Induced Drag

[Chrono]

Hi,

I've been reading this article in the NASA site about downwash and induced drag (http://www.grc.nasa.gov/WWW/K-12/airplane/downwash.html). Though I understand the general idea (how a greater angle of attack produces drag as a component of lift pointing slightly backwards), I don't understand how the wing tip vortices produce downwash, what is this downwash and how does it increase the angle of attack of the wing (I guess this means I understood nearly nothing :( ).

I really want to understand this theory, so maybe you people can help me. I'll appreciate it, as for now I'm still trying to figure out this article by myself unsuccesfully. :confused::confused:

[Brandano]

Downwash is the volume of air that the plane moves downward in order to keep airborne. Push enough air downward and you get enough reaction upward to mantain altitude.
The wing vortices are a result of the difference in air pressure between the top and the bottom of the wing. Higher pressure air escapes around the wingtip to occupy lower pressure space above the wing (this can happen behind the trailing edge, but it's easier to explain it like this). A tip vortex doesn't produce downwash, it actually uses up the energy that was stored in the downwash instead. Since to generate a vortex you need to put energy in it, and since energy doesn't come for free, the energy is subtracted from the plane's energy as drag
[edit] actually the article you linked has a nice representation of the downwash in it: http://www.grc.nasa.gov/WWW/K-12/airplane/shed.html

[markdrela]

Though I understand the general idea (how a greater angle of attack produces drag as a component of lift pointing slightly backwards) That's not correct. By definition, lift is always perpendicular to the local airflow, and does not get tilted by by the Angle of Attack (AoA). For example, a wing with a large Aspect Ratio of 40 say, at 10 degrees AoA, will have its lift vector tilted aft by only about 0.5 degrees. If you increase the AR to 400, and keep the AoA at 10 degrees, the lift vector tilt will now be only 0.05 degrees. So the AoA and the lift tilt angle are not directly related.

It is downwash that's associated with the lift tilting. To get downwash, you need the presence of wingtips, so that the air that the wing pushes down can squirt sideways and then back up and around. The spilling over and around is also what gives rise to tip vortices. For the purpose of induced drag computation it's convenient to pretend that the tip vortices cause the downwash, but physically it's more accurate say that they are a by-product of downwash. You can't have one without the other.

If there are no wingtips (i.e. the wing has infinite span), then there is
* no net downwash
* no tilt in the relative flow
* no tilt in the lift
* no induced drag
* no tip vortices.

[markdrela]

actually the article you linked has a nice representation of the downwash in it: http://www.grc.nasa.gov/WWW/K-12/airplane/shed.html
Unfortunately, that picture and explanation is misleading. I hate it when NASA does that :mad: .

In the 2D situation in the picture (infinite span), there is upwash ahead of the airfoil, and an equal and opposite downwash behind the airfoil. The net average downwash is zero. Hence, the lift tilt is zero and the induced drag is zero.

[AUAeroEng]

Ok, the article that you linked has nothing to do with wingtip vortices, though the article definitely makes it seem that way.

What this article is talking about is called "vorticity," also known as "circulation." As you know, air flowing over the top of the wing flows faster than the air flowing on the bottom of the wing. If you had a picture of an airfoil viewed from the side (like the NASA article's), and you put that airfoil in a vector field representing velocity, you would see that the velocity vectors on top of the wing are longer (bigger in magnitude, i.e. higher velocity) than those on the bottom, which are shorter (smaller in magnitude, i.e. slower velocity).

Now, if you take those velocity vectors and subtract the freestream velocity vectors, the longer vectors on top of the wing would still have a small magnitude and point in the direction of the freestream flow. The vectors on the bottom of the wing would have a small magnitude, but in the OPPOSITE direction of the free stream flow (i.e. pointing towards the leading edge of the airfoil).

This is a diagram I found on the net showing what I've just explained.
http://web.mit.edu/2.972/www/reports/airfoil/airfoil-6.gif

This "circular" flow around the airfoil is the vorticity. Because the net vorticity must be 0, you get what's known as a "starting vortex" as the air travels over the airfoil. That is what the NASA article's diagram shows.

