Lift and induced drag...

[LambOfGod]

Well, I do know how lift works. But, when an aeroplane climbs, it is producing more lift to get up there. And in cruise lift equals weight. So, in descent you'd expect it to be producing less lift. Which it is??? Is that right?
Then why is there more induced drag at higher angles of attack and descent with flaps out?
I know the flaps are there to produce more lift at slower speeds and that they do produce a hell-load of drag...

Thanks if you can answer this one... ...Properly

[keith smith]

Hi there. This much easier to understand if Icould draw a simple diagram, but I will try and describe things :
Lift L, dragD, Thrust T, Weight W, climb angle theta.
Assume thrust is along flight path.
1.Resolve along flight path results in
T=D+Wsin(theta)---means you need more thrust to climb
2.Resolve normal toflight path results in
L=Wcos(theta)--means you need slightly less lift in the climb.
Induced drag is a different matter, and for a given lift it increases with lower speed(i.e higher incidence)Hence there is a minimum total drag speed.If you are mathematically inclined Glauert describes it well in his classic book:)

Keith

[Mark1234]

Actually, in a steady state climb, the wing produces slightly *LESS* lift - because a component of the thrust is assisting the vertical picture. I would also figure that in a descent, the same occurs, for the same reason. Consider a simple thought experiment - vertical climb/descent; what is required of the wing?

As for drag, you need two answers: Why is induced drag more at low speeds, and what goes on with the flaps.

Someone else will have to explain why induced drag increases with reducing speed - I can not.. but note that it's inversely proportional to airspeed, NOT AOA.

As for the flaps, note that induced drag is something very special - drag created in the process of generating lift. It can be separated from form drag - drag due to shape if you will. Extending flaps actually creates *form* drag. The induced drag picture may change as the wing planform changes slightly, it may even reduce. The main affect of flaps is not on induced drag.

Hope that helps.

[The Real Slim Shady]

As the good Lord / Allah giveth....so he taketh away.

More lift...more induced drag...especially if you dangle bits off the back / front ends.

[Dick Deadeye]

LambofGod

when an aeroplane climbs, it is producing more lift to get up there

Nope!

Less actually! :eek:

[zerozero]

LambofGod--you got a few partial answers.

And while 'keith smith's' answer may be technically correct it's pretty hard to visualize (Apologies Keith, but at this point images work better than equations).

:)

First, you need to understand the concept of vectors. I'm going to assume you have a handle on this concept. If not, then do some research on it and if you still have questions then follow up here.

Second, Mark1234 is correct when he states that the lift produced by the wing in a climb is slightly less than in level flight due to the VERTICAL COMPONENT OF THRUST.

That is to say, when you point the nose up, thrust also has an upward vector.

In fact, airplanes climb due to EXCESS THRUST, not lift.

To answer your question about induced drag--another way to think of induced drag is to describe it as "the rearward component of lift" generated by the wings.

In a very basic way, an airfoil needs a positive angle of attack in order to produce lift (this is not the Bernoulli type of lift, but more Newtonian [for every action there is an equal and opposite reaction]--it's just that sometimes it's more convenient to describe the lifting force using Bernoulli; and sometimes more convenient to use Newton--both are valid, depending on the situation).

As flight students we're taught that LIFT (with a capital L) directly opposes Gravity (with a capital G). But that's not the entire story. In reality, it's only the VERTICAL COMPONENT of Lift that opposes Gravity. TOTAL LIFT is actually pointed slightly AFT, due to the slight angle of attack. The REARWARD COMPONENT of Lift is what we call INDUCED DRAG. It's Lift that's working to the rear instead of strictly working towards the vertical.

So, as you increase your angle of attack, you gradually point that big old TOTAL LIFT more and more to the rear--or aftwards and your rearward component of Lift grows greater and greater, increasing your induced drag.

If you draw a "Drag Curve" (Total Drag vs. IAS) it would look like a capital "U". Why? Because in high speed flight your drag is high thanks to Parasite Drag (Increases to the square of your IAS). But at slow speeds your drag is high due to Induced Drag.

That's why your best economy airspeeds are somewhat right in the middle where it's the best compromise of low Induced Drag and low Parasite Drag.

I hope all of this makes sense. It would be much easier with a chalkboard, but if you have some good textbooks maybe you can find the illustrations I'm describing.

Good luck.

[Mark1234]

So, as you increase your angle of attack, you gradually point that big old TOTAL LIFT more and more to the rear--or aftwards and your rearward component of Lift grows greater and greater, increasing your induced drag.

Doh! So blindingly obvious I'm ashamed I didn't figure that out...


More lift...more induced drag...especially if you dangle bits off the back / front ends.


Ah, but you're not increasing the lift - the mass of the plane didn't change - you simply change the manner in which it's generated. The dangly bits have little effect on induced drag.

