JNTU B.Tech III AIRCRAFT PERFORMANCE AND STABILITY Previous Question Paper (September - 2021 - R18)

According to Froude's momentum theory, the thrust T produced by an actuator disk is given by T = ρ A V_d (v_2 - V), where V_d is the velocity at the disk and v_2 is the slipstream velocity. The induced velocity at the disk is v = (v_2 - V) / 2. The thrust can be expressed as T = 2 ρ A (V + v) v. Given T = 4000 N, V = 120 m/s, and diameter D = 2.5 m, the disk area A = π * (D/2)^2 = 4.9087 m^2. At sea level, air density ρ = 1.225 kg/m^3.

Substituting the values: 4000 = 2 * 1.225 * 4.9087 * (120 + v) * v. This simplifies to 4000 = 12.026 * (120v + v^2), or v^2 + 120v - 332.6 = 0. Solving this quadratic equation for v: v = [-120 + sqrt(120^2 - 4 * 1 * (-332.6))] / 2 = 2.72 m/s. The minimum power required is the ideal power P = T * (V + v) = 4000 * (120 + 2.72) = 490,880 W, or 490.88 kW.

Drag in an airplane is categorized into two primary types: parasite drag and induced drag.

1. Parasite Drag: This is the resistance caused by the aircraft moving through the air, independent of lift generation. It includes:

• Form Drag: Caused by the shape of the object and pressure differential. Minimized by streamlining components.
• Skin Friction Drag: Caused by air viscosity and surface roughness. Minimized by using smooth materials and maintaining laminar flow.
• Interference Drag: Caused by the interaction of airflows between different components (e.g., wing-fuselage junction). Minimized by using fairings and fillets.

2. Induced Drag: A byproduct of lift generation, caused by wingtip vortices. It is inversely proportional to the square of the flight speed. Minimized by:

• Increasing the Aspect Ratio of the wing.
• Using Winglets at the tips to disrupt vortex formation.
• Optimizing the lift distribution across the span (e.g., elliptical lift distribution).