Consider a finite wing with an aspect of ratio of 7; the...

Consider a finite wing with an aspect of ratio of 7; the airfoil section of the wing is a symmetric airfoil with an infinite-wing lift slope of $0.11$ per degree. The lift-todrag ratio for this wing is 29 when the lift coefficient is equal to $0.35$. If the angle of attack remains the same and the aspect ratio is simply increased to 10 by adding extensions to the span of the wing, what is the new value of the lift-to-drag ratio? Assume that the span efficiency factors $e=e_{1}=0.9$ for both cases.

Consider a finite wing with an aspect of ratio of 7; the airfoil section of the wing is a symmetric airfoil with an infinite-wing lift slope of $0.11$ per degree. The lift-todrag ratio for this wing is 29 when the lift coefficient is equal to $0.35$. If the angle of attack remains the same and the aspect ratio is simply increased to 10 by adding extensions to the span of the wing, what is the new value of the lift-to-drag ratio?
Assume that the span efficiency factors $e=e_{1}=0.9$ for both cases.

Key Concepts

Aerodynamic Efficiency (Lift-to-Drag Ratio)

Aerodynamic efficiency, measured by the lift-to-drag (L/D) ratio, is a key performance metric in wing design and aircraft performance. It represents the trade-off between the beneficial lift generated and the drag produced by the wing. Factors such as aspect ratio, induced drag, and span efficiency directly influence the L/D ratio, making its optimization critical for efficient aerodynamic performance.

Span Efficiency Factor

The span efficiency factor (often denoted as 'e') is a correction factor that accounts for non-ideal effects, such as non-uniform lift distribution and wing planform irregularities, which can degrade aerodynamic performance. A value close to 1 indicates nearly ideal lift distribution; in practical designs, this factor is less than 1, reflecting additional drag incurred due to real-world conditions.

Finite Wing Theory

Finite wing theory deals with the aerodynamic characteristics of wings with a limited span. Unlike infinite wing analysis, where wing tip effects are absent, finite wings experience induced drag due to the creation of wingtip vortices. This theory enables the prediction of performance factors such as lift distribution and induced drag, especially when designing wings with different aspect ratios.

Aspect Ratio

Aspect ratio is defined as the ratio of the wing span to its chord (or more generally the square of the span divided by the wing area). It is a fundamental geometric parameter that influences the aerodynamic efficiency of a wing. Higher aspect ratios typically reduce induced drag because of a more favorable lift distribution and reduced wingtip vortex strength, thereby improving the lift-to-drag ratio.

Induced Drag

Induced drag is a byproduct of the generation of lift and arises due to the vortices formed at the wing tips. It is inversely proportional to the aspect ratio and directly related to the lift coefficient squared. In aerodynamic analysis, minimizing induced drag is critical for increasing the overall efficiency (lift-to-drag ratio) of the wing.

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