# sail aerodynamics

Discussion in 'Hydrodynamics and Aerodynamics' started by Guest, Mar 21, 2002.

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### PetrosSenior Member

I do not see the need for a flame suit yet... I presume we are having a civil discussion here. I know a lot of aircraft aerodynamics, and have owned and been studying sail boats for years, but I am trying to apply the acquired knowledge across an industry gap. I do not presume to know very much about sail boat dynamics (not just the air, but you have to include the effects of the water on the hull, combined it appears to be a very complex interaction). So all of my previous posting was along the lines of my musing and speculation, I was not arguing a point. So tell me if I am misunderstanding anything about effects of the sail on a boat.

I do not think your last statement is correct BTW, all devices that generate lift in a fluid (be it liquid or gas, as in air) have an L/Dmax. Trying to sail at it at all points of the wind may be another issue of course, which may be what you are referring to. You may not have enough power or thrust from the sails to reach the speed of where L/Dmax occurs. But even with very high parasitic drag you will still have a L/D max, look at the old wire braced biplanes like the Jenny and others, they were very draggy, worse than modern ultralite aircraft. But they do have an L/D max, but sometimes you may not have enough power to fly level at it (it means you will need to be in a slight dive to reach the L/D max speed). The use of a sail is quite different than a wing, even if they work the same way. A wing generates lift upward to counteract gravity, a sail generates lift to propel a sailboat at all points to the wind ideally.

Yes, you would have to consider L/D of the whole system, not just the sail. I suppose you also have to included the hull/keel interaction as well. For example if a very high aspect ratio sail causes too much heel, the hull drag will go up, so your best L/D may drop off. My test mule was going to be a catamaran so I would not expect much change in heel anyway, and to limit the heeling variable hopefully enough to ignore it.

Drag would have to be a consideration if you are trying to break a new speed sailing record, at around 50 knots all the drag, parasitic and induced, are too large to ignore. At those speeds, a one inch by three inch teardrop shaped strut for example will have less drag than an 1/8" diameter steel cable. So bracing the mast with struts rather cable will have less drag. In a recreational mono-hull that only moves along at 6 to 8 knots at best, parasitic drag is not particularly large, and cable bracing is much simpler and less expensive.

One test I could do is build my little catamaran to maximize L/D, and go out and try it with my single element sail. And install a jib or a leading edge slot to create Clmax, at the expense of L/D max. And see if it any faster at a give wind speed or around a give course. It may be we need L/D optimized for certain legs of the course, and Clmax for others. I just have never seen a complete discussion of the relevance of L/D to sailing in any of my NA books nor on this forum. It does come up occasionally, I just do not have a clear picture of its relevance to sailing performance. I suspect it may be more important than it is considered by most.

A sail plane or hang glider goes furthest when flying at L/D max, a powered aircraft consumes less fuel when flying at L/D max. So why not should a sail boat move fastest when the whole system is operating at L/D max? The power used to drive the boat is that which can be extracted from the moving air relative to the boat. The most lift that can be extracted from the wind at the least drag, it seems to me, should yield the best speed. IF you can get more total lift at the expense of even higher drag, you will not be moving as fast. Conversely, if you sail for minimum drag, you sacrifice lift and speed since that would occur at a much lower speed. So it has to be that the best speed occurs where the L/D is best because that is where the most amount of excess power is available to drive the boat. You would have to have both the best L/d of the sail rig occur at the same speed as the best L/d of the hull/keel, which may be difficult to get to occur at all points to the wind.

Or am I missing something? Perhaps I am.

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### tspeerSenior Member

You can optimize on the basis of a fixed heeling moment. That's a reason for considering the dimensional lift to be fixed in the previous discussions - it's largely dictated by the stability limits of the craft if there's enough wind.

Say you have a given mast height, and you've optimized the planform of the rig to give you the minimum induced drag for that mast height. You can reduce the induced drag while keeping the same heeling moment by using a taller, more tapered planform. The taller rig won't have the minimum drag for its height, but it will have less drag than the rig optimized for the smaller span.

And yes, its aspect ratio will be higher if the sail area is kept constant. But the induced drag will still be lower even if there's more sail area to keep the same aspect ratio, and trimmed to maintain the same heeling moment.

