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Spin and Magnus Force

Spin

Creation of Spin

Creation of Spin

How do we create spin (or rotation)?

Spin is created by applying an external force outside the centre of mass

Where this eccentric force is applied will determine the way the projectile (usually a ball) spins

Creation of Spin

Where is spin used tactically in sport?

Types of Spin

Types of Spin

List four different types of spin

Give examples of reach type of spin

  • topspin: eccentric force applied above centre of mass (spins downwards around the transverse axis)
  • backspin: eccentric force applied below centre of mass (spins upwards around the transverse axis)
  • sidespin hook: eccentric force applied right of the centre of mass (spin left around the longitudinal axis)
  • sidespin slice: eccentric force applied left of the centre of mass (spin right around the longitudinal axis)

Magnus Effect

Heinrich Magnus

Heinrich Magnus

Heinrich Magnus followed Bernoulli in the early 19th century to apply fluid mechanics to rotating projectiles

The Magnus Effect

The Magnus Effect

The Magnus effect is the underlying theory of how an additional Magnus force can deviate a spinning projectile away from its expected flight path

Magnus effect: creation of an additional Magnus force on a spinning projectile which deviates from the flight path

Magnus force: a force created from a pressure gradient on opposing surfaces of a spinning body moving through the air

Application in Sport

Application in Sport

Can you think of any examples for when you have experienced Magnus force?

When used correctly the additional Magnus force can:

  • swerve a football around a wall
  • extend the flight path of a golf drive
  • accelerate a topspin serve in tennis to mislead the opposition

Pressure Gradient

Pressure Gradient

The Magnus effect works on the same theoretical basis as the Bernoulli principle

However, instead of a projectile's specific shape we consider the effect of the projectile's rotation or spin

The way the projectile spins determines the direction, velocity and pressure of air flow around it

Again, a pressure gradient is formed either side of the spinning projectile and an additional Magnus force is created which deviates the flight path

What is a pressure gradient?

The pressure-gradient force is the force that results when there is a difference in pressure across a surface. A difference in pressure across a surface then implies a difference in force, which can result in an acceleration according to Newton's second law of motion, if there is no additional force to balance it. The resulting force is always directed from the region of higher-pressure to the region of lower-pressure

Describe what you notice about the two diagrams in your notes ?

Velocity?

Pressure?

Forces created?

Air flow?

How does this relate to Bernoulli's principle? Free kick around a wall

1. When the player kicks the ball off centre from the rotational axis of the ball, a anticlockwise spin is induced

2. As the ball spins through the air, the drag from air resistance on the right side of the ball increases while drag on the left side decreases due to the ball spinning around its rotational axis

3. This causes a drag imbalance causing the left-hand side of the ball to be a low pressure region as its velocity increase

4. This causes the high pressure region to move the ball to the left-hand side

Deviation

Deviation is what is created....

The deviation created by the pressure gradient

means all forms of spin create a non-parabolic

flight path

What do you think happens to the flight path for each spin?

  • A topspin rotation creates a downward Magnus force, shortening the flight path
  • A backspin rotation creates a upward Magnus force, lengthening the flight path
  • A sidespin rotation creates a Magnus force to the right (slice) and left (hook), swerving the projectile right (slice) and left (hook) - When drawing this with an airflow diagram be sure to draw it from the top

Topspin

Additional Dip

Additional Dip

For a ball with topspin the additional Magnus force is

created by:

  • the upper surface of the projectile rotating towards

the oncoming air flow (top to bottom), which opposes motion,

decreasing the velocity of air flow - high pressure zone is created

  • the lower surface of the projectile rotating in the same direction as the air flow, which increases the velocity of air flow and creates a zone of low pressure

  • a pressure gradient forming and an additional Magnus force being created downwards (all gases move from an area of high pressure to an area of low pressure)

Effect of downward force

Effect of downward force

The downward Magnus force adds to the weight of the projectile and the effect of gravity is increased

The projectile 'dips' in flight, giving less time in the air as the flight path shortens