The starting vortex:
http://web.mit.edu/2.972/www/reports/airfoil/airfoil-4.gif
http://web.mit.edu/2.972/www/reports/airfoil/airfoil-5.gif

[MarkusN]

I don't understand how the wing tip vortices produce downwash, what is this downwash and how does it increase the angle of attack of the wing
Look at the wing from the front and imagine the tip vortices trailing back. their rotating flow field has a "down" component behind the wing (and a corresponding "up" component outside). That's the downwash. I think you understand how this affects local airflow and thus direction of the lift vector.

[Chrono]

Ok, I think I'm getting it. This is what I understood so far, correct me if I'm wrong. I made this graphic (excuse my drawing skills).

Well first we have the wing (blue). As it moves through the air (black arrow) it generates vortices at its wingtips (assuming it is not infinite in size). This vortices create the efect called downwash (in purple). While there is downwash in the wing (which, as I read, is always present due to the wingtip vortices) the wing is affecterd rather by an "effective airflow" (I don't know what's its real name), which I assume has an angle between the real airflow and that of the downwash.

Then, as lift is perpendicular to the airflow, it tilts backwards. The horizontal component that appears with that effect is the induced drag.

The only question left is... the why the NASA web site (in the article I've mentioned) says that downwash changes the angle of attack and because of this generates drag? It shouldn't say that, its confusing :confused: . I've had a really hard time trying to understand the phenomenon because of that.

[macboffin]

A further misleading angle on the NASA article is reference to air flowing over the wing. It aint so! The wing is flowing through the air !The wing
meets the air and diverts some over itself, and some under.For most wings, since the top has more curvature than the bottom, the compression of the air to make way for the wing is greater above than below ; it thus flows faster into the low pressure area behind the wing, once it has passed, than the air below, the net effect being a downwash equal to the upwards force applied to the wing. The mixing of the two differing pressure flows at the tip results in a tip vortex.A higher angle of attack will generate a stronger vortex.
Note that flat plate or symmetrical sectioned wings fly quite well ; with a positive angle of attack. Aircraft with cambered airfoils can fly inverted also, albeit at quite high angles of attack ; obviously they have not heard of Mr.Bernoulli and his celebrated and often misquoted theory, ( which was actually descriptive of flows in pipes of differing bores.)
A higher aspect ratio, (longer thinner wing) with tips small in relation to span, will have a lower induced drag than a shorter wing with broader tips in ratio. The longer wing will however weigh more than a short wing of the same area, since the spar will be shallower as well as longer it must be of heavier construction. To some extent this factor is taken into account in the total design configuration for an aircraft for a particular role.
The available angle of attack range for the wing will be reduced as aspect ratio increases, thus affecting maximum co-efficient of lift.

[AUAeroEng]

The only question left is... the why the NASA web site (in the article I've mentioned) says that downwash changes the angle of attack and because of this generates drag? It shouldn't say that, its confusing :confused: . I've had a really hard time trying to understand the phenomenon because of that.[/QUOTE]

As I understand it, you've got the basic idea. I think you're just getting caught up in wording. The angle of attack of the airplane isn't changing, but the effect AoA of the lift vector (which is perpendicular to the airflow) is.

A further misleading angle on the NASA article is reference to air flowing over the wing. It aint so! The wing is flowing through the air !

Whether the air is running into the wing or the wing is running into the air doesn't matter. That's all based on what point you are referencing from.

Also on my above post, I thought the original poster had given the link of the second article posted.

[MarkusN]

Well, the downwash does in fact change the angle of attack effective at the wing. As the local airflow is diverted downwards, the AOA (relative to local airflow) is reduced. The amount of this reduction is called induced AOA. Downwash therefore has the additional effect of reducing lift. The lift increase per degree of (fee stream) AOA on a wing of limited span is less than that of an infinite wing for that reason. This is an effect that becomes quite noticeable on low aspect ratio wings.

[Chrono]

Well, I understand what you're saying MarkusN, but the NASA site says that the angle of attack is increased by the downwash. Quoting:

"The wing tip vortices produce a downwash of air behind the wing which is very strong near the wing tips and decreases toward the wing root. The local angle of attack of the wing is increased by the flow induced by the downwash, giving an additional, downstream-facing, component to the aerodynamic force acting over the entire wing."

Maybe this was the reason I've got confused in the first time. Anyway, thanks a lot for your help, I think I've got it now.

