How would you demonstrate the secondary affects of roll?
I'm sorry, I didn't mean to mislead by the omission. Yaw (as pitch and roll) are certainly relative to the pilot, but is that critical here? Isn't it just as easy to watch that prominent feature on the horizon moving from 10 o'clock to 2 o'clock as it is to watch the horizon moving in the windscreen (and try mentally to decouple yaw from pitch)?
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They way to teach this in the air is to demonstrate the primary effect of aileron - that it causes the aircraft to roll.
Then teach the primary effect of rudder, in that it causes yaw. What you have to show and explain here is yaw alone - ie you need to make use of crossed controls so the student only sees the yaw and not the secondary effect of yaw (roll).
Then show the secondary effect of roll which is yaw. This is not a level turn, which is where I went wrong to start of with on FI course. Just apply aileron and let the aircraft roll and then the yaw will follow.
Then demonstrate secondary effect of yaw which is roll but simply applying rudder alone.
Then do the further effect of roll and yaw which is spiral descent.
Then teach the primary effect of rudder, in that it causes yaw. What you have to show and explain here is yaw alone - ie you need to make use of crossed controls so the student only sees the yaw and not the secondary effect of yaw (roll).
Then show the secondary effect of roll which is yaw. This is not a level turn, which is where I went wrong to start of with on FI course. Just apply aileron and let the aircraft roll and then the yaw will follow.
Then demonstrate secondary effect of yaw which is roll but simply applying rudder alone.
Then do the further effect of roll and yaw which is spiral descent.
timzsta,
Finally a post to this subject that I can agree with. Simple, straightforward and easy for the student to see and understand.
I always mention the slip/skid at the appropriate moment during the demo (with the main emphasis on the roll/yaw) but doubt all but the gifted see it. Like JulieFlyGal, in my early years instructing I had trouble "eyeballing" the detail myself. Make things too complex and the average student (let alone the lowest common denominator) will neither see, understand nor remember the point. The intracacies are best left in the ground brief with the model.
Ask the average PPL holder what happens next after aileron input alone and he probably will struggle to answer correctly.
Finally a post to this subject that I can agree with. Simple, straightforward and easy for the student to see and understand.
I always mention the slip/skid at the appropriate moment during the demo (with the main emphasis on the roll/yaw) but doubt all but the gifted see it. Like JulieFlyGal, in my early years instructing I had trouble "eyeballing" the detail myself. Make things too complex and the average student (let alone the lowest common denominator) will neither see, understand nor remember the point. The intracacies are best left in the ground brief with the model.
Ask the average PPL holder what happens next after aileron input alone and he probably will struggle to answer correctly.
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Haven't yet seen anyone say 'slow the aircraft down'.
Adverse yaw (initially) then yaw in the direction of the turn, as a secondary effect of aileron use, is a lot easier to see at 90kts, however, I would argue that one demo should show adverse yaw, then the NEXT one show secondary effect, as they are 2 different things, and need to be separated.
A demo that I do to show yaw (either adverse or secondary) as an effect of roll is roll 30deg side to side, with a pause of about 2 seconds at each side. Do this in balance. Then do it with feet on the floor. Then again in balance. The role of the rudder becomes obvious pretty quickly! This does have a dual component of adverse plus secondary though, and is more of a lesson in appropriate rudder use.
Adverse yaw (initially) then yaw in the direction of the turn, as a secondary effect of aileron use, is a lot easier to see at 90kts, however, I would argue that one demo should show adverse yaw, then the NEXT one show secondary effect, as they are 2 different things, and need to be separated.
A demo that I do to show yaw (either adverse or secondary) as an effect of roll is roll 30deg side to side, with a pause of about 2 seconds at each side. Do this in balance. Then do it with feet on the floor. Then again in balance. The role of the rudder becomes obvious pretty quickly! This does have a dual component of adverse plus secondary though, and is more of a lesson in appropriate rudder use.
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I'm not an instructor , (a PPL holder) but when i was being taughtfor my IMC, the instructor showed me this.
POint the nose at a landmark on the horizon.
Bank left (no rudder) and watch the nose momentarily turn to the right before the aircraft turns left.
Repeat the excercise again this time with a bit of left rudder at the start of the turn and this time , the nose turns left striaght away.
