1. Projectile motion & Fluid mechanics
Biomechanics
Projectile motion & Fluid mechanics

2. Projectiles A projectile is anything that goes off the ground.
In sport that could be a rugby ball that has been kicked or a tennis ball that has been struck.
It could also be a high jumper or a long jumper in athletics

3. Flight Paths of Objects in Sport
Understanding flight path can help determine optimal angle of release and thus help a performer maximise distance thrown.
The flight path of a projectile follows a parabolic curve when it is only affected by gravity (air resistance not taken into consideration)

4. Factors Affects the Horizontal Displacement that a Projectile Travels
The distance that a projectile will travel is affected by 3 main factors:
angle of release
speed of release
height of release
The angle and speed of release can affect the parabolic curve that it follows

5. Optimum Angle of Release
The optimal angle of release depends on the release height and the landing height (when all other factors are equal).
When release height is equal to landing height then the optimum angle is 45 degrees (e.g. a lifted pass in hockey)
When release height is lower than landing height then the optimum angle is greater than 45 degrees (e.g. chipping out of a bunker in golf)
When release height is higher than landing height then the optimum angle is less than 45 degrees (e.g. in shot put)

6. Optimum angle of Release
Is the optimum angle of release for these examples equal to, greater than or less than 45 degrees?
Racing dive in swimming
High jump
Hockey flick/scoop
Long jump
Tennis serve

7. Attack Angle
Attack angle is the angle at which a sportsperson strikes/throws/jumps etc. Knowledge of this is crucial to success in a range of sports
Attack angle in golf
Sports science analysis of Steph Curry
In javelin the optimum release angle is about 45 degrees but in long jump it is about 22 degrees? Why?
Because, the greater the angle of release the more force is required to overcome the weight of the projectile, or if the same force is applied it will result in a lower velocity of release.
As you coach you would need to consider the weight of the projectile and the strength of the athlete when considering which is the optimum angle of release.

8. Velocity of Release
Increased velocity of release will result in increased horizontal distance travelled. E.g. greater speed in long jump run up and greater speed of rotation for a hammer throw

9. Height of Release
The greater the height of release, the greater the horizontal distance travelled. Two shot putters throwing the shot at exactly the same angle and velocity. The taller one will achieve the greatest result.

10. Projectile motion youtube clip

11. Parabolic Curves
Projectiles that have a large weight force and small air resistance force (e.g. javelin) will follow a path close to a true parabola.

12. Deviations from the Parabolic Flight Path
Some objects can deviate from the parabolic path.
Objects travelling at high speeds (e.g. golf balls)
Objects that have large cross-sectional areas (e.g. a football)
Objects that don’t have a smooth surface (e.g. shuttlecock)

13. Bernoulli Principle and Magnus Effect
Bernoulli Principle The relationship between velocity and pressure which acts on a body as it passes through fluid/air Magnus Effect The generation of a sideways force on a spinning object (can be side to side or up and down) due to pressure differences that develop as a result of velocity changes caused by the spinning object

14. Projectiles and Lift
If a projectile can gain some lift during flight it will stay in the air for longer and achieve a greater horizontal distance.
Think of how an aeroplane wing works.
The rounded shape
pushes air over it and
makes it travel further
than air under the wing.
Fast flow resulting in
low pressure is known
as the Bernoulli Principle.

15. Bernoulli Principle continued…
The air over the top travels faster as it is forced down the other side (think of water falling down a waterfall).
The fact that fast flowing air results in low pressure can seem counter-intuitive but is scientifically proven.
A spoiler on a F1 car works in the opposite way.
The Bernoulli principle is used to
explain how changes in air velocity
results in changes to pressure. The
Magnus effect follows on from this and
is more relevant to sport for us.

16. The Magnus Effect – Types of Spin
The type of spin applied to a ball will effect the path that it follows:

17. In the previous diagram the ball has backspin.
The air going towards the ball is going with the spin at the top of the ball and against the spin at the bottom.
Therefore airflow is faster at the top of the ball.
The faster flowing air creates a lower pressure
Things always move from an area of high pressure to an area of low pressure and the ball therefore moves upwards.

