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Jumping, flying and swimming

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:

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Jumping, flying and swimming

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  1. Jumping, flying and swimming Movement in “fluids”

  2. Aim • jumping • gliding • powered flight • insects • birds • drag and thrust in swimming

  3. 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 ?

  4. 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

  5. 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

  6. How far do we go? • constant acceleration due to constant gravity • not 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 • twice as far as the max height Jumping 0.12 0.1 0.08 height (m) 0.06 0.04 0.02 0 0 0.05 0.1 0.15 0.2 0.25 0.3 distance (m)

  7. How far • as before distance not affected by body mass

  8. Great locust jumping test • http://biolpc22.york.ac.uk/404/practicals/locust_jump.xls

  9. 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

  10. 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 ??

  11. Running jump • much higher/further • KE can be stored in tendons and returned during leap

  12. 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?

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

  14. Who flies? • birds • insects • bats • pterosaurs

  15. 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

  16. How does air speed up? • air slows down underneath because wing is an obstacle • air speeds up above wing • fixed amount of energy

  17. Lift and vortices • faster /slower airflow • =circulation • extends above / below for length of wing • creates wake

  18. Circulation • circulation vortex shed at wingtips

  19. 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

  20. Can nature beat man?

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

  22. 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

  23. 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

  24. Discontinuous lift • small birds with rounded wings • lift only on downstroke • vortex ring wake

  25. 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

  26. Insect flight • flexibility of wings allows extra opportunities to generate lift • rotation of wing increases circulation

  27. Insect flight lift • flexibility of wings allows extra opportunities to generate lift • fast flight of bee • downstroke • upward lift • upstroke bee move wing

  28. Clap and fling • at top of upstroke two wings “fuse” • unconventional aerodynamics • extra circulation • extra force

  29. Wake capture • wings can interact with the last vortex in the wake to catch extra lift first beat second beat

  30. 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

  31. Jet propulsion • conservation of momentum = m*v • mass of fish * velocity of fish = mass of water * velocity of water • squid • contract mantle • dragonfly larvae

  32. Paddling / rowing • depends on conservation of momentum • ducks • frogs swimming • beetles

  33. 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

  34. 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

  35. 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

  36. 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

  37. Ambush predators • keep head still • long body/dorsal fins • rapid start • flexible body, plenty of muscle • large tail fin • barracuda • pike

  38. 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

  39. 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

  40. How does a fish move? • undulations from front to back

  41. How is thrust generated? • thrust = momentum / time • anguilliform

  42. How else is thrust generated? • tail movement • Carangiform • tail generates symmetric vortex street noterotation

  43. How else is thrust generated? • tail movement acts like a hydrofoil • thunniform • cetaceans • penguins

  44. 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 total lift drag

  45. 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

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