~10 million species

~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.