Downwash, Effective AoA, Induce drag, Misconceptions..

[Vanja #66]

Do you agree with answer from PeterKampf?
https://aviation.stackexchange.com/que ... 295_44932

This one?

"However, a wing of infinite span will use an infinite amount of air for lift production, so an infinitely small amount of downward acceleration already suffices to produce lift."

Absolutely not. Multiplying by infinity is the same thing as multiplying by 0, you can't cancel it out on both sides of the equation and say whatever is left over is equal on both sides.

Take the same infinite wing and change the AoA and the C_l changes, but you can't define by how much after you divide it with infinite area.

[Fluido]

Do you agree with answer from PeterKampf?
https://aviation.stackexchange.com/que ... 295_44932

This one?

"However, a wing of infinite span will use an infinite amount of air for lift production, so an infinitely small amount of downward acceleration already suffices to produce lift."

Absolutely not. Multiplying by infinity is the same thing as multiplying by 0, you can't cancel it out on both sides of the equation and say whatever is left over is equal on both sides.

Take the same infinite wing and change the AoA and the C_l changes, but you can define by how much after you divide it with infinite area.

Yes this one .

Don't understand why so many wrong theories in aerodynamics, begining with equal transit time etc etc

I read so many explanation and still don't have idea how would I explain someone with simple example what induced drag is...

I just know that induced drag is derived from change in spanwise lift distribution,but I dont understand in real physics sense.

In my logic exist only pressure(normal to surface) and skin friction drag(tangential to surface)..

[Vanja #66]

It seems to me that even scientists who invented this theories for induced drag, don't really know what is induced drag and from what he arise from..

I read so many explanation and still don't have idea how would I explain someone with simple example what induced drag is...
I just know that induced drag is derived from change in spanwise lift distribution,but I dont understand in real physics sense.

In my logic exist only pressure(normal to surface) and skin friction drag(tangential to surface)..

These have some good explanations

https://www.grc.nasa.gov/www/k-12/Virtu ... duced.html

The vortices produce a down wash 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 induced flow of the down wash, giving an additional, downstream-facing, component to the aerodynamic force acting over the entire wing. This additional force is called induced drag because it faces downstream and has been "induced" by the action of the tip vortices. It is also called "drag due to lift" because it only occurs on finite, lifting wings and varies with the square of the lift.

Sounds good I think

[Fluido]

The vortices produce a down wash 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 induced flow of the down wash, giving an additional, downstream-facing, component to the aerodynamic force acting over the entire wing.
This additional force is called induced drag because it faces downstream and has been "induced" by the action of the tip vortices.

Sounds good I think

1. But question is how vortices behind wing induce vertical flow at the wing and in front of wing?
(induction comes from electromagnetic theory, aerodynamicist use it for induced drag..)

Last sentence indicate that drag is induced by tip vortices, as I remember in theory vertical flow is "induced" by shedding trailing edge vortices, they are consequence of change in spanwise lift distribution.

https://aviation.stackexchange.com/ques ... round-wing

Wing bending horizontal flow downward, upward reaction force is lift and backward component is induced drag.
What do you tell about this explanation?

[Vanja #66]

1. But question is how vortices behind wing induce vertical flow at the wing and in front of wing?
(induction comes from electromagnetic theory, aerodynamicist use it for induced drag..)

Last sentence indicate that drag is induced by tip vortices, as I remember in theory vertical flow is "induced" by shedding trailing edge vortices, they are consequence of change in spanwise lift distribution.

https://aviation.stackexchange.com/ques ... round-wing

Wing bending horizontal flow downward, upward reaction force is lift and backward component is induced drag.
What do you tell about this explanation?

https://i.stack.imgur.com/bZTiw.jpg

https://i.stack.imgur.com/dM5FF.jpg

GRC offered a bit simplified explanation, for a wider audience. Most of the people are happy with "induced drag is induced by vortices forming on the wing tips" and their explanation goes in more detail, but not fully.

