mawingho
Topic Author
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### Spanwise Flow

I am reading a book and it said "due to the pressure differential, some airflow will leak or spill around the wingtip from high pressure area under the wing to the low pressure area above wing. This causes a spanwise flow away from fuselage on the lower surface and a component towards the fuselage on the upper surface"

I tried to search on the web, but I still do not understand why have this cause?

Hope someone can help!

SAAFNAV
Posts: 394
Joined: Wed Mar 17, 2010 5:41 pm

### RE: Spanwise Flow

Nature abhors a vacuum.
So since you have a low pressure on top, and nature wants to equalize it, it will flow from the high pressure area at the bottom around the wing tip. Since you are also moving forward, air will flow from the forward inside to the rear outside.

Can't find the right diagram now, but will look for it.

Erich

PapaChuck
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### RE: Spanwise Flow

A gas will always try to attain a uniform pressure. An area of high pressure will expand to match the ambient pressure, just as an area of low pressure will contract. This reaction to areas of different pressure is the key here.

Differential pressure is what creates lift. The air flowing under the wing is of greater pressure than that flowing over the top. The high pressure air beneath the wing is trying to find a way to get to the top in order to equalize the pressure. It cannot flow inward toward the fuselage because, well, the fuselage is there to block it. It can, however, flow outward toward the tip since there is nothing there to block it. At the wingtip, the high pressure air under the wing will actually whip around the tip in order to reach the low pressure air on top. This phenomenon is what creates the vortices known as wake turbulence. These vortices wouldn't be formed if there weren't some span wise flow outward beneath the wing toward the tip. The high pressure air under the wing is going to expand, so it takes the path of least resistance, i.e. outward toward the wingtip.

PC
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vikkyvik
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### RE: Spanwise Flow

A force is equal to pressure differential multiplied by area. F = p*A

So, if you have a pressure differential, such as between the low-pressure air on top of a wing, and the high pressure air below the wing, you get a force.

Across the whole wing, the higher air pressure on the bottom is pushing the wing up into the lower air pressure on top. That's lift right there.

However, just outside the wingtip, the high pressure air and low pressure air have no wall between them anymore. So the high pressure air flows into the low pressure region. Since it's going around the wingtip, it creates a swirling vortex.

Now, if you take a control volume that's a box right under the wing at the wingtip, and you suddenly start moving the wing through the air, you'll see the higher pressure air in this control volume swirl up and around the wingtip. But it can't leave a vacuum in our control volume; so more air is pulled from inboard of the wingtip. This is a continuous process while the wing is generating lift, and gives you spanwise flow.
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ANITIX87
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### RE: Spanwise Flow

The way I understand it, this is what winglets really help with, right? Span-wise flow curls over the wing tip and creates the vortices we all know so well. The winglet, in turn, prevents the curling motion, right?

Is wing dihedral another contributing factor of span-wise flow? Will a plane with anhedral instead experience a smaller span-wise component (or is is the same, but towards the fuselage, which then acts as a winglet and reduces vortices)?

TIS
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tdscanuck
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### RE: Spanwise Flow

 Quoting ANITIX87 (Reply 4): The way I understand it, this is what winglets really help with, right? Span-wise flow curls over the wing tip and creates the vortices we all know so well. The winglet, in turn, prevents the curling motion, right?

Sort of. It's a popular misconception that the winglet blocks the vortex. What's really going on is the winglet alters flow pattern over the whole wing (primarily by moving the actual tip farther from the body of the wing). The result is an overall weaker vortex. The key realization is that the winglet isn't blocking anything, it's preventing part of the vortex from forming in the first place.

 Quoting ANITIX87 (Reply 4):Is wing dihedral another contributing factor of span-wise flow? Will a plane with anhedral instead experience a smaller span-wise component (or is is the same, but towards the fuselage, which then acts as a winglet and reduces vortices)?

Very technically yes, but the effect is extremely tiny in straight flight because buoyancy forces on air are very small. If you have any sideslip then it becomes much more pronounced (this is why dihedral works).

