Upload
baldwin-randall
View
218
Download
0
Tags:
Embed Size (px)
Citation preview
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
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
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
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
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
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
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
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?