JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech II FLIGHT MECHANICS I Previous Question Paper (November/December - 2020 - R13)

The aspect ratio (AR) of a wing is defined as the square of the wingspan divided by the wing area. In the context of gliding wings, which are designed for high aerodynamic efficiency, the choice of aspect ratio involves a trade-off between aerodynamic performance and structural integrity.

The merits of a high aspect ratio wing include:

• Reduced Induced Drag: Induced drag is inversely proportional to the aspect ratio. A higher AR reduces the strength of wingtip vortices, significantly improving the lift-to-drag ratio (L/D), which is critical for maximizing glide range and minimizing sink rate.
• Improved Climb Performance: By reducing induced drag, high AR wings allow for better energy retention during thermalling, enabling the aircraft to climb more efficiently in rising air.
• Enhanced Lift Curve Slope: High AR wings exhibit a steeper lift curve slope, providing more effective lift generation at lower angles of attack.

The demerits of a high aspect ratio wing include:

• Structural Weight Penalty: Increasing the span for a given wing area increases the bending moment at the wing root. This necessitates heavier structural materials or more complex spar designs to maintain wing stiffness and prevent aeroelastic phenomena like flutter.
• Reduced Roll Rate: The increased span results in a higher roll moment of inertia, making the aircraft less responsive to aileron inputs and reducing maneuverability.
• Hangar and Ground Handling Constraints: A very large wingspan makes the aircraft difficult to store in standard hangars and complicates ground handling, often requiring folding wing mechanisms or specialized transport trailers.
• Increased Parasite Drag: While induced drag decreases, the increased surface area (wetted area) of a very long, thin wing can lead to an increase in skin friction drag, which may offset the benefits of reduced induced drag at higher flight speeds.

In the International Standard Atmosphere (I.S.A.), the troposphere extends from sea level to 11,000 m with a constant lapse rate of 0.0065 K/m. Above 11,000 m, the temperature remains constant at 216.65 K (isothermal layer). To calculate the properties at 15,000 m, we must first determine the conditions at the tropopause (11,000 m).

1. Conditions at the Tropopause (h = 11,000 m):

Temperature (T₁):

Pressure (P₁):

2. Conditions at 15,000 m (h = 15,000 m):

Since 15,000 m is in the isothermal layer, the temperature is constant:

Pressure (P₁₅₀₀₀) in the isothermal layer is given by:

Using g = 9.80665 m/s² and R = 287.05 J/kg·K:

Density (ρ₁₅₀₀₀) is calculated using the equation of state: