CG question Help
#1
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From: Cookeville,
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Ive built 5 very similiar 3d profile airplanes all using hand drawn TLAR airfoils, by the time i have gotten these models balanced like i like them, the CG is between 35 and 38% MAC. The latest profile i built is very similiar to the first 5 except i drastically changed the wing. This airfoil is alot thicker and i moved the thicker part of the wing toward the leading edge i also increased the wing area from 540 to 792 sqin's. I balanced at 35% for the first flight....was a very big handful when it left the ground was worried for a few secs whether i would have the opportunity to ever fly it again, But managed to land it. I, know have the model balanced at about 27% MAC, and it flies just fine. ( i balance my models so that when i roll invrted it will still fly hands off)
My question is what has drastically changed my balance point? Is it the airfoil? Is it that the tail might be to small for the much bigger wing area? If it is realated to the tail could the ralation ship of stab size compared to elevator size have anything to do with it?
Thanks, any help appreciated
My question is what has drastically changed my balance point? Is it the airfoil? Is it that the tail might be to small for the much bigger wing area? If it is realated to the tail could the ralation ship of stab size compared to elevator size have anything to do with it?
Thanks, any help appreciated
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From: Raleigh,
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The moment you moved the thickest part of the airfoil closer to the LE you changed the center of pressure on the wing. Now your CG has to be moved forward as well or you would encounter drastic pitching moments....which I think thats what you experienced.
#4
From what I've seen around moving the thick part forward should not have THAT much effect, if any. But you say you used a much thicker airfoil as well as moving the high point forward. There may be other issues at work here. Can you offer up a pic of the airfoil section? And the airplane as a whole? Or at least what is your stabilizer area to wing area ratio?
If your shape is extreme enough you may have large separation bubbles even in level flight. With airfoil software and brand name shapes so available these days on the 'net you may want to give up on your own shapes and just use what's available and tested.
For what you're doing here, for example, I'd recomend the Eppler 474. Just pinch the trailing edge off a bit early to form a flar portion to join the ailerons to. At least you would have a proper leading edge shape that offers decent performance.
If your shape is extreme enough you may have large separation bubbles even in level flight. With airfoil software and brand name shapes so available these days on the 'net you may want to give up on your own shapes and just use what's available and tested.
For what you're doing here, for example, I'd recomend the Eppler 474. Just pinch the trailing edge off a bit early to form a flar portion to join the ailerons to. At least you would have a proper leading edge shape that offers decent performance.
#5
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From: Cookeville,
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Here are a few pics... the horizontal stab and elevator has 108 sqin surface area on both planes, the newest model(red and white) has a slightly more span and a little less cord on the stab, but roughly the same area.
The model flies great its not pitch sensitive since i moved the cg, it does all the tricks , but just doesnt "flatten" out nice in a inverted flat spin.
Thanks for the wisdom anymore comments would be appreciated.
thanks,
just wanting to learn
The model flies great its not pitch sensitive since i moved the cg, it does all the tricks , but just doesnt "flatten" out nice in a inverted flat spin.
Thanks for the wisdom anymore comments would be appreciated.
thanks,
just wanting to learn
#7
OK, in the composite pic it's obvious to me that the extra wing area of the red model has too small a stab and a shorter tail moment compared to the dayglo lime green model. That alone may be why you need a more forward CG.
I suggest you look up Tail Volume Coefficient for the horixontal tail volume (there's also a vertical tail volume coefficient for the vertical area) and compare those values. I suspect that if you increase the size of the stab on the red model so the TVC matches then it'll fly better.
Your airfoil looks fine BTW. I can see that it's no more radical than many in use these days and should fly well.
I suggest you look up Tail Volume Coefficient for the horixontal tail volume (there's also a vertical tail volume coefficient for the vertical area) and compare those values. I suspect that if you increase the size of the stab on the red model so the TVC matches then it'll fly better.
Your airfoil looks fine BTW. I can see that it's no more radical than many in use these days and should fly well.
