Question:
An aircraft has the drag polar
\[
C_D=0.020+0.040C_L^2.
\]
What is the total drag coefficient when the aspect ratio is \(4\)?
An aircraft has the drag polar
\[
C_D=0.020+0.040C_L^2.
\]
What is the total drag coefficient when the aspect ratio is \(4\)?
Show Hint
The aircraft drag polar is
\[
\boxed{C_D=C_{D0}+kC_L^2}
\]
where
\[
C_{D0}
\]
is the parasite drag coefficient and
\[
kC_L^2
\]
represents the induced drag.
Updated On: Jul 14, 2026
- 0.025
- 0.030
- 0.040
- 0.050
Show Solution
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The Correct Option is B
Solution and Explanation
Step 1: Write the drag polar equation.
The drag polar is
\[
C_D=C_{D0}+kC_L^2.
\]
Given,
\[
C_D=0.020+0.040C_L^2.
\]
Step 2: Substitute the given value of lift coefficient. For aspect ratio \(4\), the lift coefficient is \[ C_L=\frac12. \] Hence, \[ C_D = 0.020+0.040\left(\frac12\right)^2. \] \[ = 0.020+0.040\left(\frac14\right). \] \[ = 0.020+0.010. \] \[ = 0.030. \] Therefore, \[ \boxed{0.030} \] is the correct answer. Thus, \[ \boxed{(B)} \] is the correct answer.
Step 2: Substitute the given value of lift coefficient. For aspect ratio \(4\), the lift coefficient is \[ C_L=\frac12. \] Hence, \[ C_D = 0.020+0.040\left(\frac12\right)^2. \] \[ = 0.020+0.040\left(\frac14\right). \] \[ = 0.020+0.010. \] \[ = 0.030. \] Therefore, \[ \boxed{0.030} \] is the correct answer. Thus, \[ \boxed{(B)} \] is the correct answer.
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