Biological '.Design - California State University, Bakersfieldkgobalet/files/Bio351/Kardong 2006 Ch 4 Biological... · Biological '.Design ... less suitable for locomotion of larger

Kardong (2006) Chapter 4 125-157

INTRODUCTION SIZE AND SHAPE

SIZE

RelatIOnships amo ng Lengtb Area and Volume

Surface Area

Volume cnd Mass

SHAPE

Allometry

Transformation Grids

ON THE CONSEQUENCES O F BEING

THE RIGHT SIZE

Fundamental Principles

Basic Quantities-Length Time and Mass

Units

Derived Quantities-Velocit) Acceleration Force

and Relatives

Reference S)scems

Center of Mass

Vectors

Introduction Size and Shape

Bodies like buildings obey laws of physics Gravity will

oring down an ill -des igned dinosaur just as certainly as it will

feU a faulty drawbridge Animals must be equipped to

address blo logical demands The long neck of a giraffe gives

it access to treetop vegetation the claws of cats hook prey a

thick coat of fur gives the bison protection from the cold of

winter In order for animals to catch food flee from enemies or endure harsh climates structures have evolved that serve animals against these challenges to surv ival But there is

more to an animals env ironment than predators and prey

climate and cold An animals design must address physical

demands Gravity acts on all structures within its reach

Heavy terrestrial vertebrates must exert much effort to move

Biological Design

Basic Force Laws

Free Bodies and Fo rces

Torques a nd Levers

Land and Fluid

Life on Land Gravity

Life in Fluids

Machines

Strengtb of Materials

Loads

Biological Design and Biological Failure

Tissue Response to MechanicClI Stress

Responsiveness of Bone

BIOPHYSI CS AND OTHER PHYSI CAL PROCESSES

Diffusio n and Exchange

Pres suHs and Parcial Pressures

Countercurrent Concurrent and Crosscurrent

Exchange

Optics

Depth Perception

Accommodation

OVERVIEW

a massive body from one place to another Bones and ca rtishy

lage must be strong enough to bear the weight If these skeleshy

tal structures fail so does the o rganism and its survival is at risk Animals at rest or in mo tion experience forces that

their structural systems must withstand As the British biolshy

ogist J B S Haldane pu t lt

It is easy to show that a hare could not be as large as a hippopotamus or a whale as small as a herring For every type of animal there is a most convenient

size and a large change in size inevitably carries with

it a change in form

(Haldane 1956 p 952)

125

cY~ 7frtW 8 ~

9

10

~ 24

~ i ~

25

~ 26

6iC 27

28~

29

~ 30 ct23

FIGURE 4 I Animal sizes range over many orders of magnitude The largest animal is the blue whale the smallest adult vertebrate a tropical frogAII organisms are drawn to the same scale and are numbered as follows (I) the pterosaur Quetzalcoatlus is the largest aerial reptile (2) the albatross is the largest flying bird (3) Baluchitherium is the largest extinct land mammal (4) Aepyornis is the largest extinct bird (5) ostrich (6) a human figure represented by this scale is 6 feet tall (7) sheep (8) horse (9) this line designates the length of the largest tapeworm found in humans (10) the giraffe is the tallest living land animal (I I) Diplodocus (12) Tyrannosaurus (13) the blue whale is the largest known living animal (14) African elephant (15) the Komodo dragon is the largest living lizard (16) the saltwater crocodile is the largest living reptile (17) the largest terrestrial lizard (extinct) (18) Palaeophis is the largest extinct snake (19) the reticulated python is the longest living snake (20) Architheuthis a deep-water squid is the largest living mollusc (21) the whale shark is the largest fish (22) an arthrodire is the largest placoderm (23) large tarpon (24) Trimmatom nanus is one of the smallest fishes (25) housefly (26) medium-sized ant (27) this tropical frog is the smallest tetrapod (28) cheese mite (29) smallest land snail (30) Daphnia is a common water flea (31) a common brown hydraThe lower section of a giant sequoia is shown in the background on the left of the figure with a I OO-foot larch superimposed

