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Winginit

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Billski's example was of a 42-knot stall airplane travelling at 50 knots. The Helio Courier's stall spped is 30 MPH, which is 26 knots. That makes a difference in turn radius. A big difference.

Any pilot knows that.
Yes, I agree, but the idea here is that we are looking for what properties have a positive effect on spin control. The airplane in his example was unnamed and maybe even a non-existant mathematical exercise. What relevant purpose does it serve to compare a fictional airplane with no known design factors presented, when searching for somethings that may prevent spinning? My comments are that a typical conventional airplane spins when it is moving too slowly to generate enough lift...usually when banked. I then explain that a design that continues to generate sufficient lift at whatever angle of bank (0-60) is the safer airplane. If that airplane can also make smaller turns (while banked or not banked), then that shows it is less prone to spinning. The videos obviously show that the STOL airplanes are less likely to spin.

So going back to your statement
"That makes a difference in turn radius. A big difference. Any pilot knows that"
So it appears that an airplane with a slower stall speed is going to be less likely to spin, and since STOL airplanes usually generate the slowest stall speeds, they become one answer to building an airplane that is highly stall resistant.
Now I do not see how explaining a conventional airplane design with a higher stall speed which requires a huge turning radius particularly provides any useful data. The representation that because the imaginary airplane has a larger flat turn radius than it does a banked turn radius means that all airplanes will therefore do the same thing is not an accurate representation. There are lots of design factors, and every airplane will provide different results. I would think that an acrobatic airplane can reverse course in less room than it normally travels when doing a banked turn because it has features incorporated that allow extreme maneuvering.

We really seem to be going over the same territory and not covering anything new, and not having other inputs on something other than STOL airplanes.

The fact is that anything which allows you to maintain lift and control in any condition contributes to resisting spin at slow speeds. Obviously any maneuver which deviates from straight and level flight at slow speeds will increase the danger, even if its a routine maneuver. Different airplanes designs will result in differing risk levels in any maneuver. The aircraft which has higher landing speeds will by definition have more risk involved not only while landing but while making "routine" turns. The airplane that requires nearly 100 mph to land will normally require similar high speeds on the turn to final and be somewhat more difficult to make a banked turn and perfectly align with the center of the airfield. This type of airplane will probably have a higher risk factor for over banking and spinning than a slower and more docile aircraft.


Here is an automotive video on drifting. The thing I want you to watch for is the forward speed of the vehicle. As forward speed is allowed to
build the radius of the skidding turns becomes exponentially larger. When he slows the vehicle his turning radius becomes much smaller. The centrifugal forces have a large effect on both cars and airplanes, and this demonstrates that slower forward speeds enhance the ability for a smaller turning radius. Now, try to duplicate this same motion in the typical SUV (equivalent of a spam can). Not going to get the same result.

https://www.youtube.com/watch?v=g_DBLppDZAs
 
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mcrae0104

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Winginit, please do yourself (and the rest of us who find this tiresome) a favor and read Stick and Rudder as a basic introduction to the way airplanes fly and turn. Pay special attention to the parts where the author says, "your kid brother thinks..." He's speaking directly to you in these passages.
 

Winginit

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Observation 1: You quoted me, yet you say "neither of you..." Who is the other person you're addressing? Unlike you, ekiMneriB'O/MikeO'Brien/Winginit, I only have one user name.

Observation 2: Didn't you protest very recently that you didn't want to discuss the magical qualities of the Storch any longer? And yet... There you go again.

Observation 3: I invited you to carry on the conversation via PM in order not to derail REVAN's thread. Instead you carried on. Let the rest of the readers judge for themselves.



Luddite? You're too kind. The appropriate adjectives would violate HBA's rules of conduct, so I'll refrain.

[HR][/HR]
Those who post ridiculous things should not be surprised when they are ridiculed.
I don't have any interest in conversing with you by private messaging because I don't see it going anywhere. Obviously you are only looking to find any flaw or imperfection in anything I say, and refuse to accept factual visual evidence. You seem bent on trying to destroy my credibility, but I hope most of the people reading what you say will dismiss it as being mean spirited and serving no useful purpose for HBA.
I have tried to stay objective with explantions of my reasoning but you continue to seek controversy and Troll for personal responses. I would expect this kind of stuff in a high school girls locker room, but not on HBA. I think this posting actually says more about you than it does about me, so I'm going to try to just move on .
 

