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