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