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Question 1

What drives sport evolution

Answer 1

athletes, society, regulations, technology?
- technology certainly is the most powerful motor of sport evolution

_ what has become more performant
↳sailors or the boats
↳ skiers or the skis

Sport’s technology is not only about science; it should also comprehend and consider the needs and feelings of the athlets. Athlets and technology have to adapt to each other.

Question 2

Cycle of sport evolution

Answer 2

Technology innovation-Technology improvement

                                   - Athletes’adaptation to new technology
                                   - Evolution of rules & regulations

=Technical innovation

Question 3

Innovation

Answer 3

Technological innovations
Motor sports: Invention of internal combustion engine
Tennis, pole vaulting, etc:
Discovery of composite materials
Alpinism: Invention of alpine crampons
Time measurement:
Invention of photo-finish
Skiing: Invention of carving skis with heightened bindings
Sprint: Invention of the starting blocks

Technological improvement & Evolution of regulations
Engine ajustment (mix air-fuel, type of fuel, etc.)
Fabrication process to obtain best possible fibers’alignment (improved resistance & energy storage capacity)
Evolution of binding, position of points and materials
Adaptation of skis to new aerodynamic conditions to maximize lift-to-drag ratio
Introduction of chest-first rule Limitation on the height of the plates Approval of technique
Admission of the starting blocks

Technical innovations
 Ski jumping: Invention of the V-technique
High jumping:
Introduction of the Fostbury technique
Sprint: Invention of the

Question 4

Why does physics of sport matter?

Answer 4

Sport administrators
– Understand rules & regulation and adapt policy
– Set rules & regulations with full knowledge of the issues prevailing
Equipment suppliers
– Understand mechanical limits & possibilities to see where and what technical and / or technological improvement is still possible
– Technology intelligence
• Coaches
– Help correct errors and improve sport performances of athletes
– Improve approach to coaching
– Foresee changes and anticipate their integration (technology foresight)
• Athletes
– Improve technique

Question 5

Physics of running

Answer 5

Action = Reaction. Newton’s third law says that when one object exerts a force on a second object, the second object always exerts a force equal to, but in the opposite direction of the original force.

Runner’s injury. When a runner’s foot strikes the ground with the full force of the runner’s weight (F=Mg: Newton’s second law), the ground also exerts a force on the runner’s foot, which moves up the runner’s leg joints to their spine, again due to Newton’s third law.

Question 6

Physics of running

Answer 6

Impulse Momentum (p=Ft)
§ Cushioning is used in training and trial shoes to decrease the amount of force felt by the runner's feet and joints. This is accomplished by increasing the amount of time it takes for the force to reach the runner's feet. Instead of transferring it directly, the shoe cushion absorbs part of the energy and releases it on a longer time than with hard soles which transfer the force instanatneously.
§ The more the cushioning, the longer it takes for the runner to feel the force caused by striking the ground. The increased amount of time t and the decreased amount of force F (at constant impulse p) helps to minimize the wear and tear on the runner's body.

Question 7

Impact management techniques

Answer 7

Although the total force felt by the body might not change, the force applied at one instant in one place of the body can be significantly reduced by
– extending the time-frame
– Extending the area of application of this force.
§ This principle applies to most sports where catching or landing is involved, i.e. any impact situation:
• Use of gloves and « sliding into home base » technique in baseball • Entering the water vertically rather than horizontally in diving
• Flexing of legs when landing in ski jumping or gymnastics
• Break-fall technique in judo
• Soften Body checking by standing against the ice ring
• Legendary rope-a-dope of Mohamed Ali in boxing • However, cushioning impacts on efficiency

Question 8

Work efficiency

Answer 8

The efficiency h of a work is defined as the ratio of effective energy to consumed energy (or effective power to power produced). It is normally expressed in %, whereas the energy is measured in Joule or Kcal (1 J=4.18 cal) and the power in Watt (=J/s).

The efficiency is 100% when no energy is lost, that is when the energy consumed is entirely transformed into effective (useful) energy. This can never be achieved by physical activities, nor by any machine.
If different efficiencies are involved in an activity, these multiply up. For instance, the efficiency of cycling is given by the product of the human machine efficiency, the shoe efficiency to transfer power to the bike, and the bike efficiency to transfer mechanical energy into kinetic energy.

Question 9

Efficiency of various activities

Answer 9

All means of transportation do not require the same amount of energy to travel the same distance. This is due to the different weight and different efficiency of these transport systems.
• The bicycle is from far the most energy efficient means of transportation. It can be up to 5 times more efficient than walking (you will need 5 times the same amount of energy to walk a given distance than to cycle it).
• The difference between the energy necessary to cycle and to drive by car is enormous. One hundred calories can power a cyclist for 5 km, but it would only enable a car to drive 85 m!!!