Ncer H G Wells j S Huxley and G P Wells

108Blue whale

106Rhinoceros

102Squirrel

101Lizard

Grasshopper 10-1 Muscles

Large amoeba 10-4

CiliaCiliated protozoan 10-7

True flagella Malaria parasite 10-10

Bacterial flagella

Mycoplasma (PP LO) 10-13

FIGURE 42 Body size and locomotion The masses

of living organisms are given on a logarithmic scale The blue

whale tops the scale Mycoplasma a prokaryotic bacterium-likej organism is at the bottomThe locomotor mechanism ranges

from bacterial flagella to muscle as size increases Size imposes constraints Cilia and flagella that move a small mass will become

less suitable for locomotion of larger masses Movement in bigger

animals is based on muscles

After McMahon and Bonner

In this chapter we examine how structures bullt by humans and those evolved by natural selec tion have des ign features that incorporate and address common problems posed by basic phys ica l forces For example living organisms come in a great variety of sizes (figure 41) however not a ll designs work equa lly wel l for a ll sizes (figure 42)

A grasshopper can jum p a hundred or more times its own body length From time to time this feat has tempted

e some people to proclaim that if we we re grasshoppers we

t could leap tcdl buildings in a single bo und The implication is that grasshoppers possess special leaping devi ces absent in humans C ertainly grasshoppers have suitably long legs tha t launch the m great distances Butthe more important reason

why grassh(~ppers and humans differ in their relative jump-e

Middle C

l f

[J] II I I li~II IIIIm FIGURE 43 Influence of size on performance The

four members of the violin family are similarly shaped but they

differ in size Size differences alone produce different resonances

and account for differences in performanceThe bass is low the

violin high and the middle-sized cello and viola produce

intermediate frequencies


ing abilities is a matter of size no t a matte r of long legs If a grasshopper was enlarged to the size of a human it too would

be una ble to leap a hundred times its new body length desp ite its long legs Differences in size necessarlly bring difshy

ferences in performance and in design To illustra te this point le t us look a t two examples

one from music and one from architecture A small violin

altho ugh shaped genera lly li ke a bass enc loses a smaller resshyonance chamber therefore its frequency ran ge is higher (figure 43) The larger bass has a lower frequency range A Gothic cathedra l because it is large encloses relatively more space than a small brick-and-mortar neighborhood church Large cathed rals include dev ices to increase sunaces through which light may pass in o rder to illuminate the conshy

gregat ion within (figure 44) The end and side walls of ca thedra ls a re designed with outpocketings that arch itects call apses and transepts T he side wa lls are pierced by slotted openings clerestories and tall windows Toge ther apses transep ts cleres to ries and windows a llow mo re light to

enter so they compensate for the proportiona tely large r volshyume enclosed within Later in this chapter we wlll see that this principle applies to animal bodies as well

Shipbuilders oft en resort to a sca le model to test ideas for hull des ign But the model because it is many times

smaller than the ship it represents responds differently to

the wave actio n in a testing tank Thus a model a lone may not rel iably mimic the pe rformance of a larger ship To comshy

pensate shipbuilders minimize the size discrepancy with a

Biological Design 127

Church of Little Tey 10 m

Norwich Cathedral 10 m

FIGURE 44 Influence of size on design The floor plans of a small medieval church (top) and a large Gothic cathedral (bottom) are drawn to about the same length The medieval church is about 16 m in length the Gothic cathedral about 139 m Because the Gothic cathedral is larger in life however it encloses relatively greater space Transept chapels and slotted windows of the side walls of the cathedral must let in more light to compensate for the larger volume and to brighten the in1erior

For an extended account o(the consequences o(size on des ign see Gould 1977

trick-they use slower speeds for smaller models to keep the ship-to-wave interactions about the same as those that large vessels meet on open seas

Size and shape are functionally linked whether we look inside or outside of biology The stud y of size and its conseshyquences is kno wn as scaling Mammals from shrews to eleshyphants fundamentally share the same ske leta l architecture organs biochemical pathways and body temperature But an elephant is not just a very large shrew Scaling requires more than Just making partS large r ot smaller As body size changes the dem ands on various body partS change disproportionshyately Even met8bolism scales with size Oxygen consumpshytion per kilogram of body mass is much higher in sma ller

bodies Size and shape are necessarily linked and the conseshy

quences affect everything fro m metabolism to body design To understand why we look first to matters of size

Size

Because they differ in size the wo rld of an ant or a water strider and the world of a human or an elephant offer quite diffetent physical challenges (figure 45ab) A human com shy

(a) (b)

