sail aerodynamics

I am a bit confused with the explanations of how the sail actually pushes the boat forward. Do anyone have a good scientific explanation? Not just "The lower pressure on the leeward side sucks the sail forward".
/ErikW

 

Hi Erik:

The explanation is a lot simpler than many make it out to be - think of it this way. If you remember from high school physics - "For every action there is an equal and opposite reaction." (Or something like that - it's been a while.) As the wind flows over the sail it is forced to change direction by the shape of the sail, flowing over the luff (front of the sail) in one direction and exiting the leech in a different one. IOW the sail exerts a force on the wind forcing it to change direction and the wind pushes back.

This is the easier part to understand. How does this translate into the boat moving forward? For simplicity let's assume that the sail is trimmed at a 45 degree angle to the centreline of the boat. Now imagine a vector (again from high school) representing the force being exerted on the sail by the wind. . This vector will point away from the sail at a 90 degree angle (imagine the vector pulling on the sail). From the tail of the vector draw another vector at a 90 angle to the centreline of the boat and from its tip draw another one, parallel to the centreline, to the tip of the first one. Vector 2 will represent the force that heels the boat, the 3rd one represents the force that moves the boat forward. The reason the boat doesn't move through the water at a 45 degree angle is because of the keel or centreboard which also act as wings.

The above also applies to keels, centreboards, airplane wings, and your hand sticking out of the window of a car travelling on the highway.

 

....while we're at it Erik, don't get sucked into the old slot theory explanation

Subject: How Sails Work, the slot effect

I noted that this forum (another one) has had quite a bit of discussion recently of “lee side air speed”. Well, I couldn’t resist bringing up the closely related, and also much maligned subject of ‘air flow thru the slot’ created by the mainsail and the headsail.

I’ve excerpted a portion of a proposal cover letter I wrote most recently….

[Now look at the rig’s aerodynamic configuration. We’ve had many years of controversy over the flow of air in the slot between the jib and the mainsail, and many incorrect explanations. We now know irrefutably that the flow between these two sails is slowed rather than speeded up, and that results in a higher pressure on lee side of the jib and on the windward side of the main; ie, the jib’s drive is improved, and the main’s drive is degraded!! Put another way, the mainsail provides an upwash for the jib that makes the jib both more efficient and able to point higher (its operating in the safe leeward position). The jib meanwhile creates a downwash on the mainsail that decreases its efficiency. THEN WHY do we continue to make the mainsail bigger than the jib??? As if this wasn’t enough, we hide the mainsail behind a mast, and we don’t hoist it at the most favorable angle to help the jib.]
[I’ve reversed the size of these sails in proportion to their relative efficiencies. The parallel nature of the slot between my mainstaysail & its jib/genoa should further enhance the supporting role of the main and….. Still questioning the efficiency of the traditional mainsail? Look at all of the past America’s Cup boats on which $millions have been spent on sail research; going up wind you often detect huge areas of the sail right in the prime draft zones that are right on the edge of ‘backwinding’. These ‘soft’ areas are certainly not providing any significant driving force (not very efficient).]

Now lets see how many people are going to tell me I’m wrong-- that like a restricted water hose, the air is speeded up in the slot. This is another of those axioms that the textbooks have got wrong and have taught us wrong for so many years. But as Tom Speer noted, “there’s no way to finally put a stake through the heart of that old explanation—it just keeps coming back to life”.

More recently I ran across a news article in the Sept issue of Seahorse magazine which discusses the very interesting full scale prototyping work being carried out on a J-90 class boat by Eric Hall of Hall Spars. Eric is now on his third-generation, free standing ,carbon wing rotating mast, with a una-rig mainsail. His “ thought process (and maybe not entirely logical) was: If biplanes became monoplanes and monoplane wings shed wires, why not an unstayed una-rig upwind” Boy, you would surely think this was the ideal upwind rig. In responding to an inquiry on upwind performance, Eric responds, “ first, of course, the boat would be improved upwind with a No.1 jib. Generally, we could not point as high as the others here (Block Island) and therefore had difficulty holding lanes.” He goes on to say, “this is a very interesting project that we especially want to succeed. I have been accused of a missionary zeal, which frankly keeps moving it along. It’s a real problem sometimes keeping focused on what we are trying to do in view of all that is ingrained in our minds about what makes sailboats work. Anyway we are having fun…

 

Brian,

Your post confused me somewhat, with the phrase:

"the flow between these two sails is slowed rather than speeded up, and that results in a higher pressure on lee side of the jib and on the windward side of the main; ie, the jib’s drive is improved, and the main’s drive is degraded!"

