basic aerodynamics
#227

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From: Deland,
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Actually, too much can hurt, in that it will tend to make the ailerons less responsive. That goes for high or low wing planes. If you put the wingtips at approximately the same height as the CG( somewhere in the middle of the fuse - say around the thrust line), that'll be at least neutral in roll.
#229

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From: Deland,
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[:'(]JOHN ,THIS GUY WANTS TO KEEP IT SIMPLE.. HE IS ASKING A BASIC QUISTION..
[:'(]JOHN ,THIS GUY WANTS TO KEEP IT SIMPLE.. HE IS ASKING A BASIC QUISTION..
A) Middle of the fuse
or
B) The thrust line.
Also, check the pic I've attached. It's a front view of a P-51 with a line from tip to tip that shows the relation to the thrust line. If you want aerobatic, this is how. If you want tamer, add more dihedral.
If he really wanted to find the vertical CG, it would be easy enough. Mark the fuse with a vertical line at the horizontal (normal) cg location. Then let the plane hang vertical from the prop crankshaft. I line straight down from the crank - like a plumb bob - will cross the vertical CG line at the vertical location of the CG (horizontal too).
Seems that some guys get into RC partially to talk out their behinds instead of actually learning something. And then start with the sniping when someone suggests a better way. Hey Crankypants, I think you should swap usernames with this guy.
#230

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OH I SEE. SO A HIGH WING PLANE WOULD USE ANHEDRAL?? THIS WOULD PUT THE TIPS AT ENGINE CENTER LINE>>>>???? "NOT"..ITS JUST NOT THE CRITICAL..TLAR WORKS JUST FINE..FORMULAS ARE OK ,BUT NOT THE FINAL WORD.. IF THEY WERE,THERE WOULD BE NO NEED FOR WIND TUNNELS, OR TEST PILOTS.A BUICK TRUNK LID WILL FLY ,IF YOU MOVE IT FAST ENOUGH.FOMULAS ARE JOB SECURETY FOR GUYS WHO CANT BUILD, OR FLY.. RD
#231
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From: Kent,
WA
OK thanks for both your inputs on dihedral. I am absorbing all the information I can about this and other topics. I've read this entire thread. and I get both sides of the whole cg debate. As a new builder of RC planes, it really helps me to understand the thinking behind all this. After reading 8 pages of this thread, I've learned at least 2 things. 1.) There are rules about aerodynamics. 2.) These rules are not set in stone and its important to think outside the box or "wing it".(sorry I could not resist)
So thank you Dick Hanson and thank you to all that opposed him.
What, as a new builder, I was expecting to read in the aerodynamics thread were things like: airfoils. body designs, wing shapes etc. I guess I got some of that. I just don't think I need to wade through 8 pages of "I'm right, no I'm right!" to get it.
I think this thread would be more useful to new builders if we could see more testimonials and proven information that has been implemented on real RC planes. Like what has worked, what has not worked, why, and what you would do differently next time.
Rapptor tells me that 2 or 3 degree dihedral has worked for him. Johng tells me that 2 much will hurt ( i don't want my ailerons to be less responsive) and gave me an example of lining up with the centerline . both posts are useful to me. More posts would be even better.
thanks
cp
So thank you Dick Hanson and thank you to all that opposed him.
What, as a new builder, I was expecting to read in the aerodynamics thread were things like: airfoils. body designs, wing shapes etc. I guess I got some of that. I just don't think I need to wade through 8 pages of "I'm right, no I'm right!" to get it.
I think this thread would be more useful to new builders if we could see more testimonials and proven information that has been implemented on real RC planes. Like what has worked, what has not worked, why, and what you would do differently next time.
Rapptor tells me that 2 or 3 degree dihedral has worked for him. Johng tells me that 2 much will hurt ( i don't want my ailerons to be less responsive) and gave me an example of lining up with the centerline . both posts are useful to me. More posts would be even better.
thanks
cp
#233
Just a suggestion.
I would guess that you are building this model as a relaxing pastime.
So try this:
get some poster board or scrap stiff foam -or buy a little glider like the ones they used to sell for a dime.
Learn to toss it and see what happens when the wings are bent level-up-down.
The "stability" you are after , comes from the wingdihedral presenting a difference in drag, as the rudder steers it left or right .
