sail aerodynamics

PI, The site makes me wonder what he might say about the Kutta condition?

But: if he's right even a little, so this little gedanken experiment with breakfast goes, with a 165% jib, as pilots might say, is the main more Newton, and the jib more Bernoulli? With a 95%?

Paul

 

PI: I recently went through some painful 'thinking' about lift and drag, but came to very different conclusions. These are the simple examples I 'thought' my way through.
First some definitions: Drag is a force parallel to the apparent wind direction. Lift is a force perpendicular to the apparent wind. Note that the angle of attack, geometry of the aerofoil etc do not enter into this definition. When I first started investigating aerodynamics, I was confused until I picked up this definition, and thinking in these terms really helped to simplify things.
All real objects produce drag. Aerofoils also produce lift. Which is most useful to a sailboat?
Some examples:
Craft A is a raft with a crude hut built on the deck--no sail, no keel. Its 'airfoil' (hut) produces only drag, and its 'hydrofoil' (raft) produces only drag. The 'sailboat', powered by the wind, drifts straight downwind (assuming no current).
Now imagine adding a sail which can produce lift (perpendicular to the wind). Now this Craft B can be made to sail in any downwind direction. If the aero lift were equal to the aero drag, the boat could sail at 45 deg off the wind direction. If there were pure aero lift with no aero drag, in theory it could sail at 90 deg to the wind (very slowly).
For Craft C, take away the sail, but add a (steerable) keel, and you have the same performance as Craft B. Still can't go upwind, but it can sail in any downwind direction, depending on the Lift/Drag ratio of the keel.
For Craft D, you have both a sail and a keel, both capable of creating lift. Now you can sail upwind, and the better the L/D ratios of your sail and your keel/hull, the steeper you can go upwind.
Things I learned from this are:
- Lift is good, drag is bad -- even if you want to go straight downwind. A high drag (spinnaker) skiff can never reach windspeed, but a high L/D craft can go downwind faster than windspeed by moving at an angle to downwind. I've got a spreadsheet that demonstrates this, which I will try to post in the next few days.
- The keel/hull is just as important as the sail.

Hope this helps, and doesn't contradict any laws of nature.
Best,
Matt

 

Hi Matt,

Lift and drag are really just a convenient means of breaking the force into component parts. It is equally valid to chose another set of axes, which run parallel and perpendicular to the desired direction of motion. The drawing attached attempts to show this, and also clarifies, pictorially, the points I was trying to explain earlier. Drag and (predominantly) lift, both contribute to the sway force, which causes leeway and, when coupled with a keel/centreboard, produces a heeling moment. In this respect large amounts of lift are bad when sailing upwind.
In the diagram, the red zone shows the part of the sail that is wholly detrimental to upwind performance - the force is backwards and sideways, when all you really want is forward. The green zone covers the part of the sail that provides the majority of the forward surge, with little sway force (heeling moment). Note, this is not the area of maximum lift, but it is the most useful part. The amber zone contributes to forward motion, but also contributes significantly to the heeling moment, so whether it is a Good or a Bad Thing depends on the available righting moment of the boat.
What a high lft/drag ratio does is allow the force vectors to point as far forward as possible. Minimising drag is definitely the goal, but for the part of the sail in the red zone (half the sail!) lift should also be minimised. Seems to me the easiest way to minimise both lift and drag is to do without that part of the sail altogether.
The other point to note is that the air flowing round a conventional mast is seperated for most of the green zone, so presumably relies more on the amber zone for its drive, which means a much larger heeling moment for the same forward surge. Wing masts prevent thi seperation so can take advantage of the green zone.

Shoot away if I have it wrong. I don't know the answers, just putting this here for discussion.

 

Pi: Nice diagram. I think I see what you're getting at.

You're right about any set of axes being valid--I've just found that referring it to app. wind direction is the simplest when looking at sail forces. After all, the sail doesn't know which way the boat is moving. You can work out the sail force knowing only the apparent wind and the angle of attack. (well, except for interactions between main/jib changing with boat heading, etc... I'm trying to keep it simple)

The problem I think is that you can't just cut off the 'bad' parts of the sail without affecting the 'good' parts. The leading edge section which is actually pulling the sail upwind is only possible with the draggy trailing section.

