Fluid Mechanics and Movement Analysis Notes

Fluid Mechanics

B.2.2 Fluid mechanics

Syllabus Understandings

• B.2.2.1: The path of a projectile through air is determined by different factors and forces.
• B.2.2.2: Environmental conditions such as temperature, humidity, air pressure, wind, and salinity of water and altitude affect the external forces acting on an object.
• B.2.2.3: The forces of buoyancy, lift, and drag acting on a body as it moves through a fluid (air or water) have a measurable effect on its path.
• A projectile traveling through a fluid may be affected by Bernoulli's principle, the angle of attack, and the Magnus effect.

Introduction

• Humans and objects moving through a fluid (gas or liquid) experience external forces that resist their motion.
• It is important to understand the direction and magnitude of these resistive forces, and how environmental conditions might affect them.
• These forces apply when objects are in flight (e.g., diving) or translating in contact with the ground (e.g., cycling).
• Forces are measured in Newtons (N).

Projectile Motion

• A projectile is an object projected into the air or dropped, where the only forces acting on it are gravity and air resistance.
• When air resistance is negligible, the horizontal component of velocity remains constant, and only the vertical component of velocity changes.

Projectiles in Sport

• Examples of projectiles in sports include a football, a golf ball, a volleyball, and the human body during long jump or running (flight phase).
• The pathway and range of a projectile depend on:
  • Initial conditions of projection
  • Gravity
  • Air resistance

Initial Conditions of Projection

• The initial conditions of projection include:
  • Initial velocity (v)
  • Angle of projection (\theta)
  • Height of release (h)

Initial Velocity

• The flight path of a projectile is significantly affected by the initial velocity.
• The projectile's range is related to the square of the initial velocity. A small increase in initial velocity will increase the range considerably.

Angle of Projection

• The angle of projection is most significant for the maximum height of the flight and for accuracy.
• The angle of projection significantly affects the range. When the projection height is the same as the landing height, an angle of projection equal to 45° will maximize the range.
• If the landing height is higher than the projection height, the optimal release angle is greater than 45°.

Height of Release

• The height of projection also affects the projectile range; the higher the height of projection, the longer the range.
• The projection height might be important to beat an opponent or to maximize the range of values possible for the initial velocity or angle.

Optimum Angle of Projection

• To achieve maximum range, the optimum projection angle depends on the initial velocity and, more importantly, the projection height.
  • If the projection height is above the landing area or target (e.g., shot-put), the optimum projection angle is below 45°.
  • If the projection height is below the landing area or target (e.g., basketball free throw), the optimum projection angle is above 45°.
  • If the projection height is the same as the landing height (e.g., goal kick in soccer), the optimum angle is 45°.
• However, these optimum angles depend on the size of the air resistance in flight as well as other complex factors such as the strength and speed of contraction of human muscles.
• Long jumpers take off at 18°-27° rather than 45°.
• Table 1 shows typical projection angles for common sporting activities.

Centre of Mass

• The centre of mass is the mathematical point around which the mass of a body or object is evenly distributed.
• The centre of mass depends on the distribution of the material in a body or object. This will be affected by the density of the body or object and also by its shape.
• As the centre of mass is a mathematical, imaginary point, it doesn't need to lie within the material of the body or object.
• For example, the centre of mass of a boomerang is in the space between the arms and not in the material.
• For the human body, this can also be true, particularly in sporting action such as high jump or pole vault when clearing the bar.

Importance of Knowing the Position of the Centre of Mass:

• Stability of static positions: If the vertical projection of a line downwards from the centre of mass lies within the base of support, the position of the body or object is stable.
• Airborne rotations: It is the axis for all free airborne rotations of the body or object, for example, somersaulting in diving.
• Whole-body translation: The centre of mass acts as the reference point when considering whole body or object translation. For example, when performing the long jump in athletics, the trajectory of the centre of mass during take-off, flight, and landing is crucial for understanding the distance jumped.

Measurement of the Centre of Mass

• The centre of mass may be measured in several ways (e.g., calculations from segmental positions and masses, reaction board, suspension of an object or model).
• It can probably only be measured to an accuracy of 1-2 millimetres for the human body due to errors introduced by breathing, blood circulation, and inaccuracies in segment densities and positions.

Air Resistance

• Both the overall pathway and the range of the projectile are affected by air resistance.
• The ratio of weight to air resistance influences the object's flight path.
• Faster-moving objects experience more air resistance.
  • For slow-moving objects, the magnitude of air resistance is small in comparison with the force of gravity acting on the object, so the object follows a typical projectile flight path.
  • For fast-moving objects, air resistance is higher, and the pathway of the flight is affected; increased air resistance will cause a faster deceleration.
• For example, in badminton, the shuttlecock moves at high velocities, reaching a maximum of 117 \text{ m/s} ( 421.2 \text{ km/h}).
• Due to high air resistance compared with its weight, the shuttlecock will decelerate quickly. The shape of the projectile pathway is affected and is not symmetrical.