Tom.

ANITIX87
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### RE: Spanwise Flow

 Quoting tdscanuck (Reply 5):What's really going on is the winglet alters flow pattern over the whole wing (primarily by moving the actual tip farther from the body of the wing).

So what justifies the preference for winglets being vertical? Would elongating the wing axially by an identical amount have the same exact effect on flow pattern? If so, why choose vertical winglets over elongated wingtips or vice versa (let's eliminate space considerations for airports for a second)?

TIS
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jetmech
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### RE: Spanwise Flow

 Quoting PapaChuck (Reply 2):It cannot flow inward toward the fuselage because, well, the fuselage is there to block it.

Even in the absence of a fuselage, I'd say that symmetry would dictate that the spanwise component of flow on the centreline of a wing is zero.

The entire trailing edge of the wing also sheds vortices.

 Quoting tdscanuck (Reply 5):primarily by moving the actual tip farther from the body of the wing

How much would the physical movement of the vortex away from the wing contribute to the reduction of induced drag?

From an intuitive viewpoint, I seem to visualise the primary benefit of a winglet - vertical or horizontal - as the additional span provided over which one may gradually decrease the local lift coefficient. If one can do this, the rate at which the circulation changes as a function of span becomes less severe.

The rate at which circulation changes as a function of the span is related to the amount of vorticity shed off the trailing edge of the wing. Thus, to me, additional span should reduce induced drag twofold, firstly, via the more gradual change in circulation along the span, and secondly, by the less severe change in lift distribution near the wing tip.

Regards, JetMech
JetMech split the back of his pants. He can feel the wind in his hair .

vikkyvik
Posts: 12039
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### RE: Spanwise Flow

 Quoting jetmech (Reply 7):The entire trailing edge of the wing also sheds vortices.

I know. It's technically a vortex sheet or what-have-you. But you can model it as just the wingtip vortices, accounting for the total vortex flow of the wing, if memory serves. And the wingtip vortices tend to be the strongest, with the possible exception of on landing, when you have major vortices coming off the edges of flaps and such.

Anyway, not sure how that would impact anything I said.
 Quoting jetmech (Reply 7):How much would the physical movement of the vortex away from the wing contribute to the reduction of induced drag?

Induced drag is inversely proportional to the aspect ratio, which is span^2 / area. So keeping the wing area and the lift generated the same, there can be quite a difference. Hence gliders have long, thin wings.

With winglets, I've heard the rule-of-thumb that your winglet height is approximately equivalent to 1/2-winglet-height span extension (per wing, I think).
I'm watching Jeopardy. The category is worst Madonna songs. "This one from 1987 is terrible".

tdscanuck
Posts: 8572
Joined: Wed Jan 11, 2006 7:25 am

### RE: Spanwise Flow

 Quoting ANITIX87 (Reply 6):So what justifies the preference for winglets being vertical?

Two main things:
1) Span restrictions (usually gate space)
2) Vertical winglets induce less bending moment, so they don't require as much structural reinforcement, so they're easier to retrofit.

 Quoting ANITIX87 (Reply 6):Would elongating the wing axially by an identical amount have the same exact effect on flow pattern?

No. It would work much better to extend axially; that's why clean sheet designs without a span restriction (A350, 787, 747-8) use raked tips. Rule of thumb is that you need a winglet twice as tall as the span extension to get the same aerodynamic effect.

 Quoting ANITIX87 (Reply 6):If so, why choose vertical winglets over elongated wingtips or vice versa (let's eliminate space considerations for airports for a second)?

If you ignore space considerations, the only major reason is retrofitability.

 Quoting jetmech (Reply 7):Quoting tdscanuck (Reply 5): primarily by moving the actual tip farther from the body of the wing How much would the physical movement of the vortex away from the wing contribute to the reduction of induced drag?

Induced velocity from a vortex drops off a 1/distance. It makes a really big difference close to the tip, not much difference in close to the centerline (but in close you have very limited spanwise flow anyway).

