenting from scratch themselves. The second mysterious aspect of the descriptor is 0010. If you were asked to explain quickly how an aircraft's wing generates lift, you would probably produce a crude drawing showing a wing section where the bottom plane is flat, and the upper plane is humped about a third of the distance across, and you would show how the air flows faster over the hump (the camber). The aircraft wing section is obviously asymmetrical, then, and needs to be. A dinghy's foils are submerged wings working vertically. You will never need a rudder or centreboard always to have lift to port and not to starboard, or vice versa, so boat foils have symmetrical sections on 'normal' craft. The first two digits of the group of four, then, refer to the degree of asymmetry. With dinghy foils these digits will always be 00, indicating an absolutely symmetrical section, unless the designer has stepped outside normal practice and used something like leeboards, which might benefit from being asymmetrical mirror images of each other – as long as they are not down together.

Another possible cause for consternation is the use of the term 'chord'. The chord is simply the full width of the rudder or centreboard, as opposed to its length or its thickness. The last two digits tell you how thick the foil is at its widest point in relation to this width, because they are a percentage of it. The actual dimensions are irrelevant: big or small, these numbers govern the shape.

Roy may have had in mind a rudder blade width (chord) of about 250mm (9⅞"). If the blade is a NACA 0010 section, it will be 25mm (approximately 1") at its thickest point, which ideally will be 28-30% back from the leading edge. Oh, all right then, a third of the way back – 33.3%. (In the present case, we really can use the old cliché with some accuracy: this is not rocket science.) If the section was 0005, the rudder thickness would be 12.5mm at its thickest – hardly worth bothering with, as the section will taper away to nothing quickly and be fairly ineffective and weak, unless it is built in some very exotic material. If it was 0015, the same width blade would be 37.5mm at its thickest point. Any larger number would result in an obviously fat foil producing a lot of drag. So you can see that there is not a great deal of scope for variation in the dinghy scale of things, but whichever aerofoil section you choose will generate far more lift and much less drag than a flat plate. The 'coefficient of lift' is a measure of how well the foil produces lift, and there is a balancing act to be done in judging the right thickness of the foil to attain lift without sacrificing too much efficiency to drag.

In a much wider fixed keel on a yacht, 0015 or so can result in a really fat foil, which is often required on a keelboat anyway, where there is a need to fill that section with lead, or depleted uranium, or whatever else can be found in the Club skip, but here the emphasis is primarily on ballast, not on laminar flow and drag.

There are many other possible shapes. A lot of radical variations are used on high-performance craft, but this basic streamlined section under discussion – with maximum thickness 30% aft of the leading edge and no concavities or discontinuities anywhere – is seen as a conservative, efficient shape that does resist the tendency to stall and produces predictable drag characteristics which do not vary erratically. Roy's 0010 section will manage an angle of attack of about 13º without stalling. Within reason, the thicker the foil, the more it resists stalling. 0015, our example of a 'fat foil', will probably not stall at 17º, sea conditions and ventilation permitting: disturbed water has a way of laughing to scorn predicted performance.

A stalled rudder does not instantly stop steering the craft; it simply loses efficiency dramatically. We have all seen huge passenger aircraft virtually standing on their tails during take-off. Their wings are presenting such steep angles of attack at these moments that they are not working as efficient foils, but that does not prevent them generating a large amount of lift. And a good thing, too.

Which brings us back to young Hans at the helm. We left him wondering why the boat would not respond, and how soon he could expect to be given a rifle and sent to the Eastern Front. History does not record whether there were any craft dead ahead of his S-Boot when it refused to answer the helm; presumably not, as they obviously survived to tell the tale. The explanation of the boat's behaviour is simple, but not immediately obvious. As we all know, there comes a point as you slam a rudder over when it refuses to behave as a foil at all, stalled or not. It simply blocks the water it is moving through. The S-Boot's rudder went over so far and so fast that it instantly became a baffle across the water flow. However, even in that attitude it produced lift. Upwards. And so the designers learned that the hull lines as drawn were allowing the stern to squat when fully powered, to the extent that performance was being affected. As we all know, squatting sterns impede efficiency. (Now there's a text that should be nailed to the wall above every easy chair in the house.) Far from getting it in the neck, Hans was probably mentioned in despatches. All-in-all, he had an exciting day.

