Please take note that the first several paragraphs are a preamble noting a change of approach, and a caution about the misuse of standard aerodynamic data. We get into the prime subject further on at the spot marked Part II. But most of the preamble should not be missed.

I am beginning to realize that calling this series Aspect Ratio was somewhat misdirected. Aspect Ratio kicked it off, and we will come to grips with it fully, because it is very important. But to under stand it properly needs more background. Aspect ratio only has meaning within the framework of aero-hydrodynamics. With that framework in mind, you will know in your gut, as well as your head, what is going on around a boat as she sails. This must enable you to do better as designer, builder, or sailor.

So, without changing the name of the series or its identification, let's acknowledge that this is really a mini-discussion of the aero-hydrodynamics of sailing. Don't let that frighten you. It is indeed a very complex subject, vastly more so that the flight of an airplane. Yet we can simplify it and approach it in intuitive ways that you can relate to your own observations and experience. We'll use only enough mathematics to allow you to put numbers into your calculations if you care to make any. We'll make approximations and estimates sometimes. The ultimate refinement of this subject is beyond the range of anyone, no matter what computers or facilities they may have at their disposal.

I have a few more general conments before we get down to the meat of this session. There are vast quantities of both hearsay and published information about this subject, some of it really being misinformation from sources that should have known better.

There are dangers in trying to apply standard information, like airfoil section data, without a full understanding of what you are doing. Things don't "translate" always as you might expect. One of the faults may be that Aspect Ratio has not been taken properly into account.

Another mistake may rise from ignoring the effects of Reynolds Number (RN). This is earlier than I would normally have brought the subject up, but here we're only using it here to reinforce a caveat about careless misuse of aerodynamic data. Briefly, Reynolds Number is a function of (depends on) flow velocity, a characteristic length representing body size, and the mass density and viscosity of the fluid. (Vicosity is a measure of the force required to shear, or slip, one layer of molecules past its neighbouring layer.) Equal Reynolds Numbers are a statement that the ratios of viscous and dynamic forces are identical in different systems, so that the flows are the same shape, even though they are not of the same size. In other words, at equal RNs, one flow system is a scale model of the other, and we say that the flows are similar. We don't have to get heavily into the details just now.

Only if the flows are similar can two bodies have the same force coefficients. Everyone has probably heard of terms like Lift Coefficient and Drag Coefficient. These are dimensionless (meaning pure) numbers (not like pounds per square foot, or as an old Physics prof used to say when we didn't specify units properly in an answer, "What is this, cat tails per acre?"). These coefficients represent a characteristic form and effect of the fluid flow around bodies of some specific shape (but of different size) at that Reynolds Number. We pick them for their effect in useful directions, downstream = Drag, crossstream = Lift. We could, and maybe will, develop coefficients of Thrust and Side Force. Generically, we may simply speak of coefficients of Force. When multiplied into an expression containing fluid density, velocity (squared) and the area of the body, we get the Force in pounds (in the FPS foot-pound-second system which all the best old books used.)

Now prepare for the one-two punch of Reynold's Number. Consider two cylinders, like ship's masts, one two feet in diameter and the other only one foot. Common sense and a little science (being a dangerous thing?) might suggest that, in any given wind velocity, the large one should have twice the wind resistance of the thinner one (foot for foot of height of course.) Sometimes that's true.  But, at around fifty knots, the big one actually has lower resistance than the small one. How come? Well, if you can find a graph of the profile drag of cylinders plotted against Reynolds Number, you'll see. Their different RNs, caused by the size difference, place them on opposite sides of a sudden drop of Drag Coefficient on the plot. Physically, what this means is that there is a different flow shape around the larger cylinder in this range of velocities. As this Reynolds Number is exceeded, the air is suddenly able to turn further around the larger cylinder before it breaks loose. This means a narrower wake, and the width of the wake is a measure of the drag.

People who are just beginning, and aren't delving into such calculations yet, could well skip this paragraph. I'd hate to turn you off, because the good stuff is coming. For hard-case nuts like me, an excellent book, called Theory of Wing Sections, by Abbott and von Doenhoff, is published in reprint form at very reaonable cost by Dover Publications. My own copy is now 34 years old and about worn out. It is not a textbook. Those of you who have, or use it, or will get it, will find that it can be very heavy going for the non-mathematical reader in places. Still, it has many charts and diagrams and published data on NACA wing sections that can be interpreted with a little effort. There are areas of very clear explanation of things like high-lift devices, for example. If you get into the NACA airfoil data section, you will see that the graphs show different lines for RNs of 3, 6 and 9 million. You'll note that the higher efficiencies (in the form of higher Lift and lower Drag coefficients) pertain to the higher Reynold's Numbers.  The Reynold's Numbers of typical yachts both in air and water, are of the order of 1 to 2 million. So, to use NACA data for yachts, you'd have to extrapolate the downward performance trends of the curves from 9 to 6 to 3 to 1 million or so. If you wanted to be very precise, you'd have to calculate Reynold's Numbers for your size and speed and try to extrapolate the data to that Number.  You'll notice that there is one set of curves for smooth airfoils and a much worse set for "Standard roughness." Later in the AR-x series, I'll explain the fallacy of using so-called laminar-flow sections for keels and rudders of yachts. They can be worse performers in sailing reality than older sections.