18. Topspin, backspin and no spin

19. Topspin The top of the ball:
The surface of the ball is travelling in the opposite direction to the airflow
Causes air to slow down and causes high pressure
The bottom of the ball:
The surface of the ball is travelling in the same direction as the air flow
Causes air speed to speed up and causes low pressure
Consequence:
Pressure difference causes ball to deviate towards the area of low pressure.
With topspin the ball dips and the distance travelled is decreased when compared to a non-spinning flight path
Tennis players use topspin to ensure the ball dips down and stays in

21. Spin and Bounce – Friction important here
Topspin
Bottom of the ball wants to slide backwards when contact is made with ground
Friction will oppose this action and act in a forward direction (think Newton’s third Law)
This causes the ball to skim off the surface quickly at a low angle
E.g. table tennis – players like topspin as it results in ball increasing in speed as it bounces allowing less time for opposition
Table tennis topspin

22. As ball hits ground the bottom of it is pushing against the ground
Backspin
As ball hits ground the bottom of it is pushing against the ground
Friction opposes this motion and acts backwards
This causes the ball to kick up at a steeper angle
In basketball backspin is used (by flicking wrist) to ensure the ball falls down into basket after hitting backboard
In golf backspin can be used to help a ball float further and have a more controlled landing
Dustin Brown v Nadal – incredible backspin
Basketball dropped from a dam

23. Curling / Swerving an Object
The Magnus effect can also allow us to put sidespin on a projectile. Top 10 swerved free kicks in football The science behind swerved free kicks How is the spin on a table tennis shot different to spinning a cricket ball? A cricket ball gains the majority of its spin from friction when striking the ground, this is not the same as the Magnus effect.

24. Fluid Friction and Air Resistance
Some key terms: Drag force: sometimes called air resistance, this a type of friction force acting opposite to the relative motion of any object moving. Streamlining: a design created to minimise the resistance effects of air or water. Air resistance, drag and fluid resistance mean the same thing.

25. Factors affecting Air/Fluid Resistance
Velocity - the faster the body is travelling through a fluid (or air), the greater the air resistance.
Cross sectional area - the greater the cross sectional area the greater the air/fluid resistance. (in which sports do performers attempt to reduce this?)
Shape - pointy shaped objects cut through air/fluid resistance more easily, for example an F1 car or the shape of a track cyclists helmet.
Surface - a rough surface will create more air/fluid resistance or drag than a smooth surface.

26. Factors affecting Air/Fluid Resistance
The cross-sectional area, shape and surface of an object can have a major impact in sport. Millions is spent on making improvements in these 3 aspects in order to increase the speed or efficiency of a person / equipment. List examples for each of these 3 factors of sports in which changes have been made in the hope of success.

27. Air/Fluid Resistance in Sport
At the elite level the effects of air resistance can be the difference between success and failure
LZR swimsuit
Streamlining technology in swimming
British cycling marginal gains
Dimples on a golf ball
Parachutes to increase air resistance

28. Equipment and the Magnus Effect
As we know that how an object moves through the air (or a fluid) is greatly affected by its cross-sectional area, its shape and its surface we can consider how easy it is to swerve or curl. Consider these objects.

29. Football Can only apply a relatively small spin velocity to it when kicking but the rough surface allows swerve Tennis ball Can apply high velocity of spin and has quite rough surface for large amounts of swerve Golf ball Very high velocity of spin and dimpled surface enables swerve (often unwanted) Table tennis ball Smooth surface not ideal for giving spin but very high spin velocity due to rough surface of bat enables large amounts of swerve Rounders ball Reasonably rough surface but very little spin velocity can be applied and so almost impossible to apply swerve

30. The shape of an object affects airflow over it
The shape of an object affects airflow over it. Using sporting examples from individual activities, examine how athletes utilise this knowledge to adopt a technique to improve their performance. (8)

31. The flight path of a ball is affected by applying spin to it
The flight path of a ball is affected by applying spin to it. Examine the effect of backspin on a tennis ball. (8)