[NinerVictor]

The dangly bits do affect induced drag. There is a relation between Lift and Induced drag.

Cdi = Cl^2/Pi*e*AR

Cdi = Coefficient of induced drag
Cl = Coefficient of lift
Pi = 3.14...
e = Oswald Efficiency Factor
AR = Aspect Ratio

By changing slats and flaps configurations, the coefficient of lift changes and so will the coefficient of induced drag.

[LambOfGod]

Hmmmm, okay...
Well, would the CP moving aft due to the lowering of the flap + the greater use of elevator (counteracting the low nose from aft CP) part in an increase in induced drag during descent?

And I'll have to read the "Lift & Induced Drag" chapter again...

[Chesty Morgan]

Google is your friend.

Induced Drag Coefficient (http://www.grc.nasa.gov/WWW/K-12/airplane/induced.html)
Induced Drag and the Trefftz Plane (http://www.desktopaero.com/appliedaero/potential3d/induceddrag.html)
Aeronautics - The four forces of flight (INDUCED DRAG) - Level 2 (http://www.allstar.fiu.edu/aero/flight45.htm)

A quote from the middle link.

The total induced drag of a system of lifting surfaces is not changed when the elements are moved in the streamwise direction

[KristianNorway]

Hello LambOfGod

Seems like we're a couple of guys wondering about the same questions. :)

Look somewhat back in tech log, maybe three pages, and you'll find the title "strongest wing tip vortices when slow, clean and heavy. BUT WHY?" by ludovico. Maybe that can help.

I also believe that you have slightly less lift during climb, and climb is due to excess thrust.

On the other hand I'm not so sure if I agree with zerozero on the description of induced drag. He does state clearly that he describes it within the parameters of only Newtonian thought, and maybe one defines vectors different then. I'm open for discussion.

Still:

'Because lift is a force, it is a vector quantity, having both a magnitude and a direction associated with it. Lift acts through the center of pressure of the object and is directed perpendicular to the flow direction.'
What is Lift? (http://www.lerc.nasa.gov/WWW/K-12/airplane/lift1.html)

It does not tilt with angle of attack as long as the flow direction is the same (let's assume level flight at different airspeeds). That would be the resultant force from lift and drag, but not lift.

By using both Newton, Coanda and Bernoulli to describe lift it seems like we have more wingtip vortices (induced drag) when we're clean, slow and heavy.
Here's my thoughts about it in the thread mentioned above:

Hello ludovico

I asked the exact same thing here at tech log some time ago and couldn't wrap my head around it, but it seems Brian Abraham has a really good point.

I was thinking that flap couldn't affect the vortex since flying an airplane in a given IAS has to produce the same amount of lift, and hence induced drag, whether it is configured with flaps or not. Here is where I guess I was wrong:

A vortex being dependent of the downwash angle from the airfoil to the direction of flight and the pressure differential between the upper- and lower side of the airfoil, is then dependent of the aspect ratio of the wing.
As we read during our studies that's why the gliders have long wings.
But.. lowering flaps shifts the centre of pressure laterally towards the area of the flaps due to the increased camber and downwash angle. When maintaining the same amount of total lift this means less pressure differential toward the wingtips, as if there was a higher aspect ratio.
Meaning smaller vortex when lowering flaps.

As said so many times in this thread.. this is just my theory. If I am corrected I see that as a chance of learning.

I hope this may have been of some help.

[zerozero]

Hi Kristian.

You're right to pick on some of my word choice.

It's been many, many years since I've taught this stuff--and I always had the advantage of being able to draw pictures.

But when I mentioned the lifting force "tilting" back with increases in angle of attack I was picturing in my head (and probably failed to convey in words) the "total" force that I would diagram with a very large arrow.

True, Lift, (the vertical component of the total force) will always oppose Gravity, and act perpendicular to the relative wind.

That vertical component of lift I would diagram with a smaller arrow, but pointing straight up against gravity.

Likewise, induced drag, the rearward component of the greater total lifting force would also be diagrammed with a smaller arrow, pointing aftward.

The large arrow, the one that represents the total of the vertical component + the rearward component, would point mostly "up" but also slightly "to the rear".

Thus I chose the word "tilt".

But you're correct, that lift (the "vector quantity" that you mentioned) will always be strictly perpendicular to the relative wind; or flight path; or even "flow direction" as you say.

I hope I've made myself clear, because we really don't disagree, we just have a different vocabulary to describe the same thing.

If we had a chalk board in front of us, this discussion would be much shorter.

:cool:

[Mark1234]

The dangly bits do affect induced drag. There is a relation between Lift and Induced drag.

Cdi = Cl^2/Pi*e*AR

Cdi = Coefficient of induced drag
Cl = Coefficient of lift
Pi = 3.14...
e = Oswald Efficiency Factor
AR = Aspect Ratio


Indeed - no arguament there, induced drag is all about lift. however, the lift required remains the same, dangly bits or no. The dangly bits only affect HOW that lift is generated...


By changing slats and flaps configurations, the coefficient of lift changes and so will the coefficient of induced drag.

Instantaneously, yes - but if Cl increases, we've destroyed the equilibrium and all bets are off. In order to maintain equilibrium, the lift force L must remain the same - the amount of L required for a given flight path is constant, irrrespective of the wing configuration.

Now, considering that Cl = L/half rho Vsqared A
Rearranged, L = Cl half rho Vsquared A

rho (air density) will not change appreciably, nor will A (wing area), so L is proportional to Cl * vsquared.

In order to restore equilibrium, we can nose down, reducing AOA, hence returning Cl to it's original value, Or, if not, the aircraft will pitch up and slow down, Vsquared will reduce and we will find a new equilibrium where L is the required amount. The induced drag there will have increased, but due to the reduced airspeed, NOT the flaps.

So, I maintain that flaps do not *directly* affect induced drag.

[bookworm]

Likewise, induced drag, the rearward component of the greater total lifting force would also be diagrammed with a smaller arrow, pointing aftward.

The problem, zerozero, is that you don't provide an explanation of why there is a "rearward component of the greater total lifting force" or to put it another way, of why you believe the lift vector "tilts".

The lift force does not tilt with the angle of attack to remain at 90 degrees to the chord line. The lift remains at 90 degrees to the airflow. If you choose to look at the angle of the total aerodynamic force, the vector sum of lift and drag, it will indeed be tilted back. But noting that only identifies that drag exists, it doesn't explain its origin. For an infinitely long wing, there would be no induced drag at any angle of attack.

Induced drag is the result of the the modification of the local airflow direction by the vortices that result from having a finite span. The vortices tilt the air as it approaches the wing by adding a downwash. It is this difference between the freestream and the local airflow direction that manifests itself as induced drag.

[zerozero]

Bookworm--thank you for the elaboration. I had, in fact, forgotten that little piece of the mystery. As I said, it's been years since I taught this subject.

But in my defense, when I wrote my original response, I was addressing a 16 year old student pilot who wanted to know why induced drag increased at high angles of attack.

I think we got him back on track.

:ok:

[chornedsnorkack]

For an infinitely long wing, there would be no induced drag at any angle of attack.

Induced drag is the result of the the modification of the local airflow direction by the vortices that result from having a finite span. The vortices tilt the air as it approaches the wing by adding a downwash. It is this difference between the freestream and the local airflow direction that manifests itself as induced drag.

So, suppose that you are changing the angle of attack of an infinite, symmetrical airfoil.

Due to symmetry of the airfoil relative the the plane along the airfoil, the lift is zero at zero angle of attack. Drag is nonzero.

At AoA-s which are small and negative, or else close to 360 degrees, the lift shall be downwards.

Now, when the AoA is 180 degrees, lift is zero for the same symmetry reasons.

If the airfoil´s leading and trailing edge are not symmetrical, the lift would not be zero at exactly 90 degrees, but it would go through zero at near 90 degrees.

However, at small positive AoA-s, lift and drag both increase with AoA.

Is the increase of drag compared to zero-lift drag called "induced drag" in case of an infinite airfoil?

[LambOfGod]

So if induced drag & lift increase with increases in AOA, wouldn't that make the lift increase during a climb. I know the thrust is there though...
Perhaps the thrust appears to reduce the weight and the aerofoil doesn't produce as much lift...:ugh::ugh: Anyone??

[zerozero]

So if induced drag & lift increase with increases in AOA, wouldn't that make the lift increase during a climb. I know the thrust is there though...
Perhaps the thrust appears to reduce the weight and the aerofoil doesn't produce as much lift... Anyone??

Lift and drag will increase as the angle of attack is increased, but once stabilized in steady, unaccelerated flight, lift and drag will decrease slightly due to the vertical component of thrust as discussed earlier.

Keep in mind, aerodynamics are *very* DYNAMIC.

:}

[27/09]

The angle of attack is not increased in the climb. Remember AoA is measured with respect the the relative airflow or relative wind as the Americans call it. Just because the wing is at a greater angle to the horizon in the climb it does not translate that it is at a higher AoA.

The relative airflow, in crude terms, (forgetting about the upwash and downwash) is opposite to the direction of travel. During a climb the aircraft is moving forward and upward at the same time.

The AoA in the climb is about the same as it would be for the same speed in straight and level with an allowance for that proportion of weight that is being supported by part of the vertical component of thrust.

In a climb the thrust is angled upwards compared to the straight and level position. It is thrust that makes the plane climb, the more excess thrust you have over and above that required to pull the aircraft thru the air the greater your rate of climb.

