Jumping and flying

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Jumping and flying

• Movement in the air

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Aim

• jumping
• gliding
• powered flight
• insects
• birds

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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

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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

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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

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How far do we go?

• depends on take off angle
• d (v² sin 2a) /g
• jumping.xls
• maximum at 45o
• Sin 90 1
• d v2/g

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How far

• maximum distance 2KE/ (mg)
• 2 (kM)/(mg)2(k/g) (M/m)
• as before distance not affected by body mass

Alice Daddy
age 8 ??
mass 35kg 87kg
distance 1.16m ??
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Great locust jumping test
No wings
3rd instar adult
mass
distance
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How long to take off?

• depends on leg length
• time to generate force is 2s/v
• for long jump, time 2s/?(gd)
• s is leg length, d is distance jumped
• bushbaby 0.05 to 0.1s
• frog 0.06s
• flea 1 ms
• locust ??

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Jumping in locusts

• If we could jump as well, we could go over the
  Empire state building
• elastic energy storage
• co-contraction

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Running jump

• much higher/further
• KE can be stored in tendons and returned during
  leap

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Summary so far

• Jumping is energetically demanding
• muscle mass body mass is most important
• store energy in tendons if possible

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Flying

• gliding
• power flight
• hovering
• How stay up?
• Can nature do better than mankind?

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Who flies?

• insects
• birds
• bats
• pterosaurs

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Lift

• why dont birds fall due to gravity?
• where does lift come from?
• speed up air
• Bernoullis Principle
• Total energy pressure potential energy
  gravitational potential energy kinetic energy
  of fluid

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How does air speed up?

• air slows down underneath because wing is an
  obstacle
• air speeds up above wing
• fixed amount of energy

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Lift and vortices

• faster /slower airflow
• circulation
• extends above / below for length of wing
• creates wake

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Circulation

• circulation vortex shed at wingtips

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How much lift

• lift increases with speed 2
• lift increases with angle of attack

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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

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Fly optimally?
minimum power
maximum range
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Can nature beat man?
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Gliding

• soaring in thermals
• Africa thermals rise at 2-5m/s
• soaring at sea/by cliffs

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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

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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

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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

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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

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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

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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

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Hovering flight

• humming bird hovering
• generates lift on forward and back stroke
• as wings beat, vortices shed at end of stroke

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Insect flight

• flexibility of wings allows extra opportunities
  to generate lift
• rotation of wing increases circulation

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Insect flight
lift

• flexibility of wings allows extra opportunities
  to generate lift
• fast flight of bee
• downstroke
• upward lift
• upstroke

bee
move wing
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Clap and fling

• at top of upstroke two wings fuse
• unconventional aerodynamics
• extra circulation
• extra force

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Wake capture

• wings can interact with the last vortex in the
  wake to catch extra lift

first beat
second beat
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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

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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. 10113056-61
• 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

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Thanks !