Monday, July 06, 2015

Fatheads and Pinheads

On Saturday of the weekend before last I did some solo practice in my RS Aero 9 at the club. One of the very satisfying things about sailing a new class is that almost every day is a learning experience and I can see improvement in my skills every time I sail the boat.

After sailing I was starting to de-rig my boat when another club member, whom I hadn't met before, came across to chat with me and check out my boat. It happens pretty much every time I sail the RS Aero there.

But he asked me a question which initially had me stumped…

Why is the top of the sail square?

Of course he is right to ask. The tops of the sails of the other classes sailed at the club look like this…

Whereas the top of the sail of the RS Aero looks like this…


I vaguely recalled that I had read or heard somewhere why the top of the Aero sail is like that but in the moment my mind went blank.

I blurted out something like, "I have no idea. I'm not a sailmaker or an aerodynamicist."

Aerodynamicist? Where did that come from? Is it even a real thing? And even if it is, what on earth does it have to do with sailing?

And then in a desperate attempt to sound not completely ignorant about my new boat, I mumbled something along the lines of, "Well, I guess it's a way to add more sail area."

As soon as I said it I knew it couldn't be the whole story. There must be other ways to add more sail area.

But my inquisitor, who seemed to be a very nice chap conceded, "I think you could be right."

I scrambled to think of another reason the top of the sail might be square and vaguely remembered something someone had told me and hazarded a guess… "And a sail that shape spills wind well in a gust."

The very nice chap was either not detecting my total ignorance about sail design or just being polite as he said again, "I think you could be right." And he went off to do something on a boat with a pointy top to the sail.

As soon as I got home I logged on to the Google machine and did some research on why some boats have sails that are square at the top. Maybe I looked a bit of a fool the first time I was asked this question but I wasn't going to get fooled again.

I found this interesting paper by Damien Laffforgue which has a whole section on square head sails vs roached sails.

Among the advantages of the square head sail that Damien lists are these. (My comments in italics.)

1. The surface area of a square head sail will be bigger than a roached sail for the same mast length (luff), but the aspect ratio will be smaller.

2. For the same surface area, a square head sail will have a smaller mast than a roached sail, therefore the centre of gravity of the rigging, and the centre of effort of the sail will be lower, which increases the lateral stability of the boat.

I guess #1 and #2 are two sides of the same coin, so to speak.

3. The square head gives a better aerodynamic efficiency in the upper part where the wind is stronger (velocity gradient.)

Ahah. That's what I forgot when I was talking to the nice chap at the club. More sail area up high where the wind is stronger is obviously an advantage.

4. The square head does not increase the lift but reduces the drag.

I'm not sure I understand this one. Why would it be less drag? More research is indicated.

5. The square head allows a better control of the main sail twist, and self-regulates the sail shape during gusts.

I am not sure I really understand the first part of #5 but the second part is basically what I was telling the nice chap at the yacht club. The square sail top opens up in gusts and spills air.

6. The head of a square head sail is more tolerant for small angles of attack, and then produces less induced drag.

More tolerant for small angles of attack? What does that mean? And there he goes again saying that sailing a square head sail produces less drag. Why would that be?

A little more research discovered that the reasons a sail with a square top has less drag than a sail with a pointed top is something to do with the tip vortex. Here is a good explanation of this effect in an article from Sponberg Yacht Design...

In any given aerofoil planform, the airflow on both sides of the surface are at different static pressures—high pressure to windward, low pressure to leeward—and they would really like to equalize. In a triangular planform, the airflow on the high pressure side gets a chance to equalize sooner, by virtue of the shape, than on a rectangular planform for example, by skewing up toward the tip and off the surface.   
This skewing of flow from the high pressure side, mixing with the flow on the low pressure side, creates a vortex off the tip. The bigger the skew, the bigger the vortex, and the greater the induced drag. 
In his book Aero-Hydrodynamics of Sailing, C.A. Marchaj (pronounced MAR-ki) shows a photo of what the tip vortex looks like.

