Teaching the Region of Reverse Command

Save the math for building the airplane. ~.^

(And then, like all products of engineering, make it actually work right in the field by trial and error ;)

That's what I do... For work...

I also fly the **** out of everything I can get my hands on. I personally find it gratifying to "know how to build the airplane" (literally), others don't. YMMV.

Since this is a thread about teaching, I wrote:

Do not use this description on your students (well unless they like math)

If you want to ignore the first sentence of my post, that's your problem. But everyone knows no one's students like math. ;)
 
Only as much as ignoring the whole topic of the thread is yours. ;> This, my recursive point.

-Fox

The thread drifted when people started asking questions (more AOA = more lift or more drag?). I enjoyed the chance to link everything together from start (AOA) to finish (drag force). Of course nobody is going to do that while they're flying. But maybe somebody who digs aerospace engineering will benefit from how that was laid out and a lightbulb will go off for them somewhere in the chain of events.

I actually quite enjoyed your explanation, before you tainted it with your [HASHTAG]#haterade[/HASHTAG].
 
The thread drifted when people started asking questions (more AOA = more lift or more drag?). I enjoyed the chance to link everything together from start (AOA) to finish (drag force). Of course nobody is going to do that while they're flying. But maybe somebody who digs aerospace engineering will benefit from how that was laid out and a lightbulb will go off for them somewhere in the chain of events.

I actually quite enjoyed your explanation, before you tainted it with your [HASHTAG]#haterade[/HASHTAG].

I think you may have misconstrued my tone. I'm basically amused, and trying to be funny. I'm definitely not trying to bash you—it's just that generally when people think they're explaining things by using equations, they don't notice that everyone else is basically glazing over. I've tried to read a few aerodynamics publications like that, and I find it very irritating to have a simple, intuitive concept contaminated with ever-increasing levels of weird glyphs and symbols. It's the same as when I try to explain to people what I did with computers. I'd spend a whole series of excited paragraphs explaining how I was the senior systems architect for a massive global compute cloud, and talk about the provisioning system I designed, and all of the automation I built, and people would come back and say "So... you were a programmer?"

Personally, I am relatively technically ept, but to me math is like sheet music that I can't read—I am a musician, and I can play all sorts of music on all sorts of instruments, and pick it up by ear really quickly. But when people break out sheet music, I just see lines and dots and gobbledygook. I can pick through it, given enough time, and figure out about what it's supposed to sound like... and then if it's something I recognize, I can just pick it up from memory by association. But it's a lot easier to do without all the ink.

Thinking in mathematical terms is much like sight-reading—if you're trained to do it, and you practice it hard enough, often enough, and long enough, it can become a language that makes sense. Given a deep enough understanding, it can seem like the most logical, beautiful form of expression...but to most other people, you're just speaking in tongues.

I speak unix, ruby, c, objective c, bourne shell, bash, mysql, a bit of python, a bit of perl, a bit of regexp, forth, ada95, java, LaTeX, etc. These languages I know. And to me, I can communicate entire ideas and concepts in them. But mathematics is not a language I am fluent in, and that's something that I've found most pilots share. For us, if you start getting more complex than a(bc + de) = f^2 we become completely illiterate... we pick through a few basic terms to try to decipher it, then throw up our hands and move along.

I don't mean any offense.

-Fox
 
(Also, I suspect that my lack of comprehension of math ('figuring out' is not the same as 'comprehension') predisposes me to being annoyed by attempts to communicate ideas in mathematical terms. "Well, if that varies proportionally with that, why didn't he just say so??". That's my own bias, similar to most forms of willful ignorance, and one that I have in the past attempted to correct. Unfortunately, while I possess the capability of learning, I find the way math is taught to be wildly unintuitive, and often have to twist things around to teach myself before I actually understand. My own fault, to a point, due to the relationship I have with my perception of logic and the need to ask 'why' before 'what' has meaning.)
 