Basically the point of the excercise was to empahise cooridnated turns and that passengers in teh back might pick up on it and so its more comfortable to use cooridinated turns with both stick and rudder.
POint the nose at a landmark on the horizon.
Bank left (no rudder) and watch the nose momentarily turn to the right before the aircraft turns left.
Repeat the excercise again this time with a bit of left rudder at the start of the turn and this time , the nose turns left striaght away.
Basically the point of the excercise was to empahise cooridnated turns and that passengers in teh back might pick up on it and so its more comfortable to use cooridinated turns with both stick and rudder.
Adverse aileron yaw is the secondary effect of roll.
Rolling and then watching the nose drop sideways is the primary effect of gravity with a forward C of G, or if you like the secondary effect of having an angle of bank.
Roll left, aircraft yaws right. Don't let anyone tell you it will yaw left....
Pick a point on the horizon, roll left and right - nose yaws the opposite way. Practice compensating with rudder until you can keep that point on the horizon constant, then you're co-ordinating correctly.
Rolling and then watching the nose drop sideways is the primary effect of gravity with a forward C of G, or if you like the secondary effect of having an angle of bank.
Roll left, aircraft yaws right. Don't let anyone tell you it will yaw left....
Pick a point on the horizon, roll left and right - nose yaws the opposite way. Practice compensating with rudder until you can keep that point on the horizon constant, then you're co-ordinating correctly.
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Go to a safe altitude
Fly slow, as the effect of adverse yaw is higher at slow speed. (I use 60 KIAS in the C152).
Use higher than normal roll rates as the effect will also be bigger.
Tell him that you are exagerating on the control to show him the effect.
roll the aircraft at a rather positive rate to about 45º bank, and tell the student to look to the ball, it will go allmost full deflection to the other side,and the slowly comes back. Furthermore the effect is so big that most of the students will defenitely feel it. Ask him if he feels the sideways force.
Then do the same but use the rudder to keep the ball centered.
And tell him to feel the controlls while you are using the rudder, so he gets a feel of how much to use.
Watch out with students that get sick easily
Bart
Fly slow, as the effect of adverse yaw is higher at slow speed. (I use 60 KIAS in the C152).
Use higher than normal roll rates as the effect will also be bigger.
Tell him that you are exagerating on the control to show him the effect.
roll the aircraft at a rather positive rate to about 45º bank, and tell the student to look to the ball, it will go allmost full deflection to the other side,and the slowly comes back. Furthermore the effect is so big that most of the students will defenitely feel it. Ask him if he feels the sideways force.
Then do the same but use the rudder to keep the ball centered.
And tell him to feel the controlls while you are using the rudder, so he gets a feel of how much to use.
Watch out with students that get sick easily
Bart
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Dear dear. Troy, your statement "Adverse aileron yaw is the secondary effect of roll." is 100% incorrect, and if you are an instructor what you are teaching is fundamentally wrong and betrays a worrying lack of understanding. Adverse yaw has bugger all to do with roll, it is purely a result of aileron operation. Sorry if that appears insulting but if you are teaching that you really need to get it sorted out.
To all others banging on about adverse yaw, go back to post 1 and RTFQ.
To all others banging on about adverse yaw, go back to post 1 and RTFQ.
Ok, fair point: adverse yaw is the secondary effect of aileron, not of roll.
I still maintain that a slip leading to yaw is a result of angle of bank, not of roll. For example. if you're rolling from 45º left wing down to 10º left wing down (ie rolling right), the slip and therefore the yaw is still to the left throughout (aided dare I say by a bit of adverse aileron yaw also to the left).
Begging the question, is there a secondary effect of roll at all?
I still maintain that a slip leading to yaw is a result of angle of bank, not of roll. For example. if you're rolling from 45º left wing down to 10º left wing down (ie rolling right), the slip and therefore the yaw is still to the left throughout (aided dare I say by a bit of adverse aileron yaw also to the left).
Begging the question, is there a secondary effect of roll at all?
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Airbus38 - I agree with you. The way it's taught (which is the way I teach it too!) does seem a little futile. It involves deliberately mishandling the controls, and why would we do this at such an early stage of training? Much more important to demonstrate combined use aileron & rudder for adjusting bank angle - which we do in a later lesson.
As an aside - I don't say "further effect of roll". I use "further effect of bank" - because slip is a function of bank angle not of roll rate. But that doesn't contribute to the original post I'm afraid.
