Airfoils: Plotting the Four-Digit, Five-Digit, and 6-Series NACA
John Brownlee
Many of us have a penchant for collecting tables of airfoil plotting coordinates for one reason or another. The collections comprise various books and individual pages copied or cut from various sources, and they are generally incomplete. If you save the data sheet presented with this article, you will have a complete data bank for the commonly used NACA airfoils, and you can pluck out whichever one you need when the occasion arises.
Although the plotting procedure is somewhat different from the ordinary, you should have no trouble following the instructions. A few words will be said about the development of these airfoils and how they relate to model application, bearing in mind that our activities generally go on in the realm of Reynolds numbers (Rn) below one million.
As seen in using the chart, all these sections are formed by combining thickness distribution ordinates (Yt) with mean line ordinates (Ym). When the mean line is straight, the resulting shape is called symmetrical. When the mean line is curved, or cambered, the resulting shapes are called by a variety of other names depending on the combination of thickness and camber used.
Why camber an airfoil? The symmetrical shapes have minimum profile drag coefficient when operating at zero lift. The value of the coefficient depends on thickness, smoothness, shape, and Rn. As they are inclined to the wind to create lift, the drag coefficient increases. By using camber, the minimum drag coefficient of the basic shape can be maintained, for all practical purposes, to fairly high values of design lift coefficient (DLC).
Four-Digit Sections
The four-digit sections were designed to systematically investigate the effects of amount of camber and location of the point of maximum camber on a thickness distribution essentially that of the Clark Y and Göttingen 398. The first two numbers together denote the NACA mean line used. The first is the maximum amount of camber in percent of chord. The second is the location of the maximum point in tenths of chord back from the leading edge. The last two numbers are the percent thickness.
Test results showed that more forward locations of maximum camber were somewhat more efficient in moving minimum drag conditions to higher CL values. They also resulted in lower negative (nose-down) pitching moment coefficients. The examples shown on the chart are for 12% sections, with thinner sections showing somewhat higher minimum drag and thicker sections somewhat lower. The 00XX sections were, and probably still are, widely used as tail surfaces. The X4XX sections were mostly used for wings since they gave a smoother stall than those with more forward maximum camber, in addition to somewhat higher CLmax. Based on data from the NACA variable-density tunnel, however, there does not seem to be any significant difference in stalling severity between the various four-digit sections.
Five-Digit Sections
The three numbers together denote the NACA mean line for the five-digit series. The sections are cambered for a DLC which is 0.15 times the first number. The second two numbers together are twice the distance, in percent of chord, to the point of maximum camber. The last two numbers are again the thickness.
The five-digit results were successful, showing very low pitching moments, particularly in the 18–21% thickness range. Another variant, with a '1' in the middle in place of the '0', was devised to give a theoretical zero pitching moment but was not used. These five-digit sections have a reputation for "violent" stalls in full scale but should be "tame" in our realm of model Reynolds numbers.
6-Series Sections
The shape of the basic thickness distribution of the four- and five-digit sections results in minimum pressure, or maximum velocity of the airflow, at only about 7.5 to 10% back from the leading edge. At Rn in the 9 to 10 million range, flow is turbulent over about 80–85% of the surface. This is well below the flight Rn of large or fast aircraft. The objective of the 6-series sections was to develop basic thickness shapes which would have the minimum pressure point as far back as possible and provide a controlled drop in pressure so as not to trigger premature transition from laminar to turbulent flow.
The 6-series separate these sections from the 1- through 5- and 7- and 8-series. The second number denotes the minimum pressure point, in tenths of chord, of the basic thickness form. The third number, either following a comma or written as a subscript, denotes the extent above and below the DLC, in tenths, of the low-drag "bucket." The range is a function of the thickness and will be about two for 15% thickness, three for 18%, etc. This notation is omitted for basic thicknesses below 12%. The subscript ordinates represent later development efforts.
The first number after the dash is ten times the DLC. The last two digits are the thickness. When either of these is not a whole number, the value is enclosed in parentheses. The thickness ordinates are not directly scalable to other exact ordinates, but they can be scaled. If you make 12% sections from the charts, they will correctly be 6X(12)-XXX; otherwise they will be 6X12-XXX sections.
When smooth, these sections are superior in drag at very high Rn but have somewhat lower CLmax. They are far superior at high Mach numbers, delaying divergence of aerodynamic forces significantly and not changing lift and moment characteristics as severely at high subsonic speeds. They have rather large negative pitching moments, but are normally used at fairly low CL and the moment can be designed out for the most part by combining swept wings and washout. From the original 1-series development, the 16-XXX shapes were used for propellers because of their better performance at high Mach numbers; these are commonly called 16-series airfoils.
At Rn of about 1.2 million, the minimum profile drag of 6-series sections will be about the same as that of four- or five-digit sections of the same thickness. Below this they suffer earlier from laminar separation and are higher-drag shapes down to Rn of about 70,000, below which the drag of all the airfoils becomes mostly pressure drag due to laminar separation. There is, then, no strong reason to use these sections for model applications other than scale fidelity. They make nice flying wings, however, and the relatively sharp leading edges have caused me no problems with a variety of scratchbuilt planes.
To conclude, it is hoped that the tables can be of practical use to you and that the comments have been clear and of interest. The information was condensed primarily from Theory of Wing Sections by Abbott and von Doenhoff.
Transcribed from original scans by AI. Minor OCR errors may remain.
