Fluid forces • When humans exercise, birds fly, fish swim and trees sway; there are forces in operation, that we need to understand. • These forces are the bases of fluid mechanics.
Outline • Introductory material • Fluid drag force • Fluid lift force • Aerodynamics • Hydrodynamics
Introduction: • A fluid is a substance that flows when subjected to a shear stress. Therefore both gases and liquids act with similar mechanical behaviours.
Relative motion • The influence of the fluid on a body moving through it depends not only on the body’s velocity but also the velocity of the fluid. • The fluids density, specific weight and viscosity must also be taken into account. • Atmospheric pressure and temperature effect density, specific weight and viscosity of a fluid.
Background • Specific gravity • Ratio of a swimmer’s body weight to the weight of the volume of water displaced. • Density • Buoyancy is dependant on mass and volume. • Density = mass / volume • Centre of bouyancy • Determined by the centre of volume of the body • When centres of bouyancy and weight are in line the body is stable. When they are not aligned a torque is produced.
Fluid drag force • Fluid resistance is force opposing motion through a fluid and is composed of two vector components – lift (opposes weight) and drag (opposes forward motion). • Drag is a force caused by the dynamic action of a fluid that acts in the direction of the free -stream fluid flow. Drag is known as a fluid resistance force.
Drag force • FD = ½ CDρAPv2 • FD is drag force, • CD is the coefficient of drag, • ρ is fluid density, • AP is the projected area of the body or surface area orientated perpendicular to the fluid flow, and • v is relative velocity of the body with respect to the fluid. • Note: drag increases with the square of the relative velocity of motion if all other factors remain constant – known as the theoretical square law. • Drag force has several components.
Skin friction • Skin friction or surface drag is due to sliding contacts between successive layers of fluid close to the surface of a moving body (boundary layer).
Profile drag • Profile drag or form drag is the resistance created by a pressure differential between the lead and rear sides of a body moving through a fluid. Profile drag is the major contributor to overall drag for human and projectile motion.
Profile Drag • Form or profile drag depends upon the mass and shape of the object. • Note: drag force can be a motive force providing drag force acts in the same direction that the body is moving.
Wave drag • Wave drag is resistance created by the generation of waves at the interface between two different fluids, such as air and water.
Fluid lift force • Lift force acts on a body in a fluid in a direction perpendicular to the fluid flow. Lift force may be in any direction that is determined by the direction of the fluid flow and the orientation of the body.
Lift force • FL = ½ CLρAPv2 • FL is lift force, • CL is the coefficient of lift, • ρ is fluid density, • AP is the projected area of the body or surface area orientated perpendicular to the fluid flow, and • v is relative velocity of the body with respect to the fluid. • Note: The size, shape and orientation of the body (angle of attack) in the fluid are essential for generating lift force. The lift force increases with the square of the flow of velocity similar to drag force, but lift force increases are an advantage in sporting activities.
The lift/drag ratio • The aim in sport is to maximise lift force while reducing drag force. The angle of attack of projected objects (a swimmer’s hand) is constantly changing throughout the flight path, and therefore, the lift/drag ratio changes as well.
Robbins – Magnus effect • When a spherical body (such as a ball) rotates as it moves through the air, it carries with it a boundary layer of air. • The object will seek the path of least resistance, (the side of the ball that is rotating the same direction as the oncoming air). • The effect is to cause the ball to curve in the direction of this low pressure air. • Examples are tennis, golf, soccer, volleyball and football. • These are top spin or backward spin (around horizontal axis). Spin right or left known as a hook or slice is around the vertical axis. • Spin about the axis of the line of flight is called gyroscopic action and acts to stabilise the object as it moves through the air.
Aerodynamics • The following are definitions to aid in the understanding of aerodynamics.
Definitions • Aerodynamic drag force is the fluid force opposing the motion of the body moving through the air. • Aerodynamic lift force is the fluid force directed perpendicularly to the flow direction past an object with a lift-producing shape or fluid flow past a spinning ball. • Angle of attack is the angle formed between the main plane or longitudinal axis of an object and the direction of a fluid flowing past it. • Angle of projection is the angle at which an object or body is projected or released at take-off, usually measured from a horizontal frame of reference. • Attitude angle is the angle formed between the horizontal and the main plane or longitudinal axis of an airfoil or similar lift-producing object.
Definitions • Bernoulli’s principle is an expression of the inverse relationship between relative velocity and relative pressure in a fluid flow. • Boundary layer is the layer of fluid immediately adjacent to the body. • Centre of pressure (pressure is the force per unit of area) is the point of application of a fluid lift force acting on a body moving through the fluid. • Gyroscopic stability is the resistance of a rotating body to a change in its plane of rotation. • Laminar flow is the flow that is characterized by smooth, parallel layers of fluid.
