# 13.1.3: Proposed solution


Figure 13.2: XLFR5 analysis

The solution to this exercise is left open. The software is very user-friendly. Find here a video tutorial. Extension of this exercise could be the 3D analysis (wing analysis) and the Aircraft analysis. In the sequel of this Section, a very brief and schematic overview of NACA airfoils is given. Also, some XLFR5 plots are presented in Figure 13.2.

## On NACA Airfoils

The NACA airfoils are a series of airfoils created by NACA (Nacional Advisory Committee for Aeronautics), including the following series: Four-digit-series; Five-digit-series; Modifications in four and five-digit series; 1-series; 6-series; 7-series; 8-series.

4-digit series:

• First digit: describes the maximum camber as a percentage of the chord (% c).
• Second digit: describes the maximum camber’s distance measured from the leading edge in 1/10 of the percentage of the chord (% c).
• Third and fourth digit: describing the maximum thickness as a percentage of the chord (% c). [By default the maximum thickness is 30% of the chord]

Some examples include:

• NACA 2412
- Maximum camber is 2% of c. (0.02c)
- Maximum camber located at 40% (0.4c) of the leading edge.
- Maximum thickness of 12% of the chord (0.12c)
• NACA 0015
- Symmetric airfoil (00)
- Maximum thickness of 15% of the chord (0.15c)

5-digit series:

• First digit: describes the $$C_l$$ multiplying the digit by 0.15.
• Second and third digits: dividing them by 2, describes the maximum camber’s distance measured from the leading edge as percentage of the chord (% c).
• Fourth and fifth digits: describing the maximum camber as a percentage of the chord (% c).
• By default the maximum thickness is 30% of the chord.

The following example illustrates it:

• NACA 12345
- $$C_l = 0.15.$$
- Maximum camber located at 11.5% (0.115c) of the leading edge. This implies $$x_{mc} = 0.15$$.
- Maximum camber of 45% of the chord (0.45c)

Notice that camber line is defined as follows [$$y$$ and $$x$$ normalized with the chord]:

$y = \begin{cases} \tfrac{k_1}{6} \{ x^3 - 3mx^2 + m^2 (3 - m)x \} & 0 \le x \le m, \\ \tfrac{k_1 m^3}{6} (1 - x) & m \le x \le 1; \end{cases}\nonumber$

with $$m$$ is chosen so that the maximum camber takes place in $$x = c_{mc}$$.

Modifications in four and five-digit series: The fourth and fifth digit series can be modifies by adding two digits with a dash.

• First digit after the dash: describes how rounded is the shape, being 0 very sharp and 6 exactly as the original airfoil, and 9 more rounded that the original.
• Second digit after the dash: describing the maximum thickness distance measured from the leading edge in 1/10 as a percentage of the chord (% c)

The following example illustrates it:

• NACA 1234-05
- NACA 1234 with sharp leading edge shape.
- Maximum thickness located at 50% c (0.5c) measured from the leading edge.

1 series:

• First digit: describes the series.
• Second digit: describes the minimum pressure’s distance measured from the leading edge in 1/10 as a percentage of the chord (% c).
• Third digit [after a dash line]: describes $$C_l$$ in 1/10.
• Fourth and fifth digits [after a dash line]: describe the maximum thickness in 1/10 as a percentage of the chord.

Consider the following example as illustration:

• NACA 16-123
- Minimum pressure located at 60% of the chord.
- $$C_l = 0.1.$$
- $$E_{\max} = 0.23c$$ measured from the leading edge.

6 series:  It is essentially an improvement of 1-series to maximize the laminar flow:

• First digit: describes the series.
• Second digit: describes the minimum pressure’s distance measured from the leading edge in 1/10 as a percentage of the chord (% c).
• Third digit [typically as a subindex]: describes the fact that drag remains low a number of tenths below of $$C_l$$.
• Fourth digit [after a dash line]: describes $$C_l$$ in 1/10.
• Fifth and sixth digits [after a dash line]: describe the maximum thickness in 1/10 as a percentage of the chord.
• "a=. . . " [followed by a decimal number]: describes the fraction of chord in which the laminar flow remains. By default a=1.

• NACA 61 - 345 a = 0.5
- Minimum pressure located at 10% of the chord.
- $$C_l = 0.3$$. What this means is that the airfoil was designed for maximum efficiency at a lift coefficient of approximately 0.3
- $$E_{\max} = 0.45c$$ measured from the leading edge.
- The laminar flow is maintained over 50% of the chord.

7 and 8 series: Correspond to additional improvements to maximize the laminar flow both in extrados and intrados.

• First digit: describes the series.
• Second digit: describes the minimum pressure’s distance in the extrados measured from the leading edge in 1/10 as a percentage of the chord (% c).
• Third digit: describes the minimum pressure’s distance in the intrados measured from the leading edge in 1/10 as a percentage of the chord (% c).
• Letter Letter referring to an standard airfoil of previous NACA series
• Fourth digit [after a dash line]: describes Cl in 1/10.
• Fifth and sixth digits [after a dash line]: describe the maximum thickness in 1/10 as a percentage of the chord.

The following example illustrates it:

• NACA 712A345
- Minimum pressure located at 10% of the chord in the extrados.
- Minimum pressure located at 20% of the chord in the intrados.
- $$C_l = 0.3.$$
- $$E_{\max} = 0.45c$$ measured from the leading edge.

13.1.3: Proposed solution is shared under a CC BY-SA 3.0 license and was authored, remixed, and/or curated by Manuel Soler Arnedo via source content that was edited to conform to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.