For those interested in sailing models, I'll say that, because of the generally low RNs at which they operate, the application of standard airfoil data to them is questionable. As an example of this, I was told some years ago by a model airplane enthusiast friend about the remarkable wings of the best slow-speed flying endurance models. In section, their wings were like a check mark lying down. The long arm was the bottom of the wing. The short (straight) leg slanted back like a windshield from the leading edge and stopped. Now imagine what a dog that would be full size! Yet these models (built of skinny piano wire or bamboo slivers and film) stayed up in protected air, I believe for hours, on one winding of a rubber band turning huge propellors at a lazy pace. At their very low Reynolds Numbers they were the best form discovered up to the time of the story, which was some twenty-five years ago.

My caution about using standard airfoil data for models shouldn't stop anyone from designing, building and sailing them. From models, if you observe and think, you can learn more, faster, than in any other way. I did it myself. At the age of five, I was building simple models of the square-paper-sail-on-a-stick stuck in a board type. By seven, without any help or guidance, I was building fore- and-aft rigged boats of reasonable shape that would sail where I wanted, upwind or down. They were crude. This was the early hungry Thirties. There was no money for non essentials. My tools were an axe, the family carving knife, and a pair of scissors, and sometimes sandpaper.  Materials were scraps of wood, a few nails for bending into goosenecks, tins cans to cut into keel and rudder, and scraps of cloth for sails. Yet they sailed, and I learned things about how to set them up to go where I wanted that have never left me.  Even today, when I take the helm of a boat, I try to get her sailing herself. If she is not a total dog, she will usually do a better job of it, given the chance, than I, and most others, can do.

Well, so ends today's sermon. We'll get seriously to work now. Just remember, though, to wear your slicker and seaboots when you go out. Sometimes it rains aerodynamic bullshit out there.

So here's the real beginning of

In Part I, we looked at some of the macro (or outside) effects of winds, rigs, velocities and forces. Here we will begin to examine the micro or inner effects, seeing how those forces are developed and what influences them.

Probably nearly everone has heard the idea of "circulation" applied to the action of lifting surfaces. You may have seen drawings of a wing section with an oval loop drawn around it, with an arrow on the loop representing "Circulation," as an explanation of its ability to lift.* It isn't very helpful, is it? Being told that the circulation adds (vectorially) to the free stream velocity, making faster flow above the wing and slower flow below the wing, doesn't really bring it home. Even being told that Bernoulli said that the total energy around a closed loop must be constant, so that the pressure energy must be higher in areas of lower dynamic (speed) energy, and vice versa, causes only grudging acceptance. What the devil is this circulation, who let it in, and why didn't they throw it out? Can't we just say that the wind pushes on sails and let it go at that? Well, yes we could, if we were prepared to go back more than a century in science and not be able to predict or explain airfoil behaviour.

     *By convention, airfoils are drawn with their leading edges to      the right, trailing edges left, arranged so that their positive      lift is upwards in a free stream from the right. The      circulation loop we have just been discussing shows its arrow      pointing backwards above the foil, representing counter      clockwise rotation.

The truth is that we have been living with, seeing, and experiencing the effects of circulation all our lives in many ways and forms. We are going to use those common experiences now, reinforced with a couple of simple experiments that you can just imagine, or actually do, to bring airfoil behaviour home to roost in your understanding.

First thing to look at is "bluff body" behaviour. This is the barn- door-aross-the-flow idea. If you can hold a board or something similar across a water flow that is not itself too turbulent, you may see a vortex shed from one side, and then the other, in a repetitive chain. This is called a "Karmann vortex street." You have experienced a KVS every time your car has been severely buffeted by the passage of a high speed highway transport. What happens is that air coming down one side of the truck tries to turn into the dead space beind the square body, somewhat like trying a bed roll trying to roll itself up. It gets too big to hold on and and is cast off as a violently swirling mass of air that gives you a sock on one side. Then air coming down the other side does the same.  Left-right, left-right! Karmann could have given Muhamad Ali lessons. Why the formation and breaking loose is an alternating sequence is something that I would ask Mr Karmann to explain to you, only he's not here any more. I have never felt any need or desire to expend the time or energy to find out.