This figure shows quantitatively what such a tradeoff would look like. Each point plotted is a different design, optimized for a given span and gap at the foot (dashed lines), or a given heeling moment and gap (solid lines). For the example shown, the more tapered rig can be about 17% taller and reduce the induced drag by about 20% for the same heeling moment.

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### RHoughRetro Dude

What we are saying is that if the heeling moment is kept fixed at HM = RM, an increase in effective span reduces induced drag. Right?

The lift force (not Cl) is constant for both rigs, so the added span is effectively a tip loss device added to the shorter rig.

Quick sketch ... Green is optimized area for short mast. Yellow is added area for greater span. Guesstimated "CE" does not change if yellow area is washed out to zero lift. Leads me to think that twisted off main would be better than reefed main?

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### RHoughRetro Dude

LOL ... Just trying to tell you that the one thing most of us agree on is that L/D max is the fastest way to sail.

You didn't understand the statement. I know that every lifting body has an L/D max.

I too learned aero theory enough to design successful RC Sailplanes. Good thing ... my early design errors didn't kill me.

If you define L/Dmax as the point where Lift/Total Drag is highest, you can easily see that Di can be no greater than the sum of all other drag. Theoretical L/Dmax is when Di equals the sum of all other drag. Correct?

To reach L/Dmax you increase lift until Di equals Dp. Even at Lmax for the sails, the Di is lower than Dp for many boats. Thus the practical L/Dmax never reaches theoretical L/Dmax.

To help with the transition from aircraft to sailing vessels, I will be so bold as to suggest two books to you. Frank Bethwaite's "High Performance Sailing" (he also has designed RC sailplanes and speaks aircraft language) and C A Marchaj's "Sail Performance".

Bethwaite explains the limits of a boats ability to carry sail very well. I have a feeling that you are on the right track, but you have yet to grasp how limiting righting moment is. There is a very good reason that 4-5:1 is considered a high AR for sails. Above 6:1 is where aero theory works well, at extremely low AR like 1.5 - 2 (keels on monohulls) aero theory is not so great.

It is great to see someone else join the discussion with the firm conviction that starting with a sail plan that produces the required drive at it's L/D max is the way to go, I once thought that too.

I think you will find that a sailboat is much like an airplane that is has such a high wing loading that it can barely fly, even at Clmax.

Cheers

R

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### tspeerSenior Member

Yes, that's it. The optimum dihedral angle for a winglet is zero, unless the span is constrained for some reason.

The rest of the planform has area shifted farther down to make up for the moment due to the extension in span, so as to maintain the same height of the center of effort.

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### tspeerSenior Member

That's what I thought, too, until I started running a simple landyacht VPP. That's when I found out L/D max is not necessarily the fastest way to trim the sails. Max lift turned out to be faster for that configuration, even though it was past the point of best L/D.

The reason turned out to be that speed depends on both the aerodynamic L/D and the hydrodynamic L/D, but the two are not independent of each other. The hydrodynamic lift has to match the aerodynamic load. So unless the sail rig provides a side force, the hydrodynamic L/D is zero.

What was happening was by trimming at maximum lift, I was loading up the chassis, so its L/D improved. The improvement in "hydrodynamic" L/D was more than the decrease in aerodynamic L/D, so the net performance improved.

[Note that tires on a landyacht operate very similarly to the hydrodynamics of a board. There's a linear range where side force is proportional to leeward drift (this is not skidding, but comes from the flexibility of the tires), followed by a nonlinear region where the side force does not increase appreciably and can decrease as the drift becomes large (this is skidding), similar to hydrodynamic stall. The sideways drift angles are not that much different than a boat's leeway angles, either]

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### RHoughRetro Dude

LOL ...

Did you ever get down to the point of finding out what the tyre slip angle was? And did you discover the fact that a small difference in tyre tread speed to ground speed is the point of maximum traction?

In one of my many past lives, road racing was a passion for me. Years ago the drag racing guys looked at the relationship between wheel slip and acceleration. Intuition says that a spinning tyre has less traction than a tyre that is not spinning in relation to the surface. What they discovered at the time is that a 12% slip produced the maximum traction. They then proceeded to adjust the clutch systems to try to maintain 12% overspeed for the entire 1/4 mile.

We found the same thing to be true road racing, the tyres are 'skidding' at maximum accelerations, the linear part of the traction curve includes a small amount of 'skid' or drift.

