Thanks for taking an interest David (David D - there's too many Davids). (Sorry, I didn't quite mean it that way).

David D: "I think what it shows is that all the different construction methods will basically produce much the same real world camber, at least in the stiffer cloth and in the small size that you constructed.

In the real world, a minute difference ... resulting from the different construction methods, will make very little difference to real world performance for the cruising sailor." Yes, I think that is probably what we are going to find, in regard to the shape across the height of a cambered panel..

Here’s a laugh. I made a replica barrel-round panel from Tyvec, inflated it, and measured the camber at various points along the height of the panel, in the plane where the camber was greatest. I used the measurements as coordinates and was able to make a sketch of the shape. (Necessary, because photographing doesn’t show that particular shape very well).

I doubt if a shelf foot sail will demonstrate a much better distribution of camber than this, but we shall see. Imagine how stupid I felt when I went back to Arne's original notes on his "chain calculator" and found pretty much the identical curve....

I have a feeling I have not moved the frontier boundaries of knowledge very far!

Anyway, I will persist now. I am going to use 30gsm PelTec. Extremely light and pliable. I made one panel yesterday and it seems to replicate a full size panel very well.

A digression: Arne's Chain Calculator

When things don't work, go back and read the instructions! I went back and studied Arne's notes on the chain calculator (here) a bit more thoroughly because I have a feeling that nit-picking over 30 degree or 45 degree shelf is missing the point, that vertical shape probably boils down to little more than how much excess cloth can between jammed between two battens, the characteristics of the cloth used, and how the complex forces within the cloth are distributed. In his pioneering work, Arne very cleverly tried to simulate the shape by hanging a chain between two points - it takes up a curve which has been used by bridge-building engineers for centuries, called a "catenary".

(I remember learning about the catenary at secondary school, and then  a discussion with a neighbour who, a few days prior, had built the arch of a brick pottery kiln in the traditional way. He told me the curve was a catenary. Yes, I know all about that, I said - it's just the shape you get by hanging a chain between two nails! (I am afraid I haven't changed much since my school days).  He looked down at me with a glint of annoyance in his eye, and said: well son, if you know so much, tell me how you get the chain to hang upside down!)

The catenary is a somewhat complex shape, derived from a mathematical function called the "hyperbolic cosine" or "cosh". The shape Arne used to replicate the curve - and to calculate the rounding needed to give the "excess cloth" is, in mathematical terms:

y = (c/2)(e^x/c + e^−x/c 

where "c" is the amount of maximum camber, and "e" is a very special constant called "the exponential number". In terms of the "cosh" function it may be written: y = c cosh(x/c)

What has this got to do with designing a sail?  Well, if you plot this curve, you get something like this:

(I need hardly point out that an easier way of getting this curve is to hang a chain between two nails).

If you look at the interval between -3 and 3 you can see something like the shape we are pursuing here. Or, if you alter the aspect ratio of this diagram, by scaling down the vertical axis to about 15%, you get this:

It was a brilliant idea of Arne's to hang a chain between two fix points and allow sufficient slack to give the max camber he was seeking, then simply measure the length of chain to estimate the amount of rounding needed to give the necessary "excess cloth" between battens. It is only an approximation though, the shape taken up by a sail seems to be more complex - and the real shape we get in a barrel rounded sail is much better than that: camber extends out further towards the edges than the shape we see here, and more cloth can be absorbed than this curve would indicate. Which is why Arne then uses a "fudge factor" of 20% extra in the rounding. [For more detail about the origin of this fudge factor, see next post in which it is explained by Arne himself.] (Considering Arne was working entirely on his own (and tells me now that he did not know at the time that this curve was used by engineers to design arches) I consider it to have been a ground-breaking insight and a significant moment in the evolution of the modern cambered junk sail panel).

I am not expecting to see shelf foot panels yielding much different a curve than the one Arne drew in his diagram above - but I don't know yet. I will try to find out.

(PS for SJR afficionados - don't apply any of this analysis to the jib panel. The jibs are an open-at-one-end shape - the leech flies free of the boomlets, restrained only by the built-in "sheeting angle", and I believe this capricious little critter follows a different set of rules. We are focused here on closed-end panels - the panels of a contiguous sail, or the mains of a SJR.)