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From: Raleigh,
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Each airfoil has inherent characteristics and therefore different pitching moments according to their center of pressure. A wing is not balanced at the magical figure of 25% because of the wing.....the reason why its because most turbulent flow airfoils have their maximum thickness around that point and generate there maximum amount of differential pressure at that point. The first airfoil shown has the center of pressure at 27% of the chord withing the MAC. Flying it at a CG of 35% makes it marginally stable but within the allowable for 3D flying. Now, on the second airfoil the center of pressure is a lot forward, 16%, if we moved the CG at the same 35% point we are going beyond the point of neutral stability into negative stability. Thats why the model behaved the way described by Kenny. Increasing the horizontal stab area just increases the effectiveness of the flying surface but the model will remain negatively stable.
#9
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From: Cookeville,
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The yellow wing has a 15" root chord and 9 1/2" tip chord with a 44.5" span...The red wing is 18 1/2" root and 14 1/2" tip with a 49" span. Both have a straight leading edge.
I will check and see what i can find on tail volumn coeffecient, i have heard a general rule of thumb is for the stab to be roughly 25% of the wing area which i know im way below this.
Thanks again
I will check and see what i can find on tail volumn coeffecient, i have heard a general rule of thumb is for the stab to be roughly 25% of the wing area which i know im way below this.
Thanks again
#10
Kennyroy,
capio777 is leading you astray with all that nonsense about Centre of Pressure.
BMatthews is on the ball. You need to work out your Tail Volume Ratio.
Tail Volume Ratio (V-bar) is (tail area, divided by wing area) times (tail moment arm, divided by wing mean chord)
You are working out the mean chord (MAC) correctly by the looks of it, now measure the tail arm, which is the distance between the quarter chord point of the wing MAC and the quarter chord point of the tail.
That 108 in^2 tail is 20% of the small wing but only 13.4% of the big wing !!!!!
Your tail arm is short, let us say it is 1.5 times the MAC of the big wing, that gives a Tail Volume of 0.20 x 1.5 = 0.3. That is small, but not too bad. I would say that your Neutral Point (where to put the CG for zero stability) will be 35% to 40% of wing MAC. You like it that way I take it.
Next model. Same tail. Now 13.4% of wing area, and I'll bet the tail arm is now only 1.3 or 1.4 times MAC (because the MAC is bigger)
You tail Volume is reduced to 1.4 x 0.134 = 0.188
That is too small. Build a bigger tail or a longer tail arm or both!!!
My guess is that your Neutral Point has gone forward to 31% MAC so with a CG at 35% you are definitely unstable. A more forward CG should get your model stable, but I'd still suggest a bigger tail volume.
Stability is purely a matter of CG position. Anything can be made stable with a suitable CG. The sections have very little to do with it. I haven't seen a section with an Aerodynamic Centre further than 2% from the 25% (quarter chord) we all assume.
Forget Centres of Pressure. Have you heard a serious Aerodynamicist use them since the 1920s? Ignore the CP and anyone who uses it.
Believe the guys who talk about Aerodynamic Centre (or quarter chord point), tail volume, Neutral Point, Static Margin or Stability Margin (the distance of the CG ahead of the NP).
capio777 is leading you astray with all that nonsense about Centre of Pressure.
BMatthews is on the ball. You need to work out your Tail Volume Ratio.
Tail Volume Ratio (V-bar) is (tail area, divided by wing area) times (tail moment arm, divided by wing mean chord)
You are working out the mean chord (MAC) correctly by the looks of it, now measure the tail arm, which is the distance between the quarter chord point of the wing MAC and the quarter chord point of the tail.
That 108 in^2 tail is 20% of the small wing but only 13.4% of the big wing !!!!!
Your tail arm is short, let us say it is 1.5 times the MAC of the big wing, that gives a Tail Volume of 0.20 x 1.5 = 0.3. That is small, but not too bad. I would say that your Neutral Point (where to put the CG for zero stability) will be 35% to 40% of wing MAC. You like it that way I take it.
Next model. Same tail. Now 13.4% of wing area, and I'll bet the tail arm is now only 1.3 or 1.4 times MAC (because the MAC is bigger)
You tail Volume is reduced to 1.4 x 0.134 = 0.188
That is too small. Build a bigger tail or a longer tail arm or both!!!