Effect of Environmental Conditions

• Environmental conditions, such as temperature, humidity, wind, air pressure, salinity of water, and altitude, affect the forces acting on an object.
• For example, temperature affects the density of air and water.
• But, considering that there is only a small variation in density values when the temperature ranges between 0 and 30°C (temperatures in which athletes usually perform), the effect on forces will be minimal.

B.2.3 Movement analysis and its applications

Introduction

• Movement analysis requires the identification of the different phases of a physical task.
• Performance is observed or video recorded, and biomechanical flaws or inefficient movement patterns are identified for each phase independently either to prevent injuries or to improve performance.

Phases of Movement Approach

• Phases of movement can be categorized into different stages that help athletes and coaches understand and analyze the execution of specific skills:
  • Preparatory phase
  • Force production phase
  • Critical instant
  • Follow-through (for discrete skills) or Recovery phase (for continuous skills)
• Discrete skills refer to tasks and activities with a fixed beginning and end and short duration (e.g., throwing a ball or jumping).
• Continuous skills are those tasks and activities that have no clearly defined beginning and end and a longer duration (e.g., swimming or running).

Discrete Skills

Preparatory Phase

• This is the initial stage where the athlete prepares mentally and physically for the skill execution.
• Athletes focus on body position, balance, and positioning themselves optimally for the skill.
• Anticipation of the skill's demands is a key component of this phase.

Force Production Phase

• The force production phase involves the synchronized movement of the skeletal and muscular systems in producing the movement and force needed to perform the task.
• In discrete skills, such as a golf swing or a tennis serve, this phase encompasses the application of force to the object.
• For continuous skills, such as running, cycling, or swimming, force production refers to applying force against the ground, pedals, or water to move the body.
• Good technique, timing, and coordination help maximize force application and performance.

Critical Instant

• The critical instant is the culmination of the preparation and force-producing phases, and is the specific moment within the skill execution that significantly influences the skill's outcome.
• This instant determines the accuracy, power, and effectiveness of the skill.
  • The point of contact/impact in striking sports (e.g., tennis, baseball, and cricket).
  • The moment where contact is lost with the surface in jumping sports (e.g., diving, trampolining, or volleyball).
  • The point of release (e.g., when throwing a javelin).

Follow-Through

• The follow-through occurs immediately after the critical instant in discrete skills.
• It involves continuing the motion and maintaining the correct body alignment and form.
• Follow-through helps prevent injury, enhance accuracy, and improve the overall feel and control of the skill.

Discrete Skill Movement Analysis Example

• As an example, consider the phases of movement of the forehand drive in tennis.
• The forehand drive in tennis is a discrete skill with a distinct beginning and end.
• Phases of movement can be identified and performance can be observed independently for each phase.
  • Preparatory phase
  • Force production phase
  • Critical instant
  • Follow-through

Continuous Skills

• For continuous skills, such as running, cycling, or swimming, phases of movement are identified based on key events such as "heel strike" in running or "hand entry" in swimming.
• Each phase is analyzed, and inefficient movement patterns are identified.

Recovery Phase

• The recovery phase takes place after the completion of one cycle or repetition of the movement.
• For example, in swimming, the recovery phase occurs after completing one stroke, as the swimmer positions their arms for the next stroke.
• A smooth and efficient recovery is essential for maintaining momentum and rhythm in continuous skills.

Continuous Skill Movement Analysis Example

• As an example, consider the phases of movement in front crawl swimming.
• An arm stroke in front crawl swimming is a complete arm action, for example, from right hand entrance to right hand entrance.
• Each arm stroke is divided into four phases, with the positions of the hand and the shoulder on the horizontal axis used to identify the beginning of each phase.
  • Entry phase begins when the hand enters the water.
  • Pull phase begins when the hand starts moving backwards (on the horizontal axis).
  • Push phase begins when the hand is aligned vertically with the shoulder.
  • Recovery phase begins when the hand exits the water.
• Analysis of the phases could include looking at time variables (such as the duration of each phase) or spatial parameters (such as joint angles or the distance covered in each phase).

Benefits of Movement Analysis for Health and Safety

• Movement analysis can help identify biomechanical flaws or inefficient movement patterns that may contribute to the risk of injury.
• By understanding the phases of movement, healthcare professionals can collaborate with sports coaches (and athletes) to design targeted injury prevention programs, corrective exercises, and rehabilitation protocols to address specific weaknesses or imbalances.
• Video analysis, biomechanics, and motion capture technologies are often used to assess and quantify the different phases of movement precisely.

Benefits of Movement Analysis for Sporting Performance

• Movement analysis allows coaches to identify technical flaws in athletes' movements.
• By breaking down skills into phases, coaches can provide targeted feedback and design training interventions to enhance technique, consistency, and efficiency in sports-specific movements.
• Other examples of the application of movement analysis to health, safety, and sporting performance include:
  • Optimizing biomechanics to improve power, speed, and performance.
  • Developing tactical insights of games players to develop effective strategies and improve decision-making.
  • Injury management, assessing progress and readiness for an athlete to resume their sporting activities.
  • Helping to track and manage an athlete's workload and reduce the risk of overuse injuries.