AOPA Rod Machado article

[z987k]

As a follow-up question, is it possible that an aircraft such as a 182 would eventually stop accelerating due to the increased drag as airspeed increased? If it is, is it also possible to determine if that final stabilized speed could reasonably be within airframe limitations?

The 182 I flew with speed brakes would stabilize at about 140 at 22* nose down and about 185 at 30* nose down. That was about right at the bottom of the decent right as I rolled wings level. Did the same thing though, roll 80* to initiate the descent and slowly roll out until I was 22* nose down 700 agl on final or so. At no point were there any G's much above 1 due to the slow roll out at the bottom. Average descent rate was about 6000fpm.

 

[Hacker15e]

Anyone who finds that intimidating ought to be not a little embarrassed, rather than chastising me for it. Maybe this is why US students recently ranked 25th in the world in math ability?

Agreed.

 

[mshunter]

This has got to be the most absurd critique that continually crops up in so many discussions; its sole purpose seems to be to excuse laziness in pursuing knowledge. No, you don't use this information in the cockpit, you use this on the ground to better understand airplanes so that you can optimize your decision-making once you get in the air. You never know what bit of knowledge might come to your aid some day, and a professional ought to devote his life to gaining as much knowledge about his profession as he can, rather than coasting on what his private pilot instructor taught him in the dozen hours of ground school.

While this sort of discussion clearly doesn't interest you, since you have said so over and over and over, it does interest quite a lot of people, most of whom only read the discussions and don't participate.

Nowhere did I say this doesn't interest me. But I have over and over and over said that there is a simpler way to explain what you are getting at. If I really wanted to get out a calculator and work my way through tall the math equations you continually bring up, I would. But I don't need to. Why re-invent the wheel. The FAA, Jeppesen, ASA, Rod Machado and many others before me have taken the time to put it in a visual form that is easy to see, rather than taking out a calculator and working some numbers that in my brain, are just that numbers. For me, and I'd reason to say the majority of people, the numbers are not only difficult to visualize, but expensive to learn when you are paying someone usually upwards of $40 an hour. And no where did I say that your numbers have no merrit IIRC, because they do, just not at the PPL level, or even the commercial level. If they did, they'd be a part of the written test for both certificates.


I think MikeD said it best "need to know and nice to know." I don't need to know the math calculations that you presented, nor do any of my former students. Is it nice to know, sure, if you're into that kind of stuff. But math doesn't do it for me, or 95% of the pouplation. Show them a graph, and you might spike their interest though. Show them a video of what happens when you over load an airplane after you show them the graph, and again, it might spike their interest. But sit them down and start throwing all these math calculations at them, and then get them to memorize it, when more than likely they will forget it in a matter of days, weeks or months, you have essentially tought them nothing other than "what was that formula for figuring out load factor again?" And most people will daze off and start to fall asleep while learning it. I can remember when I was doing my CFI ride, I was trying to teach the examiner about w&b, and turned around to start writing formulas on the white board. I turned around about 30 seconds later, and he was pretending to be asleep. As would most people. But as soon as I puled out a graph, he was interested again. Again, I'm not saying that your formulas have no merrit, but when the majority of the people on these forums are disputing them, or disagree with the method, don't you think it might not be the best way to teach? It's not about what you know, it's about getting what you know to sink in. And IMHO, the math doesn't do the trick. We are a society of instant gratification, and I as an insructor, need to conform my teaching style to that kind of learning.

If I had someone who needed a teaching style that needed the kind of math equations that you present, I'd refer them to you. But I have yet to come across someone like that.

 

[tgrayson]

As a follow-up question, is it possible that an aircraft such as a 182 would eventually stop accelerating due to the increased drag as airspeed increased? If it is, is it also possible to determine if that final stabilized speed could reasonably be within airframe limitations?

An airplane will surely reach some sort of terminal velocity, but I suspect it's always much higher than redline. This speed is higher with the prop stopped, than windmilling. Terminal velocity generally could be calculated with the drag coefficient (Cd) and the cross sectional area (A), but Mach issues would probably complicate that simple scenario for slicker airplanes. Some of the old WWII fighters got into the transonic regime during dives, so I'm sure that modern business jets could too. Not sure about something like a C182. The upper airspeeds are probably limited by flutter.

 

[ppragman]

An airplane will surely reach some sort of terminal velocity, but I suspect it's always much higher than redline. This speed is higher with the prop stopped, than windmilling. Terminal velocity generally could be calculated with the drag coefficient (Cd) and the cross sectional area (A), but Mach issues would probably complicate that simple scenario for slicker airplanes. Some of the old WWII fighters got into the transonic regime during dives, so I'm sure that modern business jets could too. Not sure about something like a C182. The upper airspeeds are probably limited by flutter.