It sounds like the best net performance was at L/D max for the entire vehicle, although the sail was operating at the max lift the chassis could handle and at lift greater than L/D max for the sail alone.

Am I close?

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### tspeerSenior Member

Yes, in fact it was quite easy to measure. Landyachts are three-wheel vehicles, and even on a hard, dry lakebed, there are tracks left by their passage. If the slip angle is zero, the track of the front wheel will be equidistant from the tracks of the two rear wheels. But with slip, the front wheel's track is closer to the windward track than the leeward track. It's quite obvious that there's a significant slip angle.

The slip is due to flexibility of the tires. Imagine that you made a wheel by cutting the tread into small squares and mounted each square on a rod sticking out from the hub, so that the wheel was made up of a whole collection of individual feet. Now track the motion of one foot as the wheel rotates under a side load. As the foot comes around, the rod is undeflected. When the weight comes onto that foot, the rod deflects under the side load, allowing the hub to move in the direction of the applied load by the amount of the rod's deflection. When the foot comes free of the surface, the rod springs back. In this way the tire under side load walks its way sideways as each patch of tread is planted and the sidewalls flex. Each tread patch is firmly planted, with no skidding, yet the wheel has a velocity component normal to the plane of rotation.

The slip velocity due to traction or braking is due to the same flexibility. It's just that the equivalent of the rod is bending in the plane of the tire instead of at right angles to it. Of course, with a landyacht, there is no slip velocity in the plane of the wheel, because there's no torque being applied to the tire.
Yes. Actually, the sail was operating at its maximum lift, and the chassis was still in its linear range. I had deliberately arranged the aerodynamic parasite drag so that max L/D occurred below stall. With more parasite drag, the L/D would have been increasing right up to the point where the drag started to increase due to separation and stall.

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### RHoughRetro Dude

Also obvious is that since the 'bow' of the yacht has one tyre and the 'transom' has two tyres the 'centre of lateral resistance' is 2/3 of LOA aft of the 'bow' at rest (assuming equal load on each tyre). At RM max, the load should be on the leeward tyres and the 'CLR' moves foward to the midpoint. Max L/D should see both leeward tyres loaded equally at their traction limit.

I think I captured the idea in the attached sketch.

Here we disagree. What you describe are the normal forces that allow tyres to accelerate the vehicle they support. What has been found true is that some slip at the traction surface produces the greatest acceleration. The latest value is about 10%, a bit lower than the 12% the drag race guys found years ago.

Street traction and ABS systems attempt to keep this slip to 0, racing systems are set to 5-10% slip number. Yes, you can accelerate and turn and stop within the elastic 'slip' limits of the tyres. However the marks on the pavement that are left by heavy accelerations are evidence of the slip I refer to. Within the elastic limits, there is no transfer of tyre rubber to the surface. At the limit of traction there is.

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### tspeerSenior Member

Well, we're drifting away from the topic of this thread, but perhaps it's not so obvious that the center of lateral resistance is nowhere near 2/3 LOA.

The c.g. of the yacht is much farther back, and so is the center of lateral resistance. In fact, when sailing, the vast majority of the weight is taken by the leeward wheel - ideally, all of it would be. This was the big advance in performance with the "Slingshot" configuration, in which the cockpit was located behind the axle, thus moving the c.g. back relative to the axle. The windward wheel is unloaded and just skimming the ground, just like flying a hull on a beach cat. The load on the front wheel is always a compromise between having enough to steer the yacht vs giving up some righting moment.

The side force per degree of sideslip is proportional to the vertical load applied to the wheel. This tends to make the chassis somewhat self-compensating. If the c.g. is moved forward, the forward wheel also picks up proportionately more of the sideforce, moving the CLR forward, too. This is why you don't have big changes in the handling qualities of a truck when you load it up in the back.

You have the relationship of the slip angle to the distance between the tracks correct.

No, I'm talking about the side forces, not the acceleration forces. This would be equivalent to cornering with the transmission in neutral. It's what's needed to resist the side forces from the sail rig. A landyacht's tires are loaded as though the yacht is cornering even when it is traveling in a straight line. It operates on a different part of the friction circle than a dragster.

Say the curve you posted is equally valid for side force as it is for fore-aft traction. A 5% sideways slip velocity would be 3 degrees of sideslip angle. Not that different from the leeway angle of a decent keel.