Question 10

Surface characteristics

Answer 10

Elastic vs hard surface
• An elastic playing surface such as grass feels springy to run on and produces fewer injuries than more rigid surfaces such as concrete.
• But the time spent rebounding is higher on a springy surface, slowing the runner down.
• The best surface for athletics is one that is absorbent enough to limit injuries but firm enough to give athletes the best chance of achieving optimum results.
Deformable surfaces
• The least efficient surfaces are those where the deformation is plastic and not elastic, such as snow, water or sand, as a large amount of the running energy is consumed for the deformation of the surface.
• Not only does this energy expenditure not contribute to the forward movement, but it is also not restored to the body when the feet move up.
• This is why, for instance, beach volley ball is so much more energy consuming than indoor volleyball, and why jogging in the water is so demanding.

Question 11

Impulse

Answer 11

Impulse is not used only to slow down and stop
• In various sports, the duration of application of a force is crucial, e.g.
– Javelin throw – Karate

Question 12

Frictional forces

Answer 12

Static friction
Occurs between to surfaces at rest
Shoe outsoles should have static friction as large as possible to avoid slippage. The better the grip, the shorter the time the runner’s feet are in contact with the ground, the quicker they can run their legs over. Spikes, for instance, increase the grip.
No static friction, no movement whatsoever!

Static friction
Occurs between to surfaces in movement relative to each other. Kinetic friction is always opposed to the direction of the movement of the moving surface, thus slowing it down.
Skis should have kinetic friction as low as possible to maximize speed, but not to high to avoid loss of control.

No kinetic friction, no change in direction, and thus no control whatsoever !

Question 13

Frictional forces: examples

Answer 13

Tennis. Tennis shoes should prevent slippage at start of the run (high μstat), but should enable sliding at the end of the run end (low μkin). Sand stack in the shoe patterns modifies their surface roughness and thus decreases greatly the static friction coefficient. Tennis players thus hit their heels with the tennis racquet on clay surfaces to unstuck the sand.
• Basketball. Basketball shoes reflect the need to address the difference between surface types (indoor wooden court vs. outdoor concrete court), as well as the understanding need differ in different areas of the outsole, depending on the movement (no slippage at traction, no sliding at stopping, good slippage at pivoting).
• Ski, Snowboard, Windsurfing, etc. The friction coefficient does not generally depend on the area of the surfaces in contact. However, in sport where a deformation of the surface is generated (snow, water, sand, etc.), the greater the surface in contact (at equivalent weight), the smaller the pressure, the smaller the surface deformation, and thus the smaller the frictional force. This is why snowboard is better suited than skies in deep snow.
• Climbing shoes are designed to offer maximal friction. Best performances are obtained at cooler temperatures.

Question 14

Frictional forces: rolling friction

Answer 14

• Motor racing. As long as the wheel rolls, the friction is static (the wheel is moving but instantaneously the point of contact wheel-road is not). Should the wheel slide, then the friction becomes dynamic. Reminding that Fstat > Fkin, this explain why :
– The racing cars and motor bikes avoid sliding. This makes them lose both time and control.
– Because of friction, the car tires become smoother at each lap, in turn reducing friction and lap time, until it becomes worth changing tires although it costs a few seconds.
– Friction depends on the nature of the two surfaces in contact. Thus tire profiles and materials will differ on dry road, wet road, snow, etc.
– Friction depends on the temperature of the tires and is optimised for when they are warm. On the warm-up lap the cars zigzags in order to generate lateral friction and thus heat up their tires.
– The ABS braking system enables to break without sliding (the wheel remains in static friction at all time), which reduces the breaking distance compared to just blocking the wheel and allow static friction to stop the car.

Question 15

Air resistance

Answer 15

Not only friction with the ground plays a role in sport, air resistance does too. This effect is actually dominant for number of activities.
• When projectile motion is treated in basic physics courses, the influence of air resistance is often neglected in the calculations and the trajectory of a projectile becomes a parabola where the horizontal velocity component is constant and the vertical component is subject to gravity.
• However, it appears that the motion of the ball is governed not only by gravity, but also by air resistance, thus making the real path much shorter.
• More air in front implies more pressure, similarly to running in the rain.
• Air resistance being a frictional force, it also applies opposite to the motion, thus reducing the travelling speed.

