The structure of water and air

My brother-in-law recently sent me a news article from “The Economist” that seems to have some very specific application to the design and sailing of Footys. Because of the way he sent the article, and my computese inexperience, I am not able to give a reference for you to just ‘click on’. I therefore transferred the page to a photo file and attach it here. You will probably have to magnify the page to read the lettering.
The gist of the article suggests that fluids have a structure of domains and boundaries, so that any moving boat must pass from one domain into the next in its normal motion. The problem lies in the fact that each domain has its own motion, so the drag of the boat hull (as well as the sails in the air) is affected by these domain motions in a way that would make these quantities fluctuate and therefore very difficult to measure.
The article does not indicate the dimensions of these domains, but it is obvious that, if the domain size approximates that of Footy hulls, and/or the wind ripple and wavelet dimensions on the surface of our ponds, this phenomenon would affect Footy class boats much more than any of the larger classes----which seems in fact to be the general observation about Footy behaviour.
The well-known ‘bobbing’ of the hulls, as well as the difficulty of designing hulls which wont nose-dive, may be related to this phenomenon.
I will persue this phenomenon with inquiries to some of the individuals mentioned in the article.

I think you’re mixing up some things here. That’s an interesting article, but I think its main relevance to sailing footies is the manner in which the wind gusts.

I think the nose dive problem is just large rigs with a lot of sail area on short hulls which have low hull speeds, and heavy displacements which make it tough to exceed hull speed. A US1M going downwind may attain a significant fraction of the wind speed and greatly relieve the pressure, though of course if it’s gusty enough it may still nosedive.

Let’s look at a 6 lb US1m with a 65 inch mast and 600 square inches of sail area. Also a 12 inch, one pound footy with 116 square inches of area on an 18 inch mast. Assume the “pitching moment” that causes the nose dive is proportional to sail area times mast height. The moment of the footy is about .054 times the moment on the US1M. The moment to resist this will be roughly equal to the waterplane area times the square of the length. (The square of the length because any bit of volume will be that much further out and will also be submerged that much more. That is, a part of the hull 6 inches from the axis of tilt (I don’t remember ANY of the real terms, and I’m mostly just reasoning this stuff out) will have half the leverage of a part 12 inches from the axis, plus it will only be submerged half as much for a given angle of tilt. The waterplane area will be arouind the 2/3 power of the displacement. So the resistance to pitching of the footy will be around .028 times that of the US1M. If you divide the factor for the pitching moment by the resistance to it, the Footy is going to go 1.9 times as far. I haven’t counted in the hull speed factor or the weaker winds at lower heights, which to some extent will cancel each other out.

Obviously the wave height is a factor if you are using the same sized pond for your Footy.

Another factor tremendously in favor of larger boats is Reynold’s number. The viscosity of the air and water will be much more of a problem for the smaller vessels. Particularly, in the water, since a Footy is slower.

I would add that even if you manage to exceed true wind speed (multihulls, landyachts and ice boats) eventually you reach a point where the wind simply overpowers the boat, and the mast, acting like a lever begins to do it’s “lever” thing. You don’t even need the bow to go underwater, just have sufficient friction to prevent (or retard) additional acceleration. Eventually they all get overpowered and for the hard surface boats, they simply “spin out” - having lost their sideways resistance.

The article may apply much more directly to the water rather than the air. In any case, the computational power required to make sense of the phenomenon in the model sail world far exceeds anything available to us, so we will be dependent upon the conclusions reached by the big players. We will need then to interpret their conclusions in our area. My first reading of the article suggested to me that there may be a size relationship between the wind ripples on the water surface of our ponds and the dimensions of the ‘domains’ in the water, and these ripples are certainly of the dimensions of a Footy, which causes the “bobbing”.
As to the nose-dive problem, my observation is that this usually occurs suddenly, for no significantly observable reason, when the boat is sailing in a ‘stable’ manner, and that this might be related to the boat entering a domain where the direction of movement of the water is opposite to the boat’s motion. The sudden increase in the drag may then result in an abrupt nose-dive. It equally may be due to similar domains in the air, moving at a noticeably higher speed, a sort of “micro-puff”.
Whether this information would prove to be valuable in model boat design I do not know, but it might mean that stable water and air flow conditions are not something that we can count on in Footys.