Use the model held in front of you and looking at the nose straight on -you will see the underside of the left or right wing as you imitate the rudder steering it.
You need a fair bit if the rudder does all the corrections.
You need very little if the ailerons are used .
Obviously if more stability goes along with more dihedral--then the stability will fight a counter command from the ailerons.
That is a very basic view of what's happening and as was mentioned, it takes very little dihedral angle to do the job if ailerons are also used to do roll positioning.
I started building controline in 49-and freeflight shortly afterward.
One type needed no roll stability to speak of and the other needed it defined perfectly.
So sketch away and if it looks right -it likely will be flyable .
The enemy of all aircraft is weight .
The horse pucky about "heavy flys more scale like " is not true.
Your real task on a scratch design, is keeping it both light and strong.
That is the job they pay people to do at the aircraft factories.
No one was ever hired to make em weak and heavy-----
tho some do--
I would guess that you are building this model as a relaxing pastime.
So try this:
get some poster board or scrap stiff foam -or buy a little glider like the ones they used to sell for a dime.
Learn to toss it and see what happens when the wings are bent level-up-down.
The "stability" you are after , comes from the wingdihedral presenting a difference in drag, as the rudder steers it left or right .
Use the model held in front of you and looking at the nose straight on -you will see the underside of the left or right wing as you imitate the rudder steering it.
You need a fair bit if the rudder does all the corrections.
You need very little if the ailerons are used .
Obviously if more stability goes along with more dihedral--then the stability will fight a counter command from the ailerons.
That is a very basic view of what's happening and as was mentioned, it takes very little dihedral angle to do the job if ailerons are also used to do roll positioning.
I started building controline in 49-and freeflight shortly afterward.
One type needed no roll stability to speak of and the other needed it defined perfectly.
So sketch away and if it looks right -it likely will be flyable .
The enemy of all aircraft is weight .
The horse pucky about "heavy flys more scale like " is not true.
Your real task on a scratch design, is keeping it both light and strong.
That is the job they pay people to do at the aircraft factories.
No one was ever hired to make em weak and heavy-----
tho some do--
#234

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From: Deland,
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OH I SEE. SO A HIGH WING PLANE WOULD USE ANHEDRAL?? THIS WOULD PUT THE TIPS AT ENGINE CENTER LINE>>>>???? "NOT
OH I SEE. SO A HIGH WING PLANE WOULD USE ANHEDRAL?? THIS WOULD PUT THE TIPS AT ENGINE CENTER LINE>>>>???? "NOT


#235
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From: Kent,
WA
Wow! The legendary Dick Hansen replied. Thank you for your suggestion. I kinda evolved into building planes from those little radio shack rc cars. As I was getting bored with them I started taking them apart and wondered if I could use all those micro servos to make one of those 99cent gliders fly. Several proto types later (about 10 gliders) I was having no luck. Then I thought, what if I built one of those guillows 500 series gliders and use that as the air frame. As I was building it and doing research on another rc group (sorry) I concluded that to make that fly I was going to need to spend some real dough on real rc gear. The people I was talking to about the build had successfully converted and flown these planes.
Now keep in mind, at that point I had no real rc flying experience. They suggested shelving the project until I had some flight exp. I took there advice and bought an electric plane. I’ve been crashing that plane for several months now.
As usual I like to get in over my head, so I’m thinking about building a bigger plane for that ½ a contest that starts in Jan. I’m going to work with a friend of mine who has exp building and flying gas planes. I figured I’ll have him fly it, that way if the design is totally awful, his exp would keep it in the air for longer than 10 seconds.
Oh yea dihedral. What I’ve been told, is that dihedral helps a rudder only plane turn and recover from turns better. (more stable). Now if you have ailerons on you wing would dihedral be that important? My thought on it would be no. I’ve never flown a plane with ailerons so that’s why I’m asking all of you.
Oh and Dick Hansen, do the 4 basic rules apply to dihedral as well as cg?
1-If the plane is extremely light - the dihedral does not matter
2- If the plane is too heavy - it still don't matter.
3- If you got enuf power - nuthin else matters .
4-If you ain't got enough power - same thing.
Not to start another 8 pages of trouble or anything.
Thanks
Cp.
Now keep in mind, at that point I had no real rc flying experience. They suggested shelving the project until I had some flight exp. I took there advice and bought an electric plane. I’ve been crashing that plane for several months now.