CFD is used in many sports where the aerodynamic question is relevant. CFD is of course not confined to sport activities but is found in many R&D sectors of activity.
• Situation is more complex for sport where presence of other competitor affects the own aerodynamic (car racing, sailing, etc.) or when external conditions modify the aerodynamic behaviour. Real-time adaptable design would be the solution, but this often reveals too complex

Question 16

Aerodynamics

Answer 16

The aerodynamic drag on a object moving in a fluid is always opposed to direction of motion and is given by:
D=1/2pACdv2 (r o fluid density
A o effective frontal area of the object
CD oDragcoefficient
v o relative velocity (= velocity of object if fluid is at rest)

The drag coefficient CD depends on the shape and surface roughness of the object, as well as on viscosity of the fluid

Surface roughness. Generally speaking, the rougher the surface of the object, the more turbulent the fluid flow, and the greater the drag. However, at certain speed, a roughened sphere may experience less drag than a polished one. The dimples in the golf ball enables it to travel 30% faster than a smooth one.

Question 17

Air resistance

Answer 17

Without air resistance, free-fall acceleration is constant (=gravity acceleration g=9.81m/s2), and free-fall speed thus increases proportionally with time: v=gt (and the time frame for your impact on the ground is very very short…)
• In reality, air resistance is so great that it counter-balance gravity. Free-fall speed thus becomes constant.

Question 18

Slipstream in cycling ( drafting)

Answer 18

Another important aerodynamic effect in sport in the « slipstream phenomenon », which generates a forward suction effect.

To efficiently get protected from the air resistance, cyclists position themselves according to the relative direction of wind

Triathlon. It is forbidden in triathlon to ride in another rider’s slipstream. Therefore, a minimal distance (10m axial or 2m lateral) must be kept between the cyclists so that no one can benefit from suction. Surprisingly, no such rule prevail during the swimming section, although the slipstream phenomenon can be quite significant.
• Final cycling sprint. The second cyclist tries to overtake at the very last second to beneficiate as long as possible from suction effect and thus save power for the very end, while the first cyclist keeps on zigzagging to try and get the follower away from his slipstream)

Question 19

Slipstream in car racing

Answer 19

Slipstream & speed. In car racing, the slipstream phenomenon begins to be significant from 60 km/h upwards. The higher the speed, the greater the effect.
• Principle. The strategy consists in catching up with another car at the beginning of a straight line and to get as close as possible behind it, in order to no only be protected from the air resistance, but also to be situated in a small zone, a few meters long, where no turbulences occur, as eddies produced by the turbulences carry energy away and tend to slow vehicles down. Furthermore, the suction effect comes from the fact that the pressure in front of the car may be lower than that at the back, which generates a forward push, conversely to the car in front.
• Speed & power. Both cars drive at the same speed, but the second one needs less power. Therefore, when it will filter to overtake, the second car still has enough power left to accelerate, whereas the first car does not.
• Overpowered engine. The suction phenomenon results in an increase of the maximal speed, which may in turn result in overpowering the engine. To avoid this problem, the sixth gear is extended.

Question 20

Computational Fluid Dynamic (CFD)

Answer 20

Visualisation: pressure distribution cannot be physically visualised. Furthermore, the equations that govern aerodynmics are highly non-linear and cannot be solved analytically for complex bodies moving in fluid. Numerical models are therefore necessary.
• Computational Fluid Dynamics (CFD): Equations such as Bernouilli or Navier-Stokes are programmed into computers. The computers provide solutions to the problem of external airflow over vehicle shapes. The body of the configuration and the space surrounding it are represented by clusters of points, lines and surfaces; equations are solved at these points. CFD is divided into three steps. Grid generation, numerical simulation and post-process analysis.

Question 21

Air resistance in altitude

Answer 21

As the soccer ball moves through the air, the air in front of it experiences a rise in air pressure and pushes the ball in the direction opposite its motion.
• The higher the air pressure was to start with, the greater its rise in front of the ball and the stronger the backward push of air resistance. Thus if you were to play soccer in the Rocky Mountains, where the air pressure is much less, you’d be able to kick the ball significantly farther.

Positive effect: Air resistance greatly reduced
• Negative effect: Oxygen reduced => aerobic capacity greatly reduced (muscles burn sugars to produce ADP through an oxydation process)
• Insignificant effect: variation of weight
Altitude is thus well suited for sport demanding anaerobic effort and where air resistance plays a role (sprint, long jumping), but not for endurance effort (running, cycling, etc.)

