Transcript Jumping and flying

Jumping, flying and
swimming
Movement in “fluids”
Aim
 jumping
 gliding
 powered flight
 insects
 birds
 drag and thrust in swimming
References
 Schmidt - Nielsen K (1997) Animal
physiology
 McNeill Alexander R (1995) CD Rom
How Animals move
 Journals & Web links: see:
http://biolpc22.york.ac.uk/404/
First: What limits jumping ?
Jumping
 What limits how far we can jump?
 At take off have all energy stored as KE
 conversion of kinetic energy to potential
(gravitational) energy
 KE = ½ m v2
 PE = mgh
How high
 depends on KE at take off
 PE = KE therefore
mgh = ½ mv²
gh = ½ v² therefore h = ½ v2/g
 no effect of mass on how high you jump
 neglects
air resistance
How far do we go?
 constant acceleration due to constant gravity
affected by mass
 jumping in a parabola
 depends on take off angle
 d = (v² sin 2a) /g

 jumpingangle.xls
maximum at 45o
 Sin
90 = 1
 d = v2/g
Jumping
0.12
0.1
height (m)
 not
0.08
0.06
0.04
0.02
0
0
 twice as far as the max height
0.05
0.1
0.15
distance (m)
0.2
0.25
0.3
How far
 as before distance not affected
by body mass
Alice
Daddy
age
8
??
mass
35kg
87kg
distance
1.16m
??
Great locust jumping test
 http://biolpc22.york.ac.uk/404/practicals/
locust_jump.xls
Jumping in locusts
 If we could jump as
well, we could go
over the Empire
state building
 max
up is ½
horizontal distance
 elastic energy
storage
 co-contraction
How long to take off?
 depends on leg length
 time
to generate force is 2s/v
 for long jump, time = 2s/(g*d)
s
is leg length, d is distance jumped
 bushbaby 0.05 to 0.1s
 frog 0.06s
 flea 1 ms
 locust ??
Running jump
 much higher/further
 KE can be stored in tendons
and returned during leap
Summary so far
 Jumping is energetically demanding
 muscle mass : body mass is most important
 store energy in tendons if possible
Now onto: how do we fly?
Flying
 gliding
 power flight
 hovering
 How stay up?
 Can nature do better than mankind?
Who flies?
 birds
 insects
 bats
 pterosaurs
Lift
 why don’t birds fall due to gravity?
 where does lift come from?
 speed
up air
 Bernoulli’s Principle
 Total energy =
pressure potential energy +
gravitational potential energy +
kinetic energy of fluid
How does air speed up?
 air slows down underneath
because wing is an obstacle
 air speeds up above wing

fixed amount of energy
Lift and vortices
 faster /slower
airflow
 =circulation
 extends above /
below for length of
wing
 creates wake
Circulation
 circulation vortex shed at
wingtips
So to fly…
 we need to move through the air
 use PE to glide down
 as
go down, PE changed to KE
 use wings to force a forwards movement
Can nature beat man?
Gliding
 soaring in thermals

Africa: thermals rise at
2-5m/s
 soaring at sea/by cliffs
Summary so far
 Jumping is energetically demanding
 muscle
mass : body mass is most important
 store energy in tendons if possible
 Flying involves generating lift
 gliding
 use
PE to get KE to get speed to get lift
Flapping flight
 large birds fly continuously
 down
stroke air driven down and back
 up stroke
 angle
of attack
altered
 air driven
down and
forwards
 continuous vortex wake
Discontinuous lift
small birds with rounded wings
lift only on downstroke
 vortex ring wake
Summary
 Jumping is energetically demanding
 muscle
mass : body mass is most important
 store energy in tendons if possible
 Birds heavier than air
 Flying involves generating lift
 gliding
 use
PE to get KE to get speed to get lift
 flapping
propels air
Insect flight
 flexibility of wings allows extra
opportunities to generate lift
 rotation of wing increases circulation
Insect flight
 flexibility of wings
allows extra
opportunities to
generate lift
 fast flight of bee
 downstroke
 upward
 upstroke
lift
lift
move wing
bee
Clap and fling
 at top of upstroke two wings “fuse”
 unconventional
aerodynamics
 extra circulation
 extra force
Wake capture
 wings can interact with the last vortex in the
wake to catch extra lift
first beat
second beat
Summary so far
 Jumping is energetically demanding
 muscle
mass : body mass is most important
 store energy in tendons if possible
 Flying involves generating lift
 gliding
 use
PE to get KE to get speed to get lift
 flapping propels air
 insects often have unconventional
aerodynamics – can beat the “laws” of physics
 Next… Swimming
Jet propulsion
 conservation of momentum = m*v
 mass of fish * velocity of fish
= mass of water * velocity of water

squid


contract mantle
dragonfly larvae
Paddling / rowing
 depends on
conservation of
momentum
ducks
 frogs
swimming
 beetles

Drag
 friction
 turbulence
 Reynolds number gives an estimate of drag
 Re = length * speed * density / viscosity
 for
air, density / viscosity = 7*104 s / m2
 for water; density/ viscosity = 106 s/m2
Reynolds number
 Re < 1 no wake
 e.g.
protozoan
 Re < 106 flow is laminar
 e.g.
beetle
 Re > 106 flow is
turbulent
 e.g.
dolphin
 Drag depends on shape
 Drag reduced by up to
65% by mucus
Design for minimal drag
 tuna or swordfish:
 highly
efficient for high-speed cruising in
calm water
 torpedo-shaped body
 narrow caudal
peduncle
 lunate, rigid
fins
Why don't all fish look like
that?
 The design is highly inefficient:
 In
naturally turbulent water (streams, tidal
rips, etc.)
 for acceleration from stationary
 for turning
 for moving slowly
 & especially for lying still
Ambush predators
 keep head still
 long
body/dorsal fins
 rapid start
 flexible
body, plenty of muscle
 large tail fin
 barracuda
 pike
Design for manoeuvrability
 Small items don't move fast, but require
delicate, focused movements for capture.
 A short, rounded body with sculling or
undulating fins.
 Compressing the body laterally provides a
wide surface to exert force on the water
Optimal design?
 Minimise drag often in biomechanics
 No one optimal design
 efficient energetics isn’t all
 maximum speed isn’t all
 use drag on oars to achieve efficient
propulsion
How does a fish move?
 undulations from front to back
How is thrust generated?
 thrust = momentum / time
 anguilliform
How else is thrust generated?
 tail movement
 Carangiform
 tail
generates symmetric vortex street
note
rotation
How else is thrust generated?
 tail movement acts like a hydrofoil
 thunniform
 cetaceans
 penguins
Flying not swimming
 tail movement acts like a hydrofoil
 generates lift and drag
 drag
 lift
acts in line of motion
acts perpendicular (normal) to drag
total
lift
drag
Summary
 Jumping is energetically demanding
 store
energy in tendons if possible
 Flying involves generating lift
 accelerate
air to get lift
 Insects are small enough to have
unconventional aerodynamics
 Minimisation of drag
 Adaptation to environment leads to alternate
solutions of best way to swim