The NACA airfoil series

2017-02-19 by:CAE仿真在線來源:互聯(lián)網(wǎng)

The NACA airfoil series

The early NACA airfoil series, the 4-digit, 5-digit, and modified 4-/5-digit, were generated using analytical equations that describe the camber (curvature) of the mean-line (geometric centerline) of the airfoil section as well as the section's thickness distribution along the length of the airfoil. Later families, including the 6-Series, are more complicated shapes derived using theoretical rather than geometrical methods. Before the National Advisory Committee for Aeronautics (NACA) developed these series, airfoil design was rather arbitrary with nothing to guide the designer except past experience with known shapes and experimentation with modifications to those shapes.

NACA Four-Digit Series:

The first family of airfoils designed using this approach became known as the NACA Four-Digit Series. The first digit specifies the maximum camber (m) in percentage of the chord (airfoil length), the second indicates the position of the maximum camber (p) in tenths of chord, and the last two numbers provide the maximum thickness (t) of the airfoil in percentage of chord. For example, the NACA 2415 airfoil has a maximum thickness of 15% with a camber of 2% located 40% back from the airfoil leading edge (or 0.4c).

NACA Five-Digit Series:

The NACA Five-Digit Series uses the same thickness forms as the Four-Digit Series but the mean camber line is defined differently and the naming convention is a bit more complex. The first digit, when multiplied by 3/2, yields the design lift coefficient (cl) in tenths. The next two digits, when divided by 2, give the position of the maximum camber (p) in tenths of chord. The final two digits again indicate the maximum thickness (t) in percentage of chord. For example, the NACA 23012 has a maximum thickness of 12%, a design lift coefficient of 0.3, and a maximum camber located 15% back from the leading edge.

Modified NACA Four- and Five-Digit Series:

The airfoil sections you mention for the B-58 bomber are members of the Four-Digit Series, but the names are slightly different as these shapes have been modified. Let us consider the root section, the NACA 0003.46-64.069, as an example. The basic shape is the 0003, a 3% thick airfoil with 0% camber. This shape is a symmetrical airfoil that is identical above and below the mean camber line. The first modification we will consider is the 0003-64. The first digit following the dash refers to the roundedness of the nose. A value of 6 indicates that the nose radius is the same as the original airfoil while a value of 0 indicates a sharp leading edge. Increasing this value specifies an

increasingly more rounded nose. The second digit determines the location of maximum thickness in tenths of chord. The default location for all four- and five-digit airfoils is 30% back from the leading edge. In this example, the location of maximum thickness has been moved back to 40% chord. Finally, notice that the 0003.46-64.069 features two sets of digits preceeded by decimals. These merely indicate slight adjustments to the maximum thickness and location thereof. Instead of being 3% thick, this airfoil is 3.46% thick. Instead of the maximum thickness being located at 40% chord, the position on this airfoil is at 40.69% chord.

NACA 1-Series or 16-Series:

Unlike those airfoil families discussed so far, the 1-Series was developed based on airfoil theory rather than on geometrical relationships. By the time these airfoils were designed during the late 1930s, many advances had been made in inverse airfoil design methods. The basic concept behind this design approach is to specify the desired pressure distribution over the airfoil (this distribution dictates the lift characteristics of the shape) and then derive the geometrical shape that produces this pressure distribution. As a result, these airfoils were not generated using some set of analytical expressions like the Four- or Five-Digit Series. The 1-Series airfoils are identified by five digits, as

exemplified by the NACA 16-212. The first digit, 1, indicates the series (this series was designed for airfoils with regions of barely supersonic flow). The 6 specifies the location of minimum pressure in tenths of chord, i.e. 60% back from the leading edge in this case. Following a dash, the first digit indicates the design lift coefficient in tenths (0.2) and the final two digits specify the maximum thickness in tenths of chord (12%). Since the 16-XXX airfoils are the only ones that have ever seen much use, this family is often referred to as the 16-Series rather than as a subset of the 1-Series.

