# 13.1.3: Proposed solution

- Page ID
- 78423

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.

Please find below an example:

- 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.