Winginit

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Winginit, please do yourself (and the rest of us who find this tiresome) a favor and read Stick and Rudder as a basic introduction to the way airplanes fly and turn. Pay special attention to the parts where the author says, "your kid brother thinks..." He's speaking directly to you in these passages.
Have you ever noticed that in every post you make, there is comment that is meant to deride me. There are a few different types of posters on this site. There are those who spend a fair amount of their time explaining theirselves and trying to honestly create a better aviation community. People like Dan Thomas, who I often disagree with, but I respect because he works at being objective. We both frustrate one another and have some good disagreements, but we usually don't dis each other personally. Sometimes he gets the best of me, but its because he honestly believes what he is saying. Most times its a draw. We both go away believing what we belived to start with, but other readers now have some different opinions and can decide for themselves what to believe
Then there are the other posters who seldom spend more than a few moments on any post unless forced into expounding. They search the threads looking for the ligitimate posters and toss negative comments all the time. They virtually never really say anything or explain anything definitively, because that puts them at risk of being exposed. It gives others a chance to analyze their statements and point out their flaws. They prefer to stick to general references where they can't be pinned down or critized.
I believe if you analyze the bulk of my postings, I'm an idea guy and I invest the time to explain and support what I invested myself in to. I think if you look at your contributions the whole time you have been on HBA, you will find few if any times where you have invested time in explaining a point of view or supplying data and information thats helpful to people. I've created lots of threads that have produced much information thats helpful to others. I have been working on a possible sticky that would help people who have no experience with machinery to get familiar with tools and tooling as a future contribution to HBA. So I'm confident that some people have learned things from my contributions, because many of them have told me just that. But when I look at how you participate in HBA, I virtually only see you jumping in on occassion to criticize something someone else took the time to post, and most generally acting badly if anyone has an opinion different than yours.

Instead of this latest round of personal insults which I feel your own words disparage you more than me, wouldn't it have been wiser to just take the time to explain what you feel is inaccurate and why ? Or better yet, Why don't you just take the time to explain to everyone your opinion of how everything related to slow turns and skids are. Write an explanation of what you believe is the correct information that the world needs to know. It does not have to reference me or anything I have said, it just can be your definitive explanation. Then everyone can read just what you see as the correct and irrefutable application of forces. Then they can just decide for themselves. Stop being a potshotter and making everything a quick him vs me situation and just express what you believe irregardless of what anyone else believes.
 
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mcrae0104

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Alright, since you don't want to have this conversation by PM, we can do it out in the open. Here is why I take a less-than-patient approach with you, Winginit. You have a long history of posting things that are incorrect, dangerous, or in at least one case, not even legal. I have never seen you relent in your opinions when corrected by others. You deflect arguments, cast doubt on engineering and physics, and make personal attacks. If I am not mistaken, some of your posts were removed from a recent thread for this reason.

In short, by choosing to ignore facts and stubbornly making tortured arguments that go on and on across multiple threads, covering the same ground again and again, you invite this response. If you think I've been mean, use the "report" button. You're a grown man. Don't resort to calling me a school girl.

My assessment is that you simply thrive on arguing; the problem is that you don't have any idea about the content of your arguments. I've encouraged you to sharpen your arguments, to offer something more than your opinion, but you steadfastly refuse to make a case using evidence or logic. If you would do this, it would change the caliber of the discourse.

Ultimately, I would rather see you learn about flying and homebuilding than argue with you about it. Read some books. There's a great sticky here on design, and there are plenty of suggestions others can make on aviation in general. Get some flight instruction; learn what flying is really about and how it really works.

This forum was not established for people to endlessly spar about stupid things, so I will bow out of this conversation.
 

Himat

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With regards to spins, a couple of things have long been found to be true:

Easy in, easy out - This one is very common. Most airplanes with decent flying qualities and acceptable stability and that can be easily spun, can also be easily stopped. This is usually because of several features: foil gives sharp stall, wing is not designed to resist stall progression, and plenty of elevator and rudder. You thus have strong ability pitch up and induce yaw, and can make much of the inside wing go from flying to stalled with small AOA change. Aply full rudder and aileron, the inside wing stalls and the rotation commences. That same big elevator, when neutralized along with reversing that same big rudder stops the rotation, then followed with forward stick drives the airplane back across the thin dividing line between stall and attached flow and the spin transitions to a spiral dive.

Hard to enter a spin historically comes about from several features: Limited horizontal tail authority, a wing that resists outward stall progression, an airfoil that takes a lot of AOA change to go from flight to fully stalled. You can play a lot to get it to do a spin entry, it gives the pilot lots of warning that it is getting close, and then it does enter the spin, now you have to achieve a big change in AOA to unstall the stalled wing, but you have small ability to pitch down for AOA reduction and small ability to stop rotation. Hard to enter, hard to get back out.

One other issue is that entry commences with relatively small rotation speed in yaw, but as the spin progresses, the rotation rate increases, the speed difference and, unavoidably, the AOA difference between wings gets larger and more kinetic energy is stored in the rotation rate. So, once the rotation rate has built up, you have to apply more force against rotation for longer to reduce the rotation and break the spin...

Now, all of this does not mean that it must be this way, there may be ways of making the airframe design that can be tough to enter a spin, but easy to get out, but I do not know of them... It will be a great discovery if it is found.

Billski
Cut and paste with some addition from my post #379.
The trouble is that I have not read the book and seen the author’s argument, just the sum up on the web site. Still I would question his conclusion. (The difficult to spin, difficult to recover bit.)
Let look at four design elements that may make a plane more spin resistant:
(In an airplane with conventional layout.)
  • Large vertical tail volume. (Adding directional stability.)
  • Low moment of inertia in yaw.
  • Low moment of inertia in pitch.
  • Low capability for the wing to make a yawing moment. ( Low to moderate aspect ratio, bell shaped lift curve, no ailerons…)
  • Forward centre of gravity.
  • Sufficient large horisontal tail volume

I can’t see that any of those do make spin recovery more difficult and the low inertia in pitch and yaw should make it easier to recover from a spin as the aerodynamic forces will then have less inertia to overcome.
 

Dan Thomas

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Maybe the CG was a bit forward?
I often find airplanes with their control systems badly out of rig. The elevator stops on the 172 are at the elevator bellcrank, and if the upper stop is set out some so that the elevator can't reach its maximum up travel of 28°, you'll have trouble stalling the airplane. It should stall even at full forward CG. Complicating things there are the elevator balance horns, which are at an angle to the elevator's chord line. They are angled down a bit. A common mistake for the mechanic is to align that horn with the end of the stabilizer and use that as the neutral; he doesn't read the service manual and heed what it says. Those horns are down about 3° and can't be used as neutral. You have to get the elevator streamlined with the stab, meaning that the chord lines of both are the same. Using the horn as neutral will cost you 3° of up-travel, and the failure to stall is only one danger there. You might have trouble flaring properly someday, too, or can't keep the nosewheel out of the mud on a soft-field landing and flip the airplane over on its back.

Not the best picture, but you can see the angle built into the balance horn:

Cessna-elevator.jpg
 

BBerson

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High yaw inertia (tip tanks, floats) will help resist spin entry. But will delay or may prevent a developed spin recovery. Another case of "intentional spins prohibited".
 

REVAN

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Let look at four design elements that may make a plane more spin resistant:
(In an airplane with conventional layout.)
  • Large vertical tail volume. (Adding directional stability.)
  • Low moment of inertia in yaw.
  • Low moment of inertia in pitch.
  • Low capability for the wing to make a yawing moment. ( Low to moderate aspect ratio, bell shaped lift curve, no ailerons…)
  • Forward centre of gravity.
  • Sufficient large horisontal tail volume

I can’t see that any of those do make spin recovery more difficult and the low inertia in pitch and yaw should make it easier to recover from a spin as the aerodynamic forces will then have less inertia to overcome.
That's pretty much how I see it as well. I think there is a fairly common perception to attach spin resistance to stall resistance. This is reinforced by statements that if you don't want to spin, then don't stall the wing. I don't want to surrender control authority, not to avoid a stall and not to a spin either. I want to have control in the stall and I don't want to have to change control algorithms to do it. Changing algorithms causes too many problems.
 

BJC

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Cut and paste with some addition from my post #379.


