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

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patzefranpatzefran

Basically, the induced drag is created by the variation of the chordwise circulation ( otherwise the lift per unit of span length) along the span. this variayion create a vortex sheet starting from the trailing edge (leech) of the wing (sail). Energy wasted in the vortex sheet create drag.
The strongest varations of circulation occure at the tips. I don't see any evident physical nonsense in this paper !

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Mikko BrummerSenior Member

"Assuming the boat is well trimmed and properly set up, about 80 percent of the total sail area will experience relatively constant Cl. However, in the aftermost 20 percent of the sail, the velocity of the flow rapidly decreases; and with it, the lift. The rapidly changing Cl results in significant induced drag, some on the leech and some at the head and foot."

"There are two variations of induced drag:
• off the trailing edge (leech)
• off the tips (head and foot)
These are vortices, spinning counterclockwise-off that trailing edge. A deeper head section, compared to the bottom, minimizes the flow of air trying to find the shortest path from the high-pressure windward side to the low-pressure leeward side."

"Induced Drag off the Head and Foot

The second variation in induced drag is tip vortex. On a plane, these flow off the ends of the wings; on a sail, they flow off the head and foot. There is a pressure difference, or delta, from the lee side of the sail to the windward side. Nature abhors pressure deltas. It’s why we have wind. And, it’s why the flow on the high-pressure side of a sail wants to escape over the top or end to help equalize this pressure.

Almost all modern race boats employ a fractional rig. At the hounds, the main’s chord on the fractional rig is still quite long and therefore helps shed the headsail’s tip vortices. On a masthead rig, the tip vortices of the headsail are matched with the tip vortices of the mainsail. Not good!"

Hmmm...

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patzefranpatzefran

If you refer to the last sentence, I have to admit it is a dubious, main and jib acts as a whole profile like a wing with flaps, not separated wings. So there are only two strong set of tip vortex,
one at the foot of the main and another at the top of the main.
Is this what you mean ?
Otherwise please explain more clearly where is the problem.
Cheers

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Mikko BrummerSenior Member

" about 80 percent of the total sail area will experience relatively constant Cl." Really?

" However, in the aftermost 20 percent of the sail, the velocity of the flow rapidly decreases; and with it, the lift. The rapidly changing Cl results in significant induced drag". Induced drag is due to sectional variation in lift (as opposed to spanwise)?

"There are two variations of induced drag: 1) off the trailing edge (leech). 2) off the tips (head and foot)". To me it's all trailing vorticity.

"These are vortices, spinning counterclockwise-off that trailing edge." Counterclockwise? OK, maybe he is referring to some illustration. Anyhow towards the foot the vorticity will roll in one direction and towards the top in another.

"minimizes the flow of air trying to find the shortest path from the high-pressure windward side to the low-pressure leeward side." The shortest path...?

"At the hounds, the main’s chord on the fractional rig is still quite long and therefore helps shed the headsail’s tip vortices. On a masthead rig, the tip vortices of the headsail are matched with the tip vortices of the mainsail. Not good!"
Actually the headsail will shed its own distinct vorticity, even if further behind all trailing vorticity tend to tangle into one larger vortice towards the head and the foot of the sails.

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Mikko BrummerSenior Member

Simulated trailing edge vorticity on a Finn (from 23s on)

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Mikko BrummerSenior Member

And on a sloop rig:

Note that to make the strongest vortices visible, you need to filter out much of the smaller vorticity, hence what you see on a simulation depends on what you choose to look at.

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patzefranpatzefran

Amen !

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AlikSenior Member

Thanks Mikko for the review.
Unfortunately, today marketing is often using using 'scientific' words, but little sense.

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Mikko BrummerSenior Member

Here’s my take about induced drag:

On the windward side, in the upper part of the sails, the flow is bending upwards. In the lower part, closer to the foot, the air is bending downwards, slipping under the foot of the jib or the boom. This is accentuated when the boat heels, but is there even with zero heel. On the leeward side, mostly the opposite is true.

When the flows join at the leech, they are at an angle to each other, rolling into more or less horizontal vortices that propagate first in the direction of the leech exit, bending towards the apparent wind further on. This leech vorticity is the fuel of induced drag.

When the air meets at the leech, there’s also a speed difference between the windward and the leeward side - this creates vorticity in a vertical plane, adding to the viscous wake (bad air) behind the sails.

So, when the air at the leech, from the opposite side of the sail, rubs against each other forming vortices, the “vertical rubbing” is the source of the induced drag, and the “horizontal rubbing” creates the viscous “profile” drag (am I wrong to claim so?). Remember, that induced drag is actually just a mathematical construct - in the end, it’s all just pressure and skin friction.

In these simulations from some time ago, I’ve looked at the vertical velocity Vy of the flow: blue is downward in Y, red is upwards (Y-direction is up the mast), according to the legend on the right.
In the first plot, we have the vertical components of velocity near the surface, on the leeward (left) and windward (right) side of the sails.

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Last edited: May 22, 2020
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Mikko BrummerSenior Member

In the second. I’ve placed a surface right behind the mainsail leech, to look at the velocities Vy in that plane, on the opposite sides of the sail.

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Mikko BrummerSenior Member

n the third, we are looking from behind the mainsail leech, just cutting into the plane (the black outline). Large vertical velocity differences on the windward and leeward sides indicate lots of induced drag. There’s the tip vortex formation in the upper leech, that would cause a counter-clockwise vortex. In the lower leech, the air is rising on the leeward side, leading into vorticity in the clockwise direction.

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Mikko BrummerSenior Member

I then put a plane just behind the jib leech (sails in wireframe here)
Looking from aft, you can see a strong concentration of induced drag in the upper half of the jib. As the lift of the jib is high, so is the induced drag. The mainsail is much more lightly loaded.

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Mikko BrummerSenior Member

Illustration about the vertical distribution of lift & drag on a sloop-rigged boat (X-35). The graphs are the result of integrating horizontally the loading of the sails (and the hull) in the plane of lift & drag.

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philSweetSenior Member

Erm, no. The Kutta condition, in effect, says the speeds are the same on the edges of the wake, and thus the pressures are the same. If the flow is attached at the leach, the windward side air will have accelerated, and the leeward side decelerated, so that the speeds are equal on either side of the shed boundary layer (which contains the momentum defect from friction with the sail). Perpendicular to the sail, there may remain a small speed gradient on each side of the sail, but the speeds match at the wake. Any slight difference manifests as a bend in the wake just behind the leach.

So there is a clear directional change - a direction jump - from one side of the wake to the other, and this is associated with large viscous losses, but the speed gradient at the leach as you approach the sail from the windward side carries smoothly across the wake and resumes on the lee side.

The point is that the viscous losses due to transverse speed gradients aft of the leach (outside the wake) are tiny compared to the losses due to the direction jump. The transverse speed gradients can molify without viscous losses by bending the wake.

So no, there is no "horizontal rubbing" at the wake edge associated with the speed gradient analogous to the "vertical rubbing" caused by the direction jump at the wake edge.

Last edited: May 23, 2020
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