Thin Airfoil Theory

Derive the fundamental equation of thin airfoil theory and solve it for symmetric airfoil.

Show the typical distribution of pressure coefficient on the upper and the lower surfaces of an airfoil for a zero and non-zero angle of attack.

Explain with appropriate sketches how stall occurs in an airfoil at a high angle of attack.

Draw an asymmetric (cambered) airfoil and show its nomenclature. Also show the drag and lift forces when the airfoil is placed at an angle of attack greater than zero against a uniform system.

Derive the fundamental equation of thin airfoil theory for symmetrical airfoil.

Explain the Kutta condition for the flow is smoothly leaving from the trailing edge of the airfoil.

Derive the fundamental equation of thin airfoil theory.

Consider an NACA 2412 airfoil with a chord of $0.64 \text{ m}$ in an air-stream at standard sea level conditions. The free stream velocity is $70 \text{ m/s}$. The lift per unit span is $1254 \text{ N/m}$. Determine:
(i) the angle of attack and drag force per unit span, and
(ii) the moment per unit span about the aerodynamic center.

What is drag polar? Write down the drag polar of complete airplane and explain each term.

Using the momentum theory of propeller, show that
$$\eta = \frac{V}{V_a}$$
where the symbols have their usual meaning.

A propeller with a diameter of $3 \text{ m}$ produces a positive thrust of $4450 \text{ N}$ at $45 \text{ m/s}$ under standard sea level conditions ($\rho = 1.226 \text{ kg/m}^3$). Determine:
(i) the maximum efficiency
(ii) The pressure difference between atmospheric pressure and pressure immediately in front of the propeller

Define streamlined body. Differentiate between friction drag and pressure drag.

What are the sources of aerodynamic forces and moments that can be developed on aeronautical vehicles.

In low-speed, incompressible flow, the following experimental data were obtained for NACA4412 airfoil section at an angle of attack of $4^\circ$: $C_L = 0.85$ and $C_{m, c/4} = -0.09$. Determine the location of center of pressure.

Explain Magnus effect in moving fluid. How is it applied to a moving body?

An airfoil $1.5 \text{ m} \times 1.5 \text{ m}$ moves at $15 \text{ m/s}$ in stationary air of specific weight $1.15 \text{ kg/m}^3$. If the coefficients of drag and lift are $0.15$ and $0.75$ respectively, determine (i) the lift force (ii) the drag force (iii) power required to keep the airfoil in motion.

What is drag polar? Write down the drag polar of complete airplane and explain each term.

Derive the fundamental equation of thin airfoil theory.

Consider an NACA 23012 airfoil. The mean Camber line for this airfoil is given by
$z/c = 2.6595 \left[ (x/c)^3 - 0.6075 (x/c)^2 + 0.1147 (x/c) \right]$ for $0 \leq x/c \leq 0.2025$
and
$z/c = 0.02208 \left[ 1 - (x/c) \right]$ for $0.2025 \leq x/c \leq 1.0$