Transcript Mackerel at .0053 or Rainbow Trout at .15

Outline
• Kinetics (external)
– Forces in human motion
– Impulse-momentum
– Mechanical work, power, & energy
– Locomotion Energetics
• Kinetics
Outline
– 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 Resistance
Drag Force: Opposes motion
Lift 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 streamlines
2) the extent to which the relative motion of the streamlines is disturbed
Laminar flow
Uniform layers of different speed
Slowest layer closest to the surface of the object
Laminar flow:
Surface drag
dominates
Air direction
relative to ball
Velocity of air
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
Higher
Pressure
Lower
Pressure
• Turbulent flow: Non-uniform flow of fluid around
an object
• Pressure differential causes a “pressure drag
force”.
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
v = vobject - vair
vobject
Velocity (v) of fluid relative to the object
• Example: vcyclist = 7 m/s
• Still air: vair = 0
v = vobject - vair
v = 7 m/s
• Headwind: vair = -7 m/s
v = 14 m/s
• Tailwind: vair = 7 m/s
v = 0 m/s
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 Resistance
Drag Force: Opposes motion
Lift Force: perpendicular to motion
Lift Force
Asymmetric objects
Spinning object
Bernoulli’s Principle:
Pressure is inversely proportional to
the velocity of the fluid
High Velocity
Low Pressure
Low Velocity
High 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
Cycling
Racer
Recumbent
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
Fn
q
mg
Find maximum friction force in terms of mg, q, & µs.
Friction force on slope
Fn
q
mg
Fs,max = Fn • µs
Fn = mg cos q
Fs,max = µs • mg cos q
Fparallel (force pulling downhill parallel to slope) = mg sin q
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.
Recitation
• 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
Neglect or Do Not Neglect?
• 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.
Recitation
• What is the fastest velocity that can be
reached by the skier. i.e. what is terminal
velocity?