Is this the wrong way round? A reduction in velocity of the flow in the slot will result in an increase of pressure on the WINDWARD side of the jib and on the LEEWARD side of the main (the two sides that face each other when the jib is overlapped). I agree that this results in the jib's drive being improved, and the main's degraded.

 

Sorry about that mistake, you are exactly right. Thanks for bring that error to my attention. I had changed the order of listing the sails from one document to another and failed to change the windward/leeward designations correspondingly.

 

The net forces on the boat are equal to the net change in momentum of the two fluids - that's conservation of momentum. The flow also has to satisfy conservation of mass and conservation of energy. Any description of what's happening in the flow has to relate these three conservation laws in a way that is consistent everywhere. What's cause and what's effect is largely a matter of what you know or control, and what you want to know. The whole picture has to hang together, regardless. So here's the big picture, and I'll fill in more details as I go along. I hope this doesn't get too long-winded.

The sail bends the wind sideways, aft and to windward of the apparent wind direction. The change in momentum of the wind results in a force on the sail that is oriented to the side and ahead of the beam. The hull/keel/board bends the water flow toward the leeward side, and the change in the water's momentum results in a force that is oriented to windward and aft. When there's a change in the force due to the wind, the boat accelerates (both sideways and ahead) until leeway angle and boat speed arrive at a hydrodynamic reaction force that just balances the aerodynamic force applied by the sails. That's Newton's law (F=m*a), which is another form of conservation of momentum (in this case, the boat's momentum).

If you want to model the forces for engineering purposes, there are a lot of other equivalent ways of looking at it, but the conservation laws are the basic principles.

For example, in order for the wind to bend, there has to be a decreasing pressure toward the inside of the curve because if each blob of air had the same pressure on each side of it, it would just go straight. This pressure gradient provides the centripetal force to change the direction of the wind's momentum. Far away from the sail, the pressure is the ambient pressure reported by the weatherman's barometer. As you approach the sail from the lee side, you're moving toward the inside of the curve, so the pressure is dropping and is at its lowest when you arrive at the lee side of the sail. If you started far away from the sail on the windward side, you again start with the barometric pressure and as you move toward the sail you're moving toward the outside of the turn of the wind, so the pressure has to be increasing; again due to the force required to accelerate the wind to the side (higher pressure on the outside, lower pressure on the inside of each blob of air). So when you arrive at the windward side of the sail, the pressure is higher than the barometer says. The high pressure on the windward side and the low pressure on the leeward side provides most of the force acting on the sail, and when you add up the pressure difference over each part of the sail and compare it with the forces needed to divert each blob of wind, you'll find the two are equal and consistent.

For most of the flow, there's no change in energy. So if you consider all the forms of energy - potential, represented by the pressure; kinetic, represented by the velocity; thermal, represented by the temperature, and rotational (like kinetic energy, but spinning) - they all have to add up to a constant. At the speeds we're dealing with in sailboats, there's not much change in temperature or density as a result of flowing around the sail, and except for the flow very near the sail individual blobs of the air don't rotate although they do travel in a curved path (think of people riding a merry-go-round but always facing North while they do it). So a good approximation of the energy in the flow is that the potential energy has to be a constant, and this constant is called total pressure. It's the pressure you get when the flow is brought to a halt, so that there is no kinetic energy and all the energy is in the pressure term. This is the highest pressure you can generate with a given amount of wind. Where the pressure is lower, the kinetic energy has to be higher to make up the balance. So low pressures mean high velocities and high pressures mean low velocities. This is where Bernoulli's law comes from - it's an approximation of the law of conservation of energy. But it's only good where the flow is not rotating or being heated/cooled, etc. Then you have to take into account more of the thermodynamics.