If you spotted this explanation, shower yourself with praise, because in reality the Reichsmarine did not immediately get the full message. They began their modifications by adding two small auxiliary rudders adjacent to the propellers which were then turned outwards by 10-15 degrees at high speeds, with the same mystifying increase in performance. Later, they found the much simpler solution. When I had the opportunity to inspect an E-boat's hull at close quarters, I was delighted to see the two wedges fixed on the trailing edge of the stern, to port and starboard of the propellers, which showed the final outcome of that story, as they were fitted to deflect the flow downwards and so raise the stern, decrease drag, and increase speed. Using wedges, or hydraulically-controlled transom flaps, for this purpose is now commonplace, and they are frequently fitted to counter the weight of a big outboard on the transoms of fast ski-ing and fishing boats.

There are problems to overcome when making aerofoil sections for dinghy rudders and centreboards. Proprietary aerofoiled rudders and plates are obviously machined to exact tolerances, and mostly out of exotic materials, starting with marine-grade aluminium alloy. Once you assemble your home-made rudder blank out of reversed wood strips epoxied together, you're in for some fun planing it down to the right section without lumps, bumps or hollows down the full length. If the section is to be 0010 or more, it might not be acceptable to have it extending right up inside the rudder stock, as the blade would not be held very securely by the internal flat faces of the cheeks, as well as its being completely unnecessary because it is out of the water at this point. On the other hand, if you carve the section exactly up to the bottom edge of the rudder stock, then suddenly allow it to swell out inside it, you will create a line of weakness in the blade at that point across which you may as well draw a dotted line with 'tear here' written on it. A bit of forward planning and some skilful (and enjoyable) wood-carving are needed, then. And probably some templates or profiles made in advance to ensure a consistent shape along the foil length.

Fluids hate sharpness on foil sections anywhere where there is an angle of attack – and there always is, with boat foils, unless possibly sailing dead downwind in still water – and so attention must also be focused on the trailing edge. Strangely enough, it is beneficial to square off the section to produce a flat, not a sharp, trailing edge. (Even more surprisingly, this flat can be as much as 10% of the foil thickness, and can improve lift by 10% also, with practically no increase in drag.)

There is less scope for using the fatter sections in centreboards, and probably less need, as the angles of attack are shallower. A 'fat foil' centreboard would need a wide slot (over 60mm for a 400mm wide board with a 0015 section, say) most of which will be wide open when the board is lowered – too wide to be covered satisfactorily with such as mylar gasfit gaskets secured to the slot edges. The resulting turbulence at the slot would probably reduce any lift advantage gained, and you would certainly need to provide your oarspersons with oilskin shorts if they were seated over the slot when rowing in choppy water, with or without the plate down. A thinner section is preferable here, then, or even just a shaped parabolic entry up to 30% back on a relatively flat board, plus something of a tapered trailing edge, because it has been shown that the first third of the section is most instrumental in generating lift in foils at a shallow angle of attack with attached flow (such as centreboards), so you will lose less lift than you think – drag is another matter. One advantage of a daggerboard over a pivoting centreboard is that you can shape it as thickly as you like with impunity, because it fits its slot snugly – one thinks of the Laser's board, for instance. But that, and space freed up inside the boat, are the only advantages of the daggerboard.

Some sailing websites discount anything but flat plates for centreboards, in the mistaken belief that only rudder blades are used in varying angles of attack, whereas centreboards are mainly held in one plane fore and aft as they move smoothly through the water. (This is never the case, but even if they did, flat sheets always generate lots of drag.) The fact is that the centreboard in any boat beating to windward or sailing across the wind has an angle of attack caused by leeway, up to 7º or more, varying wildly in a seaway as it stalls intermittently. This is still a relatively low angle compared with rudders, of course, so even a modestly-shaped section should bring benefit. Another website fallacy I've noticed is the recommendation that the 'nose' or leading edge of the foil should always be circular in section: check the drawing here to see immediately that such a leading edge will always produce turbulence through discontinuity of flow. The shape should be ovaloid, not circular – parabolic, to be precise. So there you have it: whether you have a fat foil or not, it should at least have a parabolic nose.

(Should you wish to experiment with foils for your boat, the method of plotting the NACA aerofoil sections will be given in B188. One person's views on a technical subject are always likely to be greeted with suspicion, if not dubiety, unless the writer is an acknowledged expert in the field. As this article was written by someone who did not pass his 'O' Level in mathematics on the first attempt, it was accordingly submitted to Dave Jennings & Mukti Mitchell to be checked before publication! KM)