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You can bring the question back to rationality, however, by simply assuming a "very long" wing.

You can't if you are attempting to present the steps that lead up to understanding the aspects of the flow that introduce lift. A very long wing is a 3d model, same as a short wing; where as the former is a 2d model. They can't be interchanged. It is this distinction that leads to the realization that circulation is caused by tip vortices because, without tip vortices, without a finite wing, circulation doesn't exist, induced drag, and lift don't exist.

By the way, I forget what FAA book it was, PHAK or AFH, but one of them presented the equal transit theory in an older edition.

∆ also can be used for difference

I only pointed this out to keep with the precise terminology. Maybe to the FAA it means difference, to the scientific community it is thought of as 'little change of..". I know it was a nit pick, most of my post was. However, those distinctions are what separate a good aerodynamic discussion from one that comes from the FAA text.

My job, as I see it, is to reduce complex, 'weird' mathematical phenomena down to simple

Couldn't agree more, but the PHAK won't give you the tools to do that with any degree of accuracy. That's why I went through your post the way I did, to show you that. You've a darn good understanding, but your FAA terminology is limiting your ability to make that understanding a great one.

Don't impose that limitation on future instructors just because it's easy. Look outside of the FAA texts, there are many that exist that aren't dry. I've only focused on one because I think it's one of the easiest, most complete, and above all, it's accurate!
 
(equations) In the airplane no. However, to understand, apply, and later correlate the analytical ideas affluently present in the field of aerodynamics knowing a little algebra won't hurt you. Why does angle of attack, wing area, air density, and speed cause variations in lift and how? Why does excess power result in a climb? Rote memorization of definitions to explain these answers doesn't give you the understanding or applicable ability that two simple formula's would.

In what way does algebra -help- here? Algebra is more akin to memorization than it is to an intuitive understanding, which is what you want to have. (formulas or formulae—formula does not possess!)

Have you ever experimentally drawn a drag curve?

Yes and no. I don't think drawing a curve is useful at this phase of flight instruction. However, what I DO have them do is experiment with power required to maintain level flight relative to airspeed after explaining the drag curves on paper. How this will play out is to be determined—I'm just getting started—but so far my students have understood it perfectly, and that allows me to ask them questions about things and have them demonstrate a grasp the relationship without me having to describe each element as a separate entity.

(I'm really familiar with the experiment you're describing, though. I haven't had the sort of student for which that approach is necessary yet, and it doesn't really fit my instructional style for use on students who would otherwise get the "intuitive" model.)

Last student I did it with responded with "Holy ..... that was cool!" Then proceeded to perfectly explain angle of attack, speed, drag, and the relationship between them all including explaining the region of reverse command without being taught it yet. I mentioned the words 'reverse command' and he linked the ideas to them. What a great moment.

I think "region of reverse command" should be stricken from all verbiage. It's a terrible, terrible appellation... completely misleading. I prefer to graph the total drag curve and point out to the student that it's also the 'power required' curve.

Which is why scientific standards are so rigorously debated and subsequently used. We could learn a thing or two just from reading a college physics book. Even if you can't understand a bit of it, it is amazing how specific the explanations are. And how invariable they are from book to book (assuming the texts are well regarded).

Which is why physics students excel at racing cars!

... oh, wait. ~.^

(My roommate is a PhD physicist.. nuclear physics... so I can bounce philosophical debate off of him when I want a sanity check.)


Not from my perspective. Your conclusion screams "if you want to climb just increase lift."

I would rephrase that: If you want to climb, you need to increase the "sum of all upward forces".

I teach that flying is all about AoA and energy—airspeed is kinetic energy, altitude is potential energy. Thrust adds energy to the system, drag removes energy from the system (by converting it to heat, more or less).

Let's look at this from another perspective, exaggerating to demonstrate my philosophy: Do we teach infants to walk by teaching them the equations relating to the muscles of the leg, feet, and torso? Do we teach people how to drive by teaching them about steering wheel angles, camber, cant, relative temperatures and pressures for given speeds, etc? In the first case, you might argue that walking is intuitive and we don't need to be taught how to do it. I believe that flying is relatively intuitive as well, but perhaps that's just me. But for driving, we have a direct comparison to something that may not be considered intuitive initially. Even if you were teaching a 35-year-old engineering student to drive a car, you wouldn't go on about synchromeshes, clutch viscosity, tire friction coefficient (unless trying to explain that there was only so much "stick" to share between go, stop and turn), effective torque and engine power, stoichiometric ratios for combustion, etc.

If they want to, they're free to learn all of these things, and it may even improve their overall understanding... but it won't help them figure out if they're going to hit the car 118' in front of them or whether they should swerve to the right.