The way I understand this, vorticity causes a local area above the wing to be exposed to local downward velocity vector. This vector is most likely also increasing the resulting velocity vector over the wing, on top of generating increased angle locally and only on the top side (as far as I can tell). Unfortunately, I can't find a decent illustration online.

So the overall effect is an increase in suction on top of the wing, which is increased more and more as the AoA gets higher. So it's not that "the wing is dragging the tip vortices, causing induced drag" but instead you have an actual increase of -Cp on top which is causing bigger difference in pressure locally and therefore more drag.

So it makes sense to me that Cl squared is proportional to Cdi. I'm not familiar with the way Cdi expression is derived from Prandtl's lifting line theory, but I'm sure you can find it somewhere on internet.

[Fluido]

The way I understand this, vorticity causes a local area above the wing to be exposed to local downward velocity vector. This vector is most likely also increasing the resulting velocity vector over the wing, on top of generating increased angle locally and only on the top side (as far as I can tell). Unfortunately, I can't find a decent illustration online.

So the overall effect is an increase in suction on top of the wing, which is increased more and more as the AoA gets higher. So it's not that "the wing is dragging the tip vortices, causing induced drag" but instead you have an actual increase of -Cp on top which is causing bigger difference in pressure locally and therefore more drag.



https://wikimedia.org/api/rest_v1/media ... 3b2bca1aa1

But induced downward velocity decrease local AoA not increase, wing has smaller suction that airfoil at same AoA, so we must increase wing AoA to get same lift as airfoil.

For same lift, wing produce more drag than airfoil.

[Vanja #66]

But induced downward velocity decrease local AoA not increase, wing has smaller suction that airfoil at same AoA, so we must increase wing AoA to get same lift as airfoil.

I didn't make myself clear about that local angle increase, sorry, I will show an illustration bellow.

As for the "official" explanation, I've been reading more about it and I think a big problem is the use of the term downwash for vortex-induced-downwash, which I don't think is correct. I don't know where this originated, but I'm not going to derail this discussion with semantics. In any case, the official explanation states that the local effective relative airflow is bent downwards due to vortex-induced-downwash, which is also bending the resulting lift vector and forming a horizontal projection which is caused induced drag.



The problem here is the nature of this explanation, which is completely mathematical and depends on the reference system we chose. It offers no explanation on how this affects the pressure distribution and difference, which is the physical manifestation of drag (along with skin friction) as you noted earlier.

What I mentioned earlier for velocity can be seen on illustration bellow.



LV is Local Velocity Vector (going over the top of the wing)
VV is Vortex Velocity Vector (also locally, near the wing where it is close to vertically downward)
RV is Resulting Velocity Vector (after addition between these two)

So due to vector addition you have a resulting velocity vector which has greater magnitude than the local vector, thus increasing velocity over the wing. I'm not saying this is a valid explanation, this is how I understand the local phenomena. When you have higher AoA and lower speed, you also have a bigger influence of vortex vector in resulting vector magnitude.

I might try and do some rudimentary CFD of a rectangular wing with half-span and see what we get in terms of local pressure distribution, should be helpful.

[beschadigunc]

But induced downward velocity decrease local AoA not increase, wing has smaller suction that airfoil at same AoA, so we must increase wing AoA to get same lift as airfoil.

I didn't make myself clear about that local angle increase, sorry, I will show an illustration bellow.

As for the "official" explanation, I've been reading more about it and I think a big problem is the use of the term downwash for vortex-induced-downwash, which I don't think is correct. I don't know where this originated, but I'm not going to derail this discussion with semantics. In any case, the official explanation states that the local effective relative airflow is bent downwards due to vortex-induced-downwash, which is also bending the resulting lift vector and forming a horizontal projection which is caused induced drag.

https://upload.wikimedia.org/wikipedia/ ... wnwash.png

The problem here is the nature of this explanation, which is completely mathematical and depends on the reference system we chose. It offers no explanation on how this affects the pressure distribution and difference, which is the physical manifestation of drag (along with skin friction) as you noted earlier.