My guess is that your Neutral Point has gone forward to 31% MAC so with a CG at 35% you are definitely unstable. A more forward CG should get your model stable, but I'd still suggest a bigger tail volume.
Stability is purely a matter of CG position. Anything can be made stable with a suitable CG. The sections have very little to do with it. I haven't seen a section with an Aerodynamic Centre further than 2% from the 25% (quarter chord) we all assume.
Forget Centres of Pressure. Have you heard a serious Aerodynamicist use them since the 1920s? Ignore the CP and anyone who uses it.
Believe the guys who talk about Aerodynamic Centre (or quarter chord point), tail volume, Neutral Point, Static Margin or Stability Margin (the distance of the CG ahead of the NP).
#11
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From: Cookeville,
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Thank you for explaining to me how to figure TVR THANK YOU
I have now started me a new profile almost identical but with a bigger tail. what is a good number for TVR?
I have now started me a new profile almost identical but with a bigger tail. what is a good number for TVR?
#12
Kennyroy,
Tail Volume Ratio, TVR if you like, a capital V with a bar over it is the standard symbol in aerodynamics books, or I write it as it is said, Vbar.
0.3 is pretty minimal. Gliders and many scale aircraft range from about 0.35 (P51 Hurricane, Me 109) up to about 0.55 (P47). Most trainers are in the 0.5 to 0.6 region, pattern models about 0.7, and some free flight models with big tails or very long tail arms have a Vbar of 1 or more.
I favour 0.5 to 0.7, but almost any figure will do and you can adjust the CG to suit. A bigger Vbar seems to give a larger acceptable CG range, i.e. it is less sensitive to CG variation.
You will see several empirical CG formulae, and they are usually of the form
CG = const + factor*Vbar (which gives the answer as a decimal fraction of MAC)
The const can be 0.167 (1/6 th) or 0.15 (1/7 th) and the factor is often 0.375 (3/8 ths)
But in my personal formula the const is 0.1 and the factor is (0.25*AR^0.25) which is the fourth root of the wing's Aspect Ratio. You take the wing AR, hit square root, hit sq root again, multiply by 0.25, multiply by Vbar, and add 0.1
Sounds complicated but dead simple on a calculator.
If you want a simpler formula make the const 0.4 (assumes AR = 6.5) to get the formula
CG = 0.1 + 0.4*Vbar
More experienced folk might want to add 0.25 instead of 0.1 because that then gives the NP formula.
NP = 0.25 + 0.25*AR^0.25*Vbar
You then subtract the Static Margin (Stability Factor) that you like. I subtract 0.15, because I like to use a little poke of down elevator to hold level inverted. You don't, so you could just subtract 0.05 (5% MAC) as a Stability Factor. That doesn't leave much room for error, and any of these empirical formulae could be out by 5% MAC to start with. If you cut it that fine for first flights that's up to you.
Best of luck,
Alasdair
Tail Volume Ratio, TVR if you like, a capital V with a bar over it is the standard symbol in aerodynamics books, or I write it as it is said, Vbar.
0.3 is pretty minimal. Gliders and many scale aircraft range from about 0.35 (P51 Hurricane, Me 109) up to about 0.55 (P47). Most trainers are in the 0.5 to 0.6 region, pattern models about 0.7, and some free flight models with big tails or very long tail arms have a Vbar of 1 or more.
I favour 0.5 to 0.7, but almost any figure will do and you can adjust the CG to suit. A bigger Vbar seems to give a larger acceptable CG range, i.e. it is less sensitive to CG variation.
You will see several empirical CG formulae, and they are usually of the form
CG = const + factor*Vbar (which gives the answer as a decimal fraction of MAC)
The const can be 0.167 (1/6 th) or 0.15 (1/7 th) and the factor is often 0.375 (3/8 ths)
But in my personal formula the const is 0.1 and the factor is (0.25*AR^0.25) which is the fourth root of the wing's Aspect Ratio. You take the wing AR, hit square root, hit sq root again, multiply by 0.25, multiply by Vbar, and add 0.1
Sounds complicated but dead simple on a calculator.