As an aside - I don't say "further effect of roll". I use "further effect of bank" - because slip is a function of bank angle not of roll rate. But that doesn't contribute to the original post I'm afraid.
Well, now that we've got that sorted out, and glossed over the simple matter of what happens after you apply rudder to produce a yawing motion, let's just take a step back to think about different types of aircraft.
First, I seem to remember 2 different demonstrations in the Hawk. At a high angle of attack, it was pretty much like the light aircraft case. But at a low angle of attack, the differential wing lift was not as apparent as the force produced by the fin and rudder. The increased lift acting above the roll axis caused the aircraft to roll opposite to the applied rudder. Interesting, obvious, but ultimately useless knowledge. Send for an A cat QFI.
Then there was the Jaguar. With no ailerons, just spoilers and a differential tailplane ("tailerons") it made your head hurt to think what was happening in a turn. As to the logic of destroying lift to achieve roll, when you have little lift to start with, even if you do avoid adverse yaw .... What's more, there was the spine-bending compensation of automatic rudder application at high-G high AoA.
With the Harrier, things were fairly conventional until you used reaction controls as well as aerodynamic controls. There has recently been a long discussion on the Mil thread about the dangers of going sideways, and why the roll reaction controls can blow both up and down. But how about going backwards, when the all-flying tail operates in the opposite sense (ie stick back = nose down), and opposes the reaction controls?
Sorry, I digress, but there's always something new and interesting in aviation, and you did start by asking how one thing leads to another. Always consider the consequences.
First, I seem to remember 2 different demonstrations in the Hawk. At a high angle of attack, it was pretty much like the light aircraft case. But at a low angle of attack, the differential wing lift was not as apparent as the force produced by the fin and rudder. The increased lift acting above the roll axis caused the aircraft to roll opposite to the applied rudder. Interesting, obvious, but ultimately useless knowledge. Send for an A cat QFI.
Then there was the Jaguar. With no ailerons, just spoilers and a differential tailplane ("tailerons") it made your head hurt to think what was happening in a turn. As to the logic of destroying lift to achieve roll, when you have little lift to start with, even if you do avoid adverse yaw .... What's more, there was the spine-bending compensation of automatic rudder application at high-G high AoA.
With the Harrier, things were fairly conventional until you used reaction controls as well as aerodynamic controls. There has recently been a long discussion on the Mil thread about the dangers of going sideways, and why the roll reaction controls can blow both up and down. But how about going backwards, when the all-flying tail operates in the opposite sense (ie stick back = nose down), and opposes the reaction controls?
Sorry, I digress, but there's always something new and interesting in aviation, and you did start by asking how one thing leads to another. Always consider the consequences.
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Yaw, Roll-on
Rudders on an Eagle have quite an effect at high AOA, and there are two of them. Again, the whole concept of high AOA and rudder effectiveness is meat enough for lengthy discussion.
Then there is automatic yaw damping for the more muted flight regimes and platforms, in which case if it's working, we don't give a hoot about yaw due to roll.
Bingo
Then there is automatic yaw damping for the more muted flight regimes and platforms, in which case if it's working, we don't give a hoot about yaw due to roll.
Bingo
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Further effect of aileron
Yaw, pri eff of rudder, is a sideways movement of the nose towards a wing-tip. For further eff of ail, apply small amount of ail and KEEP IT APPLIED. As the a/c rolls, the nose drops below the horizon. When banked, this downwards movement is towards the wingtip is therefore YAW. QED! Important, warn the student that you will roll to around 45deg bank, but don't worry, it's brief and not at all uncomfortable.
Also only apply small ail, otherwise you won't have time to get the words in without reaching worrying angle of bank.
Also only apply small ail, otherwise you won't have time to get the words in without reaching worrying angle of bank.
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I was under the impression that the nose drop due to bank was because you have inclined the lift vector from the vertical and so get an apparant reduction in lift, therefore nose drop...
Nick
Nick
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"further" effect of rudder
Having demonstated the further effect is roll, bring in the "so what" factor, or "need to know" i.e. "Why does this matter?" The only time the further effect is used in practical flying is in the negative sense, as part of stall recovery when a wing has dropped. So here we have
CC forward - to unstall the wings
Full power
Ailerons neutral - because using them WHEN STALLED can aggravate
wing drop
Rudder - to prevent further wing drop (i.e. yaw/roll)
THEN when wings are unstalled, roll wings level (lots of ail and rudder to balance) and pull out.
