Outline

• Kinetics (external)– Forces in human motion– Impulse-momentum– Mechanical work, power, & energy– Locomotion Energetics

Outline• Kinetics– Forces in human motion• Gravity• Ground reaction• Inertial (F = ma)• Centripetal• Friction• Fluid Resistance

– Multi force Free body diagrams • Dynamic and Static Analysis with Newton’s Laws

Reading• Newton’s Laws

– Ch 2: pages 41-44; 46-61• Friction

– Ch 2: pages 61-62• Static/Dynamic Analyses & FBDs

– Ch 3: pages 107-124• Fluid Resistance

– Ch 2: pages 63-68• Linear Impulse/Momentum

– Ch 2: pages 68-72• Mechanical Energy/Work/Power

– Ch 2: pages 81-90• Applications (Locomotion, Jumping)

– Ch 4: pages 145-159

Human movements where fluid resistance is important?

Factors affecting fluid resistance

• Density– mass per unit volume– resistance to motion through a fluid increases with

density• Viscosity– a measure of the fluid’s resistance to flow

Figure 2.20

Components of Fluid ResistanceDrag Force: Opposes motionLift Force: perpendicular to motion

Components of drag force

• Surface drag: friction of fluid rubbing on surface• Pressure drag: front-back pressure differential• Wave drag: waves at interface of two fluids.

Streamlines

Drag force is effected by:1) different velocities of the streamlines2) the extent to which the relative motion of the streamlines is disturbed

Laminar flow

Uniform layers of different speedSlowest layer closest to the surface of the object

Air directionrelative to ball

Velocity of airLaminar flow:Surface dragdominates

Surface drag • also called skin friction • Depends on– velocity of fluid relative to surface– roughness of surface– surface area of object– properties of fluid

Reducing surface drag• Speed skater: wearing a smooth spandex suit– 10% less surface drag than wool clothes

• Cyclist: wearing Lycra long sleeved shirt, tights, and shoe covers

• Swimmer: Shaving body hair

Surface drag• Surface drag: Friction within boundary layer– human movement in air: surface drag (3-5%)– small compared to pressure drag (95-97%)

Pressure drag: dominant form of drag in human movement

• Turbulent flow: Non-uniform flow of fluid around an object

• Pressure differential causes a “pressure drag force”.

HigherPressure Lower

Pressure

Streamlining reduces turbulence and pressure drag

• Flow remains laminar for longer -- less turbulence – less pressure drag

Enoka, Figure 2.3A

Pressure drag vs. surface drag

• Pressure drag: dominates for large objects moving in low density & viscosity fluids– e.g., human running, cycling in air

• Surface drag: dominates when small objects moving in high viscosity fluids, e.g. sperm swimming

Pressure drag force• Fd = (0.5 CD)Av2

• = fluid density– air: 1.2 kg/m3

– water: 1000 kg/m3

• CD = coefficient of drag• A = projected area (m2, frontal area as

object moves through the fluid)• v = velocity of the fluid relative to the object

(m/s)

Coefficient of drag (CD): combines shape & aspect ratio index

• Unitless• Magnitude depends on– shape of object– orientation of object relative to fluid flow

• Independent of size• Streamlining reduces CD

Coefficient of drag examples

• Mackerel: 0.0053• Rainbow trout: 0.15• Pigeon or vulture: 0.4• Sphere: 0.47• Human swimmer: 0.66• Cyclist and bike: 0.9• Runner: 0.9• Flat plate: 1.0

How can we measure frontal area?

Velocity (v) of fluid relative to the object

• Example: vcyclist = 7 m/s

• Still air: vair = 0

• Headwind: vair = 7 m/s

• Tailwind: vair = 7 m/s

vobject

v = vobject - vair

Velocity (v) of fluid relative to the object

• Example: vcyclist = 7 m/s

• Still air: vair = 0 v = 7 m/s

• Headwind: vair = -7 m/s v = 14 m/s

• Tailwind: vair = 7 m/sv = 0 m/s

vobjectvair

v = vobject - vair

Components of drag force

• Surface drag: friction of fluid rubbing on surface• Pressure drag: front-back pressure differential• Wave drag: waves at interface of two fluids.

