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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 2a) /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 mass Alice 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 Profile power power Induced power Total power constant energy/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 l3 wing area l2 wing loading must go up l big birds need more wing area than little birds mass 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 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 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 !