Download - ~10 million species
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~10 million species
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after Nachtigall, 1978
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Typical insect morphology:
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What are basic jump kinematics?
initial velocity ~ 1 m sec-1
maximum height = vv2/2g
= 3.5 cm= 23 body lengths
vh
vv
From ballistics:x = vh tz = vv t – (gt2)/2
x
z
time of jump = 0.75 msecinitial acceleration = vv/t
= 1.33 105 cm sec-2
= 135 g!!!
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How much energy is required to jump, and could a flea’s muscles deliver it?
peak kinetic energy = ½ mv2
k.e. = ½ (0.45 x 10 -3grams) (1 m sec-1)2 = 2.25 ergs
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.
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Morphology of insect leg:
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What do muscles do during jump?
pleural ridge
notal ridge
resilin pad
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Resilin pad
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http://www.voyle.net/Images%202005/Oct%202005/17-10-2005-001.jpg
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Synthesis and properties of crosslinked recombinant pro-resilinChristopher M. et al.Nature 437, 999-1002 (13 October 2005)
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63d
58
62
63a
58 coxal remotor62 trochanter levator 63a trochanter depressor 63d dorso-ventral muscle
pivot point
muscles involved in jump:
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line of action of dorso-ventral
muscle
with muscle 62 active
63d
63a
pivot point
62
with muscle 63a active:
63a
pivot point
Action of Muscle 63d changes…
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resilin pad resilin pad compressed by muscle 63d
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force
length
‘stuff’ tester
stuff
length
force elasticmaterial
Area = force x distance= work of extension= energy stored
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.
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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.
length
forceIf a force, F, is storedelastically, the averageforce recovered willbe ½ F.
Therefore, average force out = .33 g.
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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.
peak kinetic energy = ½ mv2
k.e. = ½ (0.45 x 10 -3grams) (1 m sec-1)2 = 2.25 ergs
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Conclusion:
Flea jumps by slowly storing energy in resilin pad, and rapidly releasing that energy to power the jump.