Let look at four design elements that may make a plane more spin resistant:
(In an airplane with conventional layout.)
  • Large vertical tail volume. (Adding directional stability.)
  • Low moment of inertia in yaw.
  • Low moment of inertia in pitch.
  • Low capability for the wing to make a yawing moment. ( Low to moderate aspect ratio, bell shaped lift curve, no ailerons…)
  • Forward centre of gravity.
  • Sufficient large horisontal tail volume

I can’t see that any of those do make spin recovery more difficult and the low inertia in pitch and yaw should make it easier to recover from a spin as the aerodynamic forces will then have less inertia to overcome.
All good points. Just remember that tail volume needs to be measured / calculated with the airplane in all stall configurations. For example, there can be significant loss of normal flight vertical tail volume with extreme elevator deflection.


BJC
 

Winginit

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Alright, since you don't want to have this conversation by PM, we can do it out in the open. Here is why I take a less-than-patient approach with you, Winginit. You have a long history of posting things that are incorrect, dangerous, or in at least one case, not even legal. I have never seen you relent in your opinions when corrected by others. You deflect arguments, cast doubt on engineering and physics, and make personal attacks. If I am not mistaken, some of your posts were removed from a recent thread for this reason.

In short, by choosing to ignore facts and stubbornly making tortured arguments that go on and on across multiple threads, covering the same ground again and again, you invite this response. If you think I've been mean, use the "report" button. You're a grown man. Don't resort to calling me a school girl.

My assessment is that you simply thrive on arguing; the problem is that you don't have any idea about the content of your arguments. I've encouraged you to sharpen your arguments, to offer something more than your opinion, but you steadfastly refuse to make a case using evidence or logic. If you would do this, it would change the caliber of the discourse.

Ultimately, I would rather see you learn about flying and homebuilding than argue with you about it. Read some books. There's a great sticky here on design, and there are plenty of suggestions others can make on aviation in general. Get some flight instruction; learn what flying is really about and how it really works. Ok

This forum was not established for people to endlessly spar about stupid things, so I will bow out of this conversation.
No, what I do is take the time to state a position, and then furnish data to support that position. You and several others dislike me because on occasion I have proven you wrong. The egos of a few of you guys gets crushed when you are wrong, so you revert to name calling and try to bully people. It doesn't work with me and that just frustrates you guys to no end. You virtually never take the time to post anything from your own mind, you prefer to just troll along and jump in later on someone else's thread and ruin it. You have been instructed in the past to cease making personal attacks, yet you persist because of some sick need to assert superiority. Continually attacking someone over and over isn't normal. You seem transfixed on continuing this diatribe and writing every mean and nasty thing you can think of. Its really not a healthy way to exist.
You are right about me being a grown man, and as such I don't resort to childish name calling, but I do feel that what you are doing is the same type of stuff that jealous little high school girls engage in when a pretty newcomer enrolls. Can't help it if again we see things differently but thats the closest analogy I can compare your actions to. Of course I know that in your mind I must be wrong about that, because in your eyes I'm wrong about everything. The internet allows people like yourself to say things you wouldn't dare say face to face. That's one of the bad things about the internet, you can get away with impunity, but the tactics you have employed on HBA are pretty disgraceful to say the least.

You usually disagree with me on everything and then your proof is always some generic reference to physics or some book somewhere or something vague.
On the other hand I post actual data and references to support my views. You never address the supporting documents because you can't dispute what's right before your eyes. Then you just start attacking me and my credibility. This latest bruhaha revolves around the fact that I believe that a properly executed flat turn in a Slepcev Storch can be done in a smaller distance than a banked turn because the banked turn requires more speed. A very simple difference of opinion. You have absolutely nothing to base your difference of opinion on, produced no credible or relevant data, and yet you are absolutely sure I'm wrong. And with nothing to support your opinion other than occassionally shouting the word "Physics" you want to go off ranting and telling the world I have no credibility and virtually anything and everything I say and do is wrong. In your eyes everything I say and do is wrong and everything you say and do is right. Do you honestly not see anything wrong there ? I really think that's a sick outlook and obsessive to say the least.

If I am not mistaken, some of your posts were removed from a recent thread for this reason.

