About the induced drag of sails

Discussion in 'Hydrodynamics and Aerodynamics' started by Mikko Brummer, May 18, 2020.

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Mikko BrummerSenior Member

This is not at all only shear drag - mostly pressure drag. Shear drag is a small part of the sail drag - if I recall correctly, in this case, shear drag on the jib was about 7% of the total drag, while on the main it was about 4%. Drag in this illustration is just the component of the total integrated force, in the direction of the apparent wind (at 10 m height, the angle varying with height). Lift is the component perpendicular to it. Note that the two graphs are not in the same scale: The max. on the lift would be about 580 units, while on the drag it is 130 units.

On the drag curve, you can see little bumps at the spreader heights.

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tspeerSenior Member

When I first got involved with an America's Cup team, I was amazed that the sailmakers didn't speak the language of aerodynamics! I would have thought they'd say things like, "We're getting separation on this part of the sail, so we need to alter the velocity gradient ahead of that point so as to improve the boundary layer development, which means we need to change the sail shape like this." But they didn't seem to relate what they were doing to the actual aerodynamics. It was more like, "I don't like the shape I'm seeing. I think we need to bring up the mid leech a bit." Everything was done by what looked right to them and brute force Navier Stokes calculations to feed the VPP.

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tspeerSenior Member

I realize that in a Navier Stokes calculation it's not easy to separate the classical induced drag from lift-dependent drag that may be due to viscous effects.

When Munk and Jones published their criteria for minimizing induced drag (linear wake wash velocity across the span), they were basing this on the Trefftz plane that was located an infinite distance downstream. But they also assumed the wake was shed in a straight line, with no roll-up. So the wash distribution at the Trefftz plane had the same shape as the wash distribution at the trailing edge. That got me to thinking, "Can the shape of the wash distribution in the near field behind the trailing edge be used to minimize the induced drag?"

There are several practical issues with this. One is how to treat the bound vortices, which also have an effect in the near field. Another is whether the wash distribution should be taken in a plane normal to the freestream, or at a constant distance from the trailing edge, because most planforms have some sweep or curvature to the trailing edge. Shear in the apparent wind direction between foot and head complicates things, too. And then there's the issue of how one might actually measure the wake wash. However, measurement is not a problem for exploring the feasibility using CFD.

But consider the plane Mikko showed in post #11 and plot the spanwise profile of the lateral velocity behind the leech in this plane. I think you'll find this profile is not very sensitive to modest differences in the windward-leeward position of the spanwise line used for the profile, because the lateral velocity component is continuous across the wake. Once you have that profile, how linear is it? Wiggles, or curvature in general, to that profile should indicate areas of increased induced drag. The wake wash at any spanwise station is affected b the entire spanwise lift distribution, but it is most strongly affected by the lift at that particular station. So if you changed the twist or camber at a particular station in order to bring that station's wake wash more in line with a linear distribution running from foot to head, then the process ought to converge. Do this at as many spanwise locations as you have control over the sail shape, and you can get the wake wash distribution to approach the linear ideal.

That should have the effect of reducing the induced drag. And since induced drag is a large, if not the dominant, drag source, you should see a reduction in the total drag.

I've always wanted to try this as a numerical experiment using CFD. But I've never had the tools to do it. It may be a totally bogus notion. But if it works, then it could be a powerful technique in a couple of ways.

First, it could be used as an inverse design method. What I find so powerful in the wake wash criteria of Munk and Jones is it isn't necessary to actually determine the induced drag. A constant wake wash distribution (Munk) is both necessary and sufficient to ensure the induced drag is minimized for a given span. A linear wake wash distribution (Jones) is sufficient to ensure the induced drag is minimized when there is a constraint on the moment due to lift. So by manipulating the local shape to get a linear wash distribution, the induced drag can be minimized for a very complex planform or array of lifting elements.

Second, it could be used for real-time minimization of the induced drag. Lissaman showed that the linear wash distribution also produced the minimum induced drag when the freestream did not have a uniform velocity. So being able to measure the wake and adjust the trim of the sails in real time would adapt the rig to changing wind conditions. And do so in a rational way.

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PeakyJunior Member

Tom, does a spanwise linear wake wash velocity distribution also imply a linear variation of downwash angle along the span and a linear variation of induced drag?

Does the attached sketch show what you mean for a simple case?

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tspeerSenior Member

If the freestream is uniform, then linear wake wash does imply a linear downwash angle. However, if the freestream is nonuniform, then the angles won't be linear.