Talk to some sky dive pilots about what they can do with Caravans, Pilatus Porters, King Airs and Twotters.

 

[tgrayson]

he was pretending to be asleep. As would most people.

I don't think that you can really speak for most people. But a lot depends on your teaching style. I've never had anyone fall asleep on me nor have I had much problem ensuring that people pay attention. You must be a really boring presenter.

What you refer to as my "teaching style" is remarkably effective in teaching people a deep understanding of these issues, far beyond what they can get via any other means, so, no, I have no interest in whether anyone here or anywhere else disagrees with me, because they are mistaken. The reason that any person in particular can achieve better than average results is that they choose to use methods that the average person rejects.

That said, I generally only get into the math with CFI students, unless there is a particular need or interest in it earlier. There are some aspects of aircraft behavior that can only be understood with resort to high school mathematics and I feel that it's a reasonable expectation that a college graduate can perform at this level.

 

[TwoTwoLeft]

I know it does, but it doesn't help that definition make sense. ;-)

Note that a stalled airplane descends not because it lacks lift, but because it lacks the thrust to overcome the drag of the stalled wing. With enough thrust, it would still achieve level flight, assuming lateral control could be maintained.

Sure it makes sense...

Here's the scenario:

Wings level, 1G, power idle

Typical power-off stall entry. Pilot increases back pressure, increasing AOA in an attempt to stop descending. CL increases, descent is arrested. Airspeed decreases as Cd increases. CLmax is reached, pilot continues to pull, critical AOA is exceeded. The wing has now transitioned from normal to stalled flight.

The wing is now flying the back side of CLmax, there there is still lift, but not enough to counter the load imposed on it. The load here simply being the weight of the airplane (the force of gravity acting upon the airplane's mass).

 

[shdw]

I think MikeD said it best "need to know and nice to know." I don't need to know the math calculations that you presented

You might have merit arguing the students need to know. However, you, as a professional pilot, should seek this knowledge. To at least comprehend what the Wright Brothers knew, simple formulas. This is how I feel for any pilot who might put the life of myself or a loved one in his or her hands someday.

I really do find it unfortunate. Instead of repeatedly claiming it to complex, over your head, or unimportant; I wish you'd attempt to learn it. I have known you for over a year now and we have gone back and forth on this subject numerous times. Few times have you just stopped complaining about it and asked questions in an effort to understand.

You cannot appreciate what you do not know. I truly hope you find it important enough to be worth your time someday bud.

 

[USMCmech]

However, you, as a professional pilot, should seek this knowledge

Every professional pilot has their area of expertise, an area of knowledge that they have truely mastered.

As a mechanic, mine is aircraft systems, and how they work together to make the plane fly. I understand areodynamics well enough, but not anywhere near as well as some of you guys. The same could be said of any of us about any subject. Maybe you love to learn about weather, the regs, ect.

We all have our strong areas, and our week ones. So long as you recognize what areas you are lacking, and keep trying to learn, you have nothing to apologize for. There is nothing wrong with saying, "I don't know" or "You should ask Jim about that".

 

[Hacker15e]

What you refer to as my "teaching style" is remarkably effective in teaching people a deep understanding of these issues, far beyond what they can get via any other means, so, no, I have no interest in whether anyone here or anywhere else disagrees with me, because they are mistaken.

Modest and humble, too.

 

[SteveC]

An airplane will surely reach some sort of terminal velocity, but I suspect it's always much higher than redline. This speed is higher with the prop stopped, than windmilling. Terminal velocity generally could be calculated with the drag coefficient (Cd) and the cross sectional area (A), but Mach issues would probably complicate that simple scenario for slicker airplanes. Some of the old WWII fighters got into the transonic regime during dives, so I'm sure that modern business jets could too. Not sure about something like a C182. The upper airspeeds are probably limited by flutter.

Continuing with my line of questioning (having that jump plane in mind), can you tell what the acceleration rate might be? Is it possible that a 182 jump pilot could start at, say, 8,000 or 10,000 feet in level flight at slow airspeed, then transition to a 60 degree bank increasing airspeed descent, trimming as he goes and letting the airspeed rise to keep the load factor down around 1+ G, and end up at the bottom of the descent while still below redline and not experiencing any high loading?

As I said before, I'm trying to reconcile the differences here between the science and the experiential.