NACA 6-Series:

Although NACA experimented with approximate theoretical methods that produced the 2-Series through the 5-Series, none of these approaches was found to accurately produce the desired airfoil behavior. The 6-Series was derived using an improved theoretical method that, like the 1-Series, relied on specifying the desired pressure distribution and employed advanced mathematics to derive the required geometrical shape. The goal of this approach was to design airfoils that maximized the region over which the airflow remains laminar. In so doing, the drag over a small range of lift coefficients can be substantially reduced. The naming convention of the 6-Series is by far the most confusing of any of the families discussed thus far, especially since many different variations exist. One of the more common examples is the NACA 641-212, a=0.6. In this example, 6 denotes the series and indicates that this family is designed for greater laminar flow than the Four- or Five-Digit Series. The second digit, 4, is the location of the minimum pressure in tenths of chord (0.4c). The subscript 1 indicates that low drag is maintained at lift coefficients 0.1 above and below the design lift coefficient (0.2) specified by the first digit after the dash in tenths. The final two digits specify the thickness in percentage of chord, 12%. The fraction specified by

a=___ indicates the percentage of the airfoil chord over which the pressure distribution on the airfoil is uniform, 60% chord in this case. If not specified, the quantity is assumed to be 1, or the distribution is constant over the entire airfoil.

The NACA 6 and 6A-Series Mean Lines*

The 6-series mean lines were designed using thin airfoil theory to produce a constant loading from the leading edge back to x/c = a, after which the loading decreases linearly to zero at the trailing edge. Theoretically, the loading at the leading edge must be either zero or infinite within the context of thin airfoil theory analysis. The violation of the theory by the assumed finite leading edge loading is reflected by the presence of a weak singularity in the mean line at the leading edge, where the camber line has an infinite slope. Therefore, according to Abbott and von Doenhoff, the 6-series airfoils were constructed by holding the slope of the mean line constant in front of x/c = 0.005, with the value at that point. For round leading edges the Camber line values are essentially not used at points ahead of the origin of the leading edge radius. The theory is discussed by Abbott and von Doenhoff on pages 73-75, 113, and 120. Tabulated values are contained on pages 394-405. The derivation of this mean line is a good exercise in thin airfoil theory.

By simply adding various mean lines together, other load distributions can be constructed.

From Abbott and von Doenhoff: "The NACA 6-series wing sections are usually designated by a six-digit number together with a statement showing the type of mean line used. For example, in the designation NACA 65,3-218, a = 0.5, the 6 is the series designation. The 5 denotes the chordwise position of minimum pressure in tenths of the chord behind the leading edge for the basic symmetrical section at zero lift. The 3 following the comma (sometimes this is a subscript or in parenthesis) gives the range of lift coefficient in tenths above and below the design lift coefficient in which favorable pressure gradients exist on both surfaces. The 2 following the dash gives the design lift coefficient in tenths. The last two digits indicate the thickness of the wing section in percent chord. The designation a = 0.5 shows the type of mean line used. When the mean-line is not given, it is understood that the uniform-load mean line (a =1.0) has been used."

The 6A series airfoils employed an empirical modification of the a = 0.8 camber line to allow the airfoil to be constructed of nearly straight line segments near the trailing edge. This camber line is described by Loftin in NACA R-903.

NACA 7-Series:

The 7-Series was a further attempt to maximize the regions of laminar flow over an airfoil differentiating the locations of the minimum pressure on the upper and lower surfaces. An example is the NACA 747A315. The 7 denotes the series, the 4 provides the location of the minimum pressure on the upper surface in tenths of chord (40%), and the 7 provides the location of the minimum pressure on the lower surface in tenths of chord (70%). The fourth character, a letter, indicates the thickness distribution and mean line forms used. A series of standaradized forms derived from earlier families are designated by different letters. Again, the fifth digit incidates the design lift coefficient in tenths (0.3) and the final two integers are the airfoil thickness in perecentage of chord (15%).

NACA 8-Series:

A final variation on the 6- and 7-Series methodology was the NACA 8-Series designed for flight at supercritical speeds. Like the earlier airfoils, the goal was to maximize the extent of laminar flow on the upper and lower surfaces independently. The naming convention is very similar to the 7-Series, an example being the NACA 835A216. The 8 designates the series, 3 is the location of minimum pressure on the upper surface in tenths of chord (0.3c), 5 is the location of minimum pressure on the lower surface in tenths of chord (50%), the letter A distinguishes airfoils having different camber or thickness forms, 2 denotes the design lift coefficient in tenths (0.2), and 16 provides the airfoil thickness in percentage of chord (16%).

Summary:

Though we have introduced the primary airfoil families developed in the United States before the advent of supersonic flight, we haven't said anything about their uses. So let's briefly explore the advantages, disadvantages, and applications of each of these families.

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