As usual I like to get in over my head, so I’m thinking about building a bigger plane for that ½ a contest that starts in Jan. I’m going to work with a friend of mine who has exp building and flying gas planes. I figured I’ll have him fly it, that way if the design is totally awful, his exp would keep it in the air for longer than 10 seconds.
Oh yea dihedral. What I’ve been told, is that dihedral helps a rudder only plane turn and recover from turns better. (more stable). Now if you have ailerons on you wing would dihedral be that important? My thought on it would be no. I’ve never flown a plane with ailerons so that’s why I’m asking all of you.
Oh and Dick Hansen, do the 4 basic rules apply to dihedral as well as cg?
1-If the plane is extremely light - the dihedral does not matter
2- If the plane is too heavy - it still don't matter.
3- If you got enuf power - nuthin else matters .
4-If you ain't got enough power - same thing.
Not to start another 8 pages of trouble or anything.
Thanks
Cp.
#236

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CP. NO MATTER HOW STABLE YOUR PLANE IS,, "YOU" STILL HAVE TO FLY IT!!! ALL THE THINGS THAT ARE SUGGESTED HERE, ARE TO HELP YOU FLY, NOT MAKE IT FLY ITSELF.. BUILDING IT "LIGHTER" ,WILL HAVE MORE BENEFIT THAN DIHEDRAL.. IF YOU FEEL THAT DIHEDRAL WILL LOWER AIRLERON EFFECTIVENESS,MAKE THEM LARGER AND MORE THROW.. RD
#238
well - sorta -but dihedral is very friendly - and weighs nothing- so do it .
My basic rules are simply to make you think.
If it is too heavy -it won't fly - so why bother with CG
If it weighs zero or almost zero and has very low wing loading - you can take extreme liberties with CG- we have been back past 50% of MAC- and -they are still flyable - you gotta watch em -but they still fly
enough power to overcome weight -easy one -it will fly no matter how badly the designed is bungled.
If not enough power to leave the ground - none of the other stuf matters.
My basic rules are simply to make you think.
If it is too heavy -it won't fly - so why bother with CG
If it weighs zero or almost zero and has very low wing loading - you can take extreme liberties with CG- we have been back past 50% of MAC- and -they are still flyable - you gotta watch em -but they still fly
enough power to overcome weight -easy one -it will fly no matter how badly the designed is bungled.
If not enough power to leave the ground - none of the other stuf matters.
#239
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From: Kent,
WA
clarification here from cp.
I will fly the plane that I build. My friend will help with the initial test flight. I'm sure he will be training me. He has more exp than I do with flying rc planes. I'd rather have the fate of my plane in the hands of someone who has many years of flight under his belt verses my 6 months. If the plane is unstable, a person with more exp might have a better chance of landing the plane in a safer manner than I. Then he can give me sugestions on cg etc to make the plane more stable for me when I fly it solo.
Dick Hansen I understand what you are saying about cg. I threw the 4 basic rules for dihedral in there as a bad joke.
I'll keep you guys posted when I start building the plane in Jan. I'm sure I'll have many more questions then.
Thanks
cp
I will fly the plane that I build. My friend will help with the initial test flight. I'm sure he will be training me. He has more exp than I do with flying rc planes. I'd rather have the fate of my plane in the hands of someone who has many years of flight under his belt verses my 6 months. If the plane is unstable, a person with more exp might have a better chance of landing the plane in a safer manner than I. Then he can give me sugestions on cg etc to make the plane more stable for me when I fly it solo.
Dick Hansen I understand what you are saying about cg. I threw the 4 basic rules for dihedral in there as a bad joke.
I'll keep you guys posted when I start building the plane in Jan. I'm sure I'll have many more questions then.
Thanks
cp
#241
Dihedral determines lateral stability. So what is lateral stability and why and when would you want it?
Lateral stability is the tendency to roll away from a sideslip. A sideslip is when the airplane isn’t moving directly forward, but also a little to one side. When an airplane encounters a gust that causes one wing to drop, it will sideslip toward the low wing. If it has dihedral, it will roll away from the slip raising the wing back up. This tends to keep the wings level without input from the pilot.
When rudder only is applied, the airplane sideslips opposite the applied rudder. If it has dihedral it will roll in the same direction as the applied rudder (away from the sideslip). This is how an airplane is made to roll into a turn with rudder only.