[Brandano]

I think that most people make the mistake of thinking that the wingtip vortexes cause drag. Rather, they are an effect of drag. Essentially the wing acts by creating a differential in pressure between the top and bottom surface (or by deflecting the airflow downwards... it's essentially the same thing, but people tends to argue about this) To do this it converts air in a steady state in air with a potential energy state, lower pressure on top, higher pressure on the bottom. Or less mass of air on the top, more mass of air on the bottom, whatever suits you better. Essentially a wing, in the process of generating lift, adds (potential) energy to a volume of air. This energy is subtracted from the plane system, and is called induced drag. The vortexes are the result of the air returning to a steady state in the most direct way possible, and as such are a result of the drag rather than the cause.

[Chrono]

:confused: :confused: Hey!!! at the risk of becoming annoying, I have another doubt. Yes I know, but since the moment I've learned that the equal transit time theory of flight was debunked, I'm trying to update all my knowledge base on aerodynamics. :D

Well here's the issue. I've read that an airfoil generates lift by turning the moving fluid (in this case air) downwards, which in turn creates a reaction force (Newton's third law) perpendicular to the airflow. Does this also generates induced drag? I would assume so, as this would also create a tilt in the lift angle by tilting also the angle of the airflow. Or am I wrong? :confused: :confused:

Also, do you know of a really good web site or book or article that explains all this? As far as I'm concerned, NASA web site's explanations aren't as extensive as I would like, and in wikipedia the authors of the article on lift are still fighting against each other trying to establish an "official" explanation.

Thanx again for the help!!

[ciurpita]

Well here's the issue. I've read that an airfoil generates lift by turning the moving fluid (in this case air) downwards, which in turn creates a reaction force (Newton's third law) perpendicular to the airflow. Does this also generates induced drag? I would assume so, as this would also create a tilt in the lift angle by tilting also the angle of the airflow. Or am I wrong?
thanks for starting this thread. here's my non-expert take

based on what mark said, even with an infinite wing there is downwash which is related to the amount of lift generated. in other words, if there is no lift, there is no downwash. but there is also upwash preceeding the wing, so that the angle of the airflow over the wing is equally affected by the downwash and the upwash, such that airflow over the wing is still parallel to the freestream angle, the lift is perpendicular to the freestream and there is no induced drag.

however, with a finite wing, the lateral airflow around the tips adds to the downwash, making it greater than the upwash, and slightly increasing angle of the airflow over the wing such that it is at a slightly higher angle than the freestream flow and the lift vector is tilted backwards. the induced drag is due to the fact that the lift vector is no longer perpendicular to the freestrean, and is slightly rearward, as you've said.

presumably, this wing tip vortex affects the downwash more near the tips than the root, such that the the induced drag is greatest near the tip and least (zero?) at the root. (and hence why adverse yaw is more prominent with longer wings).

you might be interested in "Fundamentals of Aerodynamics" John D. Anderson

[Odysis]

Greetings all,

presumably, this wing tip vortex affects the downwash more near the tips than the root

Bang on brother. I'm going to delve into the circulation theory of lift for a second, if I may.

Imagine, if you will, the wing is replaced with a single vortex along the 1/4 chord position, which rotates the air to induce the airflow shown in the hand sketches above (just the rotating bit). The strength of this vortex is given by:
Gamma = (c(y).V.Cl)/2 where c(y) is the chord length, V is the free stream velocity, Cl is the coefficient of lift.
As with any vortex, it cannot simply stop to exist, unless it butts up against a wall (this is where wing sections in wind tunnels simulate very well infinite wings). As the vorticity changes with span, the shed vortices trail off the wing. In the real world, these wrap up, giving rise to the wingtip vortex we all know and love.

So what's this got to do with AoA changes? Once the vortices trail off the wing, they change direction from perpindicular to the free stream, so parrallel to it. This means it now induces a flow in a direction best described as "wrapping itself around the fuselage" (same direction as propwash).

OK. Now we've established the trailing vortices induce a flow in the direction perpendicular to the free stream. Once this adds to the free stream flow, it adds to the AoA in an amount defined by:
alpha(i)=w(y)/V (alpha(i) is induced alpha), and w(y) (downwash) is defined by the DE:
dw(y)=1/(4pi) * Dgamma/Dy

Doesn't mean much in that form, and I don't have a finite solution, as I used a computer to solve the discrete form.