Tennis and Table Tennis

Tennis and Table Tennis

In these sports, placing spin on the ball gives it stability in flight, guiding the air flow and reducing turbulence

The use of topspin shortens the flight path, meaning a player can hit the ball harder, thus ensuring it will still land in court or on the table; for example, a topspin serve in tennis or a topsin drive in table tennis

It can also confuse the opposition, bringing them closer to the net and unexpectedly putting them in a defensive position

Backspin

Activity

Activity

If an eccentric force is applied beneath the centre of mass, backspin is created

Explain how the additional Magnus force is created on a backspinning ball and how this is used to a player's advantage in tennis and table tennis

Use the following prompts to guide you and sketch diagrams to add to your explanation:

  • upper surface of the ball (rotates in the same direction as air flow): effect on velocity and pressure
  • underneath surface of the ball (opposes air flow): effect on velocity and pressure
  • pressure gradient forms as all gases move from an area of high pressure to low pressure, creating the additional Magnus force: direction of Magnus force and effect on time in the air and length of flight path
  • use of backspin in tennis and table tennis
  • air flow and flight path diagram

Sidespin

Sidespin

Sidespin

Sidespin is also well used for making a ball swerve in flight, both hook to the left and slice to the right. These types of spin can be viewed easily from above, as shown below:

Extend your Knowledge

Diagrams

Diagrams

Free body diagrams and resultant force diagrams can also be drawn to show the forces acting on a spinning ball in flight and the resultant force using the parallelogram law.

Biomechanists then use these diagrams to analyse performance of both athletes and equipment

Tiny changes in the surface of a

ball, for example, can have a big

impact in their flight through the

air - for example, for a ball with

backspin

Study Tip

Study Tip

When drawing an air flow diagram for a ball with topspin or backspin it is viewed from the side whereas sidespin is drawn from above

Airflow diagrams must show:

  • direction of air flow opposing the direction of motion
  • direction of rotation of the ball
  • velocity and pressure labels
  • more and tighter air flow lines with the direction of rotation side of the ball
  • Magnus force in the direction of flight path deviation from the centre of mass

Examples in Sport

Tennis

not the whole clip, just bits with practice shown

Tennis

The effects of topspin and backspin in tennis extend to the bounce of the ball:

  • A ball with topspin accelerates at a low angle on bounce as the friction with the ground surface acts in the same direction of motion. This advantages athletes with powerful serves, compact, short strokes and a variety of shots, such as Novak Djokovic, especially on the fast surface: the grass courts of Wimbledon
  • A ball with backspin decelerates and bounces at a steep angle as the friction with the ground surface acts against the direction of the ball. This advantages agile athletes who can move across the whole court rapidly to return balls that 'split up' after bounce, such as Rafeal Nadal, especially on the loose surface clay courts of Roland Garros

Other Examples

Other Examples

  • Golf: placing sidespin on the ball will allow it to swerve in flight, moving the golfball around obstacles in its path, such as trees or bends in the fairway

  • Tennis & table tennis: placing sidespin on the ball can confuse the opposition, moving them to the outside of the court or table unexpectedly after, e.g. a topspin slice serve, giving the player an open court/table to go on the attack

Extend your Knowledge - Golf

Extend your Knowledge -

How can the equipment used impact the rotation of the ball in play?

Research one of the below and describe how you think impacts the rotation?

Jabulani football

Dimples in a golf ball

Softball instead of baseball

Football

Football

Spin is most well appreciated on the football pitch

  • Sidespin is used to swerve a ball around a wall when taking a free kick or into the goal mouth from a corner kick
  • This can produce quite spectacular results and create sporting icons such as David Beckham and Roberto Carlos, famous for their free kicks and goals from unenviable positions

Homework

Homework

Research the Adidas Jabulani football from the South Africa World Cup in 2010 and compare it with the performance of the redesigned Brazuca ball used in South America in 2014

Consider their performance, stability and reliability as a spinning projectile and their effect on the game for both players and spectators

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