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David D: Wayfarer  - a famous design, even in New Zealand where we don't have them. I guess everyone is familiar with the inspiring tales of Frank (and Margaret) Dye and his Wayfarer cruises up into the Arctic Circle and Arne's territory. I wonder how many people know that this same vessel ended up in the US (or one of Dye's anyway, I believe he may have had more than one.) It was purchased by a kiwi ex-soldier and writer called Lee Hughes who took her on a solo 2,000 mile voyage up the coast of the US, and wrote a most entertaining book about the experience ("The Biggest Boat I could Afford" you can get it from Abe Books). 

I look forward to David's SJR-rigged Wayfarer sailing - and then featuring as "Boat of the Month" on the website.

Paul: "The note worthy thing about this [FanShi's] sail is it has 30° shelves, the angled shelves reduce the "baggyness" of the sail and enable it to fill quicker when the breeze gets up. "

David: Best practice, IMHO. Less baggyness than a horizontal shelf, camber over more of the height of the panel than a 45˚ shelf, easier to calculate the width of shelf than 45˚ (1/2/√3 triangle).

The above comments appeared in the recent thread “FanShi gets a new sail” and since no evidence was provided I had the temerity to question David’s comments, and to hypothesise that, in practice, there might be not much difference in the "camber over height" distribution, between 45 degree and 30 degree shelfs -  and also to offer an opinion on the relatively unimportant question of whether there is any difference in the “ease” of calculation of shelf width between 45 degree and 30 degree types of shelf foot panel. I am sure David knows what he is talking about but, hey, we live in a scientific age and I thought it might be fun to actually try to compare some scale models.

The question of camber over panel height has interested me for some time but there seems to be no actual comparative data, other than the observation that the horizontal shelf (zero degree angle) makes a pretty baggy sail. The first documented "angle shelf foot" panel was done some years ago by Slieve McGalliard on the jibs of his SJR design sail, for Poppy. 45 degrees was chosen to reduce the amount of cloth in the panels and thus to create cambers which would inflate in a lighter breeze more readily than the somewhat baggy panels of the more usual horizontal shelf method. The choice of 45 degrees was somewhat arbitrary at the time. It worked well and has been copied many times since, including on mains panels. However, there is no reason why it might not be improved. Paul's innovation of 30 degrees seems very much worth looking closely at.

With some time on my hands, due to a quick succession of two covid self-isolation requirements – and since the big table was still set up from a little dinghy sail project, I decided to use the scraps from that, and make up some 1000mm x 400mm rectangular panels, by a variety of methods, and see if we can make any side-by-side direct comparisons. I am more than happy to prove myself wrong. I also wanted to compare the "difficulty of calculating shelf widths" – and finally I also wanted to see if I could find a simple relationship between actual camber of a shelf foot sail panel (as measured) and the designed camber of a shelf foot sail panel (which may be termed the “tin plate” camber for obvious reasons). The measured camber is generally greater than the designed camber on a shelf foot sail panel, since, in reality, it is made of soft canvas, not tin or plywood, and can "bulge" a little when inflated.

The cloth used was “Maxilite 150” which is 70 (or is it 75?) gsm ripstop nylon. To give due honour to Arne who designed my dinghy sail, I chose the colour of “Stavenger blue”. This stuff is not very soft, in fact it is papery crisp and resists sheer – not particularly easy to work with at small size, and Arne expressed doubts as to whether at scale it would give a valid representation of a real-life panel. I think Arne was probably right about this, and I am now sceptical of the results (see below).

A basic and not-too-fancy foil shape, with max camber at about 1/3 chord, was mapped onto the following six models: shelf foot 30 degrees - 8% camber and 10% camber, shelf foot 45 degrees 8% camber and 10% camber, barrel-round panels 8% camber and 10% camber.

The model panels were inflated, max cambers measured, and inflated shapes were captured, as far as possible, by photographing.

