Now that we've covered the physics of banana swing, let us understand the physics behind the football curl!
What is a Football Curl?
Curl or bend associated with a football is the spin on the ball which will make it change direction. Curling or bending the ball is especially evident from free kicks, shots from outside the penalty area and crosses.
When kicking the ball, the inside of the foot is often used to curl the ball, but this can also be done by using the outside of the foot. Similar to curl, the ball can also swerve in the air, without the spin on the ball which makes the ball curl.
The image below is from the 1997 Roberto Carlos impossible goal.
The Magnus Effect
The reason that spin on a football makes it curl is known as the Magnus effect. It is the generation of a sideward force on a spinning cylindrical or spherical solid immersed in a fluid (liquid or gas) when there is relative motion between the spinning body and the fluid. The effect is named after German physicist Heinrich Gustav Magnus who described the effect in 1852. The Magnus effect is a particular manifestation of Bernoulli’s theorem. (Yes, from your Physics class!)
How is the sideward force generated?
In the case of a ball spinning through the air, the turning ball drags some of the air around with it. Viewed from the position of the ball, the air is rushing by on all sides. The drag of the side of the ball turning into the air (into the direction the ball is traveling) retards the airflow, whereas on the other side, the drag speeds up the airflow. Greater pressure on the side where the airflow is slowed down forces the ball in the direction of the low-pressure region on the opposite side, where a relative increase in airflow occurs.
Fluid dynamics behind the football curl
Calculating the trajectories of objects is a common problem in calculus where the absence of air resistance is generally assumed. Drag forces affect the path of a soccer ball and are of two main types: skin friction drag and pressure drag. Skin friction drag occurs when air molecules adhere to the surface of the ball, which results in friction from the interaction of the two bodies. Pressure drag occurs when the air reaches the rear of the ball. A large area then opens up for the airflow. Since the amount of moving air per unit area must be constant because we are not adding or removing air, the flow must slow down. Separation occurs when the air slows down so much that its speed relative to the ball falls almost to zero, which results in a wake as seen behind moving boats.
In a nutshell, a slow-moving football experiences a relatively high retarding force. But if you can hit the ball fast enough so that the airflow over it is turbulent, the ball experiences a small retarding force. A fast-moving football is therefore double trouble for a goalkeeper hoping to make a save - not only is the ball moving at high speed, it also does not slow down as much as might be expected. Perhaps the best goalkeepers intuitively understand more physics than they realize.
For the movement of the ball in the fluid, viscous forces is given by the equation: FD = CPAv2/2
where FD is the drag force, P is the density of fluid, A is the swept area and v is the velocity.
In 1976, Peter Bearman and his colleagues from Imperial College of London, carried out a classic series of experiments on golf balls. They found that increasing the spin on a ball produced a higher lift coefficient and hence a bigger Magnus force. However, increasing the velocity at a given spin reduced the lift coefficient. What this means for a football is that a slow-moving ball with a lot of spin will have a larger sideward force than a fast-moving ball with the same spin. So as a ball slows down at the end of its trajectory, the curve becomes more pronounced.
Content Source: Technical Analysis on Mechanical Model Based Football Curveball, Feng Li and Lu Liu; soccerballworld
Image Source: Soccermaniak
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