9.3 Fluid mechanics

study of forces acting on a body travelling through air or water

force that opposes direction of motion of a body through air

force that opposes direction of motion of a body through watr=er

wind tunnels

fluid dynamics programmes

• must be minimised to perfect technique and performance

• make the best equipment

• e.g track cycling

velocity

front cross sectional area

streamlining and shape

surface characteristics

the greater the velocity, the greater air resistance or drag 

E.g track cycling or speed skating all affected as high velocity 

Velocity cannot be reduced to minimise air resistance or drag

The larger the frontal cross sectional area the larger the air resistance or drag 

E.g track cycling and downhill cycling 

Frontal cross section faces the oncoming air 

Every effort is made to reduce the size of the front cross sectional area to minimise air resistance and drag 

The more streamlined aerodynamic the shape of a body in motion,the lower the air resistance or drag 

the smoother the surface the lower the air resistance or drag

Swimmers wear specifically engineered clothing to create the smoothest surface possible 

By being smoother, reduces the friction between a body surface and the fluid 

the creation of smooth air flow around an aerodynamic shape

a streamlined shape with a curved upper surface and a flat lower surface designed to give a body additional lift

tear drop shaped

• e.g a ski jumper

Travel at a high velocity 

Minimise font cross sectional area by adopting a low crouched position in jumps and straights 

Wear tear drop shaped helmets and boots to ease air flow around their body 

Lycra suits for smooth surface

Lightweight carbon fibre bikes with disc wheels and aerodynamic forks to reduce energy expenditure and minimise air resistance 

Aerodynamic riding positions with shoulders forward → minimise front cross sectional area 

Helmets that are aerodynamic glossy and smooth 

Lycra skin suits and smooth socks pulled over shoes

Temp increases → density decreases → reduces air resistance 

Altitude increases → density decreases → reduces air resistance 

movement of a body through the air following a curved flight path under the force of gravity

a body that is launched into the air losing contact with the ground surface

e.g a discus or long jumper

shown by a simple graph

height against horizontal distance

speed of release

angle of release

height of release

aerodynamic factors → bernoulli and magnus

Due to newton's second law of motion : 

the greater force applied to the projectile, the greater change in momentum and therefore the acceleration of the projectile in the air 

The greater the outgoing speed of the projectile the further it will travel 

90° → accelerate vertically upward and travel 0 m

45° → optimal angle to optimise horizontal distance 

Greater than 45° → the projectile reaches peak height too quickly and rapidly returns to the ground 

Less than 45° → the projectile does not achieve sufficient height to maximise the flight time

45° → optimal angle to optimise horizontal distance if  landing height and starting height are equal 

optimal angle is less than 45 as the projectile already has an increased flight time due to increased height of release 

• E.g javelin 

optimal angle of release is more than 45 as the projectile needs an increased slight time to overcome the obstacle 

• Golf 

a flight path symmetrical about its highest point caused by the dominant weight force

e.g shot put

a flight path asymmetrical about its highest point caused by the dominant force of air resistance on the projectile 

air resistance is much larger than weight

the velocity of the shuttle is high as it leaves the racket head

the size of AR force has decreased as

the velocity of the shuttle has reduced

it is the size of the AR force that causes the shuttle to decelerate

the AR force is now small as the velocity has decreased

the weight force has remained the same and is now larger than air resistance

the shuttle falls vertically resulting in a non-parabolic flight path

the sum of all forces acting

• net force

resultant force shows the acceleration of a projectile and direction in which the acceleration occurs

also shows flight Path

resultant force is closer to weight arrow

weight is dominant force

flight path is parabolic

if resultant force arrow is closer to the air resistance arrow

air resistance is dominant

non parabolic flight path

creation of an additional lift force on a projectile in flight resulting from bernouill’s conclusion that

• the higher velocity of air flow the lower the surrounding pressure

an additional force created by a pressure gradient forming on opposing surfaces of an aerofoil moving through a fluid

increases time a projectile spends in the air

extends flight path

larger horizontal distance covered

• e.g javelin and ski jumping

pressure decreases as velocity increases

As the aerofoil moves through the air, air is forced to part and flow at different velocities above and below the projectile to meet at the same point behind 

This affects pressure of air flow above and below the aerofoil and a pressure gradient forms to provide an additional lift force 

• air moves from an area of high pressure to an area of low pressure

forces air to travel a further distance

high velocity

low pressure zone

air flows a shorter distance

lower velocity

high pressure zone is created

the most favourable angle of release for a projectile to optimise lift force due to the bernouilli principle

17° to act as an aerofoil to maximise bernoulli's lift force in flight 

vertical force

• weight - lift force

Aerofoil shape is inverted 

• E.g an F1 car and track cycling 

Used to increase the downward force that holds to car or bike to the track 

Area of low pressure is created below the car and are of high pressure created above,so air moves down a pressure gradient and provides the downward lift force 

creation of an additional magnus force on a spinning projectile which deviates from the flight path

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

eccentric force applied right of the COM

spins left around the longitudinal axis

swerves projectile left

eccentric force applied left of the COM

spins right around the longitudinal axis

swerves projectile right

applying an eccentric force outside the centre of mass

Magnus effect works on the same principle as bernoulli 

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

A pressure gradient is formed either side of the spinning projectile and an additional magnus force is created which deviates the flight path 

This form of spins creates a non parabolic flight path

eccentric force applied above COM

spins downwards around the transverse axis

shortens flight path

eccentric force applied below COM

spins upwards around the transverse axis

lengthens flight path

rotates opposing motion of oncoming air

low velocity of air flow

high pressure zone is created

rotates with motion of oncoming air

high velocity of air flow

low pressure zone is created

a pressure gradient forms

additional magnus force is created as air moves down a pressure gradient

shortens flight path

Air flow opposes motion 

Ball rotates to the left with the air flow 

High velocity → low pressure 

Ball rotates against air flow on the right side resisting air flow

low velocity → high pressure 

Pressure gradient is formed 

Magnus force acts to deviate flight path to the left

rotates with air flow

high velocity

low pressure

rotates against air flow

low velocity

high pressure

Pressure gradient is formed 

air moves from left to right

Magnus force acts to deviate the flight path to the right 

can hit the ball harder and ball still lands in court

hit the ball higher and still lands in court

deceive opponent as ball appears to be going out

decreased angle on bounce