 Quoting vikkyvik (Reply 8):It's technically a vortex sheet or what-have-you. But you can model it as just the wingtip vortices, accounting for the total vortex flow of the wing, if memory serves.

Mathmatically you can model it that way. The problem is that that's not physical; forgetting that is where the incorrect idea of winglets as vortex blockers comes from. The wing is actually shedding a vortex sheet, which then rolls up to form the complete trailing vortex system.

 Quoting vikkyvik (Reply 8):And the wingtip vortices tend to be the strongest

Not really; the whole wing is shedding vorticity. The greatest vorticity (greatest spanwise flow difference) is out near the tips but the total shed vorticity is a lot larger than the vortex that's just coming off the tips. It takes about half a wingspan for the vortex sheet to roll up to form the complete trailing vortex.

Tom.

vikkyvik
Posts: 12039
Joined: Thu Jul 31, 2003 1:58 pm

### RE: Spanwise Flow

 Quoting tdscanuck (Reply 9):The problem is that that's not physical; forgetting that is where the incorrect idea of winglets as vortex blockers comes from. The wing is actually shedding a vortex sheet, which then rolls up to form the complete trailing vortex system.
 Quoting tdscanuck (Reply 9):Not really; the whole wing is shedding vorticity. The greatest vorticity (greatest spanwise flow difference) is out near the tips but the total shed vorticity is a lot larger than the vortex that's just coming off the tips. It takes about half a wingspan for the vortex sheet to roll up to form the complete trailing vortex.

True and fair enough - it's been awhile since I studied this stuff.
I'm watching Jeopardy. The category is worst Madonna songs. "This one from 1987 is terrible".

Starlionblue
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### RE: Spanwise Flow

So here's a question. I understand that there is flow from the bottom to the top at the tip because there's no more wing there.

However I have also read that since the wing root has most lift (typically more chord, and furthest from the tip), the pressure differential is biggest here. So on, say, the top of the wing the lowest pressure is near the root and the (relatively) highest is near the tip. That's why you get spanwise flow inwards on the top (and vice-versa on the bottom). Is this correct?
"There are no stupid questions, but there are a lot of inquisitive idiots." - John Ringo

BMI727
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### RE: Spanwise Flow

 Quoting Starlionblue (Reply 11):So on, say, the top of the wing the lowest pressure is near the root and the (relatively) highest is near the tip. That's why you get spanwise flow inwards on the top (and vice-versa on the bottom). Is this correct?

I'm not necessarily sure that it's lower pressure. Greater lifting force but wouldn't it be due to greater area rather than greater pressure differential?
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Starlionblue
Posts: 17571
Joined: Fri Feb 27, 2004 9:54 pm

### RE: Spanwise Flow

 Quoting BMI727 (Reply 12):Greater lifting force but wouldn't it be due to greater area rather than greater pressure differential?

Ok I understand that. But since there is greater lift wouldn't that imply greater pressure gradient in that area, more than can be accounted for by the increase in surface area?
"There are no stupid questions, but there are a lot of inquisitive idiots." - John Ringo

tdscanuck
Posts: 8572
Joined: Wed Jan 11, 2006 7:25 am

### RE: Spanwise Flow

 Quoting Starlionblue (Reply 11):So on, say, the top of the wing the lowest pressure is near the root and the (relatively) highest is near the tip. That's why you get spanwise flow inwards on the top (and vice-versa on the bottom). Is this correct?

That's part of it, yes, although it's mainly due to the higher angle of attack at the root (the wing is twisted). You also get some motion induced by the trailing vortex (on subsonic wings).

 Quoting BMI727 (Reply 12):I'm not necessarily sure that it's lower pressure. Greater lifting force but wouldn't it be due to greater area rather than greater pressure differential?

Generally it's both. The bigger area means more lift. The twist means (usually) higher angle of attack at the root, which means more pressure differential.