And I found a slightly less technical explanation of this issue in a comment from Rick White on the Cat Sailor Forum in a thread about the pros and cons of square top mainsails

I believe it was Dave Calvert that started the concept for windsurfers, before he started designing multihull sails. 
The theory is you have a fuller, more powerful area of the sail up high for lighter winds. 
Now, when a puff hits, because of the length of the batten sticking out from the upper mast, the wind uses that leverage to allow the top of the sail to blow off to leeward, thus depowering in the puff, lowering the center of effort, and also reducing the heeling moment. 
Sort of an automatic transmission, it shifts to a high gear in the puffs, and when the puff subside, it shift down again for more power.  
And they definitely work much better than pinheads.

So now you know.

Next time I am asked why the top of my sail is square I will be able to confuse the questioner with aerodynamic gobbledygook about tip vortices and velocity gradients and angles of attack and planforms... and pinheads.

You have been warned.


Tweezerman said...

With foils, since we don't have infinite span (infinite length of foil), we have induced drag because of tip loss (we also have frictional drag which is a function of surface area - but that is not what we are talking about here). Increasing span reduces induced drag but that is not what is going on with the fathead. In experiments with the Classic Moth sail, a fat head sail is faster than a pinhead but the span (luff length) remains the same so induced drag should be similar. It may be that a fathead gets us closer to elliptical lift distribution which is the ideal. Also, and I don't have a good explanation for this, larger twist angles than would be indicated by the predicted skewing of the wind gradient seem to be faster in high performance dinghies. A fat head does promote more twist and for dinghies that plane upwind this does seem faster, probably due to depowering. The extreme example is the top of the Windsurfer sails that are extremely twisted, bladed out and pumping in a breeze. A problem with fatheads is in light winds, when there is little wind pressure to twist, the top of the sail closes up and stalls.

Caveat, I am not an aero or hydrodynamicist but I've hung out with some smart naval architects who are well versed in the subject. (Hope I've got this right - just regurgitating from my memory, no notes used.)

Pandabonium said...

Tip vortex was the first thing that popped into my head (my father was an aeronautical engineer, and I a pilot). A sail is very much like the wing of an airplane. Why not winglets like airliners have? Because sailboats travel at very low speeds compared to jet aircraft. A squared off sail should provide added lift (forward force) by making the vortex smaller in diameter. Over my head - literally and figuratively speaking.

Unknown said...

I hate to tell you this, Tillerman, but the situation is even more complex than than you discovered, and even that complexity makes our heads hurt. For instance, in the first advantage listed, if the loss of speed is greater from the decrease in aspect ratio than the increase in speed from the larger sail area, then the square head is a disadvantage. Also if the loss of sail power due to twist (which de-powers the sail) is more than loss of power due to increased heel, again the square top loses. This type of analysis is typical of almost all sailboat technology issues, and because exact prediction of aero-hydrodynamic performance is beyond the capability of most reasonably priced software, you kinda have to do what RS on the Aero hull - try different designs on the water. That's where we all want to be anyhow.

Tillerman said...

I knew some of my blog readers would know a lot more about this than I do. But their comments do seem to confirm my suspicion that nobody really understands fully why and how certain sail designs are faster than others.

John said...

Pretty much everything is a tradeoff. You have neglected to include mast bend in your discussion. If you really want to get a headache, think about how the forces on the sail change the bend of the mast, which changes the shape of the sail, which changes the forces on the sail which then change the bend of the mast...

They probably just made it look cool.

Tillerman said...

I think John is right. The design of the RS Aero is nothing at all to do with aerodynamic and hydrodynamic efficiency. It's all about making the boat look cool. How else can you explain the cupholder?

George A said...

What's old is new again---pretty soon we'll return to gaff headed rigs--the ultimate "fat head" sail. Those old timers knew stuff that we're just now appreciating.

Post a Comment