Unless you include this, the further effect demo remains academic and
a waste of time. Hope this helps. John Gratton
CC forward - to unstall the wings
Full power
Ailerons neutral - because using them WHEN STALLED can aggravate
wing drop
Rudder - to prevent further wing drop (i.e. yaw/roll)
THEN when wings are unstalled, roll wings level (lots of ail and rudder to balance) and pull out.
Unless you include this, the further effect demo remains academic and
a waste of time. Hope this helps. John Gratton
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Hey, I'm a PPL student, at the moment I'm reading Principles of Flight and have just found a way of remembering (or demostrating for instructors) the secondary effects of roll and yaw...
Basically all you need to do is move your head to one side, if you yaw your head to the right your neck bends in a way that rolls your head to the left. If you roll your head to the right then you will see your chin yaws to the left.
I hope this helps, it's certainly worked for me. If it's wrong please let me know as I may have misunderstood something, either that or I have a major problems with my neck!
Basically all you need to do is move your head to one side, if you yaw your head to the right your neck bends in a way that rolls your head to the left. If you roll your head to the right then you will see your chin yaws to the left.
I hope this helps, it's certainly worked for me. If it's wrong please let me know as I may have misunderstood something, either that or I have a major problems with my neck!
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The secondary effect of yaw (roll) can be of great use to students when they move onto navigation.
I defy almost any student to keep the aircraft straight & level whilst holding the control wheel and looking down at their PLOG or chart. Most will involuntarily put pressure on one side of the column as they look down, resulting in a roll (usually to the left if they are using their left hand).
I teach students to ensure the aircraft is trimmed for straight and level, and then take their hand off the control column but leave their feet on the rudder pedals. The aircraft is inherently stable and should not deviate significantly during the time it takes to fill in a PLOG, plan a diversion or consult a chart. Any slight deviations can be corrected using the rudder to use the secondary effect of yaw to 'pick up' a downgoing wing. Most students find this works really well. In smooth air, some can fly for up to 10 mins without having to use the control column.
I defy almost any student to keep the aircraft straight & level whilst holding the control wheel and looking down at their PLOG or chart. Most will involuntarily put pressure on one side of the column as they look down, resulting in a roll (usually to the left if they are using their left hand).
I teach students to ensure the aircraft is trimmed for straight and level, and then take their hand off the control column but leave their feet on the rudder pedals. The aircraft is inherently stable and should not deviate significantly during the time it takes to fill in a PLOG, plan a diversion or consult a chart. Any slight deviations can be corrected using the rudder to use the secondary effect of yaw to 'pick up' a downgoing wing. Most students find this works really well. In smooth air, some can fly for up to 10 mins without having to use the control column.
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I have only skimmed through this so my apologies if I repeat a couple things. I just stumbled upon this post while preparing an advanced aerodynamics lesson for my students and realized one thing, there is allot of confusion between rudders and ailerons.
First I want to start by saying; it is called proverse roll and adverse yaw. It is not and has never really been secondary effect and in today’s aircraft effects from aileron yaw in the wind is drastically reduced. These are all just fancy new terms to make it sound easier to understand which does nothing but confuse those that actually understand it. If you want proof go turn your ailerons to full deflection in either direction, note the aileron deflects up more than down (you will understand why soon). So my advice is to ignore even discussing this with your student as its effects are minimal.
Adverse yaw (induced drag)
So now how does adverse yaw work? Well you turn the aircraft lets say to the right what happens? The left wing rises and the right wing falls, the rising (left) wing is now producing significantly more lift than the falling right wing. We have certainly taught our students by now that induced drag is drag created by lift (if not this would be a great time). So the left wing now producing more lift and drag will get pulled backwards by that drag causing the nose to rise to the left showing that you need right rudder to correct.
To answer the first question from the paragraph above, we have adverse yaw because of uneven lift causing uneven drag on each wing. A model with strings representing forces attached to the wings gives a great on the ground visual before the flight demonstration.
Adverse yaw (parasite drag)
Now you are in the turn, take your feet off the rudders and increase that turn (cfi do this) to 45-60 degrees and look at the inclometer (the ball). Notice it is still deflected to the to the right (still using the right turn from above) indicating you need right rudder. You might think, well I already handled the yaw do to rudder so why is my aircraft yawing again.
