# Riblett mean lines

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##### Well-Known Member

Does anyone know how Riblett actually calculated his GA-x mean lines? The GA-4 and GA-6 seem to match their description of being a NACA a=0.5 mean line. For the GA-2 and GA-3, however, he added 0.3% and 0.2% leading edge droop, respectively. Unfortunately, this droop means that interpolating mean lines gives odd results, and extrapolating (in my case to lower camber) gives really odd results. What I'd like to do is scale the NACA a=0.5 mean line directly, and then apply the nose droop myself (targetting ~13° leading edge slope, or equivalently a 0.25% chord mean line y-value of 0.060). But since I've been unable to reverse Riblett's process in this manner (that is, go from the GA-4 to the GA-2 by some transformation), I feel like I'm missing something.

So, what exactly does it mean arithmetically, in Riblett's context, to droop the leading edge x%?

#### Autodidact

##### Well-Known Member
My understanding was that the NACA method was tantamount to rolling a continuously expanding circle along the mean line, and used a circle for the LE radius placed so that the end point of the mean line was normal to the circles circumference (so that the end point of the mean line was slightly below the 9 o'clock), and that this caused a slight raising of the LE point and that Riblett just measured the thickness vertically up and down from the mean line and that this "corrected" the error inherent in the NACA method. So, by Riblett's assertion, he didn't add any droop, he only corrected what he saw as an error by NACA which slightly raised the LE. Maybe I'm missing something too.

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#### TinBender

##### Well-Known Member
I've done some reverse engineering on the subject.
Riblett's GA-2 mean line is defined by a parabola through 2.5% chord. The others are not parabolic.

I will IM you my data.

##### Well-Known Member
The GA-2 is definitely not parabolic at the 0.25% chord and 0.5% chord points; this is where the droop is.

Autodidact, by Riblett's assertion, he added 0.3% leading edge droop to the GA-2 and 0.2% leading edge droop to the GA-3; this is both visible and explicitly noted on the graph of the mean lines.

#### TinBender

##### Well-Known Member
What I meant was GA-2 mean line is parabolic as a piece-wise defined function, when x <= 2.5% chord. It is, near as I can tell, exactly y=-0.0293x^2+0.2471x , x<=2.5% chord

#### Autodidact

##### Well-Known Member
"This method (the NACA method - my ed.),...., is quite complicated mathematically,...... Unfortunately, it leads to a distortion at the leading edge, which is then smoothed by the so-called "slope and radius" method for forming the leading edge...... Unfortunately, this has the bad effect of super-elevating the leading edge above the original chord line."
"The next step is to control the initial slope of the mean line,... This was completely missed in the NACA work,.... Thus our GA-2 mean line incorporates .3% droop, and the GA-3 mean line has .2% leading edge droop -...."

Addaon, the NACA method resulted in the distortion of the original mean line, raising or "super-elevating" the leading edge above the original mean line. Riblett did not modify the 0.5 mean line, he corrected the distortion of that line by the NACA method. As a result of that correction, the Riblett airfoil has a droop over what the "distorted" NACA airfoil had. I don't know if the NACA 0.5 mean line is parabolic, I only know that Riblett did not modify it from it's original formulation. NACA distorted their own mean line. In other words, by "control the initial slope of the mean line", Riblett is saying to avoid distorting the original mean line.

Bret

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##### Well-Known Member
Bret, this simply doesn't match the numbers provided in the book. In particular, the GA-2 (drooped) mean line can be closely approximated by ga2(x) = 0.5 * ga4(x) + (1 - x)*0.0033 for the aft half of the mean line (x going from ~0.6 to 1); the equation gives a y value of 0.0033 at the leading edge, which corresponds to the applied 0.3% droop. The presence of this droop is not at question (in the GA-2 and GA-3 mean lines, not the GA-4 and GA-6); the question is simply how it's distributed across the mean line.

Riblett Page 52 said:
Code:
CAMBER           DERIVATION
GA-2             NACA (a=0.5) + .3% L.E. DROOP
GA-3             NACA (a=0.5) + .2% L.E. DROOP
GA-4             NACA (a=0.5)
GA-6             NACA (a=0.5)

##### Well-Known Member
What I meant was GA-2 mean line is parabolic as a piece-wise defined function, when x <= 2.5% chord. It is, near as I can tell, exactlyy=-0.0293x^2+0.2471x , x<=2.5% chord
Thank you! This is exactly what I was looking for!

#### Autodidact

##### Well-Known Member
Whew! I think you guys may have run me to ground here and I will be forced to admit that you are right! And I should also thank you for it because it means that I was wrong, which is something I would rather not be!

On page 20, Fig. 4, the initial slope of the GA30-212 mean line is 13.7° which is very close to the 13° @ 0.24% chord of the GA -2 (a=0.5) +3% L.E.drop. The super-elevation of the 2412 airfoil in the same FIg. 4 (pg. 20) is only 0.157% only about half of what the GA -2 series droop should be, so I have no excuse there.

Thank you for enlightening me. Question; why not just fair an arc into the NACA camber line? Or does TinBenders parabola fair into the camber line without increasing the height of the camber? Taken literally, an 0.3% droop would mean an 0.15% or more increase in the camber, wouldn't it?

##### Well-Known Member
Question; why not just fair an arc into the NACA camber line? Or does TinBenders parabola fair into the camber line without increasing the height of the camber? Taken literally, an 0.3% droop would mean an 0.15% or more increase in the camber, wouldn't it?
Haven't done enough analysis to figure out exactly why he took that approach; I assume (if it's a parabola) he's trying to keep the first derivative of the slope (the curvature) smooth. There are many reasonable ways to do a droop; that's why I was curious what he had done (and was having a hard time reverse engineering it).

Yes, this means that a GA-2 mean line has more than half the camber of a GA-4 mean line in Riblett's system; this is NOT true for the NACA mean lines they're based on. The GA-2 has a max camber around 1.792%; more than the 1.648% you'd expect from the GA-4 max camber of around 3.296%. The meaning of "design CL" has always been fuzzy in my mind (both in NACA's system and in Riblett's); this non-linear dependency he adds makes it even fuzzier, but at some level it does make sense. The design CL is about the "bulk camber", from, say 1% of the mean line back; Riblett also satisfies an additional constraint of initial slope of at least 12°. The droop for the leading edge doesn't much change the /behavior/ of the mean line (remember that the further forward camber is, the less effect it has on moment, etc); instead, it just changes the zero-lift angle of the airfoil.

#### TinBender

##### Well-Known Member

This Screen grab shows the mean lines of the GA-2 in red and the NACA .5 Cli 0.24.

Very different areas under the curve at the front, but nearly identical in aft portion, with removal of re-curve. The GA mean lines' forward loading may be more important to the qualities than the method of thickness distribution addition (perpendicular to chord line vs perpendicular to mean line).
The NACA mean lines are simple linear scaling of mean line with Cli = to 1. That is why a .2 naca cli mean line is not necessarily the best comparator for a GA-2, which is sized through experiment.

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