So in short - yes, Nasa has it bang on, the trailing vortices do induce a vertical flow component, which changes AoA. Further reading (with pictures!) see the attached document.

Odysis

[Odysis]

Just to clarify in advance something that may come up.

One of the diagrams in my document shows the bound vortex as shown on the NASA diagram, the trailing vortices (not shown on the NASA diagram, due their purely 3D nature) but does NOT show the shed vortex. Mine shows the trailing vortices continuing ad infinum. As mentioned, a vortex cannot end in free space, therefore this diagram is technically wrong; somewhere in space there will exist another vortex linking these trailing vortices together - this will be a mirror image of the bound vortex, and is shown in the NASA diagrams as the shed vortex.

Odysis

[Odysis]

If there are no wingtips (i.e. the wing has infinite span), then there is
* no net downwash

Sir I don't wish to argue with you - I used much of your work as a basis for mine (poorly, might I add!) during my undergrad days. I do however have a question of the above statement.

Without a net downwash, wouldn't the conservation of momentum say we then also have no net lift?

I now feel somewhat behumbled - I've just written a longwinded explaination of what I believe induced alpha is all about, just to find I don't understand how lift is created!

Odysis

[MarkusN]

Well here's the issue. I've read that an airfoil generates lift by turning the moving fluid (in this case air) downwards, which in turn creates a reaction force (Newton's third law) perpendicular to the airflow. Does this also generates induced drag? I would assume so, as this would also create a tilt in the lift angle by tilting also the angle of the airflow. Or am I wrong? :confused: :confused:

Sir I don't wish to argue with you - I used much of your work as a basis for mine (poorly, might I add!) during my undergrad days. I do however have a question of the above statement.

Without a net downwash, wouldn't the conservation of momentum say we then also have no net lift?
I had a similar issue with that, and after some racking my brain, that's my take on it:

In level flight, lift does not convert energy (is this also called performing physical labor in English? that's the term we use in German) as such, in the same way a table supporting a weight does not convert energy. It just sustains a certain gravitational potential of the body lifted.

As such there is no need for net mass being accelerated downwards to sustain lift.

And therefore upwash before the wing and downwash behind the wing can cancel each other out without violating the law of energy conservation. Actually, in an ideal fluid, they need to cancel each other out to fulfill that law.
Over the length of the wing chord there still is a considerable change of airflow direction and thus momentum, from upwash to downwash; this fulfils Newton's law of action and reaction to generate the lift.

The beauty of this: It still is valid when the plane climbs (here energy is converted). As upwash and downwash change direction now (they are rotated by the angle of climb) they don't cancel each other out anymore, and the resulting net downwash is equivalent to the energy gained by the climbing aircraft.


presumably, this wing tip vortex affects the downwash more near the tips than the root, such that the the induced drag is greatest near the tip and least (zero?) at the root. (and hence why adverse yaw is more prominent with longer wings).
One important thing to remember in that context: There is not just a "wing tip vortex". The vortex at the wing tip is easy to imagine and understand, but there is a whole field of vortices trailing back from the wing. This field is strongest at the wing tip, but there is a vortex trailing back from every spot of the wing where intensity of lift changes in spanwise direction. Prandtl was the first (AFAIK) to delve into this and he came up with the result that induced drag is lowest if this field of vortices is such that the induced AOA is constant over the span. The lift distribution fulfilling this condition is the well know elliptic distribution.

[Odysis]

Markus, (and Mark)
Force can also be expressed at m(dot).deltaV - in this case it's the m(dot) (mass flow) that got me.

As it turns out, I've been dealing with the real world too long, and forgot basic aerofoil theory. In a 2D flowfield, the air that would normally be deflected downwards to provide the upward momentum would continue to move downward forever. This means the air below it will move down to make way, as well as that above it. This in turn implies an infinite mass flow - along with it, either an infinite force, or an infinitely small deltaV. As the lift force is fixed, deltaV must be infinitely small in the 2D case.

3D the flow just spreads sideways as well, and does weird vortex things, and just works.

