Dynamic Lift

Bookmark added to your notes.
View Notes
×

What is Magnus Effect?

We all love to play with a ball, so when we throw a ball, it deviates from its original path instead of making a projectile motion. So, the deviation of this ball is called the Magnus Effect.

The Magnus Effect is an observational phenomenon that is closely related to spinning objects traveling via air or a fluid.

When we see an airplane flying in the sky, a question comes to our mind: how do wings take a lift? Is there something that lifts the wings up? Yes, there’s a force that lifts the wings of a plane.


How Wings Take Lift?

The two examples we discussed above are Dynamic Lift and Magnus Effect applications, and now we will discuss these in detail.

Airfoil technologies have drastically changed the way we live. This technology drives gas turbines, flying wind turbines, and hydraulic machines. 

An airfoil is a shape that has revolutionized the world of Engineering Physics. An airfoil is a shape that produces a lift when fluid is forced over it. So, what is the source of this lift? 

                         [Image will be Uploaded Soon]

According to Bernoulli’s principle, the particles at the upper surface should travel more distance than those at the lower surface. 


Since the particles at both the surfaces need to reach the end-point simultaneously; therefore, the velocity of upper particles should also be greater than the lower one, as it has to cover a greater distance; this means that the pressure at the top is lesser and at the bottom is high. This pressure difference generates lift. 

The argument we discussed above is called the Equal-time argument. However, this was proved wrong, as the particles on the upper and the lower surface can’t reach simultaneously; also the path wasn’t streamlined.

We can see that the high pressure brings the curvature in the fluid flow, as we can see in Fig. So, the more is the curvature, the more is the lift. 

Now, we will apply Newton’s third law to understand How Wings Take Lift?

We can see that airfoil pushes the fluid downward, so according to Newton’s third law, the air also generates an equal and opposite reaction force on the airfoil, which results in the lift. 

                 [Image will be Uploaded Soon]


What is a Dynamic Lift?

We understood how wings take the lift. Now we will study the science behind it.                          

While seeing an airplane, we ask ourselves why the wings of a plane are at a certain angle; for that, let’s take a look at a new figure:

                      [Image will be Uploaded Soon]

The wing of a plane is at a slight angle, and this causes the air streamlines at the upper surface group together, as shown below:

                    [Image will be Uploaded Soon]

We can see that the area between the streamlines has reduced a bit. So, by Bernoulli’s Principle, the mathematical expression for the same will be:

                       A1V1 = A2V2……..(1)

This equation is called the continuity equation.


Here, 

A1 is the area between the streamlines at the upper surface

V1 = Flow velocity of the streamline at the upper surface

A2 = area between the streamlines at the lower surface

V2 = Flow velocity of the streamlines at the lower surface


What happens here is, as the space or gap between the streamlines reduces, the velocity increases. From expression (1), we can understand that the area is inversely proportional to the streamline’s velocity, i.e., high velocity, low pressure and low velocity, high pressure. 

Now, considering the direction of the wings and the air molecules. If the wings are traveling in the positive x-direction, and the air molecules are rushing past to the wings. 

So, if we take the reference frame of the wing, then we are going to have streamlines of air that will rush in the direction of air molecules along the x-axis. 

Since the direction of the wing is along the direction of motion, along the x-axis and also they are bent by some angle, that’s why the streamlines at the upper surface come close to each other and are separated at the bottom surface of the airfoil. 

So, from equation (1), we understood that the pressure difference creates an invisible force, which acts along the y-direction, and that force is nothing but the lift. This lift is known as the Dynamic Lift. 

Mathematically, we can express the Dynamic Lift as:

      F = ΔPA…..(2)


So, what is Dynamic Lift? It is a force that lifts our wing, and therefore, lets our plane continue flying in the air. 


Summary

We understood from the above explanation that area reduction between the streamlines increases the velocity, and from the continuity equation, when the area decreases, the volume increases; this, in turn, increases the flow velocity of the streamline at the upper surface. Since the velocity at the upper surface is higher, that’s why the pressure will be lower, while at the lower portion, it will be higher.

As the difference arises, there is a force that lifts the wings and helps the plane continue its flight.

FAQ (Frequently Asked Questions)

Question 1: What are the Four Forces of Flight?

Answer: We know that airplanes fly because of the pressure difference in the streamlines at the upper and the lower surface of the airfoil. This pressure difference creates a force, which is the Dynamic Lift. However, there are three other forces besides the lift that help the airplane fly. These are:

  1. Thrust

  2. Drag, and

  3. Weight

These four Principles of Flying are also called the aerodynamic forces because they exist during the motion (flight) of the airplane.

Question 2: State Bernoulli’s Theorem.

Answer: Bernoulli’s theorem is consistent with the law of conservation of energy when applied to a fluid in motion. This theorem states that for a streamlined flow of an ideal liquid, the total energy viz: potential energy + pressure energy + kinetic energy per unit mass remains constant in every cross-sectional area throughout the flow.

Question 3: Write the Formula for the Lift.

Answer: The formula for the lift of a cricket ball is given as:

Lift (L) = 4/3 (4 π2b3sρv)


Where,

b = radius of the ball

v= velocity of the ball

ρ= density 

s =  rotation

Question 4: What are Lift and Drag?

Answer: Lift is a component of aerodynamic force that lies perpendicular to the direction of flow, whereas Drag is a component that stays parallel to the flow of motion.