In order to save weight and further stiffness I used no stitching and was able to rely on basting tape only, to join shelfs and middles. The panels were made fairly roughly and quickly. They all refused to inflate from the breeze of a large domestic fan. Possibly that is yet another problem in scaling. The gale from a powerful leaf-blower was needed, and it did the job satisfactorily.

45 degree shelf foot panel

With regard to lofting the shapes of the shelfs: if the calculations were to be done by hand the 45 degree shelf is easier to calculate than the 30 degree shelf. I will show the calculations if anyone is interested. However, as all of the arithmetic was done with the spread sheet anyway, that issue appears to be minor and trivial.

Barrel-rounded panels are, of course, vastly quicker and easier to make than shelf foot panels.

As expected, the shelf foot panels had greater camber (by measurement) than their designed cambers, but I am sufficiently sceptical of the measurements that I did not look for any rule of thumb here.

There was little difference in shape across the height of a panel between any of the panels. 

I formed the impression that the 30 degree shelf and the barrel-rounded panels were potentially superior to the 45 degree shelf panel in this respect, (and therefore David would be right and I would be wrong) but there was hardly any difference in the photos. I think the cloth used was responsible for the “soft chine” "tin plate" shape that all of the panels displayed and I am inclined to the opinion that these shapes do not reflect the true shape of a real-life panel. This conclusion is based on the shape of the model 45 degree shelf, which is closer to a “tin plate” panel than the much more softly curved real life 45 degree shelf mains panels on my Serendipity.

 The 45 degree model did not represent the full size shape with which I am familiar (as far as I can recall, and Serendipity is currently in mothballs so, at present,  I can't go back for another look) - and therefore the other models are likely also be unrepresentative.

Furthermore, the 10% barrel rounded panel had been almost impossible to make in Maxilite, at this size. Rather than "stretch the panels along the batten", it was necessary to compress along the head and foot, in order to induce those necessary little wrinkles. The 10% barrel rounded panel failed to produce more than 9.5% camber - due to the unsuitability of the cloth, at this small size.

It would certainly be a gross over-simplification to attribute the shape of a panel solely to shelf angle, not that anybody has said quite that.  Evidently the factors which are of importance in the final shape of a panel in vertical cross section are: choice of cloth, aspect ratio of panel, shelf camber and shelf angle (or rounding if barrel-rounded). A carefully balanced combination of all these factors might be needed to get the best shape, and this may well be what we are seeing in the much-praised sail which Paul Thompson recently made for Annie's FanShi.

I am not entirely clear what exactly is meant by the term "baggyness". At the end of the day, I would have thought that it is just a matter of how much cloth is crammed between the upper and lower battens of a panel, rather than what method is used to do it. Without doing any experiments, it is easy to calculate the distance around the vertical curve of a cambered sail and simply compare it with the direct distance between the upper and lower batten. The difference might be termed "excess cloth". Horizontal shelf is an easy way to build in a lot of excess cloth, and therefore I suppose it has the potential to be the baggyest (depending on how much camber is used, because that also is an obvious factor). 

There is still some comparative information to be had from this exercise, so I leave the results and a few photographs above. However...

I had some Tyvek left over from an experimental panel I made a few years ago. This stuff is light (42 gsm) and incredibly soft and "malleable". I thought afterwards it might have been a better choice for testing models, perhaps allowing the model panels to more closely represent real panels.

So, I used this scrap of Tyvek to make a trial barrel rounded (10%) panel.

Using Tyvek, the impossible-to-make 10% camber barrel round panel was able to be created relatively easily, it inflated easily in the light breeze of a domestic fan – and its inflated shape looked a bit more “normal” to me (with excellent camber distributed vertically, I might add). And its measured camber was 10% - exactly as it was designed to be.

As a result I have ordered some more Tyvec – and also an equivalent product called PelTek which is only 30gsm.

I intend to do the testing all over again, with this really interesting material, and see if I can get a more credible and useful set of results. I might do a couple of horizontal shelf panels as well, just as data points. I am expecting David to be proved correct regarding vertical distribution of camber, but...all bets are off...the barrel rounded panel might turn out to be a surprise!

I will have a go at that next week.

Just hoping this might be of interest.