Ich glaub, dass hat's erklaert. Zumindest verstehe ich's! Um deine Frage zu antworten, Energie (Beschleunigungsarbeit um genau zu sein) ist nicht dass, von was ich gedacht hat, sondern Impuls. Genauso dein Tisch zur Flugzeug keine Energie gibt, gibt auch der Auftriebskraft keine. Natuerlich, wann's auf Vertikalgeschindigkeit ankommt, wird's anders... Ich hoffe, dass alles klar ist?

Odysis

[Brandano]

In level flight, lift does not convert energy (is this also called performing physical lobor in English? that's the term we use in German) as such, in the same way a table supporting a weight does not convert energy. It just sustains a certain gravitational potential of the body lifted.

As such there is no need for net mass being accelerated downwards to sustain lift.
How wonderful... all that research trouble, all those years of development and the Harrier didn't really need an engine to hover after all...

What you say holds true only if the plane has no mass, otherwise you need to counterbalance the plane mass*9.81m^2 with an equivalent mass*acceleration value going downwards

[MarkusN]

How wonderful... all that research trouble, all those years of development and the Harrier didn't really need an engine to hover after all...

What you say holds true only if the plane has no mass, otherwise you need to counterbalance the plane mass*9.81m^2 with an equivalent mass*acceleration value going downwards
I was speaking of a theoretical two-dimensional flow of a wing of infinite span. Give that Harrier an exhaust nozzle of infinite expanse and the acceleration you need will become quite small. Infinitesimally small, in fact.

Odysis has given a better explanation than mine in his last post.

I am very well aware that in the real world those mind concepts don't work the same way.

[edit, much later]this is actually the part of my previous post that has the part about mass accelerated downward and thus creating the necessary reaction force:
Over the length of the wing chord there still is a considerable change of airflow direction and thus momentum, from upwash to downwash; this fulfils Newton's law of action and reaction to generate the lift.

[Chrono]

Hey, this thread turned out great. That explanation of the upwash solved all doubts I've had about the subject.

Ciurpita, the book you're suggesting ("Fundamentals of Aerodynamics" John D. Anderson), I've seen it in amazon, the book looks good but its a big deal of an investment. So do you think that book will be good for an entry level reader? As I'm no aeronautical engineer, all my knowledge base comes from the hobby. Though I'm not afraid of a few equations as I definitely love physics.

[nmasters]

I apologize in advance for muddying the water a bit more. One thing that should have been pointed out is that your vector diagram is wrong. You don’t show the upwash and your vectors are labeled wrong. It’s important to get the picture and vocabulary right so that as you delve into this stuff more deeply (and as you can see from this thread it gets really deep) you’ll run across these terms a lot. If you drill a bunch of pressure taps in a wing you get the pressure distribution (http://www.dynamicflight.com/aerodynamics/pres_patterns/) of your airfoil. Then with the knowledge that pressure is always perpendicular to the surface that it acts upon you can draw vectors at the position of each tap. Notice that most of the vectors on the lower surface point down, so they subtract from the lift. Some point forward and some point aft. When you sum all the individual vectors the result is the total force, thus your green vector is properly called the resultant vector. Then to get the lift and drag you draw a rectangle with the ends of the resultant at diagonal corners. This is actually backward from the way wind tunnel force measurements are added to find the resultant i.e. you can either break the lift and drag out of the resultant or add the lift and drag together to find the resultant. It’s this resultant vector that’s tilted aft and the lift and drag vectors are perpendicular and parallel to the free stream respectively. As you apparently understand now the downwash of the tip vortices just increases the aft tilt of the resultant by either adding to the strength of those pressure vectors that point aft or subtracting from those that point forward. Since, according to that guy Bernoulli, the relationship between pressure and velocity is reversible all the readings from those pressure taps can be converted into velocity vectors to show the bound vortex. The pressure field (and therefore the bound vortex) extends a long way out into the air, about a half span up and down and several chord lengths forward and back. It takes a lot of power to start a mass of air that big rotating and it’s not surprising that such a large volume of fluid will leak out if the ends aren’t sealed. In order to maintain level flight this fluid that leaks off at the tips has to be replenished with new air from the free stream and the replacement fluid has to be accelerated up to the circulation speed i.e. both the fluid lost and the energy it carried away must be replaced and that’s why engines are so popular.