I believe that the Froude Number is the usual index of similarity for situations where wave drag predominates, as with displacement hulls over about half hull speed. Reynolds Number is for viscous forces, so is important where friction effects predominate - such as in light air where hulls don’t get over maybe half of hull speed. Then there are other dimensionless numbers for modeling similarity of other factors, such as surface tension (Weber Number) or eddy formation (Strouhal Number). Maybe there are a pair or even two pair of these dimensionless numbers that scale the same between a target entity and a model, but that generally is not the case. One might sometimes be able to cover a pair of effects simultaneously if one can change the fluid between full scale and model. Generally, one must be content with looking at one effect at a time, such as wave drag, while trying to minimize effects that scale differently, such as form drag (proportional to hull speed squared) and skin friction (proportional to hull speed).

The Froude Number is calculated as F = velocity / sq rt(length * gravitational constant g).

When I compare a US 1M or IOM traveling at, say, 4 ft/sec to a Footy, I get the following:

Vfooty / sq rt(1 ft) = 4 ft/sec / sq rt(3ft), from which I calculate the speed the Footy would have to travel at for similar wave drag conditions to be 2.3 ft/sec. And from that I estimate that Footy hulls just won’t behave much like 1M hulls. Note that while the Froude Number does not require any number for the beam of the vessel, it is implicit in the term “model” that the hulls are identical except for scale. Footy hulls don’t look much like 1M hulls, so maybe shouldn’t be expected to behave like them.

Bobbing, hobby-horsing, and the like are natural frequency responses based on inertia and flotation, and the frequencies are probably not all that difficult to estimate. But it’s probably easier to take a few boats, get some videos of them bobbing and hobby-horsing, and then calculate those frequencies. Anytime waves or ripples containing those frequencies come by, the behavior will be elicited. The thing is, these effects probably scale differently from Froude effects and Reynolds effects, so it is difficult to derive any great benefit from data on bigger boats. It’s probably also difficult to change any of those frequencies enough that they won’t continue to be a problem. You might raise or lower one of them a tad, and that might help with one set of conditions, but a small change in wind speed and the ripple frequency would change just enough to raise the problem again.

I think it would be a real hoot to set up some test tanks for our little boats. Sometimes I put myself back to sleep in the middle of the night by thinking about how one might do some testing in swimming pools. Maybe pulleys and falling weights to get constant drag… maybe a long box so that we might rig a cart, so that a hull could be heeled before being towed, with strain gauges to measure side force and torque… maybe a little electric motor driving a board back and forth to make waves… and then I go to sleep and don’t think about it anymore.

