sail aerodynamics

[brian eiland]

Lift Forces, aircraft vs sailing

First off, let me apologize to you Mark. I had not realized your very extensive background in aerodynamics.

Actually, not so much. The "normal-velocity at slat TE" effect described by AMO Smith actually has little effect on the lift. See the attached panel solution. Whether the jib's leech is just under the mast or just above the mast doesn't affect the lift very much, despite a very large change in the normal velocity seen by the leech.

In light of classical thin-airfoil theory, none of this is very surprising. This theory indicates that for a given AoA, lift is almost entirely determined by the camber at the rear of the airfoil. Modifying the shape near front like in this case has almost no effect. In the context of this theory, a small slot between the jib and mainsail is just a tiny interval where the modeling vortex sheet has zero strength. This small interval will only affect the flow in its immediate vicinity, but it cannot influence the overall circulation and lift.

So I looked back at this posting of yours, and I still have a question.
1) Is this lift force you are talking about here primarily a force that would act perpendicular to an aircraft wing giving it lift?
2) Would much, or any, of this lift force at the rear of the sail's airfoil be driving a boat forward?

Perhaps what I am having trouble visualizing is how is the lift force that is being generated by the cambered sail getting transferred to the vessel. That force has to act upon something to transmit its force to the vessel. In the case of an airplane its the wing, in the case of a sailboat its the sail itself that's the initial element acted upon. I had asked related questions here:
Sail Loading on the Rig, Rig Loading on the Vessel

I assume there are a whole lot of little lift forces generated across the surface of the sail, that taken in total add up to the sum-total lift force. But those little lift force elements at the leech of the sail do little for forward drive of the vessel in my opinion?? Maybe this image I visualize very often has confused me?

 

[SukiSolo]

I'd definitely agree with Mikko about twist and leech control being paramount, although on a una rig (fully battened) I find keeping the chord reasonably forward (and being able to hold it there) also very useful. My newest sail is easily the quickest I've had and requires careful use of leech tension (kicker primarily) but rewards good adjustment. It also is cut (correctly) to allow side bend of the mast to open and close the leech in the over power situation. You can visually see it, and feel it, quite easily. In disturbed air, rolling over trees and such I prefer to keep a more twisted leech shape (on all points), whereas in more laminar air a straighter tighter leech seems faster. Using the tell tales is not enough to guide you (completely) to the optimum - unless you use your head and experiment a little.

I had one sail, a light Mylar tri radial cut circa 1990 which was very quick especially in a 5 - 6 upwind with a motoring top leech....
However the key was that the leech opened up properly below the motoring top panel and it was this that stayed in a 'fast' position. Eventually the material which was a laminated Mylar around Kevlar strands at 90 deg stretched and the sail lost it's edge. Stretched quite a way without breaking though, which I thought it would.

On a una rig, there will be no (or virtually no) leech return IF you define leech return as crossing the centreline axis (or plane) in a strong breeze - because the boom will be further out from that plane. So in a Force 5+ all drive vectors will be forward, with maybe the extreme end of the (bottom) leech neutral.

Right now, I'm more convinced (than ever) that the exit flow off a sail is the most critical part in reducing drag. Really nice to see some top notch theorising, thinking and practical work and computation looking at these problems.

 

[brian eiland]

How Sails Work

.... Maybe this image I visualize very often has confused me?

So I guess the images in this PDF have some misconceptions??

 

[markdrela]

I would really like to hear from Mr. Drela and Mikko a rational explanation about why the above reasoning does not work in practice.

First of all, you're making a 2D airfoil argument, so I'll assume the flow is 2D.

As you move away from the airfoil's near-field, the V1-V2 velocity difference, or flow turning, is entirely related to the overall circulation Gamma. When V1 and V2 are defined on a circle of radius r which is large relative to the chord, the relation is

dV = V1 - V2 = j Gamma / ( pi r )

where j is the unit vector normal to the bulk flow (i.e. in the lift direction).

