A look at how a football swerves and how a tennis racket behaves. Explaining the mechanics behind these games.

2. Flight of a Football

3. • Round! And remain round!
• Bouncy
But not too much!
• Water Proof
• Swift Through the Air
…Aaaand here comes the physics!

4. • Weight Acts downwards always
Depends on how heavy the ball is
• Magnus Force The direction depends on the motion of ball
Depends on the spin on the ball
Force is perpendicular
to both spin and velocity
Simple application of
Bernoulli’s principle
Higher
Pressure
Lower
Pressure

5. • Question: Is it always true that the harder you kick the ball, the faster it goes?
NO!
• A new force enters the scene: the Drag Force!
• Rule of thumb:
The greater the
turbulence, the
greater drag force!
• Drag Force is proportional to square of velocity. Faster the ball, greater the drag
• Surprise! Drag suddenly decreases as the separation points coincide!
(Image courtesy:
Ken Bray article –
A Fly Walks Around A Football)

6. A Rougher Ball is better than a Smooth One
• Drag Coefficient = Measure of how much drag there is
• Drag Coefficient falls sooner for a rougher ball than a smooth one
• Drag Crisis: The fall is rapid!
Which is a better football? A Smooth One or a Rough One?
The rougher ball moves
more smoothly than a
smooth one!!
Drag crisis
(Graph courtesy:
A Fly Walks Around A Football and
Journal fo Fluid Mechanics)

7. Taking a free-kick =
Aiming for a letterbox slit!
• Weight, spin and drag affect ball trajectory
• A free kick is not as easy as it seems!
• Smooth is not always desirable

9. All That Racquet
Tennis

10. • Rigidity of the stem and flexibility of the head increased
• Increase in the area of the head
• Greater adjustability of the tension in the strings
Wooden Aluminium Graphite

11. Dead Spot
More bounce
Sweet Spot
Centre of mass
Grip

12. Impact! Translation Rotation Final movement= + =
If the ball is hit just right, there will be no impact on the grip
Standard Physics: Every movement can be broken down to a translation and a rotation
Vcm = V Vb = ω b Sweet spot:Vcm = VbBam!

13. • The racquet also vibrates!
Impact Vibration
• Third type of motion
• Gives rise to two sweet spots
• Can’t have both

14. Making the case for the central sweet spot even better!
Hit the ball right from the middle of the racquet!
Hold racquet at the proper grip position

16. Sources:
http://sport.maths.org/content/
Articles on football flight by Ken Bray
Physics of racket-ball interaction – by H.Brody, University of Pennsylvania
Sweet spots of rackets – Hesston College article
Big Thanks to my friends – too many to name and they know!
Thanks to Arnab Sir and Kulkarni Sir