# 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

I have found it's easy to understand that "vortices consume energy", and when you manage to explain how leech vorticity is formed, you are a long way to explaining induced drag.

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### Mikko BrummerSenior Member

Any comments anyone, about the illustration in post #14, the vertical distribution of lift and drag. The maximum amount of lift would seem to be generated about 40% up the sail plan, the maximum drag roughly the same. There's a bulge in the drag curve in the top of the mainsail, this is rather due to the separated flow there than the "tip vortex".

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### patzefranpatzefran

Mikko, perhaps if you draw the vertical distribution of D/L, the vortex tip effect on drag in % of lift should be more visible.

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### Mikko BrummerSenior Member

That's a good idea, I will look into that.

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### Will GilmoreSenior Member

I would love to see a comparison of that illustration with one of just a headsail and just a main, of equal sail area.

On the sailboatowners forum, they are running a thread about the "slot effect" and talking about Arvel Gentry.
Sail Trim and Aeronautic Theories. https://forums.sailboatowners.com/threads/sail-trim-and-aeronautic-theories.1249924109/#post-1632875

I'm just trying to glean some small nugget of understanding from all this.

-Will (Dragonfly)

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### JotMJunior Member

I know a was struck by a post by Mark Drela a couple of years ago (which was almost the single reason for me to try taking his class online), in which he stated:

[...] The reality is that the overall lift of a rig is almost entirely determined by its planform and by the local incidence of the rearmost portions of the rearmost sail. In contrast, 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

(by the way, if you would scroll 4 messages up from that one, there's a picture that looks somewhat familiar to one that has appeared in this thread )

I have been fooling around, both with the software he mentioned in that post and out on the water, with the "local incidence of the rearmost portions of the rearmost sail" bit of that. Which, I tend to believe, did help getting a bit of extra speed out of the boat in some situations.

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### PeakyJunior Member

If the drag is predominantly induced drag and that is a result of “leakage” around the head and foot, wouldn’t you expect drag to be lowest in the middle (roughly) and highest at the top and bottom?
Also noticeable that the best lift:drag ratio is in the area of separated flow.

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### JotMJunior Member

So what would the vertical distribution of the lift-to-drag ratio look like?

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### DCockeySenior Member

A vortex along the leach results from locally separated flow. It is not directly related to induced drag.

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### TeddyDiverGollywobbler

For me it looks mostly vorticities of foot and tops of both sails. No "leech effect" but the separated boundary layer on the sails..

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### philSweetSenior Member

No, it can not be localized like that. A change in the flow in one area affects the pressure over the entire sail. The pressure distribution over the entire sail is contributing to induced drag. Induced drag is the sum of the crossflow over the entire fluid domain and is caused by the pressure distribution over the entire sail.

Keep in mind that there is only one pressure across a patch of sail. That pressure is producing both the local lift force and the local pressure drag (there is a shear drag as well). Anywhere there is leakage from the windward to the leeward side, the pressure tends to be weaker and both lift and pressure drag are reduced.

Mikko Brummer likes this.
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### PeakyJunior Member

If only the shear drag can be localised, then is Mikko’s plot showing that shear drag is highest in the middle and lowest at the ends? Why would that be?

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### patzefranpatzefran

Looks like Mikko's plot shows the total load, not the shear load only. Even if Drag over lift ratio is lower in the middle than at the tips , drag could be higher, simply because lift is higher in the middle (lift is near zero at the tip !).
IMHO, the meaning curve is D/l, not D !

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### Mikko BrummerSenior Member

I agree that some of the wake originates from the separation vortices on the inside of the sails (windward side, on the leeward side the flow is attached). But it seems to me these vortices are sucked into the leach vorticity & the tip vortex, rather than being its source?

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### Mikko BrummerSenior Member

Thank you Philsweet, it makes sense that induced drag cannot be localized like that, but is simply a (big) part of the total pressure drag.

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