 

[tgrayson]

The wing is now flying the back side of CLmax, there there is still lift, but not enough to counter the load imposed on it. The load here simply being the weight of the airplane (the force of gravity acting upon the airplane's mass).

If this were truly the case, the airplane would be accelerating downwards, since unequal forces produce accelerations. This only happens briefly, whereupon a steady descent rate is encountered. Steady descents aren't caused by a lack of lift, but by a lack of thrust. Although the wing isn't generating Clmax (although it could be, since the lift curve sometimes recovers after the stall), we fly airplanes all the time at less than Clmax. Like, most of the time. Look at any lift curve and you see that the lift curve dips after Clmax, but rather gently. You can fly a particular lift coefficient on either side of the peak.

 

[tgrayson]

can you tell what the acceleration rate might be?

Not with any degree of accuracy. I have data for the parasite drag coefficient of a C182 and the frontal area, so I could probably calculate a nose dive at zero AoA, but up until that point, induced drag is a large component of the drag, which would be decreasing as the airspeed picks up. I don't have any induced drag data for a C182, although I might could make some up to produce a reasonableness check.

I don't think there is a discrepancy to be explained...most people agreed that it was a non-stabilized maneuver and airspeed was increasing. Only USMCmec claimed a constant airspeed, but I view the subjective data on load factor to be very unreliable. It's not like the rest of us don't do 60 degree descending turns. I do them all the time when doing steep spirals with Commercial or CFI students. At the steepest, these are 60 degree banked turns and we're descending power off at a high rate, constant airspeed, and I have no problem accepting that the load factor is pretty much 2.

 

[z987k]

Continuing with my line of questioning (having that jump plane in mind), can you tell what the acceleration rate might be? Is it possible that a 182 jump pilot could start at, say, 8,000 or 10,000 feet in level flight at slow airspeed, then transition to a 60 degree bank increasing airspeed descent, trimming as he goes and letting the airspeed rise to keep the load factor down around 1+ G, and end up at the bottom of the descent while still below redline and not experiencing any high loading?

As I said before, I'm trying to reconcile the differences here between the science and the experiential.

I can attest, that yes you can do this... even from 12k to sea level. ~1 g throughout.
Also a commercial steep spiral is nothing like after a jump run... you don't have parachutes on.

 

[shdw]

We all have our strong areas, and our week ones. So long as you recognize what areas you are lacking, and keep trying to learn, you have nothing to apologize for. There is nothing wrong with saying, "I don't know" or "You should ask Jim about that".

Exactly. Bold added for emphasis. I certainly have voids in my own knowledge, as we all do. Though I feel my time is better spent questioning what I don't know rather than questioning it's usefulness.

The problem, as I see it, is pilots believing aerodynamics, beyond what the FAA requires, is only useful to engineers and designers.

 

[mshunter]

Exactly. Bold added for emphasis. I certainly have voids in my own knowledge, as we all do. Though I feel my time is better spent questioning what I don't know rather than questioning it's usefulness.

The problem, as I see it, is pilots believing aerodynamics, beyond what the FAA requires, is only useful to engineers and designers.

Here's the thing. It's not that I don't think understanding them is't usefull. I feel I have a decent grasp of it actually. But I fail to see the legitimacy of knowing all the math calculations when I can use charts and graphs to understand it at a level that actually interests me. I am not arguing that the math has no place. What I am saying is that your average person will see the math, do the math, but have a hard time corelating it to actually flying. I sure do. And the reason why I say it's more for an engineer or desginer is because their brains are usually more apt to understand these numbers. Some people see the world in numbers, some in shapes, some in figures, etc. I would reason to bet that engineers see it in numbers, desginers in shapes, etc. Thats where that comment comes from.

I just don't see numbers as a way for me to learn, and haven't come across someone who does yet, aside from a very limited few in these forums. And those in these forums think it's the gospel and there is no other way to learn it because it's all wrong unless it's there way(or the highway). Maybe I'm just a blue collar dummy who spent half his life getting greasy bent over the hood of a car and is a dumb knuckle dragger? Who knows. What I do know is while I was a CFI, I had one person who busted a checkride out of the many I signed off, and I sitll can't figure out why he busted it. But it is what it is. The bottom line in my point of view, it doesn't matter how you teach someone, it matters that they understand it and can apply it.


P.S. The knuckle dragger dummy comment is not directed at you shdw. (Brian right?)