When an airplane is flown in “knife edge†flight it is in a continuous sideslip and if it is laterally stable it will continue to try to roll out, and that tendency must be resisted with aileron. Lateral stability in this cause is often referred to as “roll couplingâ€.
An airplane that has lateral stability when upright due to dihedral becomes laterally unstable when flying inverted.
For a beginning pilot and/or for just relaxing easy flights, some lateral stability is desired. For better aerobatic performance, a minimum of lateral stability is desired.
Dihedral is the usual way of achieving lateral stability. When the wing is mounted above the fuselage, dihedral effect is enhanced, so that there is some lateral stability even with a flat wing. If the wing is mounted below the fuselage, dihedral effect is reduced so that a flat wing may have no lateral stability or even be slightly unstable. This is why low wing airplanes are usually built with more dihedral than high wing airplanes.
Another way to provide lateral stability is sweepback. A low wing airplane with a flat wing and some sweepback may be laterally stable. An advantage to this configuration is that the airplane is also stable when inverted. (This is one reason many pattern models have low mounted swept wings.)
The amount of dihedral is determined by the purpose of the airplane, and for experienced flyers is largely a matter of personal preference. For a low wing training or rudder only machine, Johng’s suggestion is a good starting place as is 2-3 degrees for a high wing model.
If you fly coordinating aileron and rudder (to produce a pure rolling motion), dihedral doesn’t have much effect on roll rate. (It doesn’t really effect roll damping,) However if you fly banking the wings with ailerons only, the resulting adverse yaw (which is actually a sideslip) will cause an opposing moment that will reduce aileron effectiveness.
Lateral stability is the tendency to roll away from a sideslip. A sideslip is when the airplane isn’t moving directly forward, but also a little to one side. When an airplane encounters a gust that causes one wing to drop, it will sideslip toward the low wing. If it has dihedral, it will roll away from the slip raising the wing back up. This tends to keep the wings level without input from the pilot.
When rudder only is applied, the airplane sideslips opposite the applied rudder. If it has dihedral it will roll in the same direction as the applied rudder (away from the sideslip). This is how an airplane is made to roll into a turn with rudder only.
When an airplane is flown in “knife edge†flight it is in a continuous sideslip and if it is laterally stable it will continue to try to roll out, and that tendency must be resisted with aileron. Lateral stability in this cause is often referred to as “roll couplingâ€.
An airplane that has lateral stability when upright due to dihedral becomes laterally unstable when flying inverted.
For a beginning pilot and/or for just relaxing easy flights, some lateral stability is desired. For better aerobatic performance, a minimum of lateral stability is desired.
Dihedral is the usual way of achieving lateral stability. When the wing is mounted above the fuselage, dihedral effect is enhanced, so that there is some lateral stability even with a flat wing. If the wing is mounted below the fuselage, dihedral effect is reduced so that a flat wing may have no lateral stability or even be slightly unstable. This is why low wing airplanes are usually built with more dihedral than high wing airplanes.
Another way to provide lateral stability is sweepback. A low wing airplane with a flat wing and some sweepback may be laterally stable. An advantage to this configuration is that the airplane is also stable when inverted. (This is one reason many pattern models have low mounted swept wings.)
The amount of dihedral is determined by the purpose of the airplane, and for experienced flyers is largely a matter of personal preference. For a low wing training or rudder only machine, Johng’s suggestion is a good starting place as is 2-3 degrees for a high wing model.
If you fly coordinating aileron and rudder (to produce a pure rolling motion), dihedral doesn’t have much effect on roll rate. (It doesn’t really effect roll damping,) However if you fly banking the wings with ailerons only, the resulting adverse yaw (which is actually a sideslip) will cause an opposing moment that will reduce aileron effectiveness.
#242
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From: Chesterland, OH
Oh lordy, what am I doing to myself...but I gotta get into this one.
I started reading the thread 8 or 9 pages ago and decided to jump to the end...and the beat goies on! CG is still a hot subject.
I would have to side with the group that says, CG DOES matter. The couple of points, 'if it weighs nothing, CG don't matter', while true, is not a realistic scenario. Unless you are able to conjur up some serious magic. Not being realistic, I would have to file it under the 'nonsense' heading. 'If it don't have enough power to get off the ground, again, it (CG) don't matter'. See the previous sentence.