Definitions • Magnus force is the lift force produced by spinning balls, discs and cylinders. • Magnus effect is the deviation in the trajectory of a spinning object toward the direction of spin resulting from the Magnus force. • Projection angle is the angle formed between the centre of gravities instantaneous projection velocity vector and the horizontal plane. • Projection velocity is the speed and direction of an object at the instant of projection. • Profile drag is the net force caused by a difference in pressure from the leading side of the body to the trailing side; the greater the differential, the greater the drag.
Draw the attitude angle, centre of pressure and comment on the pitching moment
Questions • 1) Clearly explain the mechanical concept of the “floating” volleyball or soccer ball. • 2) Explain why the dimples on a golf ball do not increase its drag force. • 3) A shot put mass is stipulated by the IAAA to be a certain weight for male and female competitors. Would the distribution of this mass effect the throw? Explain your answer.
Questions • 4) A middle distance runner is running a 10 km race on a track. There is a tail wind on the home straight and a head wind on the back straight. In this situation would the conditions cancel out any drag effects? • 5) List some variables that would change the CD for a downhill skier. • 6) Summarise the flight of the discus and javelin from release to landing. Include in your answer the angle of attack, angle of release. Attitude angle and the relative application of drag and lift forces.
Questions • 7) Describe the complete action of a shot putter, javelin or discus thrower and determine the essential mechanical components involved in the throw. • 8) For balls thrown with different types of spin, discuss the effects of spin direction (axis of rotation), spin velocity, and velocity of projection on the spatial path of the ball. Discuss different kinds of baseball pitches relative to the same factors. • 9) Draw a top-spinning ball during its ascent and descent in its trajectory. Draw in the Magnus force vector on each diagram. Then, resolve each Magnus force vector into its horizontal and vertical components. Compare the horizontal components on the two diagrams, and explain the effect of each one on the path of the ball. • 10) Describe the tennis players segmental movement pattern for a hitting a forehand top spin shot.
Hydrodynamics • The following are useful definitions.
Definitions • Angle of attack is the angle between the longitudinal axis of a body and the direction of the fluid flow. • Archimedes principle is a physical law stating the buoyant force acting on a body is equal to the weight of the fluid displaced by the body. • Bernoulli’s principle is an expression of the inverse relationship between relative velocity and relative pressure in a fluid flow. • Boundary layer is the layer of fluid immediately adjacent to a body. • Buoyancy is a fluid force that acts vertically upwards.
Definitions • Centre of volume is the point around which a body’s volume is equally distributed and at which the buoyant force acts. • Coefficient of drag is a unitless number that is an index of a body’s ability to generate fluid resistance. • Coefficient of lift is a unitless number that is an index of a body’s ability to generate lift. • Density is mass per unit of volume
Definitions • Foil is a shape capable of generating lift in the presence of fluid flow. • Form/profile drag is the resistance created by a pressure differential between the lead and rear sides of a body moving through a fluid. • Lift/drag ratio is the magnitude of the lift force divided by the magnitude of the total drag force acting on a body at a given time. • Lift force is the force acting on a body in a direction perpendicular to the fluid flow.
Definitions • Propulsive drag is the force acting in the direction of a body’s motion. • Skin friction/surface drag is the resistance derived from friction between adjacent layers of fluid near a body moving through a fluid. • Theoretical square law is that drag increases approximately with the square of velocity when relative velocity is low. • Vortex theory is that swirling masses of water from the interaction of the body with the surrounding water which creates propulsion. • Wave drag is the resistance created by the generation of waves at the surface between two different fluids, such as air and water.
Questions • 1) Why would a “sinker” sink faster in the vertical position than in a horizontal position? • 2) Discuss the situation where, a swimmer swims front crawl with the head out and then the head in at the same velocity. Which style would take more strokes for the same distance? • 3) The same person performs a number of push and glides from the pool side, with arms out, together stretched out in front, and head up. Explain why one push and glide is more efficient than the others.
Questions • 4) Explain how drag force can be a propulsive force in swimming. • 5) Explain how lift force is produced by the swimmer’s hand. • 6) Identify the forces that act directly on the swimmer’s trunk to cause it to move forward relative to the water with one arm cycle. • 7) Imagine you are teaching an adult the front crawl stroke. List six steps to learning the stroke, and give appropriate drills for each step with mechanical reasons for each of the steps and drills. • 8) Discuss swimming velocity in terms of stroke length stroke frequency. Comment using mechanical reasons which is more important, if one is more important.