[Lowest common denominator/teach to test] is a poor and all to often accepted excuse to teach something incorrectly. Why not teach it correctly with the caveat that giving too much detail to the examiner can be a slippery slope. Then the CFI applicate has ideas that properly link together and can choose how detailed to make his or her example. This is invariably better than fragmented ideas aimed to teach to the stupidest...erm lowest common denominator...level. ;)

I would never excuse teaching anything incorrectly, and that's a large part of my retort—teaching someone incompletely may sound bad, but in the end an intuitive understanding based on incomplete (but fundamentally correct) instruction is often better than an analytical knowledge base with no intuitive ability to apply it.


Yes, but you never said it. Two paragraphs to say zero lift AOA is the angle which an airfoil produces no lift. If the student ever got curious they could google zero lift AOA and find tons of information. Reading your reply what should they google? No gravity with atmosphere AOA?

Gravity is a confounding factor, albeit the one airplanes were designed to overcome. ^.^

But it's so wholly misunderstood by so many that it's sometimes better to assume a spherical universe in a vacuum for the purposes of making a point... to me, it's implied that if, without gravity, the lift required for level flight (symmetrical airfoil) occurs at zero degrees AoA .. then clearly that's the zero-lift AoA.

I put it there to show you that mentioning CG's arm effects on rudder is an unnecessary addition. It's effects are negligible and worth mentioning only to mention that they are negligible.

I don't know if I'd call them negligible in, say, an aft-of-CG Vmc scenario. Perhaps if I knew the equation, I could solve for the actual effect ... but if I -need- to do that, I can always look it up.

True if you're not doing tail wheel or acro GP is relatively non existent.
Considering my preferences, I'm fond of teaching it ... but only when appropriate. I think effects of that nature should be taught from most to least significance.

However, you describe p-factor in terms of head wind and tail wind.

... Bearing in mind that most of my goal is to get the OP to read the PHAK, where these things are detailed with graphs and such. :>

>snip<

Heaviest and slow. Exactly. Slats decrease AOA and flaps increase it. Speeds relatively the same at landing as climb (yes not identical). However, weight is dramatically lower after a long haul in a big bird. That's your difference, and that's what matters. Being in a climb and being clean configuration are irrelevant and unnecessary additions.

Now here's where perhaps I'm misunderstanding something. The way I understand it, flaps increase the -effective- AoA of a segment of airfoil, allowing the same lift production at a lower overall angle of attack, and also effectively increasing drag by the same mechanism.

... you're selling yourself short by saying algebra has no place in the airplane. Sure, not in the plane.

Well... ? :>

What about for a simple 3 or 4 variable formula to explain the analytical side?

If the student is an engineer by trade—and in particular, an engineer who has become accustomed to developing understanding through mathematical relationship—I will happily dig out formulae to explain various phenomena.

I mean it's math the chinese learn in 5th and 6th grade.

Is that why they're renowned as exceptional aviators and aviation students? ~.^

(I think China is doing almost everything -wrong- in an elevation-of-the-species sense, but we can table that discussion for another time if you like.)

Surely we can expect a high school or college graduate to be able to comprehend it in it's simplest forms.

I am neither. (That doesn't mean I don't understand it, but while I feel that graphs are sometimes useful for the purposes of illustrating relationships, the equations used to create them are superfluous)

I don't need to know ρ, nor what a slug is, nor how many furlongs per fortnight I'm traveling to know that:
A> Air is a fluid
B> Air has weight

The things that are less intuitive are questions like "Why is humid air less dense than dry air", until you look at the molecular weights. For those sorts of questions, that explanation alone is usually sufficient, and, as I prefer to say, "there's plenty of information out there, and it's left as an exercise for the reader."

Keep in mind, to make your AOA discussion mean something you need to start with the desire to seek equilibrium between the four forces. Specifically that lift equals drag. All analysis should revolve around this concept, leave the instantaneous analysis' for a later discussion.

I know what you're saying, but that reads funny. But yes, that's how I teach it.

I stick this last because it is the most important part. And trust me when I say I speak imprecisely all the time. That said, when dealing with this topic it should be our aim to speak as precisely as possible.

Absolutely.

-Fox
 
I only pointed this out to keep with the precise terminology. Maybe to the FAA it means difference, to the scientific community it is thought of as 'little change of..". I know it was a nit pick, most of my post was. However, those distinctions are what separate a good aerodynamic discussion from one that comes from the FAA text.

I bounced this one off my physicist roommate before replying, because I wanted to check myself. He says that ∆ perfectly acceptable as a measurement of difference. He is my representative sample of the scientific community.