Once thrust exceeds weight you are able to climb vertically, in this instance the wings are producing no lift that supports the aircrafts weight.

[zerozero]

Think about pulling g's in a steep turn.

A 2000 pound (kilos, whatever...) airplane in steady, unaccelerated flight (therefore pulling 1g) must produce 2000 pounds of lift.

But a 2000 pound airplane in a 60 degree bank will pull 2g's and therefore must produce 4000 pounds of lift.

It must produce DOUBLE the lift even though it's not climbing. And while we may say it's in a steady state, it's still considered to be "accelerating" (i.e. changing direction).

But if you were to take that same airplane in steady, level flight and simply yank back on the yoke, yes you'd climb (for a little while) but more importantly you just increased the lift in a really uncomfortable way--and you could feel the g's in your seat, the same way you can feel them in a steep turn.

But if you want to continue that climb, you're gonna have to add power, and when you do, you'll stop pulling so hard on the yoke, producing extra lift that's smashing you into your seat.

All of this will eventually translate into basic aircraft control.

Pitch + Power = Performance.

After you master the pitch and power relationship everything else is just details. Really try to understand this relationship the best you can.

[bookworm]

Is the increase of drag compared to zero-lift drag called "induced drag" in case of an infinite airfoil?

I think you'd need to be a lexicographer to get excited about this one. ;)

If you take "induced drag" as being literally "the drag associated with the production of lift", then you would have to say yes.

If you prefer McCormick's version: "Induced Drag: The drag that results from the generation of a trailing vortex system downstream of a lifting surface of finite aspect ratio" then pretty much by definition, you'd have to say "no".

I prefer the latter.

[chornedsnorkack]

The AoA in the climb is about the same as it would be for the same speed in straight and level with an allowance for that proportion of weight that is being supported by part of the vertical component of thrust.

In a climb the thrust is angled upwards compared to the straight and level position.

Not only in climb.

Consider plane in a steady level flight. At some AoA, suppose that the thrust is exactly horizontal.

Since the flight is level, drag is exactly horizontal (and equal to thrust) while lift is exactly vertical (and equal to weight).

Now, pitch the plane up, increasing Cl, and slow it down, decreasing Vsquared, so that the plane is again in steady level flight.

Since the flight is again level, the drag must needs be exactly horizontal. But the thrust is now angled upwards, since we just pitched the whole plane with its engines. Therefore some of the weight of the plane is supported by the vertical component of the thrust. Lift must be smaller than weight - in level steady flight.

Indeed, as you pitch up to steady hover, both lift and drag must go to zero (because airspeed is zero) and thrust must be exactly equal to lift.

But when you go to steady vertical climb, lift and drag are no longer required to be zero because there is nonzero airspeed. Drag is opposed to airspeed, which means directly down. Lift must be at a right angle to airspeed, so horizontal. Thrust no longer needs to be directly vertical when there is lift present.

[27/09]

chornedsnorkack

You missed the condition I placed in my statement. for the same speed in straight and level

My statement was about the fact that AoA doesn't really change from straight and level to a what it is in a steady climb so long as the aircraft flys at the same IAS in both cases.

You talk about varying speeds for straight and level and as a result are also talking about varying the AoA.

[hawk37]

Bookworm, you seem to be saying that an aircraft/airfoil combination with no wingtip vortices (consider the academic case of a perfect winglet) would have no induced drag. Or, an airfoil that stretched from one side of a windtunnel to the other (no wingtip vortices) has no induced drag. Am I understanding you correctly?

[bookworm]

Bookworm, you seem to be saying that an aircraft/airfoil combination with no wingtip vortices (consider the academic case of a perfect winglet) would have no induced drag. Or, an airfoil that stretched from one side of a windtunnel to the other (no wingtip vortices) has no induced drag. Am I understanding you correctly?

I didn't say "wingtip vortices" but "trailing vortex system" (or rather Barnes McCormick did). Vortices don't have to be shed at the tip. I have no idea what a "perfect winglet" might be -- if it's infinitely long then you might as well have an infinite span. As for windtunnels, there may be some practical effects that spoil the two-dimensional nature of the flow, but yes, perfect 2D flow means no induced drag. In a real wing of finite length, there must be vortices in order for there to be lift, hence there must be induced drag dependent on lift.

[cwatters]

I'm wondering if the OP wasn't after a much simpler answer...

On one level you can consider the lift produced by a wing to be more or less constant and equal to the weight of the aircraft even when climbing.

Increasing the angle of attack allows a wing to produce that amount of lift at slower speed but only within limits due to the stall.

Deploying flaps allows the wing to produce that amount of lift at an even slower speed to make landing and takeoff safer.

The extra drag produced by the flaps is worth it.