Lecture 3 (Wing & Lift)

Date:06.02.2020

  Aspect Ratio: The aspect ratio is the ratio of the wingspan and chord length. if the wingspan is 'b'  and the chord length is 'c'. then, 

    

$$\begin{align*} Aspect Ratio & = \frac{Wing Span}{Chord Length}\\ & = \frac{b}{c}\\ & = \frac{b^2}{bc}\\ & = \frac{b^2 }{S} ~~~~[b.c ~=~ S(Area~of~wing)] \end{align*}$$

    Angle of Attack (AOA): 

AOA or Angle of Attack is a term used in aerodynamics to describe the and between the chord line of the aerofoil and vector presenting the direction of airflow.

    

    Body Frame:

(1) Longitudinal axis (x) parallel to the fuselage.

(2) Lateral axis (y) cross to the fuselage.

(3) directional axis (z) or vertical axis.

    Angle of Incidence (AOI):

An angle between the chord line of an airfoil and the longitudinal axis is termed as angle of incidence.

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Newton's First Law: 

"Without any external force, a body at rest. and a body in motion will remain in motion in a straight or linear path."

    Modified: If a body at rest wants a motion, a force is needed. And if airflow gets bend or turned there must be a force acting on it.

        (1) Consider symmetric aerofoil at $0^{\circ}$ Angle of Attack:

In this case, speed of airflow on the upper surface and lower surface of the wing will be same. Thus the force of the upper surface $(F_1)$ and lower surface $(F_2)$ is equal. That means $F_1 = F_2$. So there will be no lift.

        (2) Consider Asymmetric aerofoil at $0^{\circ}$ Angle of Attack:

In this case, as the bending surface on upper side is higher, So there will be some differences in force on the upper surface $F_1$ and the lower surface $F_2$ because of the speed of two surfaces. That means $F_1<F_2$. So there will be lift.

    Lift: 

Lift is the component of the total aerodynamic force that acts perpendicular to direction of airflow. The lift force or simply lift is a mechanical force generated solid objects as they move through air. Lift acts in the perpendicular direction of the flying object or body.

    The Equation of lift is,  $$L = \frac{1}{2} C_L \rho v^2S$$  

Where, $C_L = \frac{2L}{\rho v^2S}$

Here in this equation, 

$$\begin{align*} L & = Lift \\ \rho & = ~Density ~of ~air~ (Kg~m^{-3}) \\ v & = ~Velocity ~of~ air ~(m~s^{-1}) \\ S & = ~Area~ of~ wing~ (b.c) \\ C_L & = ~Cofficient~ of~ lift~ or~ Efficiency~ in~ \\ & ~~~~~~~generating~ lift~(no~ unit~ or~ Dimensionless) \end{align*}$$

    Drag: Drag is the component of the total aerodynamic force that acts parallel to the direction of airflow.

    How lift is generated:

Newton's First Law states that "without any external force, a body at rest will remain at rest. and a body in motion will remain in motion in a straight or linear path."

If we can modify the statement we can say, "If an object or mass in air starts moving from rest there must be a force acting on it. Similarly, if a flow of air gets bent or turned over a wing, it is due to a force acting on it. Newton's third law states that, 

"Every action has its equal and opposite reaction."

By the third law, the force will be countered by an equal and opposite force, In case of an airfoil, the airflow gets bent or turned due to its shape. The force acting in opposite direction creates lift in the aerofoil.