Note that the leech return angle does not directly appear here. And in fact, dV decreases to zero as the chosen r is made large, so clearly it doesn't make sense to use direct airfoil geometry arguments when examining distant velocity triangles.

The "leech return" angle affects dV and the lift only via its influence on Gamma. This influence is quantified by 2D thin airfoil theory. If the sail airfoil is flat, so the leech return angle is also the overall angle of attack alpha, then we have an analytic solution:

Gamma = pi V c alpha

which is equivalent to the familar

cl = 2 pi alpha



The shape of the wake does not affect the above arguments.

 

[markdrela]

I assume there are a whole lot of little lift forces generated across the surface of the sail, that taken in total add up to the sum-total lift force. But those little lift force elements at the leech of the sail do little for forward drive of the vessel in my opinion?? Maybe this image I visualize very often has confused me?

It's not very useful to consider the loadings on the "leech" and "luff" regions separately, or on the mainsail and jib separately, because they always interact very strongly. The mainsail generates a big "drag", but in doing so it causes the jib to have a big "thrust". Of course what matters is the overall load, which is completely defined by the lift force perpendicular to the apparent wind, and the drag force parallel to the apparent wind.

In the 2D airfoil pressure force vector diagram you show, some of the arrows have a large "drag" and some have a large "thrust". But since this is a 2D inviscid flow, you can be 100% sure that the "drag" and "thrust" forces cancel EXACTLY, and the net drag is zero. It's not worth considering further.

Similarly, to determine the drive of any sail rig all we need to worry about is the overall circulation (which is determined mainly by the "leech return angle"), since this is what determines the overall lift. Twiddling with the jib shapes, slots, overlaps, etc., merely spreads this given lift among the various sheets, but it cannot change the overall lift.

The jib, slots, etc., are important only in that they affect the overall viscous drag of the rig. Redistributing the loads will also affect the yawing moment and the helm trim, so that's another but probably secondary consideration.

 

[markdrela]

So I guess the images in this PDF have some misconceptions??

Bogotaj's article is correct from what I can see.

 

[DCockey]

Remember that changing the shape near the leech affects the flow and pressure distribution over the entire sail.

Also, lift is defined as the force component normal to the approaching free stream, not normal to the local surface.

Edit - Mark responded before I clicked Post.

 

[daiquiri]

The shape of the wake does not affect the above arguments.

Thanks for the reply. This is the part which I would like to discuss a bit. It somehow relates to this reply too:

Remember that changing the shape near the leech affects the flow and pressure distribution over the entire sail.

What I am thinking about are two sails, the first one with a nicely streamlined mast (like a wingmast) and the second one with a separation-inducing mast. they will have two flow patterns which can be very roughly sketched like this:


In both cases, the resulting aerodynamic force will be V2-V1 (vectorial). And in both cases the vector V1 is the same. But the vector V2 cannot be the same, IMO.
The wake behind the second sail extends and expands to the far field behind the sail and hence the V2,w and V2,l will keep diverging.
Now, IMO, the vector V2 to be used in the calculation V2-V1 is the mean vector between V2,w and V2,l as shown in the pic.

In the first case (streamlined mast) the flow is attached at the trailing edge, we have:
V2 = V2,w = V2,l
- hence, the exit angle of the vector V2 coincides with the leech angle.

But when there is a wake V2 no longer coincides with the V2,w and has a smaller exit angle (being an average of V2,w and V2,l). Hence, the resulting force is smaller.
In terms of circulation, the separation decreases the circulation around the sail section, hence it decreases lift.

That's why I still struggle to understand the phrase

The shape of the wake does not affect the above arguments.

True, the wake absolutely does not affect the validity of the arguments based on the general circulation theory, but it should affect the value of circulation - and hence the of the resulting lift force.
So what am I missing there?