When we get into the other stuff, very light, I am of the opinion, as are most people with a real life background in aerodynamics, that CG ALWAYS matters.
There is no question that an extremely forward or aft CG can be compensated for but that does not mean it is flying well. In many cases, an aft CG can be very useful. For instance, in aircraft being used for aerobatics an aft CG, say 35% of MAC (mean aerodynaic chord), allows maneuvers that would not be possible with a more forward CG. But place that CG in that same airplane at 100% of MAC and I suggest it would simply be unable to fly. At best, given enough runway and speed, it attain enough of a nose up attitude to flop into the ground inverted.
Conversely place the CG at 0% MAC, it'd be a ground loving missle.
Given sufficient power and angle of attack, a CG at 0% could be made to fly but a positive angle of attack effectively moves the CG rearward. And 'sufficient power' most likely would entail a power to weight ratio of 1:1 or better.
Yep, the Buick trunk lid, along with barn doors an other items, will fly with enough power. But I prefer to make the distinction between 'flying' and 'flying well'.
There used to be, and may still be out there yet, the idea that tail heavy aircraft fly faster at the same power setting and weight since when trimming nose down to compensate for the aft CG, the horizontal stab is now generating lift and more engine power can be converted to speed. This may be why so many unlimited racers in the 40's and 50's experienced low altitude accelerated stall/snaps when rounding the pylons. Easy to overcontrol the pitch.
Say what you will about thinking outside the box, expanding your horizons, seeing things in a new light, etc., but I will continue to advocate a good flying airplane and CG control is one of the major issues to that end.
I do enjoy the the electric foamies with very light wing loading and if you are flying in a confined space and hanging on the prop with an angle of attack of +45 degrees, I'll agree the CG is of little consequence. But then I would suggest you are not really 'flying'.
That's my story and I'm stickin' to it!
Joe
AMA L166
I started reading the thread 8 or 9 pages ago and decided to jump to the end...and the beat goies on! CG is still a hot subject.
I would have to side with the group that says, CG DOES matter. The couple of points, 'if it weighs nothing, CG don't matter', while true, is not a realistic scenario. Unless you are able to conjur up some serious magic. Not being realistic, I would have to file it under the 'nonsense' heading. 'If it don't have enough power to get off the ground, again, it (CG) don't matter'. See the previous sentence.
When we get into the other stuff, very light, I am of the opinion, as are most people with a real life background in aerodynamics, that CG ALWAYS matters.
There is no question that an extremely forward or aft CG can be compensated for but that does not mean it is flying well. In many cases, an aft CG can be very useful. For instance, in aircraft being used for aerobatics an aft CG, say 35% of MAC (mean aerodynaic chord), allows maneuvers that would not be possible with a more forward CG. But place that CG in that same airplane at 100% of MAC and I suggest it would simply be unable to fly. At best, given enough runway and speed, it attain enough of a nose up attitude to flop into the ground inverted.
Conversely place the CG at 0% MAC, it'd be a ground loving missle.
Given sufficient power and angle of attack, a CG at 0% could be made to fly but a positive angle of attack effectively moves the CG rearward. And 'sufficient power' most likely would entail a power to weight ratio of 1:1 or better.
Yep, the Buick trunk lid, along with barn doors an other items, will fly with enough power. But I prefer to make the distinction between 'flying' and 'flying well'.
There used to be, and may still be out there yet, the idea that tail heavy aircraft fly faster at the same power setting and weight since when trimming nose down to compensate for the aft CG, the horizontal stab is now generating lift and more engine power can be converted to speed. This may be why so many unlimited racers in the 40's and 50's experienced low altitude accelerated stall/snaps when rounding the pylons. Easy to overcontrol the pitch.
Say what you will about thinking outside the box, expanding your horizons, seeing things in a new light, etc., but I will continue to advocate a good flying airplane and CG control is one of the major issues to that end.
I do enjoy the the electric foamies with very light wing loading and if you are flying in a confined space and hanging on the prop with an angle of attack of +45 degrees, I'll agree the CG is of little consequence. But then I would suggest you are not really 'flying'.
That's my story and I'm stickin' to it!
Joe
AMA L166
#243
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From: Binangonan, PHILIPPINES
Hello, I've just registered today in this site, the RCU. 
