Is circulation real?

And in a similar spirit, I will respond separately.

If I understand correctly, you are suggesting that 100% of the propulsive force generated by the engines is counteracted by the drag?
What therefore, in terms of classical physics, and balancing the four fundamental components of flight (lift, drag, thrust and weight) is the source of the 11,000 Newtons of force required to counteract the weight (around 1,100 kg at 9.8 m/sec2 ) of a light aircraft such as a Cessna 172?
If all the force of the thrust is balanced by the drag, then what is generating the lift force balancing the weight?

Are you suggesting that Einstein's development of the General Theory of Relativity that contradicted the Newtonian tenet that all velocities are relative, was an "extension fully compatible" with Newton's laws?

Or that Michelson & Morley's conclusions that contradicted the established tenet that light requires a medium through which to propagate, were an "extension fully compatible" with the theory of the Aether?

Or that the Copernican theory that contradicted the established tenet that the Earth is the centre of the universe was an "extension fully compatible" with the Church's theory of the universe?

No, of course you are not.

Are you are suggesting that by contradicting one of the tenets of Kelvin's circulation principle, that it only applies in the presence of conservative forces, Prandtl's interpretation was an "extension fully compatible" with Kelvin's theory.

Of course you aren't .
So what is it you are saying?

I'm not sure what the ellipsis refers to. The property of mass times momentum would have the dimensions of [M] x [MLT-1] = [M2LT-1] . Force is rate of change of momentum, or [MLT-2]. I'm pretty sure Newton didn't make that claim.

 

Circulation is observed most of the time. I'm uninterested in word salad that is contrary to reality based observation.

 

I'm confused. You said "And let's not forget that lift without circulation also happens."
Can you give an example of where lift occurs without circulation please?

 

No. I take here the small example off an aircraft in wings level flight on a rectilinear horizontal trajectory, unaccelerated. The drag I'm refering to is the total drag, ie the sum of the parasitic drag and the lift-induced drag. Correct me if i'm wrong, but at a flight speed V, the thrust is given by Tr = W/E, where W is the weight of the aircraft and E the efficiency, E = CL/CD. CL : Lift coefficient ; CD : Drag coefficient. With CD = CD0 + CL²/(pi*AR*e), where the drag coefficient has to contribution, one called "zero-lift drag", and the other "lift dependent drag", in aeronautics.
The simpliest expression of this lift dependent drag is given here, in accordance, as you surely know being a pilot, with observations. And as you know, this lift dependent drag is the projection of the lift vector, in the direction of flight. So because the lift can be calculated by the circulation theory, the same goes for the lift dependent drag.

These are subjects that have been already debated, and it is interessant to notice, that, , in science, setting a foot back, the more a proposition can be related to existing work, the less debate it produces. New paradigms are hard to be understood and accepted, even if they give better explanation of observation. To a point that makes Max Planck conclude that it could require the work of some human generations of scientists for new paradigm to reach their rightfull place in the world of science. So "fully compatible extension" are to be prefered, and tested first, before shaking the whole place upside down. This is the true meaning of my remark.

Sorry for the poverty of my wording in english. The momentum is by definition the product of the mass and the velocity. The change of momentum is the derivative of the momentum with respect to time, with the dimension that you gave [M][L][T-2]. Newton has not directly maid that claim, you're right. But from his work, emerges the notion of force F, that creates changes in momemtum. F = md²V/dt². Because vortices cannot be modelized in a potential flow, the mathematical approach of the circulation consists in transferring its properties to a so called bound vortex (or bound circulation), while conserving the total momentum. Again, from this point of view also, circulation appears as idealization, an abstraction, built upon some mathematical properties. This approach, that uses the Circulation, is proven to be sufficient to calculate with a certain approximation the lift produced by a wing in incidence. I agree that it does not explain the origin of lift in the physical world. As an curious engineer, i wish i know some more profound mechanisms involved in lift creation, but only to push the limit of my designs, my first priority being the identification of the most reliable tool that is to be used in a given situation. And Circulation, by its simplicity, is sufficient in a numerous situation, to deal with a given real problem, in the shortest time.

 

Ludwig Prandtl and Max Michael Munk taught us that the wings (daggerboards, rudders, sails) can be replaced by a column of air that rotates interacting with the wind.

And so we see that the Wings do four things four:

1) deflect the wind: Up-wash
2) accelerate the wind
3) deflect the wind: Down-wash
4) slow down the wind

The second thing to know is that the High pressure depends on the Angle of Attack and the Low pressure depends on the curve.

 

When diverting a fluid, the interaction produces a Force (F).