Figure 2.20

Components of Fluid ResistanceDrag Force: Opposes motionLift Force: perpendicular to motion

Lift Force

Asymmetric objectsSpinning object

Bernoulli’s Principle:

Pressure is inversely proportional to the velocity of the fluid

Low VelocityHigh Pressure

High VelocityLow Pressure

Figure 2.22

• Drag acts in horizontal (x) direction, opposite to the direction of locomotion Drag

Drag in locomotion (Fd = 0.5 CDAv2)

• Walking or running in air (CD = 0.9, = 1.2 kg/m3)– 0.5 CD = 0.55 kg/m3

– Fd = 0.55Av2

• Frontal area (A) = 0.4 m2

– Fd (Newtons) = 0.22 * v2

Role of Fd in locomotion• Person in still air– Walk (1.25 m/s): Fd ~ 0.001 Fg,x

– Run (4 m/s): Fd ~ 0.01 Fg,x

– Run (8 m/s): Fd ~ 0.025 Fg,x

• Person in headwind of 17 m/s (~ 35 mph)– Run (8 m/s): Fd ~ 0.25 Fg,x

Role of Fd in locomotion

Drag in cycling (Fd = 0.5 CDAv2)

• For cyclist in air (CD = 0.9, = 1.2 kg/m3)– 0.5 CD = 0.55 kg/m3

– Fd = 0.55Av2

• Frontal area (A) of cyclist & bike– Touring position (upright): 0.5 m2

– Racing position: 0.3 m2

– Recumbent position: 0.2 m2

Touring

Racer

Recumbent

Cycling

Swimming• Water density >> air density– greater pressure drag

• Fd = 0.5 CDAv2

– = 1000 kg/m3

– CD = 0.66– A = 0.073 m2

• Fd (swimming) = 24* v2

– Comparison: Fd (walk, run) = 0.22 * v2

Drag: walking vs. swimming• Drag force comparison at a given speed– Fd (swimming) ~ 100 x > Fd (walk, run in air)

• Reasons– Water density >> air density– frontal area less– Cd less for swimming position

Total force: walking vs. swimming• Swimming– Drag: largest force– 2 m/s --->

Fd ~ 0.14 * body weight• Walking– Ground reaction force: largest force– 2 m/s --->

Fg ~ 1.5 * body weight

Figure 2.23

Figure 2.24

Problem: Friction force on slope

q

Fn

mg

Find maximum friction force in terms of mg, q, & µs.

Friction force on slope

Fs,max = Fn • µs

Fn = mg cos qFs,max = µs • mg cos qFparallel (force pulling downhill parallel to slope) = mg sin q

q

Fn

mg

Friction vs. Gravity force parallel

• m=70kg

• µs = 0.5• theta = 30 degrees• Solve for static friction force and the component

of gravitational force pulling parallel to the slope.

Recitation

• a skier starts at the top of a 30 degree incline,init. vel. = 0

• considering gravity, air resist. & friction, draw a FBD.

• a skier starts at the top of a 30 degree incline,init. vel. = 0

• considering gravity, air resist. & friction, draw a FBD

• If m = 0.050 and mass is 70.0kg, what is max. frictional force? add that number to FBD

Recitation

• If frontal area is 0.600 m^2, air density is 1.200 kg/m^3, Cd is 0.9, what is air resist force when velocity = 10 m/sec

• add this # value to your FBD

Recitation

• if we include air resistance, kinematic problems get more difficult.

• In the bike lab we will take aero force into account and use an iterative computer approach.

Neglect or Do Not Neglect?

• What is the fastest velocity that can be reached by the skier. i.e. what is terminal velocity?

Recitation