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5. (8 points) The mean camber line of an airfoil consists of two parabolas joined at their vertices as shown. The maximum mean camber is $kc$ (where $k$ is a constant and $c$ is the chord) is located at 0.4$c$ behind the leading edge. For this airfoil find $\alpha_{ZL}$ (angle for zero lift) and $C_{mac}$ in terms of $k$. \begin{equation} \frac{z_c}{c} = \begin{cases} k \left[1 - \frac{\left(\frac{x}{c} - 0.4\right)^2}{0.16}\right] & \text{for } 0 \le \frac{x}{c} \le 0.4\\k \left[1 - \frac{\left(\frac{x}{c} - 0.4\right)^2}{0.36}\right] & \text{for } 0.4 \le \frac{x}{c} \le 1 \end{cases} \end{equation}

          5. (8 points) The mean camber line of an airfoil consists of two parabolas joined at their vertices as shown. The maximum mean camber is $kc$ (where $k$ is a constant and $c$ is the chord) is located at 0.4$c$ behind the leading edge. For this airfoil find $\alpha_{ZL}$ (angle for zero lift) and $C_{mac}$ in terms of $k$.

\begin{equation*}
\frac{z_c}{c} = \begin{cases}
k \left[1 - \frac{\left(\frac{x}{c} - 0.4\right)^2}{0.16}\right] & \text{for } 0 \le \frac{x}{c} \le 0.4\\k \left[1 - \frac{\left(\frac{x}{c} - 0.4\right)^2}{0.36}\right] & \text{for } 0.4 \le \frac{x}{c} \le 1
\end{cases}
\end{equation*}

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5. (8 points) The mean camber line of an airfoil consists of two parabolas joined at their vertices as shown. The maximum mean camber is kc (where k is a constant and c is the chord) is located at 0.4c behind the leading edge. For this airfoil find αZL (angle for zero lift) and Cmac in terms of k.

(zc)/(c) =
k [1 - (((x)/(c) - 0.4)^2)/(0.16)] for 0 ≤(x)/(c)≤ 0.4
k [1 - (((x)/(c) - 0.4)^2)/(0.36)] for 0.4 ≤(x)/(c)≤ 1

Added by Juan B.

University Physics with Modern Physics

Hugh D. Young 14th Edition

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Solved by Expert Dwijendra Rao

Step 1

The angle for zero lift is the angle at which the mean camber line intersects the chord line. In this case, the mean camber line consists of two parabolas joined at their vertices. Since the maximum mean camber is located at 0.4c behind the leading edge, we can Show more…

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5. 8 points) The mean camber line of an airfoil consists of two parabolas joined at their vertices as shown. The maximum mean camber is kc (where k is a constant and c is the chord) and is located at 0.4c behind the leading edge. For this airfoil, find Î¸L (angle for zero lift) and Cmae in terms of k. TIE 0.4| for 0 < Î¸ < 0.4. 0.16 _0.| for 0.4 < Î¸ < 1 0.36

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