Most of you probably know that (L/D)max occurs right where that total drag curve is the lowest, which also happens to be your best glide speed, and max range speed (in props). In jets it gives you max endurance.

Where drag is lowest is not best glide speed. It is minimum sink speed. Best glide is always faster than that, assuming no wind.
 
I am working on my CFI rating and am having a difficult time putting the concept of the region of reverse command into a logical, easy to understand explanation. Any thoughts or ideas you guys have used to explain this would be greatly appreciated. Thanks.

The way that I explain it - when you think of lift as an arrow point vertically up from the wing, the arrow is actually pointing slightly aft. So while most of the lift while the wing is level is pulling the aircraft up, some small amount is pulling it backwards. When the aircraft is inclined nose higher (high AoA), that arrow is now pointing much more aft than it was when level. So, more thrust is now required to overcome that.
 
Got this from a rod machado book.
 

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(Also, I suspect that my lack of comprehension of math ('figuring out' is not the same as 'comprehension') predisposes me to being annoyed by attempts to communicate ideas in mathematical terms. "Well, if that varies proportionally with that, why didn't he just say so??". That's my own bias, similar to most forms of willful ignorance, and one that I have in the past attempted to correct. Unfortunately, while I possess the capability of learning, I find the way math is taught to be wildly unintuitive, and often have to twist things around to teach myself before I actually understand. My own fault, to a point, due to the relationship I have with my perception of logic and the need to ask 'why' before 'what' has meaning.)

I didn't come from a math background either, and as a result I had to take a number of years of the stuff as pre-reqs to get my degree. It was painful, but i eventually learned to "cooperate and graduate." Maybe I got Stockholm syndrome as a result? :)

It's certainly interesting how much people will glaze over (or even get upset) by math, and it's a valuable lesson in educational psychology. But just like your programming language analogy, everything has its strengths and weaknesses, and there's definitely something elegant about being able to symbolically convey "here's everything that drives induced drag. These things are all the result of the way the airplane was built or the atmosphere. These leftover things (AOA and airspeed) are all you can control." Meh maybe I just should have said that. :)
 
Where drag is lowest is not best glide speed. It is minimum sink speed. Best glide is always faster than that, assuming no wind.

Do you have a source for that? My understanding is that L/Dmax minimizes glide angle which maximizes range (I.e. "Best Glide") while Min Sink keeps you aloft for a longer period of time, but because you're flying slower you won't go as far.

NASA Glenn Research Center has a cool page about gliding flight:
https://www.grc.nasa.gov/www/K-12/airplane/ldrat.html

I'd check the glider flying handbook, but it's at home. Plus I've got the glider add-on checkride coming up in the next couple months, so I should probably know for sure. :)
 
LaTeX is a macro package designed, and only really useful, for typesetting mathematics. Why else would anyone ever use it?

I could just say "wrong." and be right, but I'll engage, instead.

I used to use LaTeX for everything that I wanted to look good. It isn't only for mathematics—that's just flat wrong. Really, your entire characterization is incorrect, and shows a geeky sort of myopia typical of the math addicts. I moved to InDesign when I started working on publishing print books, but LaTeX served me well for years as it has for countless others who have published books, papers, letters, magazines and newsletters, formal documents, sheet music and so on.

Math. Not even once.

-Fox
 
I could just say "wrong." and be right, but I'll engage, instead.

I used to use LaTeX for everything that I wanted to look good. It isn't only for mathematics—that's just flat wrong. Really, your entire characterization is incorrect, and shows a geeky sort of myopia typical of the math addicts. I moved to InDesign when I started working on publishing print books, but LaTeX served me well for years as it has for countless others who have published books, papers, letters, magazines and newsletters, formal documents, sheet music and so on.

Math. Not even once.