The induced drag distribution is not linear because the induced drag is the product of the downwash and the local lift, and the lift distribution is not linear. Take the classical isolated elliptical wing, for example. The downwash is uniform, but the induced drag is not uniform along the span. Instead, the induced drag varies in an elliptical manner because of the lift distribution.

Yes.

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PeakyJunior Member

Thanks Tom.

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Mikko BrummerSenior Member

I will seek that old simulation for you and plot it.

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tspeerSenior Member

Thanks.

What would be really interesting is if you used that profile to modify the sail trim so as to smooth out the wake wash profile, and then compared the drag with the original computation. That might indicate whether the concept has merit.

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fastsailingSenior Member

I realize that in a Navier Stokes calculation it's not easy to separate the classical induced drag from lift-dependent drag that may be due to viscous effects.

When Munk and Jones published their criteria for minimizing induced drag (linear wake wash velocity across the span), they were basing this on the Trefftz plane that was located an infinite distance downstream. But they also assumed the wake was shed in a straight line, with no roll-up. So the wash distribution at the Trefftz plane had the same shape as the wash distribution at the trailing edge. That got me to thinking, "Can the shape of the wash distribution in the near field behind the trailing edge be used to minimize the induced drag?"

There are several practical issues with this. One is how to treat the bound vortices, which also have an effect in the near field. Another is whether the wash distribution should be taken in a plane normal to the freestream, or at a constant distance from the trailing edge, because most planforms have some sweep or curvature to the trailing edge. Shear in the apparent wind direction between foot and head complicates things, too. And then there's the issue of how one might actually measure the wake wash. However, measurement is not a problem for exploring the feasibility using CFD.

But consider the plane Mikko showed in post #11 and plot the spanwise profile of the lateral velocity behind the leech in this plane. I think you'll find this profile is not very sensitive to modest differences in the windward-leeward position of the spanwise line used for the profile, because the lateral velocity component is continuous across the wake. Once you have that profile, how linear is it? Wiggles, or curvature in general, to that profile should indicate areas of increased induced drag. The wake wash at any spanwise station is affected b the entire spanwise lift distribution, but it is most strongly affected by the lift at that particular station. So if you changed the twist or camber at a particular station in order to bring that station's wake wash more in line with a linear distribution running from foot to head, then the process ought to converge. Do this at as many spanwise locations as you have control over the sail shape, and you can get the wake wash distribution to approach the linear ideal.

That should have the effect of reducing the induced drag. And since induced drag is a large, if not the dominant, drag source, you should see a reduction in the total drag.

I've always wanted to try this as a numerical experiment using CFD. But I've never had the tools to do it. It may be a totally bogus notion. But if it works, then it could be a powerful technique in a couple of ways.

First, it could be used as an inverse design method. What I find so powerful in the wake wash criteria of Munk and Jones is it isn't necessary to actually determine the induced drag. A constant wake wash distribution (Munk) is both necessary and sufficient to ensure the induced drag is minimized for a given span. A linear wake wash distribution (Jones) is sufficient to ensure the induced drag is minimized when there is a constraint on the moment due to lift. So by manipulating the local shape to get a linear wash distribution, the induced drag can be minimized for a very complex planform or array of lifting elements.
When freestream does not have a uniform velocity, what is the definition of induced drag you and quoted Lissaman are using?
Am I correct to assume it's somehow related to minimizing total amount of energy wasted as induced vortices, even though the induced drag is still by definition a component of a total force vector?

Perhaps simply adding induced drag vectors at all heights or rather integrating them with respect to variable in vertical direction?
Does it make any sense for trying to minimize induced drag of such definition for a sailor?

Case example (not realistic, but as simplified as possible), uniform freestream speed, but varying direction along span (height above sealevel), and thus varying freestream velocity. Wind direction at sea level south, at mast tip southwest. Boat is heading approximately southsoutheast. A sailor would not want to minimize energy of added vortices, but get significantly more lift higher up despite of resulting increased induced drag, because total sailforce high up is directed closer to the direction the boat is going than closer to sealevel anyway, even with low L/D high up. In other words, a sailor would initially seek to find best driving force under constraint of a given maximum heeling moment (in intended conditions, not in all conditions). And after realizing consentrating aerodynamic lift higher up also leads to less healing force (under the same constraint) and thus less hydrodynamic lift and thus less hydrodynamic drag, a sailor would adjust aerodynamic lift distribution even further top loaded to maximize upwind VMG (small drop in aerodynamic driving force more than compensated by a little larger drop in hydrodynamic drag).
It is my understanding that the optimum distribution of lift that results maximum upwind VMG does not involve minimum induced drag in this case, and the reason is the non-uniform freestream condition.