And then some gentlemen in white coats come along and have the mania of analyzing this Force in the laboratory in two components: Lift (L) and Drag (D)

 

“A real understanding of aerodynamics must go beyond mastering the mathematical formalism of the theories and come to grips with the physical cause and effect relationships that the theories represent. In addition to the math, which applies most directly at the local level, intuitive physical interpretations and explanations are required if we are to understand what happens at the flow field level.” ( from ‘Understanding Aerodynamics’ Doug McLean, which I’m s-l-o-w-l-y going through)

anyway, if anybody hasn’t run across this ^, it might be worth a read. But given the number of master’s theses focusing on wind tunnel agreement with CFD code(s)…. , modeling assumptions (philosophical stances?) are still iffy (?).

 

It definitely lacks some poetry in this field. The very last artist that has worked on flight science may be Leonardo da Vinci, in his Codice Volo Uccelli.

 

Unless you have not already done so, before getting totally bemused by his book, watch his video. From around 26:00 he struggles to explain the presence of pressure differences and resorts to “reciprocal cause and effect“, "pressure fields", "diffuse clouds of low pressure" !
Arrant nonsense!
And he knows it when he says it’s “kind of the weak link” and “the part I'm least satisfied with” and asks his readers for feedback on "how to strengthen this part”.
And return to the book and

1. do a word search in his book for "clouds ....pressure" in section 7.3.3 and 8.1.4
2. And think about the meaning of "reciprocal cause-and-effect relationship" that pops up at critical junctures such as in 7.3.3.5 :
   "The velocity field and the pressure field support each other in a reciprocal cause-and-effect relationship, an interaction in accordance with Newton's second law of motion."

It’s pure fiction!

 

Fun though it is, debunking Prandtl's application of Kelvin's theory of conservation of circulation to aerodynamics is not my primary goal. I would much rather engage in a critical discussion of of what I believe is a the far more reasonable derivation of the pressure differences over here.

 

I know this is off the subject of circulation, and I'm sure I have pointed this out before, but there's a big hole in Anderson's book. In a number of sections he refers back to Section 1.5 to explain the source of the aerodynamic force : e.g.

6.7:
and 9.7:
However, while section 1.5 goes into detail about how the aerodynamic force can be resolved into lift and drag, and how the aerodynamic force is the result of pressure differences around the wing, he never explains how the net aerodynamic force, acting outwards from the wing, in fig 1.10:


is derived from the pressure acting Towards the wing in Fig 1.12:

(I take these images from the first edition since, by the 6th edition the graphical artists have mis-transcribed the direction of the arrowhead from towards the wing to away from the wing.
Who draws an arrow like this? )
Anderson claims that the explanation is in Section 1.5, but there is no explanation.

 

Sir George Cayley, a philosopher at least, was fascinated by flight-

On Aerial Navigation, Part 1 https://invention.psychology.msstate.edu/i/Cayley/CayleyP1.html

I’ve always liked Vaughan-Williams ‘Lark Ascending’…

 

Al, I’d argue that this ^ fits in with his quote that I posted above- math in aerodynamics is a description of a real event. You agree, apparently, that understanding aerodynamics is difficult, and yet, when someone shows you the limit of their knowledge/approach, you mock them. Ever think that he’s actually asking for a colloquy?

One of the basic pillars of Quantum Theory is the slit experiment, where light can act as a particle or a wave. Perhaps the nature of lift can be understood in parallel models of duality? For example, I see waves in cloud formations, but they can be understood as a particles at the same time. I posted an Indian Master’s thesis about this months ago.

 

You have misidentified the object of my mockery. I am not mocking the humility he demonstrates by acknowledging the limit of his knowledge and requesting assistance from his audience. I am mocking his professional and academic lack of rigour in presenting the material without providing any hint of his uncertainty about its validity. Remember he is writing as a Technical Fellow (retired), Boeing Commercial Aeroplanes, USA, with a foreword by John J. Tracy, Chief Technology Officer The Boeing Company, so it carries some authority.

Yet in this video, published some years after the publication, he freely admits to serious concerns about the material already published with such authority!

I am not mocking humility and admission of lack of knowledge while preparing the book, both of which are laudable attributes, but his professional and academic lack of rigour in not revealing this lack of conviction when writing the book.
Those are, I suggest, valid targets for mockery.

 

And actually, I couldn't get my hand on your post. Could you please post the link or the document again ? Would be greatly appreciated. Few weeks ago, I searched for this exact post that you mention, because I was just amazed reading it... I don't have a proper background on fractals, i've played with them when I was young, guided by a special edition of American Scientist. Later, I bought a book on Fractals "Dimension non entière et applications" from G. Cherbit. Maths seemed to me so complicated at the time that I just gave up. But since then, I kept the curiosity for this, having a strong feeling that it has to do with Nature. It's pure Alchemy. "As above, as below" (The Kybalion).
I wonder if this master's thesis could help me "generalize" Einstein Equations, -Schwarzschild metric-, or Maxwell's equations, -spherical harmonics-. I know I won't be able to develop the equations by myself, but at least, I could re-write the existing formulations to try to get a new perspective of them.