If you want a simpler formula make the const 0.4 (assumes AR = 6.5) to get the formula
CG = 0.1 + 0.4*Vbar
More experienced folk might want to add 0.25 instead of 0.1 because that then gives the NP formula.
NP = 0.25 + 0.25*AR^0.25*Vbar
You then subtract the Static Margin (Stability Factor) that you like. I subtract 0.15, because I like to use a little poke of down elevator to hold level inverted. You don't, so you could just subtract 0.05 (5% MAC) as a Stability Factor. That doesn't leave much room for error, and any of these empirical formulae could be out by 5% MAC to start with. If you cut it that fine for first flights that's up to you.
Best of luck,
Alasdair
#13
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From: Raleigh,
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Its true, dont pay attention to what I say, afterall an airfoil doesnt mean anything in flying. All we need is a flat surface and plenty of tail area to control it. Thats how my team and I managed to do work stability problems on the predator. A good design is mostly just guessing until you hit the magic number....right? Who needs center of pressure? [:-]
#14
Perhaps there is some disagreement about terminology here. "Center of Pressure" and "Aerodynamic Center" refer to completely different concepts, both of which have utility in different contexts. For 2 dimensional wing sections I think the difference is pretty easy to understand.
Center of Pressure: The position along the chord of a wing section about which the pitching moment is zero. Linear analysis of thin wing sections predicts that the Center of Pressure will (in general) move as the angle of attack is changed. One exception to this is a symmetrical (uncambered) wing section.
Aerodynamic Center: The position along the chord of a wing section about which the pitching moment does not change as the angle of attack is changed. The pitching moment about the Aerodynamic center may or may not be zero. If it is zero, then the Aerodynamic Center and the Center of Pressure happen to be at the same point. Linear analysis of thin wing sections shows that the Aerodynamic Center is at c/4, or "quarter chord", and doesn't change with angle of attack.
Both concepts can be extended to 3D aircraft and thick airfoils. One thing that changes as you go to a 3D aircraft from a 2D wing section is that the Aerodynamic Center (usually) no longer falls at the quarter chord. Another difference is that the location of the Aerodynamic Center is no longer strictly independent of angle of attack. However, it remains fairly stationary even for fairly thick airfoils over a wide angle of attack range (as alasdair points out).
THE condition for static longitudinal stability is that the Center of Gravity is forward of the Aerodynamic Center. The location of the CG in relation to the Center of Pressure will determine the static tail load, but is unrelated to stability. So Capio777, I've got to agree with alasdair that Center of Pressure is not directly relevant to the stability discussion.
Center of Pressure: The position along the chord of a wing section about which the pitching moment is zero. Linear analysis of thin wing sections predicts that the Center of Pressure will (in general) move as the angle of attack is changed. One exception to this is a symmetrical (uncambered) wing section.
Aerodynamic Center: The position along the chord of a wing section about which the pitching moment does not change as the angle of attack is changed. The pitching moment about the Aerodynamic center may or may not be zero. If it is zero, then the Aerodynamic Center and the Center of Pressure happen to be at the same point. Linear analysis of thin wing sections shows that the Aerodynamic Center is at c/4, or "quarter chord", and doesn't change with angle of attack.
Both concepts can be extended to 3D aircraft and thick airfoils. One thing that changes as you go to a 3D aircraft from a 2D wing section is that the Aerodynamic Center (usually) no longer falls at the quarter chord. Another difference is that the location of the Aerodynamic Center is no longer strictly independent of angle of attack. However, it remains fairly stationary even for fairly thick airfoils over a wide angle of attack range (as alasdair points out).
THE condition for static longitudinal stability is that the Center of Gravity is forward of the Aerodynamic Center. The location of the CG in relation to the Center of Pressure will determine the static tail load, but is unrelated to stability. So Capio777, I've got to agree with alasdair that Center of Pressure is not directly relevant to the stability discussion.
#15
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From: Raleigh,
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I apologize for mixing the the term center of pressure here. My point is to ilustrate that there is a difference of pitching moments according to the airfoil selected. If the same CG is maintained while changing the shape of the airfoil the pitch will be affected. Take this two airfoils used in the design of an aircraft named "One Design" featured in Sport Aviation february 1994 edition.