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tspeerSenior Member

This is an issue I've wondered about myself. In the Lissaman paper, the magnitude of the freestream varied, but not the direction.

Induced drag is really a bookkeeping issue. It comes about from the rotation of the lift vector due to local changes in the apparent wind direction. When referenced back to the nominal freestream direction, the local lift has a component parallel to the freestream and is classified as a drag component.

If the apparent wind direction is skewed, there isn't a single apparent wind direction and the definition of lift and drag becomes a bit ambiguous. The common practice in meteorology is measure the wind strength and direction at a height of 10 m above the surface. That could be adopted for the purpose of measuring lift and drag as well. Lift could be the component of the total aerodynamic force that is perpendicular to the apparent wind at 10 m, and drag could be defined as the component of the total aerodynamic force that is parallel to the apparent wind at 10 m. As a practical matter, one could pick any reference direction for the apparent wind so long as one was consistent throughout the process of calculating the total aerodynamic force.

Whether the linear wake wash distribution gives minimum induced drag in a skewed flow is something that remains to be seen. I've not found many papers that consider wings in a skewed freestream.

One effect of a skewed wind field is to make the performance polar asymmetrical. I had a similar conceptual problem with understanding the best course to sail, and the meaning of Vmg, when the polar is asymmetrical. What I realized is the notion of Vmg being parallel to the true wind is purely an artifact of the symmetrical polar. Say you're sailing upwind and the polar is asymmetrical. One possible strategy would be to draw a line perpendicular to the true wind and tangent to each lobe of the polar. That would be the conventional way of defining Vmg, and would lead one to sail the course where the tangent lines touch the lobe for each tack.

But there is another approach to maximizing windward performance, and that is to draw the convex hull that encloses the polar. This results in a straight line that is tangent to the two lobes. It is not perpendicular to the true wind because of the unequal size of the lobes for each tack. Compared to the symmetrical polar case, the tangent point of the tack with better performance is closer to the wind, and the tangent point of the lesser tack is further off the wind.

What I came to realize is the straight line tangent to the two lobes for both the symmetrical and asymmetrical polars is a legitimate part of the polar itself. It's true that the boat's performance will suffer if it tries to sail on any of the true wind directions subtended by the line. However, the line does represent the average velocity of a boat that spends part of the time at one tangent point and part of the time at the other tangent point. If you pick a direction that is near one end of the line, the boat will spend most of its time sailing at the nearby tangent point and only occasionally sail on the opposite tack. If you pick a direction that is the midpoint of the line, then the boat will spend equal time on both tacks.

This means that for an asymmetrical polar, the boat should pinch on the favored tack and foot on the lesser tack. It also means that when sailing in an averaged direction that is subtended by the line, what one wants to do is to advance perpendicular to the line as much as possible. So Vmg is really the velocity component perpendicular to the line, not parallel to the wind direction.

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DCockeySenior Member

Whether the performance polar will be asymmetric depend on thefreestream in a fixed reference frame, not a reference frame moving with the boat. If the speed of freestream varies with height but the direction does not vary then the apparent wind variation with height and performance polar will be symmetric relative to the true wind direction. If the freestream direction varies with height then the apparent wind variation with height and performance polar will not be symmetric relative to the true wind direction. The latter situation may be more common.

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tspeerSenior Member

I was talking about the case where the true wind direction is skewed. Of course there is twist in the apparent wind due to the wind gradient.

I once asked Stan Honey, "What is the job of the navigator on an inshore race?" He said, "The navigator's job is to determine the wind shear so as to know the course for the opposite tack." He was talking about asymmetrical polars.

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Will GilmoreSenior Member

I think, by definition, apparent wind is measured at the point of interference or contact with the moving object. With regards to a sailboat, practically has it measured at the masthead. Any other definition would be a calculated AW, not an actual AW.

Of course, that doesn't mean the related forces couldn't be measured elsewhere. However, again, those would probably be calculated forces, not measured forces.

-Will (Dragonfly)

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Doug HalseySenior Member

Do you have a link to the Lissaman paper? I can't seem to find one & I've misplaced my paper copy.

Years ago, I had my doubts about the legitimacy of methods like this that have sheared onset flows & potential flow perturbations. Discussing it with John Hess, who was one of the originators of the Douglas Neumann Program (the first 3D panel method), he also wasn't sure but finally agreed that it wasn't necessarily wrong. Are you aware of any further "endorsements" of this approach?

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patzefranpatzefran

Doug, I have attached a copy of Lissaman paper.....

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