So this is the model I’ve been using for a while: When the plane rotates for takeoff a vortex forms on top of the trailing edge (this is called the starting vortex or startup vortex). When the plane has traveled about 5 to 7 chord lengths from where the TE vortex started the vortex separates from the TE but its ends are still attached to the wing tips. During this 5-7 chord length period the bound vortex has started and gained enough strength to lift the plane. Thus you have a big toroidal vortex i. e. a doughnut. The doughnut is divided into quadrants. One quadrant is the bound vortex and the opposite side of the doughnut is the starting vortex and for a few minutes after takeoff they are connected by the tip vortices. The starting vortex stays on the runway near the point of liftoff until it is slowed down by internal friction and becomes indistinguishable from the rest of the atmosphere. The tip vortices can’t just end so they snake around until they find each other and hook up to form another closed torus. The air flow is descending into the hole of the doughnut and ascending around the outer edges. If you were to leave this toroidal vortex alone (take the plane out) it would persist for a while and, due to its own circulation, actually travel some distance. But you’re not leaving it alone you’re forcing it to do work. The plane rides inside this big torus and the engine constantly pushes it forward into the rising air at the front. This is similar to a phenomena sailors call “deadwater” (http://www.seafriends.org.nz/oceano/waves2.htm#internal) except that in deadwater the internal wave (http://en.wikipedia.org/wiki/Internal_wave) only creates drag on the ship but the airplane rides in a different position in the wave and derives both lift and part of its total drag from it. Dolphins surf in the bow waves of ships (http://images.google.com/images?q=dolphin+%22bow+wave%22&ndsp=20&svnum=10&um=1&hl=en&client=netscape-pp&rls=com.netscape:en-US&start=0&sa=N) And in storm waves.


http://www.arvelgentry.com/origins_of_lift.htm Is a good explanation of the origin of lift and induced drag since they are both just different aspects of the same phenomenon

As for books that are more accessible than "Fundamentals of Aerodynamics" you might look at “The simple science of flight” (http://www.google.com/search?hl=en&rls=com.netscape%3Aen-US&q=%E2%80%9CThe+simple+science+of+flight%E2%80%9D+b y+Henk+Tennekes&btnG=Search) by Henk Tennekes and “Stop abusing Bernoulli!” (http://www.google.com/search?hl=en&rls=com.netscape%3Aen-US&q=%E2%80%9CStop+abusing+Bernoulli%21+%E2%80%9D+by+ Gale+Craig&btnG=Search) by Gale Craig


No mater which books you read somebody will tell you that it’s nonsense.This stuff is the most difficult problem in classical physics so there are a lot of people with only a partial grasp (like me) and many (unlike me) will argue that everybody who doesn’t subscribe to their myopic point of view are wrong.


--Norm

[ciurpita]

Ciurpita, the book you're suggesting ("Fundamentals of Aerodynamics" John D. Anderson), I've seen it in amazon, the book looks good but its a big deal of an investment.

all engineering books are expensive. i look for used copies on half.com

[Odysis]

all engineering books are expensive.

And just to make it worse, the authors will generally only give a detailed explanation of their take on things. As you've seen here, there are many ways to explain what we see. None more right or wrong than the others, simply better suited for a particular task.

A thought - nothing that has been said in the way of vortex interaction, lift generation etc is prescriptive, it's all descriptive. That means they are ways of explaining what we see, i.e. that a wing keeps an aircraft aloft. None of them are telling the air what to do, rather trying to help us understand what it's already doing. Is the wing moving forward, or the air moving backward? Chicken or egg? Circulation or pressure differential?

Odysis

[Tom Harper]

nmasters,

Thanks for the interesting discussion. Like you said it does not match with all others.

I don't have the grandiose theory but I do have some observations. You can see the tip vortices in contrails. They remain separated for many miles and then turn inward and connect to complete the torus and form the trailing vortex that rolls along following the airplane. Sometimes it is like a text book illustration.

When a passenger I have observed the airflow over the wing in fog and when the pressure differential caused condensation (vaps). The vortex sheet at the trailing edge does not produce visible vortices. I'm not saying they are not there. I just have never seen them. The downwash appears as an even plane. The tip vortex begins at a point near or at the TE of the wing tip. I have never observed the vortex starting forward of the trailing edge. I don't think there is any spanwise 'leakage'.

[AUAeroEng]

Hey, this thread turned out great. That explanation of the upwash solved all doubts I've had about the subject.