Looking at the whole sail, rather than just parts of it, the net sail force will always be somewhat downwind. The theoretical ideal would be a sail that is all lift and no drag. (I added a page 2 to your diagram and attached) Even this idealized sail does not give a net upwind force.

As the boat points higher and higher upwind, the lift has less and less of a forward component and more of a heeling component. Nonetheless, drag is worse, since it has a heeling plus a backwards component, for a net loss.

That's a good point about the mast causing separation in a critical area. I have often wondered if having a giant luff sleeve could help this, or would it assume the wrong shape? Maybe some balance between aerodynamic forces (suction pulling the luff sleeve forward and leeward -good) and sail tension (pulling the luff sleeve back -bad). Has anyone tried/studied this?

Matt

 

Cheers Matt. The direction that the boat is moving is critical. For example, if the boat is travelling perpendicular to the app wind, then lift should be maximised (all over the sail), where as, as explained above, when travelling upwind there is different criteria. So whilst the sail still generates forces in exactly the same way irrespective of the direction of travel, the requirements of the sail differ.

Marchaj has done some research into luff sleeves, but concluded they didn't work due to the blunt leading edge of the round masts. However, he seemed to use pretty big diameter masts, and of course windsurfers use luff sleeves and sail quicker than most dinghies.

 

Hi everybody., I haven't been able to read all posts on this subject, but now that you are discussing luff sleeves, i would like to throw in another idea.(apologies if already mentioned/discussed)
I guess our sails have somewhat more in common with STOL aircaft (short takeoff and landing) than any other aircraft due to relatively slow flow of air over the foils.
This type of craft, and indeed all modern passenger planes have leading edge slats, which are deployed where maximum leading edge (lift) performance is required, which is during take off.
We know that we have a problem with our masts, so why dont we use slats attached/ hinged to the mast, which can also be tacked from one position to another and regulate the inflow of air entering the equation, thereby making the mast itself less significant.
I am not intending to produce design objectives here, but just an idea of introducing a control surface before the mast to enable a better controlled entry into the mainsail.

 

Actually, a modern state-of-the-art boardsail has a cambered sleeve with a max thickness exceeding the mast diameter. The wider the sleeve chordwise, the greater the effect. Here is an illustration:

 

I have got to agree 100% with Hansen having owned and sailed every sailboard sail type ever made since 1980. The mast in most sailboard designs, even going back 20 years, was not really an impediment to performance of the sail. At one stage super skinny masts were introduced to the market and sails were made to fit these skinny masts. To my best knowledge these rigs were NOT noticably faster than conventional diameter mast rigs for sailboards.
Maybe Marchaj was plain wrong, and was unable to foresee future mast and rig develpments.

 

Perfectly true. However, lift and drag are very useful for calculating performance because you don't need to know the orientation of the sail or the boat. All you need to know is the point of sail, lift/drag ratio of everything in the air, and the lift/drag ratio of everything in the water to calculate the boat-speed/wind-speed ratio.

BTW, the name typically given to the force component that is parallel to the chord is axial force, and the component that is at right angles to the chord is normal force.

The problem with the drawing (assuming it depicts attached flow) is that if you add up all the vectors shown, the drag is near zero (exactly zero if you use inviscid flow assumptions to calculate the vectors). The aerodynamic drag of a sail comes mostly from aerodynamic forces that are tangential to the sail (skin friction), and from the fact that the local apparent wind direction is not the same as the difference between the boat's velocity and the true wind direction (the free-stream apparent wind direction). The skin friction isn't shown at all on the diagram.

The boat sails in a header of its own making, tilting the aerodynamic force vector aft, and the component parallel to the free-stream apparent wind that results from this tilt is generally accounted for as part of the drag. This induced drag is a major source of drag, and it's not shown directly on the diagram, either.

So the diagram is somewhat misleading because it implies that the shape of the camber has a major impact on the drag or thrust because of the way that the pressures are oriented along the chord of the sail. I turns out this isn't really the case at all. Although camber affects the lift at a given angle of attack, the angle of attack can, in principle, be adjusted to restore any given amount of lift.