To answer this go outside have your student grab onto a near by poll (telephone poll, lamp post, etc) and hold one arm out and walk around the poll. Explain how the outside arm travels a farther distance than the inside arm and must therefore go faster. Now relate this to your aircraft in a turn and how parasite drag on the higher (left) wing will be greater because it is traveling faster than the right wing. Therefore parasite drag is the reason for needing continuous rudder through turns (especially steeper turns as the steeper the turn the greater the differential).
This here is also why the ailerons are deflected more up than down. By deflecting more up the aileron on the inside wing of a turn will create more drag attempting to offset adverse yaw effects.
Proverse roll
You push on that right rudder and the nose shifts right then seconds later the right wing drops and you start turning right. This happens simply because of the right wing being on the inside of a now skidding turn (great way to demonstrate slip and skid, skid is like what you see driving a car to explain it on a level your student might get) is moving slower then the left wing on the outside. So the faster moving left wing generates more lift and you are in a turn.
Conclusion of roll/yaw
As far as those two go that is all I would think to discuss with a new student a few lessons in. I also introduce this to my students starting at lesson 1; there is no better time to learn how and why your airplane does what it does than the first lesson. Too many people are making it through their private without knowing thoroughly how their aircraft flies.
Restatement of previous thoughts
As far as the names of them, if you want to use obscure names that are not recognized in the engineering world, fine. But the engineering side is much easier to teach than any of these obscure new and old names coming out. Teach the 3 forces, not 4, lift and drag are byproducts of aerodynamic force acting off the aerodynamic center, teach that.
We are taught in our CFI course to teach things right first because of primacy. So go study up on stability and control, everything in relation to aerodynamic force/center, center of pressure, coupled effects (dutch roll spiral divergence primarily), and learn how they work not only by themselves but together.
Why I feel this way - example
Draw on a piece of paper an airplane put a circle just behind the wing for cg and draw a line down for weight, then a circle just behind that (open circle) for aerodynamic center and draw a line diagonally back for aerodynamic force, and finally on the tail draw another circle and arrow pointing down for the tail down force. From this you can explain why the tail exhibits a down force, cause if it didn't the plane would just flip end over end all day. *Edited out missinformation: A far aft cg will not cause an end over end rotation. My apologies for any confusion this may have caused.* You can show how moving the cg aft decreases the work needed to be done by the tail down force allowing the aircraft to fly at a lower angle of attack which shows why it gets better performance and lower stall speeds at an aft cg. Hopefully I have made my point, learn this stuff and teach it, which is basic enough to teach to a freshman in high school, if their younger than that find a sea saw and I bet you can teach them.
Hopefully this wasn’t too lengthy for everyone if you want to know more please ask there are ways to break down every component of aerodynamics so that it can be taught even to someone who knows nothing about aircraft. Also here is just a starting point for what I think every instructor should know:
Click here:http://www.mypilotforum.com/phpBB3/d...file.php?id=53 for a link to download a power point presentation I did on aerodynamics. Obviously you can’t see all the background work I prepared to demonstrate all of it, but at least you can take it and use it as a starting point of what you should know about an aircraft. That is my own personal site all information is safe but please virus scan anyways as you should do with anything you download.
Good Luck
~Brian
First I want to start by saying; it is called proverse roll and adverse yaw. It is not and has never really been secondary effect and in today’s aircraft effects from aileron yaw in the wind is drastically reduced. These are all just fancy new terms to make it sound easier to understand which does nothing but confuse those that actually understand it. If you want proof go turn your ailerons to full deflection in either direction, note the aileron deflects up more than down (you will understand why soon). So my advice is to ignore even discussing this with your student as its effects are minimal.
Adverse yaw (induced drag)
So now how does adverse yaw work? Well you turn the aircraft lets say to the right what happens? The left wing rises and the right wing falls, the rising (left) wing is now producing significantly more lift than the falling right wing. We have certainly taught our students by now that induced drag is drag created by lift (if not this would be a great time). So the left wing now producing more lift and drag will get pulled backwards by that drag causing the nose to rise to the left showing that you need right rudder to correct.