There is a disagreeable appearance of the Karmann vortex street in downwind sailing. When going straight downwind, as under "twin self steering staysails" the powerful impulses caused by the alternating shedding of these vortices causes horrendous rolling. "Rolling down the Trades" under twins was a true description of a nightmare. Spinnakers can do it too if they are presented merely as bluff bodies. Then they set up rhythmic swinging and then rolling of the vessel. Far better to tack downwind and get some Lift in the action, so the sails are steadying, rather than rolling agents.

Now we're going in search of Lift. Every time you stroke an oar in water, or move a canoe paddle, you see a vortex, a little whirlpool spinning at the surface. That spin, or vortex, is historical evidence of an earlier forceful action between a solid and a fluid.

Let's establish that it is one of the laws of physics that a vortex cannot end in a fluid, but only at an interface with another fluid or at a solid boundary.

Now let's do or imagine an experiment that will show us some interesting things. Our equipment is (we should be so lucky) a sailboat moving not too quickly in fairly calm water, and an oar. (One with a straight, clean-edged blade is best.) If you actually do this, let me caution you to be careful, not going too fast, or too reckless in turning the oar, or you may end up swimming. At the rail, holding the oar vertical, blade arrayed parallel to the flow, insert it into the water about a foot and a half, and a decent distance away from the side of the boat. There will be some turbulence and some drag. Now rotate the oar, perhaps ten degrees outboard at the leading edge - be careful! Don't be distracted by nearly taking the plunge, but hold still and watch closely. You will see a vortex, called the "starting vortex" cast off from the trailing edge. It will remain where it started as you sail away. No other vortex appears from the other side, as it did with bluff bodies. Look closer, and you will see a spinning filament connecting the bottom of the oar to the bottom of the starting vortex. That is called the "trailing vortex." It keeps on spewing off the oar as long as you keep on going. Theoretically, in an "ideal fluid" the connection to the starting vortex remains, but in reality the starting vortex is eventually worn down by friction.

But what of the vortex seemingly leaving the oar tip? We have said that a vortex cannot end in a fluid. Yet it seems to disappear. The oar, being a lifting device, is not the sort of solid boundary at which a vortex can terminate. Where is it? Well, it is enclosing the oar blade and terminating at the water-air interface. It is the "circulation," causing differential velocities (high outboard and low inboard) creating inboard high pressure and outboard low pressure. These show themselves as the Lift that is trying to pull you overboard. You can see the effect of the low outboard pressure, because the water level is lower on the outboard side of the oar. If you look carefully in clear water, you may actually see that the trailing vortex is apparently screwing itself off the oar blade as the circulation gets shed into the trailing vortex.

What causes the shedding of the starting vortex and start of circulation, connected as they are by the trailing vortex? It is the combination of the shape of the blade (foil) and the way it is presented to the flow. [We'll be doing more on these things in detail later, so please don't worry about lack of explanation here.] What I am trying to dispose of here is the lingering notion that it is the foil, and not the circulation that causes the lift.  The idea of circulation causing lift still sounds a little flakey, doesn't it? If the foil weren't there, and you could just replace it with a circulation somehow, would there still be a Lift?

The answer is yes, if there is something to push on. Another experiment similar to the last one will show it. For this we will replace our oar blade with a mop handle. (Whisker poles are much too expensive to lose.) Let's do this experiment on the port side so flow is coming from our right, just like all the illustrations of airfoils. Stick the mop handle down into the water. Convince yourself that your age old experience is still valid. Drag still pushes the mop handle straight aft. There isn't any magic. Now we're going to spin it. You may not be able to do it well enough in your hands. It would help to have something to overcome the drag. Passing the handle through a ring secured on a lanyard to a rail fitting further forward would do it. Now, if you spin the handle counter-clockwise, the end in the water will walk away from the boat. The spinning action is dragging water into a circulation, and generating Lift. If you'd really like to see some action, make up something like a boy scout fire-starting bow, and give a good sustained spin first in one direction and then the other. The mop handle will walk back and forth across the flow.

The idea that the action of the foil is to produce circulation, and the circulation produces the Lift, is the basis of the "lifting line" theory of airfoils that we'll look at in AR-3. About that time (I hope) we'll actually start talking about Aspect Ratio in a meaningful way (for those who have been waiting so patiently.) However, these vortices that we've been talking about are very much involved with Aspect Ratio.