Anyway I have seen an unfinished site: http://www.rcaeronautics4dummies.fil...rianrecipe.com
If you like to have a fun time or laugh at the site, just take a peek.

Anyway I have seen an unfinished site: http://www.rcaeronautics4dummies.fil...rianrecipe.com
If you like to have a fun time or laugh at the site, just take a peek.
#244
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From: antwerp, BELGIUM
Indeed,even a brick can `fly` if you bolt enough power on it...
take the purest form of flying: gliding. here there is no thrust, so no power to weigth ratio...those planes are very sensitive with respect to CG, if they want to fly efficient
take the purest form of flying: gliding. here there is no thrust, so no power to weigth ratio...those planes are very sensitive with respect to CG, if they want to fly efficient
#245
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From: KENILWORTH, UNITED KINGDOM
Hey Dick, If C of G does not really matter then why do Airlines have a load control chart to work out C of G, taking in weights pax/luggage /fuel etc? on every flight... or am I missing something here after 30 years in mil and civil aviation? (Oh and 50 years of model aircraft construction? When most of that time modelling was modelling and not gluing polystyrene together)!
#247
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From: KuressaareSaaremaa, ESTONIA
I read Anderson book about anhedral in big airplanes- there was nothing about wingtips and CG, instead, as a jet powered cargo plane has a swept back wing, the anhedral is used to decrease lateral stability. There is not much, if any, anhedral in prop driven high wing planes, which usually doesn't have swept back wings. Anhedral is to cancel the effect of swept back wing on lateral stability, as LouW excellently described above.
And position of CG in respect to aerodynamic center (or neutral point) does matter- Dick should fly those extreme planes with pusher prop to prove opposite!
Normal, orthodox, designed in the box planes have no problems of using pusher props. Being heavy and without excess of power. And they still fly.
And position of CG in respect to aerodynamic center (or neutral point) does matter- Dick should fly those extreme planes with pusher prop to prove opposite!
Normal, orthodox, designed in the box planes have no problems of using pusher props. Being heavy and without excess of power. And they still fly.
#248
prove?
prove what.
If you don't build and fly the extreme airplanes -you really don't uderstand what I am talking about.
Don't let a formal education get in the way of learning something.
I had a full , formal music education--but I was still able to play jazz/country/ folk etc..
Just because you can't find something in a textbook does not mean it does not exist .
prove what.
If you don't build and fly the extreme airplanes -you really don't uderstand what I am talking about.
Don't let a formal education get in the way of learning something.
I had a full , formal music education--but I was still able to play jazz/country/ folk etc..
Just because you can't find something in a textbook does not mean it does not exist .
#249
I wonder how many of Newtons peers thought he was a little off his rocker? Did the Wright brothers have a formal education in aerodynamics? How many "rules", or bones, did they break with their designs? By reading this thread I have learned that no matter how well your plane could fly, or how well your airfoil is engineered there is this nasty little thing called CG. At my field there are four of us who fly Tiger 60's on a regular basis. We all hate each others planes. None of them handle like they should, except mine. I have my CG set perfectly. Of course in the real world each of these planes have the correct CG for their respective pilots' tastes as none of these guys would tolerate a plane that did not fly well. Didn't some expert state that Windows would never catch on? Innovators are all idiots to someone, but the ones that are right can change our perception of reality. If I put a cat in a box and walk away, will it still be there the next day? (edited to make a very good theory more PC) How much of an effect does proportional (a bigger plane will have a proportionally thicker wing, and vise versa) wing thickness have on a plane's ability to perform well in precision aerobatics? What happens when I narrow it, or thicken it?
#250
I forgot to mention the Katana I have on the build list that has plans for both a tapered and constant cord wing. Fully symmetrical wing that has a leading to trailing edge taper from fuse(root?) to tip without either of them being 90 degrees from the fuse. I am really a beginner, 1 year flying, four planes and one kit, in this so please keep it simple. The math doesn't scare me as I have an Electronics Engineering Degree, but the theories are a little out of my field. The tapered cord is scale, like an Extra's, but I have been led to believe that a tapered cord is unforgiving, without further explanation.



CP,YOU HAVE MADE A VERY WISE CHOICE.. IM SORRY FOR NOT BEING MORE HELP..GOOD LUCK AND MOST OF ALL,-----------HAVE FUN!!!!!!!!!! RD