PS: the moderator removed my last post on another thread because I had used Bold Letters to make a point, and I never knew that using the options provided by the thread could be interpreted as unacceptable. What Mac isn't saying is that the reason I used the bold lettering which contained nothing crude or normally unacceptable was simply because Mac was doing the same type of stuff he is doing here. The Mod then closed the whole thread. Now I ask anyone still reading this thread, do you really believe that a mod would close a thread because of one posting ? He closed the thread because it had deteriorated to a pissing contest, and the same people were involved. And thats one of the times when Mac was warned about the personal diatribes. Yep, in Macs eys what I say is always wrong and its his job to correct me and tell the whole world about it, over and over. Is that normal ?
 
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Winginit

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Proposing a non standard (and known to be risky) flying technique, I think the burden of proof is on you.

Dana
I don't feel anything that I say will satisfy the people who really want to just be disruptive and negative. I have posted explanations and videos numerous times and they are ignored.
I have also said that my opinion is based on viewing these videos which demonstrate that very small turning radaii can be obtained with both the flat turn and a skiding turn. Anyone who watches the video cannot deny that the the Storch performs the maneuvers easily. The question then becomes "is it a dangerous maneuver"? I have said numerous times that it is a dangerous maneuver in a typical spam can and I don't reccommend it for them. I further stated numerous times that the purpose of these maneuvers was for a pilot who had already placed himself in a dangerous position and the additional control at slow speeds and low altitudes could help the pilot get through the problem. I never advocated that every time someone lands their airplane they should ignore standard landing procedures and try flat turns and skids. Having an airplane that is controllable at exceptionally slow speeds is a benefit, not a negative.
Then the topic turned to whether the Storch could make a smaller turn by banking or flat turning. Again I pointed to the airshow video which demonstrates that because of very slow forward motion, the Slepcev has little centrifugal force to deal with when turning and turns very tightly. Now, logically if the designer wanted to demonstrate the tightest turning radius his airplane could perform, thats the one he would demonstrate to his customers. If it was a banking turn, thats what he would have demonstrated, but he didn't do a banking turn. You will also notice in the video that the pilot actually slowed his airplane to perform the maneuver rather than speed up for a banking turn.All of that seems pretty logical to me. I think the video demonstrates exactly what I'm saying. Thats my opinion and thats my version of a reasonable basis for that opinion.

All I get in return are mathmatical calculations where they admit that they don't know any specifics about a Storch and want to apply a general trend and say ALL airplanes therefore must operate the same way. Thats their opinion, but like my "evidence", its not absolute proof. So we have different opinions.

Then there are the comments that a skid is a dangerous maneuver. Well I agree that in the typical general aviation spam can it is a dangerous maneuver, but we have no way of knowing if its always dangerous in a STOL airplane. If someone attempted slipping in a stol, they would most likely be near the ground and very slow, limiting the danger involved. So here is how I see it. The STOL "banks" his wings and performs the base to final turn normally, and continues to land using normal procedures. He is not attempting to perform a sideshow supershort landing but instead is just trying to reach the ground as smoothly as possible with a reasonably slow touchdown. He is after all landing in a field where he has never landed before. About ten feet off the ground he spies an old fence post or a bolder directly in his path. He is too low to bank the wing but needs to change direction. He does not need to turn 180 degrees or even 90 degrees, just maybe 15-20 degrees and he can miss the post. A simple skid is employed, and since the wing still has sufficient lift, it doesn't drop like a Cessna might. Thats not nearly as dangerous as doing nothing and hitting the post. The pilot could probably do the same maneuver successfully at thirty feet. If he is at fifty feet there is no need to perform the maneuver. I don't see why anyone would dispute that logic, but the people with different opinions will distort it a thousand ways, and nothing will satisfy them. (Note: Earlier on another post I provided a video. It was a "training"video discussing the method of touchdown in an off airport/backwoods landing. Just about 15 feet altitude, the pilot needed to make a slight course correction because of a dogleg in the road. He came very close to losing his wing because his airplane was equipt to do the maneuver.)

One further thing, there are actually schools that teach the flat turn as an acceptable maneuver, so apparently I'm not alone in seeing some benefit to flying planes that are capable of doing flat turns. One fellow has 16,000 flight hours and specalizes in teaching slow flight over airports and one of his specialties is teaching the flat turn. Apparently he has found some benefits there, and even wrote a book about it. Then there is the attached article from backcountry pilot discussing the benefits of mastering the flat turn. There are other examples available but apparently its not as cut and dried as many lead you to believe.