Ironically, one of the areas where the flow is rotational, and therefore Bernoulli's law isn't a good approximation, is in the flow right next to the sail. In this boundary layer, the fluid actually touching the sail doesn't move relative to the sail, and there's a rapid change in the velocity as you move out away from the surface. But there's very little change in pressure because some of the energy is going into rotational energy and some of it is being converted into heat, resulting in a loss of total pressure. So as the air in this boundary layer exits the leech of the sail, it's been slowed as well as had its direction changed, and this loss of momentum is the skin friction acting on the sail. But since the pressure doesn't change very much across the boundary layer, the flow acts much like it would about a body that had no boundary layer at all, but whose shape was like that of the sail plus the boundary layer thickness.

Because the boundary layer effectively changes the shape, almost everything else about sail trim and sail shape is all about keeping the boundary layer thin so that effective shape of the sail is much like the physical shape. When you put telltales on the sail, you're looking to see what's happening in the boundary layer. If the yarn lays back flat, then the flow in the boundary layer is smoothly following the sail's shape, and the air is being bent the way you want it to and you're getting the desired force on the sail. If the yarn is going nuts or pointing foward, the boundary layer is doing something quite different, and you have to go some distance out from the sail to get into the outer flow - so the effective shape doesn't look anything like the physical shape of the sail. This is what happens when the sail stalls and the effective shape looks like a big fat wedge whose lee side isn't bending the wind near as much as you'd like, so the lift (component of the force at right angles to the apparent wind) is much less and the drag (component of the force parallel to the apparent wind) is excessive. The combination of the two is smaller and points aft, robbing the boat of the drive you'd like to see.

I think I'll stop there. If this makes sense to you, I can go into more detail on the care and feeding of the boundary layer.

 

While we are on the subject of old theories that didn't pan out like the slot theory (and the flat earth theory), I would like to get other peoples opinions on some other theories that really bother me. The more I read the more irritated I get with some of the vortex and circulation theories I hear.
The Helmhold vortex theorem states that "vorticies end on boundries or form a closed path". This theory is just plain wrong. A funnel cloud is a vortex that does not end on a boundry or form a closed loop. The vortex I create with a boat paddle does not extend to the bottom of the lake. I know that most text state that this theorem can be proven mathematically, but all you can prove is that the mathematical model you have chosen to represent the vortex does not accurately discribe the phenomena. From this misguided theory came another bizarre theory that "the circulation around the wing, the vortex shed off the wing tips and the start vortex back on the ground are a closed path therefore allowing lift to be generated. PUT DOWN THE CRACK PIPE. The start vortex has nothing to do with lift. What would hapen if a seagull flew through the start vortex after the plane was 1000ft in the air. Would the plane fall to the ground because the closed loop was broken?
But we aren't done with the stupid theories yet. The Kutta-Joukowski hypothesis about the start vortex acting like a gear to start a circulation around the wing that creates lift. These guys are some real glue sniffers. There is no real circulation around a wing. I know that by subtracting the average velocity vector it then looks like there is circulation, but that same trick can be used to argue that the cars in the right lane of the interstate are going backwards. The cars in the right lane aren't really going backwards and there isn't really any circulation just upwash down wash and a slight difference in velocity above and below the wing. I would venture to say that never in the history of aviation has a single particle ever traveled a circular path around a wing. Even if the start vortex did create this imaginary circulation, once the start vortex is shed what would sustain the circulation? is it some sort of pepetual motion?
I guess I'm just a slow learner but I have trouble accepting ideas that contradict all common sense (and sometime the laws of physics). Does anyone out there also have trouble believing the earth is flat or vortices are infinite.

 

I agree that any description of fluid mechanics has to agree with what we all observe in practice. However, the vortex theories with which you take issue have been well substantiated by experiment and form the basis of most practical fluid dynamic engineering calculations. I respect your legitimate questions, and my appologies to the rest of the board if I'm responding to an obvious troll.