To answer the first question from the paragraph above, we have adverse yaw because of uneven lift causing uneven drag on each wing. A model with strings representing forces attached to the wings gives a great on the ground visual before the flight demonstration.
Adverse yaw (parasite drag)
Now you are in the turn, take your feet off the rudders and increase that turn (cfi do this) to 45-60 degrees and look at the inclometer (the ball). Notice it is still deflected to the to the right (still using the right turn from above) indicating you need right rudder. You might think, well I already handled the yaw do to rudder so why is my aircraft yawing again.
To answer this go outside have your student grab onto a near by poll (telephone poll, lamp post, etc) and hold one arm out and walk around the poll. Explain how the outside arm travels a farther distance than the inside arm and must therefore go faster. Now relate this to your aircraft in a turn and how parasite drag on the higher (left) wing will be greater because it is traveling faster than the right wing. Therefore parasite drag is the reason for needing continuous rudder through turns (especially steeper turns as the steeper the turn the greater the differential).
This here is also why the ailerons are deflected more up than down. By deflecting more up the aileron on the inside wing of a turn will create more drag attempting to offset adverse yaw effects.
Proverse roll
You push on that right rudder and the nose shifts right then seconds later the right wing drops and you start turning right. This happens simply because of the right wing being on the inside of a now skidding turn (great way to demonstrate slip and skid, skid is like what you see driving a car to explain it on a level your student might get) is moving slower then the left wing on the outside. So the faster moving left wing generates more lift and you are in a turn.
Conclusion of roll/yaw
As far as those two go that is all I would think to discuss with a new student a few lessons in. I also introduce this to my students starting at lesson 1; there is no better time to learn how and why your airplane does what it does than the first lesson. Too many people are making it through their private without knowing thoroughly how their aircraft flies.
Restatement of previous thoughts
As far as the names of them, if you want to use obscure names that are not recognized in the engineering world, fine. But the engineering side is much easier to teach than any of these obscure new and old names coming out. Teach the 3 forces, not 4, lift and drag are byproducts of aerodynamic force acting off the aerodynamic center, teach that.
We are taught in our CFI course to teach things right first because of primacy. So go study up on stability and control, everything in relation to aerodynamic force/center, center of pressure, coupled effects (dutch roll spiral divergence primarily), and learn how they work not only by themselves but together.
Why I feel this way - example
Draw on a piece of paper an airplane put a circle just behind the wing for cg and draw a line down for weight, then a circle just behind that (open circle) for aerodynamic center and draw a line diagonally back for aerodynamic force, and finally on the tail draw another circle and arrow pointing down for the tail down force. From this you can explain why the tail exhibits a down force, cause if it didn't the plane would just flip end over end all day. *Edited out missinformation: A far aft cg will not cause an end over end rotation. My apologies for any confusion this may have caused.* You can show how moving the cg aft decreases the work needed to be done by the tail down force allowing the aircraft to fly at a lower angle of attack which shows why it gets better performance and lower stall speeds at an aft cg. Hopefully I have made my point, learn this stuff and teach it, which is basic enough to teach to a freshman in high school, if their younger than that find a sea saw and I bet you can teach them.
Hopefully this wasn’t too lengthy for everyone if you want to know more please ask there are ways to break down every component of aerodynamics so that it can be taught even to someone who knows nothing about aircraft. Also here is just a starting point for what I think every instructor should know:
Click here:http://www.mypilotforum.com/phpBB3/d...file.php?id=53 for a link to download a power point presentation I did on aerodynamics. Obviously you can’t see all the background work I prepared to demonstrate all of it, but at least you can take it and use it as a starting point of what you should know about an aircraft. That is my own personal site all information is safe but please virus scan anyways as you should do with anything you download.
Good Luck
~Brian
Last edited by shdw; 18th Mar 2009 at 04:21.
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Surely the aim of the lesson (in JAA land the very first lesson given after famil?) is to demonstrate that any application of aileron requires balancing with rudder? The way I was taught to demonstrate this was to pick a feature, then roll left and right in an 'oscillatory' manner. The nose would weave all over the place. Repeat by applying rudder in concert with aileron to keep the nose in the same place. From a student PPL's perspective we can argue about the finer points of adverse yaw vs. slip but all we are trying to achieve is a student who can recognise the need to maintain balanced flight.
Am I being too simplistic?
Am I being too simplistic?