Back Country Pilot

Skidding in energy management turns.
I took the new instructor at Aurora Aviation, 2H2, out to the Hangar Kafe yesterday. Teaching energy management turns always requires admonishment to use more rudder, but he was a fast learner. It is a turn to target deal, not a turn to heading. If turning level is your norm, you are used to limiting angle of bank to prevent load factor and bleeding energy in the level turn. By allowing the nose to go down naturally in the turn we eliminate that problem. Now rather than a bank and then turn deal, we are in a continuous banking/descending to turn to target. As long as we continue to move the aileron, we need continue pushing the nose around with rudder. Also, as the bank steepens past forty five degrees, the rudder helps push the nose down.

I said Parker was a fast learner. When I asked him to "push that nose around with rudder," he skidded quite a bit. I was then able to point out that the airplane is not going to stall or spin with the nose well down and the elevator released completely. The skidding in the turn is far less problematic than slipping in the turn when at low altitude. We need to push the nose around and onto target prior to having to pull up to prevent impact with terrain.

The problem, for those who fly low, with not training for this situation is that a pilot can come unglued and reactively pull up while still in a bank and stall or spin the airplane. Or he can put a wing into terrain or a wire still trying to complete the turn with too little rudder in the direction of bank.
Jim Dulin.jpg

Now there is what I'm basing my opinion on.

Note: I have absolutely no doubt that the same people who disagree with everything I say will now berate these two professional pilot/authors who make their living training other pilots . At least then I'll know its not just me thats not allowed to have a different viewpoint, it the rest of the world too.
 
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Toobuilder

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Eki

The reason we are so frustrated with your "opinion" is because the basis of it is so poor compared to ours. You have CLEARLY never flown an airplane, and youtube demonstrations of skidding turns are not reasonable "evidence" to support your opinion. These videos don't illustrate measured comparisons between the two turning techniques - they are simply demo stunts.

Further, your "imaginary fence post at 10 feet" probably makes sense to you as a non pilot, but I can assure you that there is plenty of room to bank at that altitude. In fact, I am sometimes still in my final turn at 10 feet.

Finally, the reference you posted above is somewhat accurate (in context). It describes letting the nose drop as you roll further into a bank as a means of unloading the wing to prevent a stall. I use this exact technique often - and its why I can bank 60+ degrees on the final turn without fear or danger of stall. I also know whats coming in the next few steps and am ready for it. Its called energy management for a reason. The cited passage DOES NOT describe the circus stunt that the SS shows in the video - it is the exact opposite, in fact. If you ever start flying, these things will become readilly apparent to you. I suspect you will find great embarassment then in spouting these beliefs of yours today.

Others have reccomended doing some basic reading on flying - Stick and Rudder among them. I'd add my endorsement of that and also encourage you to get an introductory flight in a little airplane. You will quickly see that a little experience and knowledge washes away the youtube nonsense.
 
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Dan Thomas

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These two little sentences fly in the face of all that is known about turning:

I was then able to point out that the airplane is not going to stall or spin with the nose well down and the elevator released completely. The skidding in the turn is far less problematic than slipping in the turn when at low altitude. We need to push the nose around and onto target prior to having to pull up to prevent impact with terrain.

If you are in a turn and release the elevator completely, you get a spiral. That's not something you want at 400 feet. And stating that "skidding is less problematic than slipping in a turn" is completely backwards.

Writing a book does not make someone an expert. These days, anyone can write a book and self-publish it, and the world is full of such erroneous publications.
 

BBerson

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The Jim Dulin book "Contact Flying" has some bizarre phrases, "hover taxi", for example.
Too confusing for a new student, I think. Apparently written as a collection of his strange alternative ideas for other instructors. (Some good ideas)
In the first chapter he advocates using the rudder for turns on final approach. But no aileron! (important detail that eki should note)
And final approach at 45 mph..... That's for advanced bush training.

I could not load beyond the second chapter.
 

Toobuilder

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I read the passage above Dan, and I gave it more credit than the writing style deserves, but unloading the wing (abandoning glideslope) is an effective way of eliminating the stall. It does rapidly set you up for an ever steepening descent however, and that is a "bill you are going to have to pay" before roundout. It's non stable and dynamic, but effective. As for the "elevator released completely" statement, I glossed over that as hyperbole. If he was serious, then yes, I agree that its bad advice. And yep, I glossed over the skid/slip advice. Good catch.
 
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