9.3 Fluid mechanics

fluid mechanics definition

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

air resistance

• force that opposes direction of motion of a body through air

drag

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

How are air resistance and drag analysed

• wind tunnels

• fluid dynamics programmes

  • must be minimised to perfect technique and performance

  • make the best equipment

  • e.g track cycling

4 factors affecting drag or air resistance

• velocity

• front cross sectional area

• streamlining and shape

• surface characteristics

How velocity affects drag or air resistance

• 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

How front cross sectional area affects drag or air resistance

• 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 

How stream lining and shape affects drag or air resistance

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

How surface characteristics affects drag or air resistance

• 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 

stream lining definition

• the creation of smooth air flow around an aerodynamic shape

Aerofoil

• 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

Downhill skiing and minimising air resistance

• 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

track cycling and minimising air resistance

• 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

affect of temperature on air resistance

• Temp increases → density decreases → reduces air resistance 

affect of altitude on air resistance

• Altitude increases → density decreases → reduces air resistance 

projectile motion definition

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

projectile

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

• e.g a discus or long jumper

graph showing projectile motion

• shown by a simple graph

• height against horizontal distance

4 factors affecting horizontal distance travelled

• speed of release

• angle of release

• height of release

• aerodynamic factors → bernoulli and magnus

How speed of release affects horizontal distance travelled

• 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 

How angle of release affects horizontal distance travelled

• 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

Height of release and horizontal distance : landing = starting height

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

Height of release and horizontal distance : landing below starting height

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

  • E.g javelin 

Height of release and horizontal distance : landing above starting height

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

  • Golf 

parabolic flight path

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

• e.g shot put

non-parabolic flight paths

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

flight path of a shuttle cock initial

• air resistance is much larger than weight

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

flight path of a shuttle cock mid flight

• 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

flight path of a shuttle cock landing

• 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

resultant force

• 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 : shot put

• resultant force is closer to weight arrow

• weight is dominant force

• flight path is parabolic

Resultant force : shuttle cock

• if resultant force arrow is closer to the air resistance arrow

• air resistance is dominant

• non parabolic flight path

steps for drawing resultant force

1. Draw a free body diagram showing the forces of weight and air resistance 

2. Adding dotted parallel lines to the weight and air resistance arrows to create a parallelogram

3. Draw a diagonal line from the origin of weight and air resistance (COM) to the opposite corner of the parallelogram with a double arrow labelled the resultant force

Bernoulli principle

• 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

lift force

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

benefits of an additional lift force

• increases time a projectile spends in the air

• extends flight path

• larger horizontal distance covered

  • e.g javelin and ski jumping

Relationship of velocity and pressure

• pressure decreases as velocity increases

Aerofoil shape and Bernoulli: general

• 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

Aerofoil shape and Bernoulli: curved top surface

• forces air to travel a further distance

• high velocity

• low pressure zone

Aerofoil shape and Bernoulli: flat bottom surface

• air flows a shorter distance

• lower velocity

• high pressure zone is created

angle of attack

• 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 

free body diagram showing effect of lift force

• vertical force

  • weight - lift force

downward 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 

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

sidespin: hook

• eccentric force applied right of the COM

• spins left around the longitudinal axis

• swerves projectile left

sidespin: slice

• eccentric force applied left of the COM

• spins right around the longitudinal axis

• swerves projectile right

how is spin created

• applying an eccentric force outside the centre of mass

magnus effect: general

• 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

4 types of spin

1. top spin

2. back spin

3. sidespin : hook

4. sidespin: slice

top spin

• eccentric force applied above COM

• spins downwards around the transverse axis

• shortens flight path

back spin

• eccentric force applied below COM

• spins upwards around the transverse axis

• lengthens flight path

topspin + additional magnus force : upper surface

• rotates opposing motion of oncoming air

• low velocity of air flow

• high pressure zone is created

topspin + additional magnus force : lower surface

• rotates with motion of oncoming air

• high velocity of air flow

• low pressure zone is created

topspin + additional magnus force : effect

• a pressure gradient forms

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

• shortens flight path

backspin and a free body diagram

Hook + additional magnus force : left side of ball

• Air flow opposes motion 

• Ball rotates to the left with the air flow 

• High velocity → low pressure 

Hook + additional magnus force : right side of ball

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

• low velocity → high pressure 

Hook + additional magnus force : effect

• Pressure gradient is formed 

• Magnus force acts to deviate flight path to the left

Slice + additional magnus force : right side of ball

• rotates with air flow

• high velocity

• low pressure

Slice + additional magnus force : left side of ball

• rotates against air flow

• low velocity

• high pressure

Slice + additional magnus force : effect

• Pressure gradient is formed 

• air moves from left to right

• Magnus force acts to deviate the flight path to the right 

benefits of topspin

• 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