The anti-skid systems I'm used to dealing with - those on aircraft - aim to operate at the peak of the curve. When the wheel starts to skid, it decelerates rapidly, leading to the large slip velocity you've shown. The anti-skid compares the deceleration of the wheel with the maximum deceleration that should be achievable on dry pavement. If the wheel's deceleration exceeds that amount, the anti-skid system then releases the brake pressure.

Early anti-skid systems dumped all the brake pressure, causing the operating point to traverse all the way to the origin, then re-applied the brakes. This led to a pulsing of the brakes that caused the operating point to run back and forth over the curve. More modern systems have a proportional valve that smoothly dumps brake pressure to get back to the front side, but don't go all the way to zero and provide better performance.

You wouldn't want to reduce the slip velocity to zero because that means zero braking - it would be worse than a skid. Instead, you want to operate at the peak of the curve, which is above the flat zone that corresponds to full skidding. That's the advantage of ABS over manual braking.

I suspect the tire starts leaving rubber on the surface when the curve starts to become nonlinear. That means some part of the contact patch is starting to slide, while other parts are still experiencing increased resistance in their local linear range. Once more of the patch is sliding than is increasing its resistance, then the curve has rounded the corner and started downhill.

But we're getting off of sail aerodynamics, so let's take any more discussion of tires to a new thread. I only broached the subject to point out the similarity between the landyacht VPP I was using and a watercraft VPP.

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### RHoughRetro Dude

It was a good detour.

I'll stop after this comment.

In practice, it is not possible to turn a racing car if the front tyres are at the limit of traction under braking. The braking torque must be reduced so lateral force can be developed. The magnitude of the traction vector does not change, only the direction. It includes slip at the contact surface.

Back on topic ... Sail Aerodynamics ...

With a gap at the foot of the main, I have a clear picture of the spanwise lift distribution.

Since the fordeck of a modern tri looks like it lacks the ability to seal a genoa or jib at deck level, can I assume that the lift distribution is similar to that of any other sail with a gap at the foot? ie, the centre is about 40% of the span above the foot?

Can I safely use the total projected area and assume the AC is close to the 1/4 chord line of the sailplan at about 40% of span? That would surely make guestimates easier.

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### Paul ScottSenior Member

Tom, what happens to the airflow around a landsailor's wing when the craft experiences roughness on the ground of the racecourse?

Paul

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### Mikko BrummerSenior Member

About the parasitic drag of the mast ... I was a bit surprised (dissapointed?) my insert did not raise any discussion.

I looked recently at the sails of a classic 6 meter, which has a rather large and blunt mast. In case of the 6 meter, CFD shows a 2,8 kgf drive for the mast, which amounts to 4,5% of the total drive of the sails (rig). Using the IMS (nowadays called ORCi) VPP parasitic drag coefficients, they would predict a negative drive in the order of -3,8 kgf... So the IMS VPP (like most commercial VPPs which are based on the iMS), would underpredict drive in the 6 meter case by some 6.6 kgf - that is 10,5% of the total (CFD predicted) drive. If my CFD is right, that is.

A similar error would be introduced in windtunnel measurements, where common practice is to measure the bare pole drag without sails and then substract it from the measured total drag, to get the sail drag coefficients.

It seems to me the mast should be considered as part of the mainsail profile, rather than a necessary drag device. There could be benefits in trying to shape the mast for max. drive in conjunction with the sail behind it, rather than try to minimize the drag of the bare mast, as seems to have been the practice earlier on.

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### tspeerSenior Member

I agree completely. The leading edge suction on the mast is a significant contributor to the drive of the whole sail rig. And I'll take it a step farther.

With a rotating wingmast, it's possible to achieve fully attached flow on both sides of the mast, at least at high-ish Reynolds numbers. For such a mast, its drag is mostly due to skin friction and the pressure drag of boundary layer growth, without the drag of separation bubbles between the mast and mainsail.

One can also apply the same principles to the design of headfoils, although I've not yet tried to tackle that particular problem.

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### RHoughRetro Dude

This is obvious, the only people that would debate it are proponents of rigs that claim to sail better because the sails are not set behind the mast. The aft-masts, the a-frames, and the Mainstay(tm) rigs come to mind.

The rating rules for fast boats include the mast area as part of the total sail area for a reason. The mast helps drive the boat.

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