GATE 2026 AE – Question 54
For an airfoil section the pitching moment coefficient is determined about a reference point that is 0.3 times the chord behind the leading edge. It varies with the lift coefficient as shown in the table below. The distance of the aerodynamic center from the leading edge of the airfoil as a fraction of the chord is ________ (rounded off to one decimal place).
| $c_l$ | 0.2 | 0.4 | 0.6 | 0.8 |
|---|---|---|---|---|
| $c_m$ | -0.02 | 0 | 0.02 | 0.04 |
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Correct answer: 0.39 to 0.41
Explanation
About a point at $x_{ref}$ the moment coefficient is $c_{m} = c_{m,ac} + c_l\left(\frac{x_{ac} - x_{ref}}{c}\right)$, so the slope $\frac{dc_m}{dc_l} = \frac{x_{ac} - x_{ref}}{c}$. From the table the slope is $\frac{0.04 - (-0.02)}{0.8 - 0.2} = 0.1$, so $\frac{x_{ac}}{c} = 0.3 + 0.1 = 0.4$.