When I was in college, one of the professors, Dr. C. T. Tsu, was doing research into tornadoes. He had made an experimental rig with a blower that exhausted through a duct with a spinning honeycomb disk inside, followed by an exquistely machined plexiglass nozzle. Below the vertically oriented nozzle was a ground board that could be moved up and down to vary the distance to the nozzle. To make a long story short, he found that he didn't need the nozzle, and he didn't even need the blower - all that was necessary was the rotating disk. It turns out tornadoes are a boundary layer phenomenon, and all you need is a rotating air mass in close proximity to a surface. That's why so much of the damage in hurricanes is actually due to tornadoes spawned by the hurricane's rotation. His rig produced tiny little tornadoes that had all the characteristics of the real thing, including the sheath at the bottom where debris (ground walnut shells, for the model) is picked up. So it's not correct to say that the tornado doesn't obey Helmholz' laws. One end does end at the boundary to the fluid and the other end is the concentration of the vorticity already contained in the airmass. You need both - the surface and the rotation. If the surface is too far away from the rotating airmass you don't get tornadoes. If this still seems to contradict the Helmholtz theorem, remember that the theorem specifically assumed an irrotational fluid in which the net vorticity had to add up to zero. That assumption is violated by the conditions that spawn tornadoes, just as it is violated inside the boundary layer of the wind flowing around a sail.

As for the paddle, the two vortices you see at the surface are in fact the ends of one vortex that goes down the side of the paddle, wraps around the tip, and comes up the other side. Prandtl even used the analogy of the flow about a downward-moving paddle to describe the vortex wake left by a wing:

"Instead of a downward acceleration of the wing itself in its various consecutive positions we shall consider an instantenous acceleration (impulse) of the whole surface of separation [meaning the depressed wake behind the wing - TS]. In other words, this surface of separation is momentarily solidified into a 'board,' and this board is given a downward impulse (In order to take care of the variation of w1 with x, the 'board' may be considered elastic)." (Prandtl, L.and Tietjens, O. G., "Applied Hydro- and Aeromechanics," Dover Publications, Inc., NY, 1934.Section 111, pp. 192)

So, you're right - the vortices don't go all the way to the bottom of the lake. They are a continuous loop and only have ends at the boundary of the fluid, just as the Helmholtz theory says they must.

I think it would be perfectly valid to describe automobile traffic by a mean velocity and a perturbation, both positive and negative, with respect to that mean velocity. So relative to the mean flow, yes, some cars would be moving backward and some moving forward. That doesn't mean that their total speed is negative any more than it does for the flow on the windward side of a sail.

The vortices used in the Helmholtz theorem are one solution to the approximation of the flow phyics that result from assuming an inviscid fluid. It's one component used to describe the flowfield by superposition, in addition to a uniform flow and sources/sinks. The circulation about a wing and the Kutta condition used to determine its value are really just approximations used to model the vorticity generated in the boundary layer. By combining all three of these elements, one can put together a very realistic approximation to the flow that accounts quite well for lift and induced drag.

Presumably your argument about interrupting the starting vortex means that the entire vortex structure would have to fall apart. But that belies a misunderstanding of the starting vortex. First of all, there isn't a large, distinct starting vortex in most cases because the lift comes on gradually, generating a diffuse vortex sheet instead of the single large vortex of an idealized impulsive startup. And this diffuse sheet decays away because of the viscosity in the air. Large vortices also spawn smaller ones through instabilities in the flow. As Lewis Richardson put it,

Big whorls have little whorls,
Which feed on their velocity,
And little whorls have lesser whorls,
And so on to viscosity.

(see, for example, http://mixing.oce.orst.edu/people/jmoum/courseinfo/3Dturbulence.pdf)

Second, under the assumption of an inviscid irrotational fluid, the flow about your proverbial seagull would be the sum of both the flow about the seagull in the absence of the vortex and the vortex itself, so the seagull would not destroy the vortex just by flying through it. The seagull would experience quite a jolt going through the core, but the lifting surface that generated the vortex would not be affected.