 Quoting Starlionblue (Reply 13):But since there is greater lift wouldn't that imply greater pressure gradient in that area, more than can be accounted for by the increase in surface area?

Since the wing is physically larger at the root, you can have the same gradient (pressure change per unit distance) but end up with a larger pressure differential. Greater lift does not necessarily mean more gradient.

Tom.

DocLightning
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### RE: Spanwise Flow

 Quoting tdscanuck (Reply 5):Sort of. It's a popular misconception that the winglet blocks the vortex.

I've heard you say this a number of times. Yet NASA seems to disagree.
http://www.nasa.gov/centers/dryden/a...hnology/Facts/TF-2004-15-DFRC.html
"The Benefits of Winglets" 4th paragraph.

I also read a technical document from Embraer (I think) that gave the same explanation. The winglet redirects some of the vortex into thrust.

That said, I've also read other documents, like this one: http://www.mh-aerotools.de/airfoils/winglets.htm.
These documents agree with you.

The best I can make of it all (as someone with scientific training in a wholly unrelated field) is that either there are two different effects at play or that there is still controversy among aerodynamicists about how exactly winglets work. I know that even now, there is still controversy about the finer points about how a wing creates lift, even though the applied science of wing design is quite mature.
-Doc Lightning-

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tdscanuck
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### RE: Spanwise Flow

 Quoting DocLightning (Reply 15):I've heard you say this a number of times. Yet NASA seems to disagree. http://www.nasa.gov/centers/dryden/a....html

I don't see anything in there that disagrees with what I'm saying. I suspect you're looking at this sentence:
"Winglets, which are airfoils operating just like a sailboat tacking upwind, produce a forward thrust inside the circulation field of the vortices and reduce their strength."

This is absolutely true. The key is that they're talking about the *circulation field of the vortices*. The winglet changes the vortex itself; it's not as if the winglet is just hanging out capturing the existing vortex (which is essentially the same as the "vortex blocker" theory of winglet operation).

 Quoting DocLightning (Reply 15):I also read a technical document from Embraer (I think) that gave the same explanation. The winglet redirects some of the vortex into thrust.

This is kind of semantically iffy; it's physically valid, though absolutely not how I'd choose to explain it. It doesn't contradict anything in my head.

 Quoting DocLightning (Reply 15):The best I can make of it all (as someone with scientific training in a wholly unrelated field) is that either there are two different effects at play or that there is still controversy among aerodynamicists about how exactly winglets work.

I don't think it's either; it's a controversy about how to explain it. There is no controversy among aerodynamicists about how wings work either, but you'll start a riot if you try to claim there is a "right" way to explain it.

Tom.

vikkyvik
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### RE: Spanwise Flow

 Quoting DocLightning (Reply 15):I've heard you say this a number of times. Yet NASA seems to disagree. http://www.nasa.gov/centers/dryden/a...hnology/Facts/TF-2004-15-DFRC.html "The Benefits of Winglets" 4th paragraph.

Quoted:

Winglets, which are airfoils operating just like a sailboat tacking upwind, produce a forward thrust inside the circulation field of the vortices and reduce their strength. Weaker vortices mean less drag at the wingtips and lift is restored. Improved wing efficiency translates to more payload, reduced fuel consumption, and a longer cruising range that can allow an air carrier to expand routes and destinations.

That's not in opposition to what Tom said. When someone says "block the vortex", it seems to imply that the vortex hits a wall and has nowhere to go, so stops dead in its tracks. That's not accurate. Instead, the winglet uses the vortex flow to generate a forward thrust. If the vortices stopped spinning, the winglet would likely be pretty useless.

Winglets don't block the vortex flow, in much the same way that wings don't block the freestream airflow. Instead, they utilize it.

In addition, the winglet acts as a span extension, which reduces the effect of the vortices on the wing, reducing induced drag.

Of course, the tip of the winglet will generate a vortex as well.....
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WingedMigrator
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### RE: Spanwise Flow

 Quoting tdscanuck (Reply 16):you'll start a riot if you try to claim there is a "right" way to explain it.