Question 22

Bouncing balls

Answer 22

Bouncing. Ball bounce is important in many sports including soccer. The ideal height of bounce varies for different sports but should be constant from one part of the field to the other.
• Measurement. The Coefficient Of Restitution (COR) is a measure of the elasticity of the collision between the ball and the ground. Elasticity is a measure of how much bounce there is, or in other words, how much of the kinetic energy of the colliding objects before the collision remains as kinetic energy of the objects after the collision.
• Elastic vs. plastic bounce. A perfectly elastic collision has a coefficient of restitution of 1. A perfectly plastic, or inelastic, collision has COR=0. Example: two lumps of clay that don’t bounce at all, but stick together. So the coefficient of restitution will always be between zero and one.
• BBR. Another measure of the bouncing quality of a ball is given by the Ball Bounce Resilience (BBR). It is equal to the COR squared, and then expressed as a percentage. For example, if a ball is dropped from 3 meters, hits the ground, and bounces up 1 meter, the BBR is 33.3%.
COR 2 = Height of bounce = BBR Height of drop 100

Question 23

Coefficient of restitution (COR)

Answer 23

Influent factors.
For a given ball, the COR varies with
• The surface characteristics (material, thickness, moisture, etc.)
• The temperature, which influences the internal pressure of the ball (e.g. squash)
• The atmospheric pressure
 Type of ball
COR
Basketball
0.75
Golfball
0.60
Tennis ball
0.70
Soccer ball
0.75
Baseball
0.57
Superball
0.90
   Tennis balls. This is why tennis balls are less inflated in altitude to compensate for the lower atmospheric pressure and thus ensure a constant COR
If your ball has a whole, even the tiniest, than it COR drops because the inner and outer pressures become the same (atmospheric pressure)

Question 24

Aerodynamic lift

Answer 24

The Bernouilli effect for fluid dynamics means that: if a fluid (gaz or liquid) flows around an object at different speed (due to assymetry of object), the slower moving fluid will exert more pressure than the faster moving fluid on the object, which forces the object towards the faster moving fluid. This expresses nothing else but the conservation of energy. Bernouilli’s equation along a streamline of constant elevation writes:
Where p is the local pressure, r is the fluid density and v is the fluid speed.

The lift is what makes any flying object fly. The flying condition is that the aerodynmic lift is equal (or greater at take-off) than the object’s weight.
Li

Question 25

Grounding effect in Formula-1 cars

Answer 25

Invertedwings.Duetotheirveryhighspeed,F1carscanalsogenerate lift, which can be vefry dangerous. To avoid this problem, inverted wings have been introduced, which produces a downforce instead of lift. This downforce helps stabilizing the car and increases cornering speeds.
• Venturitunnels.FromBernouilli,fluidspeedincreaseswhenitflowsthroughanarrowor restricted area (Venturi effect). The increased speed results in a reduction in pressure. A narrow tunnel, called Venturi tunnel, is placed under the side pod, shaped like an inverted wing. As air enters and is forced through the narrow center,its speed increases, creating a low pressure area between the chassis of the car and the track. This creates a suction effect, which holds the car to the track.
• Downforce/drag.Thegreaterthedownforce,thegreaterthedrag,whichreducesthespeedat given engine power. A compromise have thus to be found to reach optimum downforce-to- drag ratio. The same applies for any flying object where the lift-to-drag ratio should be maximised.

The different circuit place a different demand on the aerodynmic setup of the car. A road course with low speed corners requires high grounding effect to maintain speed in corners and to reduce wear on the brakes. On high speed circuit, it is more important to reduce the drag as it is proportional to the square of the speed.
• If the aerodynamical setup is badly computed, the risk is to generate lift in certain conditions. In particular, at very high speed, supersonic shock waves can be produced underneath the chassis, which may results in high pressure increase, and thus generate a lift force instead of a downforce.

Question 26

Saling

Answer 26

Because of the difference of pressure between the two sides of the sail created by the Bernouilli effect, the boat feels a lift force in the direction A.
Breaking down A into two equivallent forces in the direction B and C, and considering that the keel (underwater wing) prevents the boat moving in direction C, the boat has no choice but move in the direction B.

Sailing upwind
Angle of attack. The keel cannot, however, prevent 100% of motion in the direction C. Therefore, no sailboat can have an angle of attack (angle between wind direction and boatspeed) less than 30°, and most have 45° as a threshold. That nevertheless leaves about 270° degrees of direction in which to sail.
Tacking. Therefore, it is possible to reach a destination just into the windeye by going 45° off the wind to the right, then « tacking » to 45° to the left and so on. Seen from above, the boat’s path will thus form a zigzag.
45°

Sailing upwind
• Sailing downwind, with wind blowing from behind, is not the most efficient
– The sails are highly unstable, with consequent loss of energy carried away by turbulent eddies
– The speed of the boat is limited by the speed of the wind.
• Wind is not the sole factor that should be considered when sailing. Current is another. Great torques can be generated when sailing
up-stream.