 

[MikeD]

Here's the thing. It's not that I don't think understanding them is't usefull. I feel I have a decent grasp of it actually. But I fail to see the legitimacy of knowing all the math calculations when I can use charts and graphs to understand it at a level that actually interests me. I am not arguing that the math has no place. What I am saying is that your average person will see the math, do the math, but have a hard time corelating it to actually flying. I sure do. And the reason why I say it's more for an engineer or desginer is because their brains are usually more apt to understand these numbers. Some people see the world in numbers, some in shapes, some in figures, etc. I would reason to bet that engineers see it in numbers, desginers in shapes, etc. Thats where that comment comes from.

I just don't see numbers as a way for me to learn, and haven't come across someone who does yet, aside from a very limited few in these forums. And those in these forums think it's the gospel and there is no other way to learn it because it's all wrong unless it's there way(or the highway). Maybe I'm just a blue collar dummy who spent half his life getting greasy bent over the hood of a car and is a dumb knuckle dragger? Who knows. What I do know is while I was a CFI, I had one person who busted a checkride out of the many I signed off, and I sitll can't figure out why he busted it. But it is what it is. The bottom line in my point of view, it doesn't matter how you teach someone, it matters that they understand it and can apply it.


P.S. The knuckle dragger dummy comment is not directed at you shdw. (Brian right?)

As I said, nice-to-know vs need-to-know.

Is it need-to-know for a pilot to know the math equations for aerodynamics? No. Is it nice-to-know? Sure. It can be a good complement to the hands in the cockpit and give a general understanding of why something is happening. But its not required, and doesn't really need to be.

By the same token, are the same math calculations need-to-know for an engineer building the plane? I would hope so! What the pilot does in the aircraft with it is nice-to-know for them, but not required and also doesn't need to be.

The point being, each has its respective place. They can also be combined up to suit an individual's desire to any number of levels.

 

[shdw]

I just don't see numbers as a way for me to learn, and haven't come across someone who does yet, aside from a very limited few in these forums. And those in these forums think it's the gospel and there is no other way to learn it because it's all wrong unless it's there way(or the highway).

It really has nothing to do with being one way. I personally prefer to give graphs, pictures, and simple formulas. Wrapping as many learning styles (an interesting article, I think) as I can into one lesson and favoring whichever method the student seems to prefer. I am still knew at this with much to learn, but it seems to work in all venues I've taught in, to include aviation (most of my teaching did not occur within aviation).

I find it unlikely that you've not encountered anyone who can, or enjoys, working with numbers. This type of learning style is deemed a logical one and between 15 and 30 percent of the population falls within this category. The difference in percentage depends on source, age, and culture. For you, in California, with a high percentage of Chinese American, there is an even greater probability for encountering the logical learner.

What I find far more likely is that you don't teach that way, don't look for people who learn that way, and thus, are unlikely to notice such a student. This is not to fault who you are in any way. However, as stated previously, I do wish you saw purpose in broadening your horizons. Especially as it directly pertains to your chosen profession.

P.S. The knuckle dragger dummy comment is not directed at you shdw. (Brian right?)

It sounds like you are directing it at yourself? If this be the case, then, to quote Denzel Washington in the movie The Great Debaters, "You wouldn't punch yourself in a street fight so don't punch yourself in a word fight. Use humor against your opponent, not yourself."

Yes, it is Brian. I don't remember your name. Though I do remember one post you did tell the community your name and some of what you said in that post, but I can't find it. You were being a wise ass (big surprise with us debating huh? lol) and linked us to your schools homepage after a debate about Rich Stowell. It was a classic too, I wish I could find it.

 

[FDX8891]

I don't think that you can really speak for most people....

What you refer to as my "teaching style" is remarkably effective in teaching people a deep understanding of these issues, far beyond what they can get via any other means, so, no, I have no interest in whether anyone here or anywhere else disagrees with me, because they are mistaken.

Yeah, I'll go with Hacker on this one...modest and humble too.

You tell Mshunter that he can't speak for most people, but then you go right ahead and say that any teaching style other than yours is inferior. Now that's a joke...Not the fact that the US ranks 25th in the world in Math. By the way, how many countries are there in the world? We rank 25th, and you're complaining?!...God help us.....

Yeah, your equations can give one a deep understanding of the subject matter, but that's the thing - In order to be a safe and proficient pilot you don't need to be an engineer or mathematician. You don't even need to know the lift formula, which is very basic.

Maybe if you didn't talk down to people who "know" less on this forum (like me) then maybe my ignorance would be more welcoming to your omnipotence.

 

[SteveC]

...Not the fact that the US ranks 25th in the world in Math. By the way, how many countries are there in the world? ...

Between 190 and 200. Depends on who is doing the counting.