Flight of a Football

• Round! And remain round!

• Bouncy

But not too much!

• Water Proof

• Swift Through the Air

…Aaaand here comes the physics!

• Weight Acts downwards alwaysDepends on how heavy the ball is

• Magnus Force The direction depends on the motion of ballDepends on the spin on the ball

Force is perpendicularto both spin and velocity

Simple application ofBernoulli’s principle

Higher Pressure

Lower Pressure

• 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)

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 movesmore smoothly than a smooth one!!

Drag crisis

(Graph courtesy:A Fly Walks Around A Football and Journal fo Fluid Mechanics)

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

All That RacquetTennis

• 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

Dead Spot

More bounce

Sweet Spot

Centre of mass

Grip

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!

• The racquet also vibrates!

Impact Vibration

• Third type of motion

• Gives rise to two sweet spots

• Can’t have both

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

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