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.