~10 million species
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~10 million species
after Nachtigall, 1978
Typical insect morphology:
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!!!
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.
Morphology of insect leg:
What do muscles do during jump?
pleural ridge
notal ridge
resilin pad
Resilin pad
http://www.voyle.net/Images%202005/Oct%202005/17-10-2005-001.jpg
Synthesis and properties of crosslinked recombinant pro-resilinChristopher M. et al.Nature 437, 999-1002 (13 October 2005)
63d
58
62
63a
58 coxal remotor62 trochanter levator 63a trochanter depressor 63d dorso-ventral muscle
pivot point
muscles involved in jump:
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…
resilin pad resilin pad compressed by muscle 63d
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.
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.
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
Conclusion:
Flea jumps by slowly storing energy in resilin pad, and rapidly releasing that energy to power the jump.
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