Question 27

Why do shots curve?

Answer 27

• Newton’s 1st Law. If no side force is acting on the ball, it would fly in a straight line. Therefore, they must be a lateral force.
• Bernouilli?Apriori,itcannotbeBernouillieffectas the ball is symetrical, which should result in no speed difference along the two sides of the ball ?!
• Magnuseffect.However,iftheballisrotatingona vertical axis, then a special case of the Bernouilli effect occurs, called Magnus effect, which generates a sideway force equivallent to a lift.This will curve the trajectory of the ball.The effect becomes significant after about 10m, that is about when is passes the wall of defenders !

Question 28

Magnus effect for side spin

Answer 28

A kick or a through transfers a certain amount of energy to the ball. This energy is either in the form of kinetik energy (velocity) or rotational energy (angular momentum. See thereafter). Therefore, the greater the spin, the greater the deflection, but the slower the speed. This explains the difference between fast and slow ballers.

The length of a shot varies depending on the spin of the ball around its horizontal axis perpendicular to the direction of motion. This explains, for instance, why lifted lobs fall in the court.

Question 29

Rotational inertia in various sports

Answer 29

• In cycling, it is important that the inertia of the wheel, at given weight, be as high as possible. It will require more energy to accelerate it, but once the cruising speed reached, the speed will easier to maintain as less affected by frictional forces.
• Hammer throw. Until the rules were changed, tungsten head and super-light titanium handles were used, which enables to put virtually all the weight in the head, without changing the 7 kg official weight. Problem was that the hammers would bury themselves deep in the field, like meteorites, giving a hard time to the officials to take them out!
• Downhill skis are much more inertial than slalom skis, which are themselves much lighter than artistic jumping skis, where rotation has to be performed in a minimum time (the time of flight).

Question 30

Rotational inertia in various sports

Answer 30

stored during the swing and transferred to the ball, thus increasing the length of the shot.
• Baseball bats used by professionals tend to be shorter than the permitted 42 inches and weight around 33 oz, although no weight restriction exists. The reason is that the speed of pitches are so high that the batter has only a fraction of second to react. Longer and heavier bats inevitably take longer to accelerate and thus necessitates tremendous power.
• Racquet sports. The same applies to racquets of all kinds. In badminton and squash, racquets tend to have lighter frame weight as very fast moves and swings are necessary. In tennis, “back of the court players” tend to have racquets with slightly heavier heads as they have enough time to prepare their shots. Conversely, “net-type” tennis players will prefer lighter racquets, giving them more control and enabling faster

The greater the rotational inertia of a club, raquet, bat, hockey stick, etc., the less control, the more power (or time) needed to swing it and stop it, but the greater the energy and momentum transfered to the ball.
The power of sportmen being finite, there is always a trade-off to find between the weight of the bat, its mass distribution and the rate at which it is swung.
Furthermore, rules and regulations exist in sport to limit the diameter and mass of balls and wheels.

Question 31

Conservation of Angular Momentum ( figure skating)

Answer 31

Onceintheair,angularmomentumisconserved => angular momentum must be initiated while still on the ground, actually just when quitting the ground.
• Twistmustthusbeinitiatedbytheupperbody
– because feet must produce the reaction on the ground which enable to generate the rotation.
– because the upper body has 3 times more rotational inertia than the legs.

Question 32

Angular momentum and stability

Answer 32

Not only does conservation of angular momentum enable to vary the angular velocity, but it also gives stability as spinning objects react to any force that tend to change the angular momentum.
Conservation of angular momentum is the reason why cyclists or bikers remain stable, whereas they have to put a foot down at soon as they stop at the red light.

Question 33

Stability

Answer 33

• Athletes can increase their stability by:

1. Making sure their line of gravity falls in the center of their base of support (Tower of Pisa, weight lifting)
2. Increasing the size of their base of support (wrestling, weight lifting, rugby, etc.)
3. Lowering their center of gravity (judo, landing at ski jumping, weight lifting).

Question 34

Conservation of energy

Answer 34

When all forces acting on a system are conservative (non-conservative forces are forces like friction, air resistance), then the mechanical energy of this system remains constant
Where m is the mass of the object, v its speed and h the height above ground of its center of mass. Ekin represents the kinetic energy, Epot the gravitational potential energy and Eelast the energy stored in an object in the form of elastic deformation.