Ciurpita, the book you're suggesting ("Fundamentals of Aerodynamics" John D. Anderson), I've seen it in amazon, the book looks good but its a big deal of an investment. So do you think that book will be good for an entry level reader? As I'm no aeronautical engineer, all my knowledge base comes from the hobby. Though I'm not afraid of a few equations as I definitely love physics.


Chrono,
Check out "Aircraft Design: A Conceptual Approach" by Daniel P. Raymer (the fourth edition is the latest, but earlier edition are alright as well). It explains a lot of the practical aspects of designing aircraft with theory thrown into to back it up.

And I second ciurpita's suggestion of half.com.

[biber]

Cool thread!
Very good explanation and links, Norm.

biber

[nmasters]

Chicken or egg? Circulation or pressure differential?

Why not both? That arvelgentry.com page I pointed to yesterday describes a simple experiment that shows the starting and bound vortices. While the wing is moving through the water there’s a pressure field around it but when you pull the wing out, thus removing the solid surface that was separating the pressure differential, the pressure transforms into rotary motion.

--Norm

[MarkusN]

When a passenger I have observed the airflow over the wing in fog and when the pressure differential caused condensation (vaps). The vortex sheet at the trailing edge does not produce visible vortices. I'm not saying they are not there. I just have never seen them. The downwash appears as an even plane. The tip vortex begins at a point near or at the TE of the wing tip. I have never observed the vortex starting forward of the trailing edge. I don't think there is any spanwise 'leakage'.
You are right of course. One must remember that what we are discussing here is the flow field of a lifting line, a theoretical concept to make lift accessible to calculation. In realitity we have a lifting surface, or exacltly speaking even a lifting body.

The spanwise vortex field I spoke of manifest itself only in the form of spanwise components of velocity: on the underside of the wing flow has an outwards component, on the upper side a corresponding inward component. I assume that these would roll in to form vortices only quite a bit downstream. Also, since this is a field, there probably are no individual vortices with a core, instead all vortices will indeed unify with the tip vortex downstream.

[macboffin]

Relevance is this ; a moving wing meets static air, with inertia, and accelerates and deaccelerates that air. The air in a wind tunnel is moving,(due to scale effects often pretty rapidly) and thus has kinetic energy ; which makes it's behaviour in response to passing around a wing section somewhat different to that obtaining for a wing in free flight.
Hence the discrepancies between wind tunnel results and practical flight tests.

[biber]

I'd say that's the wrong explanation for true statement.

It doesn't count if the air moves or the wing, with in each case the other thing beeing static.
That's just an issue of dealing with different inertial frames of reference and
choosing one or the other, having one and the same physical experiment at hand.

The differences between wind tunnels and aircraft flying in the free atmosphere are more related to restrictions that wind tunnels have in the amount of turbulence and achievable reynolds numbers, e.g.

biber

[MarkusN]

I..in the amount of turbulence and achievable reynolds numbers, e.g. ...
that, and the limited size of the flow field. In free air there are no walls restricting the sideways movement of air 'dodging' the plane.
An open test section wind tunnel without walls OTOH has its own set of problems.

[Chrono]

No mater which books you read somebody will tell you that it’s nonsense.This stuff is the most difficult problem in classical physics so there are a lot of people with only a partial grasp (like me) and many (unlike me) will argue that everybody who doesn’t subscribe to their myopic point of view are wrong.


Yeah, it seems so. I was also reading an article in wikipedia about lift and in the discussion section there was a big fight between the editors of the article. I guess that makes even harder for people like me to understand the subject, as many people hold their theories true ans the others wrong, while in reality they're only explaining a different point of view which isn't unique nor excluding.

Hey, if it isn't too much to ask Norm, could you add one simple drawing for the second paragraph of your explanation?

Thanks a lot to everyone for your links, explanations and your time.

