Jumping and flying

Movement in the air

Aim jumping gliding powered flight

insects birds

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/632/movelectures/fly/

Extra reference: Videler, J (1993) Fish swimming Chapman &

Hall

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 or gh =

½ v²

If muscle is M, let work done be kM mgh = kM or h =kM/(mg) = (k/g)*(M/m) If same proportion of body is jumping

muscle, height should be the same no effect of mass on how high you jump

neglects air resistance

How far do we go? depends on take off angle d = (v² sin 2) /g

jumping.xls maximum at 45o

Sin 90 = 1 d = v2/g

How far maximum distance =2KE/ (mg) =2 (kM)/(mg)=2(k/g) * (M/m) as before distance not affected by body

massAlice Daddy

age 8 ??

mass 35kg 87kg

distance 1.16m ??

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 ??

Jumping in locusts If we could jump

as well, we could go over the Empire state building

elastic energy storage

co-contraction

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

Flying gliding power flight hovering

How stay up? Can nature do better than mankind?

Who flies? insects birds 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

How much lift lift increases with speed 2

lift increases with angle of attack

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

Fly optimally?

speed

po

we

r

Profile power

Induced power

Total power

constantenergy/distance

minimum power

maximum range

Can nature beat man?

Gliding soaring in thermals

Africa: thermals rise at 2-5m/s

soaring at sea/by cliffs

Bigger is better? big wings act on more air

called lower wing loading long thin wings have less induced

power called aspect ratio more economical,

but have to fly faster

Bigger is worse As bird size (l) gets bigger

mass l3

wing area l2

wing loading must go up l big birds need more wing area than

little birds harder to flap

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 http://www.biology.leeds.ac.uk/

staff/jmvr/Flight/modelling.htm

Bounding flight glide, flap, glide, flap, flap - several times, then glide full muscle power would make bird

climb more efficient to use muscle at best

shortening rate

Hovering flight humming bird hovering generates lift on forward

and back stroke as wings beat, vortices

shed at end of stroke

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 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

Exam papers… Neuroscience (i):  Matsuda K, Buckingham SD, Kleier D,

Rauh JJ, Grauso M, Sattelle DB. (2001) Neonicotinoids: insecticides acting on insect nicotinic acetylcholine receptors  Trends Pharmacol Sci.  22: 573-80

Neuroscience (ii): Cho, W, Heberlein U, Wolf, FW (2004) Habituation of an odorant-induced startle response in Drosophila Genes, Brain, And Behavior 3: 127-137 [paper copy here]

Muscle:  Kappler, JA; Starr, CJ; Chan, DK; Kollmar, R Hudspeth, A J (2004) A nonsense mutation in the gene encoding a zebrafish myosin VI isoform causes defects inhair-cell mechanotransduction Proc Natl Acad Sci U S A. 101:13056-61

Movement:  Prestwich, KN & O'Sullivan, K (2005) Simultaneous measurement of metabolic and acoustic power and the efficiency of sound production in two mole cricket species (Orthoptera: Gryllotalpidae) J exp Biol 208, 1495-1512

Thanks !