What I mentioned earlier for velocity can be seen on illustration bellow.

https://i.ibb.co/s3Zk03F/wingtip-vortices.png

LV is Local Velocity Vector (going over the top of the wing)
VV is Vortex Velocity Vector (also locally, near the wing where it is close to vertically downward)
RV is Resulting Velocity Vector (after addition between these two)

So due to vector addition you have a resulting velocity vector which has greater magnitude than the local vector, thus increasing velocity over the wing. I'm not saying this is a valid explanation, this is how I understand the local phenomena. When you have higher AoA and lower speed, you also have a bigger influence of vortex vector in resulting vector magnitude.

I might try and do some rudimentary CFD of a rectangular wing with half-span and see what we get in terms of local pressure distribution, should be helpful.

These explanations are modeling of the drag force. As per my first message. It is nothing but surface static cp . Which has many factors in play. In that instance over a single foil they can be modelled with what you all are showing but to get the real understanding fluido needs he needs to go back to basics from what I mentioned in my first reply

[Fluido]

https://i.ibb.co/s3Zk03F/wingtip-vortices.png

LV is Local Velocity Vector (going over the top of the wing)
VV is Vortex Velocity Vector (also locally, near the wing where it is close to vertically downward)
RV is Resulting Velocity Vector (after addition between these two)

Yes I agree with that but this just happen at wing tip area not at middle sections. Wing tip vortex is not in touch with inboard sections of wing. Induced drag is not happen only at wing tips.

[Vanja #66]

Yes I agree with that but this just happen at wing tip area not at middle sections. Wing tip vortex is not in touch with inboard sections of wing. Induced drag is not happen only at wing tips.

The effect is the strongest near the wing tips, so this is where I illustrated it. It has a certain effect over the entire wing, but it is very weak towards the symmetry plane, especially on wide span aircraft.

https://www.researchgate.net/figure/Spa ... _330199264

These explanations are modeling of the drag force. As per my first message. It is nothing but surface static cp . Which has many factors in play. In that instance over a single foil they can be modelled with what you all are showing but to get the real understanding fluido needs he needs to go back to basics from what I mentioned in my first reply

We are exactly discussing one specific phenomenon related to Cp distribution, the one relating to induced drag. Fluido rightly asked about it, since the typical explanations lack either depth or logic when it comes to explaining the influence on pressure distribution.

[Stu]

Would it be sensible to think that vortice induced drag across the span can be found by using the theoretical ‘infinite span’ model (as no tip vortex can be present), or am I being completely stupid?

[Vanja #66]

Would it be sensible to think that vortice induced drag across the span can be found by using the theoretical ‘infinite span’ model (as no tip vortex can be present), or am I being completely stupid?

For an isolated wing outside transonic and compressibility effects, without any other element (fuselage, tail, etc) this would be an acceptable comparison, since you don't have interference drag and you have the same skin friction drag. So you are left with form (pressure) drag and induced drag, However, we know a 2D wing and a 3D wing have different pressure fields, so the form drag is different as well. If you accept to make a comparison of induced drag as part of the form drag between the two cases, you are ok.

[Fluido]

https://i.ibb.co/s3Zk03F/wingtip-vortices.png

Indeed wing tip vortex interact with very little surface at straight wing.

[Vanja #66]

Indeed wing tip vortex interact with very little surface at straight wing.
https://i.stack.imgur.com/bydZb.jpg

Lovely stuff! I'm thinking also the flow from bottom to top side gets accelerated along the curvatures of the tip, which could also take part in the increase in drag. I think in your case also the core of the vortex is in contact with the top surface, additionally increasing the local suction.

The downside with the (vortex) induced drag is that it forms on the second part of the chord of the wing tip, and this part of the surface is almost always the part where the top surface is already "going down" so it's only oriented rearwards and the whole suction is attributing to drag only.

I will find the time in the next few days to do a comparison of half-span 3D vs 2D wing in a few different AoA simulations.