For the NACA \(2412\) airfoil, the lift coefficient and moment coefficient about the quarter-chord at \(−6 ^{\circ}\) angle of attack are \(−0.39\) and \(−0.045\),respectively. At \(4^{\circ}\) angle of attack, these coefficients are \(0.65\) and \(−0.037\),respectively. Calculate the location of the aerodynamic center.
For the NACA \(2412\) airfoil, the lift coefficient and moment coefficient about the quarter-chord at \(−6 ^{\circ}\) angle of attack are \(−0.39\) and \(−0.045\),respectively. At \(4^{\circ}\) angle of attack, these coefficients are \(0.65\) and \(−0.037\),respectively. Calculate the location of the aerodynamic center.
We need to find here the location of aerodynamic center. Slope of the lift curve is \[a_{0}=\frac{0.65-(-0.39)}{4-(-6)}=0.104\;\textrm{per degree}\]
Slope of the moment coefficient curve \[m_{0}=\frac{-0.037-(-0.045)}{4-(-6)}=8\times10^{-4}\;\textrm{per degree}\]
Location of aerodynamic center is given as \[\bar{x}_{ac}=-\frac{m_{0}}{a_{0}}+0.25
\\\Rightarrow \bar{x}_{ac}= -\frac{8\times10^{-4}}{0.104}+0.25=0.242\]