[nmasters]

Tada :D

The first drawing from my vortex lift page isn’t quite right. The trailing vortices move closer together as the plane moves away from them. I realized the error a few days after I posted it years ago but I’m too lazy to redraw it. The second drawing is from a discussion of sweep effect we had on homebuiltairplanes.com a while back. The volume of air involved in the circulation is much bigger than it appears in this drawing. For instance when the B-2 bomber is refueling from a KC-135 the tanker pilot can feel the other plane below him. Not surprising really, when they’re hooked up they look like some sort of nightmare biplane

--Norm

[Derfy]

Here's a nice little streaming video about vorticity which includes a bit on circulation and also shows the starting (and stopping) vortex for an airfoil. From about 3 minutes in.
Unfortunately you'll need RealPlayer (or similar) to view. :(

http://modular.mit.edu:8080/ramgen/ifluids/Vorticity_Part_2.rm

In fact the page that this video comes from has a few topics that may be of general interest to us amateurs :D :

National Committee for Fluid Mechanics Films

http://web.mit.edu/fluids/www/Shapiro/ncfmf.html

:cool:

[Ricardo RW]

Wow, there's a lot of stuff here to my brain... but brain succeed better than brawn...

[Chrono]

hey!! all said, the physics behind lift and flying are, in fact, very complex (glad I'm understanding it). :eek: That makes me think it was almost a miracle that men could learn how to fly.

[Ricardo RW]

..That makes me think it was almost a miracle that men could learn how to fly.More than learn to fly I think the real issue is understand why it's flying :p

Saludos vecino (Regards neighbor) :)

[Brandano]

Well, man had lots of hints about how to achieve flight. Birds, some seed pods.. seems like the Egyptians had already gliding toys, and I bet that some form of paper plane was flying much earlier than any attempt at human controlled gliding. Not to mention kites

[MarkusN]

True, but the pioneers that really managed breakthroug (Lilienthal and the Wright brothers) took a very systematic aproach at at least understanding what forces are generated on lifting surfaces in flight. Not the circulation and potential theory stuff that we are discussing here yet, but they tried very hard to understand the phenomena.

[Chrono]

Well, man had lots of hints about how to achieve flight. Birds, some seed pods.. seems like the Egyptians had already gliding toys, and I bet that some form of paper plane was flying much earlier than any attempt at human controlled gliding. Not to mention kites
Yeah, but there where mostly spectacular failures in the beginning (and a few small successes), like that of Abbas Ibn Firnas. I think the first true pioneer was sir George Cayley. I wonder what would he think if we gave him a copy of "Fundamentals of of Aerodynamics". :D
Saludos vecino (Regards neighbor)
And Ricardo: que tal vecino (How's it going neighbor?)

[nmasters]

As with most other technologies primitive hardware preceded theory by many years. The earliest recorded “flying machine” was Archytas' "pigeon" (http://www.tmth.edu.gr/en/aet/1/14.html) in 425 BC. Before the mid 19th century progress was pretty sporadic and halting. There’s a story that a Chinese general strapped one of his solders to a kite in about 200 BC and some time later there are court records of people being sentenced to fly as punishment. Marco Polo described a good luck ceremony in which a drunken sailor was tide to a kite and flown over the harbor (sounds more like a prank to me but he could have made some weather observations). Over the centuries several tower jumpers apparently survived and a few accounts even say they managed to fly some distance from the starting point. I can’t remember who these people were but when I read about them (there were two that were witnessed and one repeated for a total of three “flights”) I calculated the glide slope from the witnesses’ comments. It was 4:1, about the same as a butterfly, assuming a straight line. The line that finally lead to controlled heavier than air flight really started with Sir George Cayley (http://en.wikipedia.org/wiki/George_Cayley) in the late 1700s. He discovered the importance of camber and in the 1840s threw a small child down a hill (or his chauffer (or maybe his chauffeur was a 10 year old boy)). Anyway up to the mid 1800s there was no theoretical bases and none of the previous attempts had any sort of control. In the 1850s Lord Kelvin and Hermann Von Helmholtz (http://en.wikipedia.org/wiki/Helmholtz%27s_theorems) developed the circulation theorem apparently based partially on previous work with electromagnetic induction. The Navier-Stokes (http://en.wikipedia.org/wiki/Navier_Stokes ) equations were also worked out in the mid 19th century. 70 years later a really clever guy named Ludwig Prandtl (http://en.wikipedia.org/wiki/Ludwig_Prandtl) worked out the lifting line theory (http://www.onemetre.net/Design/Downwash/LiftLine/Liftline.htm) which allows you to predict the performance of a wing before you actually build it (about 20 years too late to help the Wright brothers). Of course we all know how things turned out once the theories were all in place.

--Norm