I was going to ask about how winglets help shove more air down, which we all know is how airplanes achieve flight

DocLightning
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### RE: Spanwise Flow

 Quoting tdscanuck (Reply 16):I don't think it's either; it's a controversy about how to explain it. There is no controversy among aerodynamicists about how wings work either, but you'll start a riot if you try to claim there is a "right" way to explain it.

OK, I guess that makes more sense and reconciles the two explanations I've been encountering. As usual, your posts are informative.
-Doc Lightning-

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jetmech
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### RE: Spanwise Flow

 Quoting vikkyvik (Reply 8):Anyway, not sure how that would impact anything I said.

No impact at all. I was just trying to add to your description   .

 Quoting Starlionblue (Reply 11): So on, say, the top of the wing the lowest pressure is near the root and the (relatively) highest is near the tip. That's why you get spanwise flow inwards on the top (and vice-versa on the bottom). Is this correct?

I'd say the main driver of spanwise flow is the static pressures on the upper and lower surfaces of the wing relative to ambient static. There may certainly be spanwise gradients in pressure along the upper or lower surfaces, but it is the overall static pressure relative to ambient that drives the lateral component of flow.

Regards, JetMech
JetMech split the back of his pants. He can feel the wind in his hair .

vikkyvik
Posts: 12039
Joined: Thu Jul 31, 2003 1:58 pm

### RE: Spanwise Flow

 Quoting WingedMigrator (Reply 18):I was going to ask about how winglets help shove more air down, which we all know is how airplanes achieve flight

If you look reeeaally closely, you'll see that the winglets are, in fact, flapping in flight.

 Quoting jetmech (Reply 20):I'd say the main driver of spanwise flow is the static pressures on the upper and lower surfaces of the wing relative to ambient static. There may certainly be spanwise gradients in pressure along the upper or lower surfaces, but it is the overall static pressure relative to ambient that drives the lateral component of flow.

Not necessarily. The static pressure on the bottom surface of the wing can also be lower than ambient. Just not as low as the static pressure on the top surface.

Ah ok, no worries.
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jetmech
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### RE: Spanwise Flow

 Quoting vikkyvik (Reply 21):The static pressure on the bottom surface of the wing can also be lower than ambient. Just not as low as the static pressure on the top surface.

Sure, but even in this case there would still be vortices shed off the trailing edge and tip of the wing. Although the overall spanwise components of flow would be from the wingtip to the root on both the upper and lower surfaces, the difference in the magnitude of these components would still produce vortices and hence, induced drag.

Regards, JetMech
JetMech split the back of his pants. He can feel the wind in his hair .

Faro
Posts: 1565
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### RE: Spanwise Flow

 Quoting mawingho (Thread starter):"due to the pressure differential, some airflow will leak or spill around the wingtip from high pressure area under the wing to the low pressure area above wing. This causes a spanwise flow away from fuselage on the lower surface and a component towards the fuselage on the upper surface"

Funny one would have thought that the bigger contributor to spanwise flow by far would be the fuselage/wing junction. I imagined that air deflected off the fuselage sides would "overflow" onto the wing root, causing a high-pressure area "pushing" air outward toward the wingtips. Wouldn't this contribute (in a major way) to spanwise flow?

Faro
The chalice not my son

Starlionblue
Posts: 17571
Joined: Fri Feb 27, 2004 9:54 pm

### RE: Spanwise Flow

 Quoting faro (Reply 23):Funny one would have thought that the bigger contributor to spanwise flow by far would be the fuselage/wing junction. I imagined that air deflected off the fuselage sides would "overflow" onto the wing root, causing a high-pressure area "pushing" air outward toward the wingtips. Wouldn't this contribute (in a major way) to spanwise flow?

I would think that the air stays relatively attached due to the shape of the wing root fairing. Air that hits the wing moves around the airfoil. But that's just my speculation.
"There are no stupid questions, but there are a lot of inquisitive idiots." - John Ringo

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