 

[Jamie Kennedy]

Interesting discussion. I've always felt it useful to look at things from both momentum theory and energy theory, similar to what you might do with solids and liquid kinematics and dynamics. Some of the old slot theories and such can be done away with though, especially when sailing an Optimist or Laser. ;-)

I find the above diagram very useful, but better if you also look at it with the parasitic, skin, and form drags of mast and sail cloth thrown in as well.

 

[markdrela]

True, the wake absolutely does not affect the validity of the arguments based on the general circulation theory, but it should affect the value of circulation - and hence the of the resulting lift force. So what am I missing there?

Yes, the boundary layer on the airfoil affects Gamma and hence lift because its displacement thickness changes the apparent shape of the airfoil.

My main issue with your arguments is that the V1-V2 difference completely depends on where you pick points 1 and 2. If you pick points 1 and 2 far from the airfoil, then V1-V2 is zero. The presence of the wake does not change this fact.

BTW...
Your sketch shows that V2,l and V2,w continue to diverge in the wake. That's not what happens. Typically the displacement thickness is maximum at the trailing edge, and then decreases in the near wake and ultimately asymptotes to a constant (equal to half the airfoil's drag area). So V2,l and V2,w will converge shortly downstream of the trailing edge, and then asymptotically become parallel far downstream.

 

[Doug Halsey]

the lift is almost unaffected by:
* the incidence of the front parts of the sail (i.e. the jib or jibs)
* the size, number, or orientation of the slots, if any
* any overlap between the sheets

This appears to contradict the experimental results shown in the attached figure, which was taken from the frequently-quoted 1975 Wright Brothers Lecture on "High-Lift Aerodynamics" by A.M.O. Smith.

 

[markdrela]

This appears to contradict the experimental results shown in the attached figure, which was taken from the frequently-quoted 1975 Wright Brothers Lecture on "High-Lift Aerodynamics" by A.M.O. Smith.

In the unstalled region, pretty much all the curves fall into one broad line, which is what I was referring to. For a given alpha and "leech return angle", the CL doesn't change much.

In that post I also said:

The primary function of slots is to better manage boundary layers, and thus allow larger rear-sheet incidence angles and hence larger lift without separation.

which is clearly what's happening in the figure. More slots mainly increases CLmax, not unstalled CL(alpha).

The various wiggles in the curves indicate that significant separation is present thoughout the higher alpha range. Also at alpha=12 deg, the lift drops for 0 to 1 to 2 slots. This indicates that they in the process of adding the first few slots, the net rear camber was also decreased. Apples and oranges, etc.

 

[Doug Halsey]

The number of slots on this wing clearly affects whether particular values of CL are achievable, so in that sense I would say it affects "the lift."

Maybe we're just bickering over semantics though

 

[Petros]

Perhaps what I am having trouble visualizing is how is the lift force that is being generated by the cambered sail getting transferred to the vessel. That force has to act upon something to transmit its force to the vessel. In the case of an airplane its the wing, in the case of a sailboat its the sail itself that's the initial element acted upon.

Brian,

I did not see your question answered yet, it appears these knwolegable folks may have given you too much information as a means of explaination.

as far as how a sail generates forward thrust to keep you underway, it might be useful to keep basics in mind:

1. when you curve or accelerate a fluid with mass (this could be air, or water), there is an equal and opposite reaction. that is how fluid mechanics works. F=ma, the force generated is the mass of the air you accelerated by curving it over the surface of the sail.

2. when you "bend" (or accelerate) the moving air, the sail reacts in the manner described elsewhere here, creating the thrust or low pressure area distributed over the surface (often this low pressure area is distributed in a very irregular way). The shape of that distribution is often the material of debate and tweaking to improve the total thrust you get off the sail, and why proper sail trim is so important to good performance.

3. This low pressure area is transmitted to the mast and boom through the fabric, and than through the rigging, sheets and lines to the hull. So if you can envision pulling on the mast for example, the force on the mast is than transmitted to the hull though the shrouds, stays, step, and sheets, pulling the boat forward.