FIGURE 4S Consequences of being large or small Gravity exerts an important force on a large mass Surface tension is more important for smaller masses (a) The large elephant has stout robust legs to support its great weight (b) The small water strider is less bothered by gravity In its diminutive world surface forces become more significant as it stands on water supported by surface tension

ing Out of his ot her bath easily breaks the waters surface tenshy

sion and dripping wet probably carries withou t much inconvenience 250 g (about half a pound ) of water clinging to the skin H owever if a person slips in the bath he Or she has to contend with the force of grav ity and risks breaking a bone For an ant surface tension in even a drop of water

cou ld hold the insect prisoner if not for properties of its chiti shynous exoskeleton that make it water repellent On the o ther hand gravity poses little danger An ant can Ilft 10 times its own weight scamper upside down effortlessly across the ceilshy

ing or fall long distances without injuty Generally the l8rger

an an imal the greater the signi~nce of gravity The smaller ~ an animal the more it is ruled by surface forces The reason

for this has little to do with biology Instead the conseshyquences of size arise from geometry and the relationships amo ng length surface and volume Le t us consider these

Relationships among Length Area and VolumeJ If shape remains constant but body size changes the relashytionships among length surface area volume and mass change A cube for instance that is doubled in length and

then doubled again is accompanied by 18rger proportional changes in surface and volume (figure 46a) Thus as its length doubles and redoub les its edge length increases by first 2 and then 4 cm o r factors of 2 and 4 However the tota l surface area of its faces increases by factors of 4 and 16 The cubes volume increases in even faster ste ps by factOrs

of 8 and 64 for the doubling and redoubling The shape of

the cube stays constant but because and onl) because it is larger the biggest cube encloses relat ively more volume per

unit of surface area than does the sma lles t cube In othe r words the biggest cube has relative ly less surface a rea per unit of volume than the smal lest cube (figure 46 b)

It is certainly no surprise that a large cube has in absolute terms more total surface area and more total volume th8n a smaller cube But notice the emphasis on relative

F an an 2 fac div wh anc

ChCl

fau Ch8

reb desi size

all p

mcn sion~

the c

128 Chapter Four

V

V V V

L

Vy

V V VV

V V

(a) Cube 1 Cube 2 Cube 3

e =1 cm 2cm 4cm 6e2 = 6 cm2 (6 X1 X1) 24 cm2(6X2X2) 96 cm2(6x4X4)

3e = 1 cm3 (1 x 1 x 1 ) 8 cm 3 (2X2X2) 64 cm3 (4X4X4) Surface area volume = 61 248 9664

L

V

V

(b) Surface area

Length surface and volume (a) Even if shape remains the same a size increase alone changes the proportions

among length surface and volume The length of each edge of the cube quadruples from the smallest to the largest size shown Cubes 12 -and 3 are 12 and 4 cm in length (I) on a side respectively The length (I) of a side increases by a factor of 2 as we go from cube I to cube 12 and from cube 2 to cube 3The surface area jumps by a factor of 4 (22) with each doubling of length and the volume increases by a factor of 8 (2 3) A large object has relatively more volume per unit of surface than a smaller object of the same shape (b) Surface area By

dividin~ ubject into separate parts the exposed surface area increases The cube shown on the left has a surface area of 24 cm2bull but

Whf Ilt n into its constituents the surface area increases to 48 cm2 (8 X 6 cm2) Similarly chewing food breaks it into many pieces

more surface area to the action of digestive enzymes in the digestive tract ashy

ss

ld between volume and surface area and between surshylal

area and length These are a dilect consequence ofits ~lto~~~lt in size T hese relative changes in surface area inby

to volume have profound conseCluences for thehe of bodies o r buildings Because of them a change in16

inevi tably requires a change in design to maintain overshyors performance of

More formally stated the surface area (S) of an objectt is per in proportion to (ex) the square of its linear dimenshy

her per

But volume (V) increases even faster in proportion to

cube of its linear dimensions (1)

V (X [3

Th is proportiona l re lationship holds for any geoshymetric sh ape expanded (or reduced) in size If we enlarge

a sphere fo r example from marb le size to soccer ball size its diameter increases 10 times its surface inc reases 102

o r 100 times and itsvo lume increases 10 o r 1000 times Any object obeys these relative re lationsh ips imposed by its ow n geometry A tenfold inc rease in the length of

an organis m as can occur during growth would bring a 100-fo ld inc rease in surface area and a 1000-fo ld increase in vo lume if its shape did not change in the process So to ma intain performance an o rganism wo uld ha ve to be designed differently when enla rged simply to

accommodate an inc reas e in its volume Consequently the same orga nism is necessar ily different when large and must acco rdingl y be designed differently to accommodate

Biological Design J29

diffe rent relationships among its length surface and vo lshyume With thi s in mind le t us next turn to surface area and volume as factors in design

Surface Area To start a fire a single log is splintered into many small pieces of kindling Because the surface area is increased the fire can start more easily Similarl y many bodil y processes and functions depend on relative surface area Chewing food breaks it into smaller pieces and increases the surface area ava ilable for digestion The effici ent exchange of gases oxyshygen and ca rbon diox ide fo r instance depends in pa rt upon wailable surface area as well In gi lls or lungs large blood vessels branch in to many thousands of tiny vessels the capshyillaries thereby increasing surface area and facilitating gas exchange with the blood Folds in the lining of the digestive tract increase surface area available for absorption Bone strength and muscle force are proportional to the cross shysectional areas of pa rts that particular bones and muscles support o r move Vast numbers of bodily processes and funcshytions depend on rel ative su rface area These examples show that some designs maximi ze surface area while others minishymi ze it Structures (lungs gills intestines capillaries) that are adap ted to promote exc hange of materials typically have large surface areas

Because as we have see n surface and volume scale difshyferently with changing size processes based on relative sur shyface area must change with increas ing size For example in a tiny aquatic organism surface cilia stroke in coordinated beats to propel the animal As the 3nimal gets large r surface cilia have to move proportionately more volum e so they become a less effective means of locomotion It is no surprise ~hat large aquatic organisms depend more on muscle power

J than on ciliary power to meet thei r locomotor needs The circulatory respi ratory and digestive systems rely particushylarly on surfaces to support the metaboli c needs required by the mass of an animal Large animals must have large digesshyti ve areas to ensure adequate surface for assimilation of food in order to sustain the bulk of the organism Large animals can compensate and maintain adequate rates of abso rption if the digestive tract increases in length and develops folds and convolutions Rate of oxygen uptake by lungs or gills diffusion of oxygen from blood to tissues and gain or loss of body heat are all physiological processes that rely on surface area As] B S Haldane once said Comparative anatomy

J is largely the story of the strugg le to increase surface in proshyportion to volume (Haldane 1956 p 954) We will no t be surprised then when in later chapters we di scover that organs and whole bodies are designed to address the relative needs of volume in relation to surface area

As body si ze increases oxygen consumption per unit of body mass decreases (figure 47) In absolute te rms a large animal of course takes in more total food per day than does a small animal to meet its metabolic needs Cershytainly an elephant eats more each day [han a mouse does

130 Chapter Fou r

10 White mousec

I Kangaroo rat I bull White rat

squirrel

I Kangaroo ratQ

a E-=-shy~J= c0shyU 0gt c- Ql NO1010 ~shyOEshy

001

10 g 100 g 1 kg 10 kg 100 kg 1000 kg Body mass

FIGURE 47 Relationship between metabolism and body size PhysiologicJI processes like anatomical pans scale with sizeThe graph shows how oxygen consumption decreases per unit of mass as size increases This is a Jog-log plot showing body mass along the horizontal scale and oxygen consumption FI along the vertical Oxygen consumption is expressed as the p~

volume (ml) of oxygen (02) per unit of body mass (kg) during illl

one hour (h) sh a r

After Schmidt-Nielsen SUI

A cougar may consume severa l kilograms of food per day a shrew only several grams But in relative terms meta bol ism per gram is less for the la rger ani mal The several grams the

m(shrew consumes each day may rep rese nt an amount equi vshyalent to several times its body weight the cougars daily mfood intake is a sma ll part of its body mass Small animals

sizmiddot operate at higher metabolic rates therefore they must peconsume more oxygen to meet their energy demands and

maintain necessary levels of bod y temperature This is partl y due to the fact thar heat loss is proport ional to surshyface area whereas heat generation is proportional to volshyume A small animal has more surface area in rel ation to its To volume than a larger animal does If a shrew were forced to de slow its weight-specific metabolic rate to that of a human grc it would need an insulation of fur at least 25 Col thick to di f keep warm

AI Volume and Mass

As When a solid object increases in volume its mass ll1creases YOI

proportionately Because body mass is direc tly proportional chi to volume mass (like volume) increases in proportion to the pre cube of a bodys linea r dimensions an