The NACA airfoil has the max thickness at 30% while the "one design" has it at 20%. As you can see the moment coefficient is positive and keeps increasing as the AOA increases while the "one design" coefficient goes negative until it reaches 14 degrees. Adding this pitching moment to a 3D model which tends towards neutral stability can bring it towards the negative stability region.
The NACA airfoil has the max thickness at 30% while the "one design" has it at 20%. As you can see the moment coefficient is positive and keeps increasing as the AOA increases while the "one design" coefficient goes negative until it reaches 14 degrees. Adding this pitching moment to a 3D model which tends towards neutral stability can bring it towards the negative stability region.
#16
Capio777,
I still think you are missing the big picture. The condition for static longitudinal stability is that the Center of Gravity be forward of the Aerodynamic Center. Another way of saying this is that the derivative of the aircraft pitching moment about the center of gravity with respect to angle of attack be negative (dCM/dAlpha<0).
Your plots show the variation of section moment coefficient with angle of attack (dCm/dAlpha). These plots can be used to calculate the effective shift of the section Aerodynamic Center:
The change in moment coefficient resulting from a shift in reference point can be computed as follows:
(1) Cm = Cm_o + (Cl)*delta
where Cm_o is the moment coefficient about the original reference point, Cl is the section lift coefficient, and delta is the distance the reference point was shifted aft normalized by the chord. Taking the derivative with respect to angle of attack:
(2) dCm/dAlpha = dCm_o/dAlpha + delta*(dCl/dAlpha).
The Aerodynamic Center of a wing section is defined as the point where dCm/dAlpha = 0. Setting equation (2) equal to zero and solving for delta gives:
(3) delta = -dCm_o/dAlpha / dCl/dAlpha
For the plots you showed, the biggest difference between the two sections in dCm/dAlpha is less than 0.001 per degree. dCl/dAlpha is at least 0.10 per degree for almost all wing sections. This gives a delta of less then 0.01, or a shift of Aerodynamic Center between the two sections of less than 1% of the chord. Will this have an effect on longitudinal stability? Yes it will, but for an aircraft, it is an extremely small effect compared to the effect of a change in geometry such as that shown by KennyRoy above. Your thoughts?
I still think you are missing the big picture. The condition for static longitudinal stability is that the Center of Gravity be forward of the Aerodynamic Center. Another way of saying this is that the derivative of the aircraft pitching moment about the center of gravity with respect to angle of attack be negative (dCM/dAlpha<0).
Your plots show the variation of section moment coefficient with angle of attack (dCm/dAlpha). These plots can be used to calculate the effective shift of the section Aerodynamic Center:
The change in moment coefficient resulting from a shift in reference point can be computed as follows:
(1) Cm = Cm_o + (Cl)*delta
where Cm_o is the moment coefficient about the original reference point, Cl is the section lift coefficient, and delta is the distance the reference point was shifted aft normalized by the chord. Taking the derivative with respect to angle of attack:
(2) dCm/dAlpha = dCm_o/dAlpha + delta*(dCl/dAlpha).
The Aerodynamic Center of a wing section is defined as the point where dCm/dAlpha = 0. Setting equation (2) equal to zero and solving for delta gives:
(3) delta = -dCm_o/dAlpha / dCl/dAlpha
For the plots you showed, the biggest difference between the two sections in dCm/dAlpha is less than 0.001 per degree. dCl/dAlpha is at least 0.10 per degree for almost all wing sections. This gives a delta of less then 0.01, or a shift of Aerodynamic Center between the two sections of less than 1% of the chord. Will this have an effect on longitudinal stability? Yes it will, but for an aircraft, it is an extremely small effect compared to the effect of a change in geometry such as that shown by KennyRoy above. Your thoughts?
#17
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From: Raleigh,
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Yes, I do agree with your explanation. Normally the effect on a real aircraft or even the average r/c model is extremely small and in some instances is beneficial for stability. My view is that a 3-D model has already the CG aft enough to make it marginally stable and the small contribution by the increase in pitching moment can turn the model toward negative stability. We did wind tunnel experiments with different wing crossections of same thickness and chord length and while keeping the same AC for each one it was found that there was a relation between position of max thickness and pitch sensitivity.