The infinite vortices are just an approximation that simplify the flow physics so to be able to make decent engineering calculations with a reasonable effort. Just like most of us function quite well using the flat earth approximation for our maps and just about everything we do in everyday life. It's only if we have to concern ourselves with more extreme situations like orbital mechanics or the difference between the rhumb line and great circle route of a trans-oceanic crossing that the flat earth assumption proves inadequate and we have to assume a round earth. Which is itself an approximation that doesn't give good enough results in even more demanding situations.

 

Erik wrote:
I am a bit confused with the explanations of how the sail actually pushes the boat forward. Do anyone have a good scientific explanation? Not just "The lower pressure on the leeward side sucks the sail forward".
/ErikW
_______________________________________
I would encourage anyone interested in this subject, and that is looking for a simplified explanation of 'lift' to read these two articles:

1) Taking Flight, New Scientist magazine 5 May 2001

http://www.steamradio.com/pipermail/multihulls/2001-June/003583.html



2) The Physics of Airplanes---Why We Go Up, Discover magazine Apr 2001

http://www.discover.com/apr_01/featphysics.html

Enjoy, I did, Brian

 

Hi Brian,

Can you expand on this a bit. I'm reading you as saying that a sloop rig can point higher than the equivalent uni-rig... Small cat context.

Regards,
Colin
www.sailwave.com

 

Colin wrote: I'm reading you as saying that a sloop rig can point higher than the equivalent uni-rig

Yes, the very existance of the two sails means there exist a slot between them. This slot will normally be of such a nature as to restrict a full flow between them; so it diverts some of this flow around the outer sides of the two sails. If one looks at the fow patterns of this diverted flow, it is termed an upwash on the leading sail.....this upwash is a slight change in the incident angle of attack of the leading sail, or in other words the sail can be pointed slightly higher into this 'new wind direction' that it sees.

The trailing sail (mainsail) experiences a downwash which makes it more difficult for it to point as high. And in some cases can 'appear' as backwinded.

Is that understandable? or should I try a different wording?

 

Hi Brian,

Thanks very much for the reply; I think I see the argument...

But just to clarify: consider a uni-rig sailing up-wind such that at that angle its VMG is better than any other angle. Now consider that same boat as a sloop also sailing up-wind at an angle that maximises its VMG. In the right circumstances (sea-state, tuning, etc) it's possible that the sloop is pointing higher than the uni-rig.

And the reason is that the advantages provided to the jib by the angle of the upwash from the main (and high pressure from the windward side of the main?) outweigh the disadvantages provided to the main by the downwash of the jib.

So what about the 'slot effect' everybody seems to assume in our club - i.e. that the jib accelerates air over the lee of the main, reducing pressure and increasing left. Is that happening as well further away from the sails?

I've seen the "slot effect" referred to as a "myth" recently but folk seem to sail fast by using it as a mental model... Is it a myth?

Please excuse my ignorance here; two weeks ago I looked on-line to confirm my understanding about how aero/airfoils + slot worked and got hit by a maelstrom of different arguments; all of which I suspect have an element of truth to them...

Regards,
Colin
www.sailwave.com

 

I'm not sure if it's apropo, but one thing a monohull sailor has to learn when sailing a performance cat is that you want to sheet in as hard as you can without stalling, not a little as you can without luffing.

 

The problem with many theories, is that the proponents of them refuse to observe reality. Seems that the theorethical "proof" takes the place of experimenting. If the Wright brothers had payed attention to the scientists of the time, we'd still be ground bound. I grew up listening to the wind slot theories, but they didn't make sense to me. However, just look at the telltales on you leeward shrouds. They don't show more speed. Sit between the jib and the main, and the wind feels less not more. I agree there is a modification of flow, and it helps to point higher. It makes the air flow separation on the leeward side of the main shift aft.

 

Yes indeed. So many aerodynamic explanations are like one of Kipling's "Just-So Stories".

The best explanation I've seen of high-lift aerodynamics and the interaction between multiple surfaces is A.M.O Smith's 1975 Wright Brother's Lecture, "High Lift Aerodynamics", AIAA Journal of Aircraft. (Don't have the precise reference handy- Sept. if I recall correctly)