The amount and shape of the camber influences the drag, but does so indirectly through its effect on the boundary layer by way of the shaping of the pressure distribution and the effect of the pressure distribution on the boundary layer development. If it weren't for the boundary layer, it wouldn't matter at all what shape the pressure distribution was, and thus what the camber shape was.

The chord-wise component of the pressure at the leading edge is known as leading edge thrust. Thin, sharp leading edges tend to promote a separation bubble on the lee side of the leading edge that can produce low pressures that result in comparable lift to a thick leading edge, but are not oriented as much in the forward direction, reducing leading edge thrust and increasing drag. In inviscid flow theory, the thin leading edge produces infinite velocity around zero area, and the combination just balances all the other aft-directed pressure components. In practical flows, this isn't the case, and the improvement in leading edge thrust is, indeed, the major advantage of the wingmast.

Wilkinson uses a schematic diagram similar to yours, but broken up into nine zones, shown below (1., 2.). The flat regions (II, V, VII) are separated flow. Zone I provides the leading edge thrust. A wingmast makes zone II much smaller and allows the pressure distribution in zone I to be much higher.

The second figure below of a wingmast pressure distribution has the features of Wilkinson's illustration. Zone II is very small - it just bridges the crease in the lee-side mast/sail junction. There's an additional separation bubble on the mast itself, due to laminar separation and transition to a turbulent boundary layer. This particular example is taken below the onset of stall, so there's no zone V.

1. Wilkinson, Stuart, "Partially Separated Flows Around 2D Masts and Sails", PhD thesis, Ship Science Department, University of Southampton, 1984)

2. Wilkinson, Stuart, "Static Pressure Distributions over 2D Mast/Sail Geometries", Marine Technology, Vol. 26, No. 4, Oct., 1989, pp. 333 - 337.

 

Hi Tom,

Thanks for your input - much appreciated as always.

The advantages of using lift and drag for aeroplane wings is clear, but I think axial/normal is more useful for boats, precisely because the orienation of the boat to the wind is so important. Assume that (upwind) the sail is sheeted to the centreline so that the boat and sail point (and travel) in the same direction. The aim is (obviously) to maximise VMG to windward, which is entirely dependent on the boat's heading as this affects both the angle of attack of the sail and the cosine of the angle to dead up wind.

"The boat sails in a header of its own making, tilting the aerodynamic force vector aft, and the component parallel to the free-stream apparent wind that results from this tilt is generally accounted for as part of the drag. This induced drag is a major source of drag, and it's not shown directly on the diagram, either."

My understanding is that induced drag is a function of AR and planform, not section shape, therefore I was simplifying to 2d. Presumably induced drag is constant across the chord length and can simply be superimposed with the effect of tilting the pressure vectors aft?

Also, I’m assuming that skin friction is a function of surface roughness and surface area. Provided the same material is used, surface roughness is constant across different section shapes. Surface area increases with camber (for constant chord, not constant force), so a flatter sail is better in this respect, although I guess skin friction is a fairly small total of overall drag so can be ignored for comparative purposes.

"So the diagram is somewhat misleading because it implies that the shape of the camber has a major impact on the drag or thrust because of the way that the pressures are oriented along the chord of the sail. I turns out this isn't really the case at all. Although camber affects the lift at a given angle of attack, the angle of attack can, in principle, be adjusted to restore any given amount of lift."

This is exactly the point I was trying to make, but I draw a different conclusion. If you have to increase the angle of attack by bearing away, this is a bad thing because you are not sailing as close to the wind, hence VMG is worse. The shape of the sail camber DOES have an affect on the thrust and drag.

At least we agree about the positive impact of wing masts!

Thanks for the references. The problem I always have with pressures illustrated this way, is that you have no idea of the axial/normal components, which (IMHO) is the vital info for boats.

 

Not entirely right, since for the same span and lift and induced drag, you can trade chord for CL.

 

Soft Wing Sail

Brian Eiland suggested this might interest you all.