-Fox

Kudos to Leslie Lamport then I guess, the computer scientist with a PhD in mathematics who wrote it, for making it useful for others besides his own kind. ;)
 
Kudos to Leslie Lamport then I guess, the computer scientist with a PhD in mathematics who wrote it, for making it useful for others besides his own kind. ;)

Contrary to popular opinion, one CAN actually succeed in being useful even if one has an education in advanced mathematics... it's just very rare. ;p

-Fox
 
Higher AoA = higher lift as well right? Induced drag is a 'by product of lift' to use the FAA definition.
Higher AoA = higher coefficient of lift, not necessarily more lift. Lift will equal the weight of the aircraft, assuming unaccellerated flight. To fly at the higher angle of attack, your velocity will have to decrease.
lift-equation.png
 
Higher AoA = higher coefficient of lift, not necessarily more lift. Lift will equal the weight of the aircraft, assuming unaccellerated flight. To fly at the higher angle of attack, your velocity will have to decrease.
lift-equation.png

No offense, but I see math equations like this and I just shake my head. 99% of the people I instructed would be asleep by the time I finished writing that on the white board.
 
No offense, but I see math equations like this and I just shake my head. 99% of the people I instructed would be asleep by the time I finished writing that on the white board.
There are essentially 4 variables on the right side of the equation. If you can't comprehend that, I heard Wendy's is hiring. It is very simple. This is 3rd grade math. There are only 2 things the pilot has control of: the CL and V. To make it simple, AoA and Velocity. If one goes up, the other will go down, and vice-versa, as the Lift on the left side of the equation will almost always equal the weight of the aircraft in almost every phase of flight.
 
There are essentially 4 variables on the right side of the equation. If you can't comprehend that, I heard Wendy's is hiring. It is very simple. This is 3rd grade math. There are only 2 things the pilot has control of: the CL and V. To make it simple, AoA and Velocity. If one goes up, the other will go down, and vice-versa, as the Lift on the left side of the equation will almost always equal the weight of the aircraft in almost every phase of flight.

Yeah, but it's boring. Most people don't do boring. I comprehend algebra just fine, a bit more than 3rd grade (I have a 3rd grade GATE student, he's just learning multiplication). I wasn't trying to go all agro on you(hence the "no offense"). Just pointing out that a lot of people get bored with seeing a bunch of math on a white board. Every time I started with it, I got blank stares.
 
There are only 2 things the pilot has control of: the CL and V.

In my opinion, you can't oversimplify the relationship between the pilot, CL and V.

I prefer to say that in straight flight, the pilot has control over only two things: Tailplane AoA and thrust. Everything else is increasingly indirect, including velocity.

If you want to really break it down into component forces, you absolutely can, and you can make it pretty darn interesting. We're describing the function of a relatively simple machine, made of a handful of the simplest ones. Throwing math at people and going "Here you go!" doesn't build a functional, intuitive understanding of the machine, in my opinion, any more than diving into the minutiae of shear forces, 3D rotation, Navier-Stokes equations, helps to "understand" lift. Understanding the airplane as a machine, as a whole, and just accepting that lift "is" is all that's really needed.


Viscosity, leverage, relating the flow of air around an airfoil to the flow of water around various objects, equating the forces on the airplane with one another and demonstrating how everything comes back to AoA. Relating altitude and airspeed to potential and kinetic energy, and fuel to stored energy. Diagrams a-plenty. A fan and a balsa-wood airplane. Don't give them the answers—present them problems and make them think through them. Suddenly, you've explained the foundation of weight and balance, stability, lift, angle-of-attack, etc., in one 1.5 hour lesson. Not in depth, but you build on those understandings as you go along.

I'm not saying that teaching should condescend—I'm saying that teaching should focus on what matters to the student. You said above that the pilot has control of V, but that's imprecise—the pilot's control of V is actually indirect. The pilot also has indirect control of density, and in many cases direct control of wing surface area (S). So if you tell a student what you just told them, you run the risk of creating a misunderstanding by your very attempt to be clear. You may create artificial barriers to understanding among those who don't perceive reality as a function of mathematics, and you may create false understanding in those who do.

Knowing the equation does not equate to understanding the problem.

-Fox
 
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