Mike Biggs

It is exactly the difficulties that you have described which make the Footy such an interesting subject for study.
First, the Footy is not a model of anything, it is what it is. Any numbers obtained are about the Footy itself, with no need to extrapolate to to the “full size”.
The behaviour of the Footy hull and sails are a complete subject for study, in themselves, with no need to think of anything else.
The suggestions in the article on Lagrange coherent structures suggest that Footy behaviour may be affected more directly by the discontinuities of water and air than is the case for One Metre and larger yachts. As most people are not in the slightest interested in the hydro and aerodynamics of one foot long structures at very low speeds, This seems to be a subject upon which Footydom may make a contribution that is unique to our small group.
When I first read the article, it struck me as entirely reasonable that the amplitude and spacing of wind ripples on the water of our fairly small sheltered ponds may be directly related to the size of the Lagrange structures—or why would we even observe ripples of those dimensions? (Why does a 1 kph wind not produce ripples that are 1 metre long from crest to crest?)
In this and other threads I have described the methodology that I plan to use to determine drag data for Footy hulls using the “steady” flow of my local river at thigh-deep levels to measure drag forces on actual Footy hulls, which then may be compared with the calculated numbers available in CAD programs such as Hullform. Existing hulls may be “reverse-designed” into the Hullform CAD program (or any other) so that calculation may be compared with some measured numbers.
The major point of uncetainty seems to be the actual measurement of forces in the 10-50 gram range while standing thigh deep in a flowing river. So far I have been able to make very light helical springs from nylon-covered stainless-steel fishing leader which stretches about 10 centimetres under forces of about 50 grams. I can measure stream flow velocity by dropping a plastic fishing float on the end of a 2 metre cord which travels to the end of the cord in about 4 to 8 seconds (which is close to Footy hull speed)
MY ponds here are frozen for the winter and I’m not going to stand in the ice-cold river water, so proceedings will have to wait until spring.
Your thoughts about testing tanks and motorized towing carts, while admirable, are way beyond the financial resources that any sane person would devote to a “toy boat”. Not to “rain on your parade”, but I would be delighted to have a colleague who was interested in carrying part of the load in this enterprize.
Whether we would get any useable results is another matter, but, hey, what do we have to lose? I’m a retired biologist, and what other problems do I have a real opportunity to work upon?
I hope to hear more from you, Mike, as your suggestions would indicate that you are an “experiment-minded” person.
Rod Harle

“Your thoughts about testing tanks and motorized towing carts, while admirable, are way beyond the financial resources that any sane person would devote to a ‘toy boat’.”

Well, yes and no. Of first importance is the fact that I was somewhat less than totally serious in my post. But I do think some fairly sophisticated testing is within the reach of many clubs.

Strain gauges are actually inexpensive, consisting in their most common form as printed circuit “wires” on a flexible backing that is glued to whatever you want to measure the strain in. “Strain,” in this case, is engineering jargon for stretch or compression, generally as a result of an imposed load. And that means that with some bits of metal, a power source such as a battery, and something like an oscilloscope, you can take dynamic data about the load on an object. With a little skill and knowledge, one can build his own force transducers. I’m just about certain that searching on “strain gauges” will not only turn up the devices, but show how they are wired to measure force or torque; the central idea is to convert the (very small) changes in resistance under strain into voltage changes, which are more easily measured, possibly after amplification.

I suspect that scanners use stepper motors, although I don’t really know that. And I further suspect that a small stepper motor would make a fine towing device for small hull models - although it would require some knowledgable electronics types to put together the control circuits for the stepper motors. Such a stepper motor should produce a constant speed when fed a steady series of pulses.

While an oscilloscope is one way to read transducers during towing, even better would be an A to D board in a PC, as that would allow the data to be preserved digitally, and also allow the data to be analyzed for frequency. Here’s one website advertisng inexpensive boards for PCs to do just that: Please note that I know nothing at all about these folks, their site was just the first one I found when I searched on “A to D converter” and PC. Also note that their software works only with old operating systems, or so it seems to indicate. But if everything is legitimate, you can get 8 channels of digital data recording for $110.

I’d say that a couple hundred dollars and a couple hundred person-hours would set a club up for some fine model sailboat hull testing. Right now that 200 hours of work is a whole lot more than I want to spend on my toy boats. But it also looks to me like many clubs could find the expertise to do the work, and the cost of the materials isn’t really all that high.

I’m interested in all this, just not interested right now in doing any of the work. Sort of the story of my life…

Mike Biggs

You might be able to replace a stepper motor with an easier to find, less difficult continuous robot servo. You don’t need the torque, but using a fixed diameter drum you can calculate how much string per turn is taken up, and the drum speed would be a constant (unless batteries get low). A much longer tow tank could then be used and distance times - I suppose electronically which giving the known distance of travel and the time taken, could result in some form of technical data to be compared to other designs. Likewise a camera with wide angle lens could be mounted above the tank to get photos of bow and stern waves for transparency overlay comparison. Video camera might be a good substitute as they shoot at a known number of frames per minute which could also verify to time recorded.

Maybe not as sophisticated as your thoughts, and perhaps probably not as accurate, but able to produce comparisons perhaps.