JNTU B.Tech II FLIGHT MECHANICS-I Previous Question Paper (November/December - 2020 - R15)

The aspect ratio (AR) of a wing is defined as the square of the wingspan divided by the wing area. For a gliding wing, which requires high aerodynamic efficiency, the choice of aspect ratio involves a critical trade-off between performance and structural integrity.

Merits of High Aspect Ratio:

1. Reduced Induced Drag: High aspect ratio wings significantly reduce the strength of wingtip vortices. Since induced drag is inversely proportional to the aspect ratio, a higher AR leads to a higher lift-to-drag ratio, which is essential for achieving a flat glide angle and maximizing range.
2. Improved Climb Performance: By minimizing induced drag, the aircraft retains more energy during flight, allowing for better performance in thermals and increased endurance.
3. Enhanced Lift-to-Drag Ratio: A higher lift-to-drag ratio allows the glider to cover greater horizontal distances for every unit of altitude lost.

Demerits of High Aspect Ratio:

1. Structural Weight Penalty: Increasing the span for a given wing area increases the bending moment at the wing root. To maintain structural rigidity and prevent aeroelastic failure (such as wing flutter), the wing must be built with heavier materials or thicker spars, which increases the overall structural weight.
2. Increased Parasite Drag: While induced drag decreases, the increased wetted area of a longer, thinner wing can lead to higher skin friction (parasite) drag at higher airspeeds.
3. Reduced Maneuverability: High aspect ratio wings have a higher roll inertia, making the aircraft less responsive to lateral control inputs.
4. Storage and Handling: The increased span makes the aircraft more difficult to hangar, transport, and maneuver on the ground.

In summary, while a high aspect ratio is vital for the aerodynamic efficiency required for long-distance gliding, it is constrained by the structural weight penalty and the practical limitations of wing stiffness and handling.

In the International Standard Atmosphere (I.S.A.), the altitude of 15,000 m lies within the troposphere, where the temperature decreases linearly with altitude at a constant lapse rate. The standard sea-level values are: pressure (P₀) = 101325 N/m², temperature (T₀) = 288 K, and lapse rate (L) = 0.0065 K/m. The gas constant for air (R) is 287 J/(kg·K) and the acceleration due to gravity (g) is 9.80665 m/s².

1. Temperature (T) at 15,000 m:

2. Pressure (P) at 15,000 m:

The pressure is calculated using the hydrostatic equation for a constant lapse rate atmosphere:

3. Density (ρ) at 15,000 m:

Using the equation of state for a perfect gas: