bio inspired design - lecture5. bio scaling
TRANSCRIPT
Vermelding onderdeel organisatie
Bio-Inspired DesignBioscaling: does size matter?
Faculty of Mechanical, Maritime, and Materials EngineeringDepartment of BioMechanical Engineering
Just Herder
February 17, 2010 2
© 2008 Just L. Herder
Scaling effects
“Fleas can jump 130 times as high as their height (St Paul’s for a human) and 350 times as far as their body length (football field for a human)”
Kangaroos can jump only around 10 m far…
February 17, 2010 3
© 2008 Just L. Herder
Scaling effects
Fleas can jump > 100 timestheir body height and length
Why cannot elephants do the same thing?
Very often: Area to volume ratio
February 17, 2010 4
© 2008 Just L. Herder
Scaling effects
Example: spherical organisms (0.4 um – 14 mm)A=4πR2
V= 4πR3/3Hence A/V=3/R
Oxygen uptake proportional with volumeOxygen transport proportional with area
From: W. Nachtigall, Biomechanik, 2000
February 17, 2010 5
© 2008 Just L. Herder
Scaling effects
Example: spherical organisms (0.4 um – 14 mm)A=4πR2
V= 4πR3/3Hence A/V=3/R
Oxygen uptake proportional with volumeOxygen transport proportional with area
Organisms greater than around 20 mm need organsdedicated to oxygen uptake (e.g. lungs).
From: W. Nachtigall, Biomechanik, 2000
February 17, 2010 6
© 2008 Just L. Herder
Scaling effects
• trees
The Giant Trees of the Styx Valley in Souther Tasmania
The world’s most slender chimney (HalsbruckeEsse near Freiberg, Sachsen, compared with grass and upscaled Fagus Sylvatica
February 17, 2010 7
© 2008 Just L. Herder
Scaling effects
• Trees: height versus trunk diameter
From: W. Nachtigall, Biomechanik, 2000
February 17, 2010 8
© 2008 Just L. Herder
Scaling effects
Constant ratio of deflection/length would require β=2
McMahon and Kronauer, 1976
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© 2008 Just L. Herder
Scaling effects
However, measurements (via eigenfrequency) suggest D=L3/2 or L=D2/3
McMahon and Kronauer, 1976
February 17, 2010 10
© 2008 Just L. Herder
Scaling effects
Heart beat versus body massSimplifying assumption: Assumescaling law for accellerating mass:
13
2 2
2
2 2
1
:
m
F mx mr VrF VrA A
S S S S
Equal and
S S S
σ ρ ω
ω
ω ρ ω
ρ ωσ
σ ρ−−
= = =
= =
=
= =
l
l
&&
JC Cool, 2004
February 17, 2010 11
© 2008 Just L. Herder
Scaling effects
10-2 10-1 1 10 102 103 104
103
102
10
1
hear
t be
at [
1/m
in]
body mass [kg]
mousehedgehog
cat
humanhorse
elephanttheoretical
actual
JC Cool, 2004
February 17, 2010 12
© 2008 Just L. Herder
Scaling effects
Energetical scaling lawsHeat production versus heat transfer through skin
Per kg larger animals need less food (more efficient)No warm-blooded animals smaller than ≈ mouse-size
2
21
3
:
:
V
V
m
Demand S S
S SThen SS S
−
=
= =
l
ll
l
JC Cool, 2004
February 17, 2010 13
© 2008 Just L. Herder
Scaling effects
10-2 10-1 1 10 102 103 104
2*106
5*105
105
2*104Oxy
gen
upta
ke [
mm
3 /kg
hr]
body mass [kg]
mouserat
rabbit
humanhorse
elephanttheoretical
actualdog
131V
mm
S S SS
−−= =l
JC Cool, 2004
February 17, 2010 14
© 2008 Just L. Herder
Scaling effects
Gulliver: 12 times bigger than lilliputters. According to the story he needs 123 times as much food, is that correct?
February 17, 2010 15
© 2008 Just L. Herder
Scaling effects
Gulliver: 12 times bigger than lilliputters. According to the story he needs 123 times as much food, but in ‘reality’ he would need only 122.