From Duckworks, details of a Wing sail from Israel.
http://www.omerwingsail.com/

Pericles

 

Soft Wing Sail

Ilan Gonen has replied.

http://www.boatdesign.net/forums/showthread.php?p=152300&highlight=pericles#post152300

Pericles

 

Sail Induced Drag & Split Tips

Hi Everybody,
Reading your thread, I feel like a MIT student. many things to learn for me. In order to bring my little contribution, I would like to mention the following concept, I didn't see yet, it is:
" Non Linear Aerodynamic consideration" or "higher order effects on vortex drag", as rocket scientists call it.
Or it is also observed on eagle wing tip feathers.

I recommend to read page 19 of the PDF attached, where a split tip wing vortex is modelized. Conclusion is a significant reduction in induced drag and/or increase in L/D.

Trying to understand this issue, I guess that a vortex is a 3 dimensions "item", one dimension is related to apparent windspeed, but the other dimensions are likely to be related to pressure difference between the 2 sides of the sail/wing section at the tip, combined with the chord's lenght at the tip, which is likely to drive vortex diameter
So if you halve the chord at the tip, (everything else constant, ...)each vortex is likely to be twice smaller in diameter, compared to the basic wingtip vortex (reference vortex), and therefore the volume of air involved is proportional to Diameter squared, so each small vortex generates 4 times less induced drag than the reference vortex.

Separation of vortex wakes, using some diehdral for the split tip might also help to reduce drag ?

May be we could find here a simple and cost effective way to improve sails'performance.

For a catamaran I imagine that it could be possible to use a split foot sail, combined with trampoline effect, to improve the low component of induced drag.
For the top of the sail, it seems more challenging as you are supposed to have the fore part of the split-tip bending on the leeside while the aft part of the split is supposed to come windward, in order to avoid vortex interferences.

Sorry, my English is far from perfect, I hope it remains understandable.

 

I think one of the most important papers on the subject is Max Munk's "Minimum Induced drag of Aerofoils," NACA-TR-121, 1923. Ignore all of the sextuple integrals and read the words - especially the ones in italics. His theory applies to nonplanar as well as planar lifting surfaces.

To minimize the induced drag, the induced velocity at right angles to the surface ("downwash") shoud be uniform across the span and proportional to the cosine of the dihedral angle. And for multiple lifting surfaces, the induced velocity should be the same for all the surfaces. All of the nonplanar surfaces in Ilan Kroo's paper could have been analyzed, and their loadings optimized, using these principles.

Probably the most important predictor of lift/drag ratio is the wetted aspect ratio: span^2/(total wetted area). For example, the induced drag of a ring is equivalent to that of a planar surface whose span is sqrt(2) times the diameter of the ring - so the ring has much less drag for the same span. But the circumfrence of the ring is pi times the diameter. So the ring will have more than double the wetted area of a planar wing with the same induced drag. This is typically the case with nonplanar surfaces. The induced drag of the nonplanar surface is lower for the same span, but the same result could have been obtained with less surface area by extending the span of the planar surface. So nonplanar surfaces are most useful if there is some limitation on the span.

Sail rigs are limited by the stability of the hull when the wind gets above a certain speed. So a key criterion for a sail rig is not minimum induced drag, but the minimum induced drag for a given heeling moment. There's not a unique solution to this problem. R. T. Jones showed the minimum drag for a given moment is obtained with a linear variation in the induced velocity across the span. (Jones, Robert T., "The Spanwise Distribution Of Lift For Minimum Induced Drag Of Wings Having A Given Lift And A Given Bending Moment", NACA-TN-2249, 1950) You can get any moment you desire, including zero, if you wish. However, there are practical limits for sail rigs, such as zero lift at the head instead of negative lift.

If you combine the results of Munk and Jones, you can take into account factors like the gap between the foot and the water's surface, heel angle, and heeling moment. This spreadsheet implements a lifting line analysis that allows you to define an induced velocity profile in the Trefftz plane, and then calculate the spanwise loading and planar planform to implement it. The spreadsheet could easily be extended to nonplanar surfaces.

This would allow you to optimize a nonplanar rig for minimum drag given a constrained heeling moment. This will not necessarily result in a symmetrical geometry, however. For example, say you were optimizing a "T" shape, like a keel with wings. The optimum loading of the wings for a given tack may not result in the same planform shape for the windward and leeward wings. But it may be possible to use Excel's solver to find the optimum shape with practical geometric constraints.