Couldn't agree more, but the PHAK won't give you the tools to do that with any degree of accuracy.

I think we have different models of the same process. I would like to hope that we (and our students) arrive at the same point, terminology aside.

Don't impose that limitation on future instructors just because it's easy. Look outside of the FAA texts, there are many that exist that aren't dry. I've only focused on one because I think it's one of the easiest, most complete, and above all, it's accurate!

Consider my position—OP is looking for recommendations on preparing for his CFI ride. I just finished mine, and I found that most conventional advice was inadequate or incomplete. OP mentions weakness in aerodynamics and cites Bernoulli. I'm not going to do harm by pointing him to the PHAK. If he were going to try and get a job as an aeronautical engineer, then I would certainly point him elsewhere... but any examiner -should- accept the FAA terminology and explanations (which I don't believe are in any way flat wrong), or they're not doing their job. Conversely, they're not required to accept more "precise, correct" sources.

I think a CFI with a decent understanding of aerodynamics (as opposed to just memorization) out of the PHAK will be a far better instructor than most of the instructors out there who are still teaching the "equal transit" farce. I was working with a very, very experienced CFI-who-shall-not-be-named a few months ago (Gold Seal, Master CFI, and a really nice guy), who was baffled when I suggested that (no wind) descending at a speed greater than best glide speed would result in -decreased- glide distance. We debated for about two or three hours on the subject (with me paying ~$100/hr) while I tried to explain by graphs and everything else and came up blank. Eventually I just told him that I could talk to airplanes, and they wanted best glide. He believ^H^H^H^H^H sidetracked. Anyway, the final part of the discussion went like this:

Me> "Alright ... look, power-off glide, no wind... the airplane is flying at best glide, and let's just assume for the sake of argument that it has a 10:1 glide ratio." <points at "Best Glide" on the drag curve> "What happens if we go slower than best glide?" <Moves finger up the drag curve to the left>
He> "Well, we'll land shorter."
Me> "And the glide ratio will decrease, right?"
He> "Yes, of course."
Me> "Ok ... what happens if we increase speed?" <Moves finger up the other side of the drag curve>
He> "We'll go farther."
Me> "?! And the glide ratio will...?"
He> "Well, it will have to increase to 20:1."
Me> *Stare*

A solid understanding of the intuitive nature of aerodynamics will, however incomplete, beat the pants off a rote or surface-level "understanding" of AFNA or aerodynamics texts. I'm not just being contrarian here ... not intentionally, anyway. Analysis is the weak mode of the human brain ... intuition is far, far more powerful, far faster, and largely correct. It can also be refined to grasp new concepts and tuned to address inherent misconceptions, and the corrections are often fed by the analytical process... and that's the strength of the analytical process. Unfortunately, we as a culture are currently placing far too much value on analysis and all but discarding intuition... which in my view is as equally incorrect as if it were the other way 'round.

My goal is to teach what is fundamentally correct, and help the student (or reader) attune their understanding to the intricacies of flight through reasoned analysis of a simplified dataset.

Respectfully,
~Fox
 
My goal is to teach what is fundamentally correct

I'm trying to show you that you're not achieving this goal. I see it's you're goal, which is why I took the time to reply in so much depth to your post. However, you limiting your understanding to FAA verbiage (which I beg you not to do to the OP or any CFI candidate) is killing your chances. Unfortunately, you won't understand what this means till you broaden your scope.

Defend your positions less, ask questions more. The questions you contended, slip stream for instance, I replied with a quote. Your comment regarding CG and it's role in yaw during VMC, read a half a dozen or so pages before in AFNA and you'll have your supporting evidence for that. In short they exist, but are negligible within the range of CG determined by pitch stability.

Check AFNA for what slats do. You note flaps increase effective AOA. Yes, they do. What do slats do though? This won't answer your question though, but it's good knowledge for your next step. Your question is answered by lift equals weight. Whether you have flaps, slats, and landing gear down or are completely clean. If the weight were the same and the speed were the same then the lift coefficient (Cl is how you calculate drag coefficient for induced drag...this is clear in the induced drag formula AFNA p58 Cd = Cl squared divided by pie times the aspect ratio) will be the same. This lift equals weight condition can be assumed true for any pitch attitude less than +/- 15 degrees (another AFNA reference here).

My physics books are at work, so I can't cite you for delta atm. It was Flightwise's author, however, who I first read delta as "small change in something". I know in mathematics it's viewed as a difference though. So I'll yield to you on that one. :)

As for the rest, I'll leave those for you to discover or ask more questions about. What I hope you'll soon realize is there exists no middle ground between fundamentally and analytically correct. You're either both or you're neither.
 
