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
constant acceleration due to constant gravity not affected by mass
jumping in a parabola depends on take off angle d = (v² sin 2) /g
jumpingangle.xls maximum at 45o
Sin 90 = 1 d = v2/g
twice as far as the max height
How far do we go?
Jumping
0
0.02
0.04
0.06
0.08
0.1
0.12
0 0.05 0.1 0.15 0.2 0.25 0.3
distance (m)
hei
gh
t (m
)
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 lift upstroke
lift
move wingbee
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
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
friction
turbulence
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
noterotation
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 acts in line of motion lift acts perpendicular (normal) to drag
draglifttotal
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