#18
Shoe,
Thank you for that input. Spot on.
When I did my aeronautics degree (admitedly a long time ago) the AC is the point on a section or surface (a 3-D wing) about which dCm/dCl is zero, while the Neutral Point is the point on the whole aircraft about which dCm/dCl is zero.
i.e. the NP is the AC of the combination of wing plus tail.
So each surface has its own AC, and when I combine them into a whole aircraft I refer to the NP, and potion the CG relative to that.
Alasdair
Thank you for that input. Spot on.
When I did my aeronautics degree (admitedly a long time ago) the AC is the point on a section or surface (a 3-D wing) about which dCm/dCl is zero, while the Neutral Point is the point on the whole aircraft about which dCm/dCl is zero.
i.e. the NP is the AC of the combination of wing plus tail.
So each surface has its own AC, and when I combine them into a whole aircraft I refer to the NP, and potion the CG relative to that.
Alasdair
#19
Alasdair,
Good point, I was being sloppy with my terminology. Thanks.
Cappio777,
I see your point that even a small change may be important if your aircraft already has a small static margin. My experience has been that crossing the region from statically stable to statically unstable is not like falling off a cliff. The aircraft still flies like an aircraft, it just requires more and more attention as the CG is moved aft (obviously at some point you won't be able to keep the poles in the left half-plane). I really doubt that you would notice much of a change in flying qualities for a shift in Neutral Point by a percent or two of the MAC (even if the aircraft went from statically stable to statically unstable as a result of the shift).
Good point, I was being sloppy with my terminology. Thanks.
Cappio777,
I see your point that even a small change may be important if your aircraft already has a small static margin. My experience has been that crossing the region from statically stable to statically unstable is not like falling off a cliff. The aircraft still flies like an aircraft, it just requires more and more attention as the CG is moved aft (obviously at some point you won't be able to keep the poles in the left half-plane). I really doubt that you would notice much of a change in flying qualities for a shift in Neutral Point by a percent or two of the MAC (even if the aircraft went from statically stable to statically unstable as a result of the shift).
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From: Deland,
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Back to the original post. Kenny took the same airplane design and replaced the wing with a bigger one. In order to keep the CG at the same %MAC, the tail size and moment would need to be scaled up as well. Relative to wing area, a smaller tail size means the CG needs to move forward. Thus the needs for TVR calculations or more in-depth calcs. I think the TVR effect will far outstrip the effect of the airfoil pitching moment here.
Don't be afraid to make the tail even bigger than TVR calculations suggest. A big stab allows a much further aft CG, and also damps dynamic motions, further allowing agressive balancing -- With an oversized stab, even an out of balance airplane is manageable. Plus, you can get a lot of elevator power to boot.
Don't be afraid to make the tail even bigger than TVR calculations suggest. A big stab allows a much further aft CG, and also damps dynamic motions, further allowing agressive balancing -- With an oversized stab, even an out of balance airplane is manageable. Plus, you can get a lot of elevator power to boot.
#21
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From: Cookeville,
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Thanks everyone !! Keep debating and talking cause im enjoying the reading. Im working on the new model and now have the wing and fuse ready to cover. If im understanding right here if i use an "oversized" tail , for lack of a better word i could maybe get away with a CG of say 38 or 39 percent and still be stable enough to fly?
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From: St. Charles, MO
John, you forgot to mention that small tails look funny too. There is a kind of rythm about airplane sizes and shapes. Make some of the shapes look funny and it might not work nicely.
End of metaphysical analysis.
End of metaphysical analysis.
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From: Cookeville,
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I have finished my latest model and have about 10 flights on it now. Thanks to the info i got in this forum I beleive I have built my best plane to date. Back to my origianl question I feel like my problem was the TVC was to small, because i used the same airfoil. I have this new model balanced at 35% and am going to move it back a little more. The palne is still flying very nicely at this cg (not pitch sensitive) but is not neutral yet (still takes a little up to maintain level flight inverted).
Thanks to all of you!
Kenny
Thanks to all of you!
Kenny