I'm trying to show you that you're not achieving this goal.
... snip ...
What I hope you'll soon realize is there exists no middle ground between fundamentally and analytically correct. You're either both or you're neither.

Unfortunately, we'll have to part ways on this point, as I do not agree with that philosophy. Rest assured, most of society sees it the same way you do... but what I said above is basically what I have to say on the issue.

I haven't seen anything in your responses that I have disagreed with, nor any specific points you've disagreed with anything apart from my phrasing, one example of poor wording, and my general choice of examples... but if you find fault with my attempt to clarify basic aerodynamics for someone who finds analytical sources too dry, then I encourage you to jump in and do it yourself, or to fill in the gaps, or correct anything you see as misinformation. I don't really see that happening here, but again, perhaps I simply don't know what I don't know. Still, I have to draw a line somewhere, and this is how I teach it. I do not teach AFNA, nor do I teach navigation from H.O. Pub. No. 216: AIR NAVIGATION (Department of the Navy, Hydrographic Office). I'm confident, however, that my students will leave with a functioning grasp of aerodynamics that will serve them well as pilots... and that if they need or want to learn more, will not interfere with anything they learn in the future.

-Fox
 
I do not teach AFNA

And I don't suggest you do, never did either. I suggest you learn from it. As I said before, use it as a reference for accurate information on specific subject matter. The book I mentioned; "Illustrated Guide to Aerodynamics" is a better, 'learn from' book. AFNA's robust index makes it a superb resource for the purposes of reference material, however.

We aren't discussing what to teach a private or commercial pilot. We are discussing what a teacher should learn. A k-8 teacher learns calculus, doubt they are teaching that, but they learn it. Why? How can you know what basics are important if all you ever learn is those basics? You must see where it goes, at least slightly beyond those basics, to see what is and what isn't important.

For instance, you're misunderstanding with the flaps begins with your not realizing the importance of emphasizing the lift equaling weight condition. A student should have this drilled in before they even hear about AOA. Even the FAA starts with the forces on an aircraft, but you can't know why just from reading the PHAK. I pointed this issue out on my very first reply. Most of those original points have gotcha's like this down the road.
 
Few things here as I feel like I kinda started a poo storm (Actually I did start it). Sorry if I did not read the whole exchange.

I think the PHAK is great for learning the basic stuff. Now once I understand the concept I'll mess with other sources. After all this stuff is like any other concept we learned in school. You can't learn calculus without learning basic math. You can't be a doctor unless you learning basic anatomy.

So in short you both have some good points.
 
You can't learn calculus without learning basic math.

You can't learn calculus at all if your learning of the basics is tainted with a poor conceptual understanding. This is what you face reading FAA material, other than AFNA, on this topic. Agreeably, AFNA is boring, which is why I'd highly recommend another source. I think you'd be surprised how well written the source is that I recommended. Make no mistake, it's not an advanced book. It simply covers the basics with a high degree of accuracy. And for 25 bucks...sure beats some of these 100+ dollar text books. Amazon has offers as low as 7 bucks.
 
Fox,

Would it be feasible to base that whole lesson around the airport diagram? To show how to anticipate, asses, aid in active listening versus, and maintain overall SA in the environment?
 
Fox,

Would it be feasible to base that whole lesson around the airport diagram? To show how to anticipate, asses, aid in active listening versus, and maintain overall SA in the environment?

In my opinion, yes—the airport diagram and a scenario that allow you to explore the details... just make sure to hit every bullet point on it and cover all the ground that needs to be covered in the course of the lesson as points in your scenario... and it doesn't hurt to have addenda if you can't quite get it all, or an alternative scenario to branch to.

Doing it that way allows you to ask questions, help the student explore the information and come up with their own answers, etc. ... whereas a teaching lecture is fairly static, and can bounce right off. One thing my examiner liked on my checkride was my line "He learns best who teaches himself." ... later he told me that he had background in education, and that that line sold my case pretty well... because it's an important concept. You're not -teaching- the student... you're helping the student learn. You're not generally going to drill the knowledge into their heads, you're going to guide them to it and let them explore. (generally)

Anyway, the subject of the whole affray being passing the CFI ride, I think it's critical that you demonstrate not just that you know the material—that's assumed, and woe betide they who don't—but that you understand the material and you're prepared to think like a teacher, and that you are able to build that level of knowledge within the learner... and that you're abreast of the techniques the FAA recommends.

Just my 2¢.

-Fox
 
@Acrofox

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;) :D
 
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