4. it is useful to keep in mind that the lift off the sail is considered perpendicular to the plane of the sail, which is rarely aligned to the direction of travel, so the forward component of that lift is actually what drives you forward, the other component is what causes the boat to heel over, resisted by the keel or dagger boards in the water (which keep the hull from sliding sideways over the water). The more lift off the sail, and the higher the center of this lift acts, the more heeling or sideways force will be acting on the hull.

Personally I think too that the drag of the sails and rigging also add to the heeling of the hull. But at lower speeds of most cursing boats the effect is small, but it does appear that more recently there has been some effort to reduce the drag of all the rigging to improve the sails efficiency for racing boats (meaning that it will extract more forward motion out of the same size sail in the same wind).

if you can visualize the sail surface as a lifting surface that generates lift perpendicular to it surface (based on how much camber there is in it and the angle of attack it has on the free steam air flow), that lifting force is transmitted to the mast and boom. The mast and boom is held in place by the shrouds, sheets and rigging, which is attached to the hull. So if you could put little strain gags at the mast step, the shroud and stay anchors in the hull, and where the sheets attach to the hull or traveler, you would see that each one is contributing to pulling the hull forward, and if there is much side force on the rig, you will see that it also heels the hull over. That is basiclally the load path from moving air to hull of the driving force that move the sailboat forward.

is this what you are looking for?

 

[brian eiland]

.....
Similarly, to determine the drive of any sail rig all we need to worry about is the overall circulation (which is determined mainly by the "leech return angle"), since this is what determines the overall lift. Twiddling with the jib shapes, slots, overlaps, etc., merely spreads this given lift among the various sheets, but it cannot change the overall lift.

The jib, slots, etc., are important only in that they affect the overall viscous drag of the rig.....

Bogotaj's article is correct from what I can see.

Then I am trying to understand these quotes from Bogotaj's article. Are they all in accordance with the 'leech return' explanations?

Sails in Combination
Each sail by itself is much simpler than the combination of a foresail and mainsail as in the sloop rig. The sails are operating so close to each other that they both have significant interaction with the other.
The most interesting feature of this is that the two sails together produce more force to pull the boat than the sum of their forces if they were each alone.
The net result is that the total force of the two-sail system is increased, with the foresail gaining more than the mainsail loses.

Since the purpose of the sail is to develop force to move the boat in a forward direction, it would be most effective to have as much of the sail as possible operating with the largest possible pressure difference across it. The way to achieve that is to accelerate the air quickly around the curved leading edge of the sail in order to generate low pressure on the leeward side close to the luff and then maintain it back over a significant portion of the sail. This is achieved by imparting high curvature to the front of the sail. Once the flow is accelerated curvature can diminish and the flow will continue quickly around the leeward side of the sail. The back of the sail needs to be flatter in order to allow the flow to gradually decelerate to avoid stall as already described. These details are the basic factors that define the rounded entry with forward draft (position of maximum camber depth) and straight leech profile that has proven fast in typical sailing applications.

This is one of the reasons I have placed more emphasis on that nice big overlapping genoa of my aftmast rig, and brought the overlap back significantly, unlike some modern smaller jib vessels.

It is evident that a sail shape with more curvature aft keeps the air accelerated longer, which may produce a higher amount of total force due to a larger region of negative pressure. The problem is that the negative pressure vectors on the aft portion of the sail are angled more aft than those toward the front of the sail, so the amount of forward force that is produced in the direction that the boat travels is less, while the amount of sideways force that contributes to heeling and leeway is greater. It is also apparent that a shape with its camber aft has a shorter, steeper pressure recovery that will lead to earlier separation and stall.

I will say that I understand his explanations better than a lot of others being presented here.

Paul combines his practical understanding of sailing from his
experience as a successful racing sailor with his awareness of fluid dynamic
principles as an engineer to provide explanations of how sailboats work that are understandable to the average sailor.