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~10 million species

~10 million species. after Nachtigall, 1978. Typical insect morphology:. From ballistics: x = v h t z = v v t – (gt 2 )/2. v v. v h. z. x. What are basic jump kinematics?. initial velocity ~ 1 m sec -1 maximum height = v v 2 /2g = 3.5 cm = 23 body lengths.

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~10 million species

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  1. ~10 million species

  2. after Nachtigall, 1978

  3. Typical insect morphology:

  4. From ballistics: x = vh t z = vv t – (gt2)/2 vv vh z x What are basic jump kinematics? initial velocity ~ 1 m sec-1 maximum height = vv2/2g = 3.5 cm = 23 body lengths time of jump = 0.75 msec initial acceleration = vv/Dt = 1.33 105 cm sec-2 = 135 g!!!

  5. peak kinetic energy = ½ mv2 k.e. = ½ (0.45 x 10 -3grams) (1 m sec-1)2 = 2.25 ergs How much energy is required to jump, and could a flea’s muscles deliver it? Typical insect muscle can deliver 6 x 10 5 ergs gram-1 sec-1 = mass specific power 20% of 0.45 mg flea is muscle. Therefore, flea’s muscle could deliver 56 ergs sec-1.. Flea would need 50 msec to generate 2.25 ergs at this rate. But jump lasts only 0.75 msec. In 0.75 msec, muscle could only deliver 0.041 ergs. Also, typical muscles require 3 msec to reach peak force! Thus….muscle could not DIRECTLY power the jump.

  6. Morphology of insect leg:

  7. What do muscles do during jump? pleural ridge resilin pad notal ridge

  8. Resilin pad

  9. http://www.voyle.net/Images%202005/Oct%202005/17-10-2005-001.jpghttp://www.voyle.net/Images%202005/Oct%202005/17-10-2005-001.jpg

  10. Synthesis and properties of crosslinked recombinant pro-resilin Christopher M. et al. Nature 437, 999-1002 (13 October 2005)

  11. muscles involved in jump: 63d 58 coxal remotor 62 trochanter levator 63a trochanter depressor 63d dorso-ventral muscle 58 62 63a pivot point

  12. with muscle 62 active 63d with muscle 63a active: 63a 62 63a pivot point pivot point line of action of dorso-ventral muscle Action of Muscle 63d changes…

  13. resilin pad compressed by muscle 63d resilin pad

  14. force elastic material force Area = force x distance = work of extension = energy stored length stuff length ‘stuff’ tester Could resilin store enough energy to power jump? Bulk resilin can store 1.5 x 104 ergs mm-3 Flea resilin pad = 1.4 x 10-4 mm3 Therefore, could store 2.1 ergs per leg, or total of 4.2 ergs. This is more than the 2.25 ergs required for jump.

  15. If a force, F, is stored elastically, the average force recovered will be ½ F. Therefore, average force out = .33 g. force length Could muscle store this much energy in the resilin pad? Cross section of muscle 63d = 2.2. x10-4 cm2. Typical muscle can generate 3000 g cm-2. Therefore, muscle can generate .66 g of force.

  16. peak kinetic energy = ½ mv2 k.e. = ½ (0.45 x 10 -3grams) (1 m sec-1)2 = 2.25 ergs Assume that tendon moves 0.034 mm. Then work = 0.33 g x 0.0034 mm = 1.24 ergs per leg = 2.24 ergs per flea.

  17. Conclusion: Flea jumps by slowly storing energy in resilin pad, and rapidly releasing that energy to power the jump.

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