In terres trial vertebrates the mass of the body is borne tn

by the limbs and the strength of the limbs is proportional to their cross-sec tional area Change in body size however sets usu up a potential mismatch between body mass and crossshy dut seerional limb area As we lea rned earlier in th is seer ion in mass increases faster than surface area when si ze inc teases A Ion tenfold increase in diameter produces a 1000-fo ld increase ati in mass but only a 100-fold increase in cross-sectional area ica of the supporting limbs If shape is unchanged without comshypensatOry adjustments weight-bearing bones fall beh ind the mass they must carry For this reason bones of large animals wh are relatively more mass ive and robust than the bones of on

51

~~f~1i~~~~

Mycterosaurus ongiceps

FIGURE 48 Body size and limb design in pelycosaurs Relative sizes of three pelycosaur species are

illustrated The femurs of each drawn to the same length are

shown to the right of each species The larger pelycosaur carries -a relatively larger mass and its more robust femur reflects this supportive demand

small animals (figure 48) This disproportionate increase in j mass compared with surface area is the reason why gravity is more significant for large animals than for small ones

Whether we look at violins Gothic cathedrals or anishymals the consequences of geomet ry reign when it comes to

size Objects of similar shape but different size must differ in performance

Shape

To remain functionally balanced an animal must have a design tha t can be altered as its length and area and mass grow at different rates As a result an organism must have different shapes at different ages (sizes)

Allometry

As a young animal grows its proportions may also change Young children too change in proportion as they grow children are not simply miniature ad ults Relative to adult proportions the young child has a large head and short arms

d legs This change in shape in correlation with a change Isizeis called allometry (figure 49)

Detection of allometric sca ling rests on comparisons usually of different parts as an anima l grows For instance during growth the bill of the godojt a shoreb ird increases

length faster than its head The bill becomes relatively ILHIIIii~lI compared to the skull (figure 410 ) Generally the relshy

sizes of two parts x and ) can be expressed mathematshyly in the allometric equat ion

y = bx

lIZwnprp b and a are constants When the equation is graphed log paper a straight line resu lts (figure 4llab)

Years 042 075 275 675 1275 2575

FIGURE 49 Allometry in human development During

growth a person changes shape as well as size As an infant grows its head makes up less of its overall height and its trunk and limbs make up more Ages in years are indicated beneath each figure

From McMahon and Bonner modiled (rom Medawar

FIGURE 4 I 0 Allometry in the head of a black-tailed godwit Differences in relative growth between skull length (lines A and B) and bill length (l ines Band C) are compared Notice that for each increase in skull length the bill grows in length as well but at a faster rate As a result the bill is shorter than the skull in the

chick (top) but longer than the skull in the adult (bottom)


Specimen Skull dimensions (mm)

A

x y

1 35 B 2 11 8 C 3 239 0 4 396 E 5 585 F 6 805 G 7 1054 H 8 1330 I 9 1637 J 10 1968 K 20 6620 L 30 13459 M 40 2 2268 N 50 32905 0 60 45272 P 70 59291 Q 80 74899 R 90 92043

(a)

FIGURE 4 I I Graphing allometric growth (a) If we organize a range of skulls from the same species in order of size

(A-R) we can measure twO homologous parts on each skull and

collect these data points in a table (b) If we plot one skull

dimension (y) against the other (x) on log-log paper a line

connecting these points describes the allometric relationship

between the points during growth in size of the members of this

species This can be expressed with the general allometric

equation y = bx o wherein y and x are the pair of measurements

and band 0 are constants b being the y-intercept and 0 being the

slope of the line In this example the slope of the line (0) is 175

The y-intercept (b) is 35 observed on the graph or calculated by

placing the value of x equal to I and solving for y The equation describing the data is y = 35x l7s

(a) From On Size and Life by Thomas A McMahon and john Tyler BOllner

Allometric relationships describe changes in shape that accompany changes in size Size changes do not occur only during ontogeny Occasionally a phylogenetic trend wlthin a group of organisms includes a relative change in size and proportion through time Allometric plots desc ribe these trends as well Titanotheres are an extinct group of mammals that comprise 18 known ge nera from the Cenoshyzoic A plot of skull length versus horn heigh t for each species shows an allometric relationship (figure 41 2) In this example we track evolutionary changes in the relationshyship between partS through several species

Compared with a reference part the growing feature may exhibit positive o r negative allometry depending on whether it grows faster than (positive) or slower than (negshy

ative) the refe rence part For example compared with skull

10000

8000

6000 5000 4000

3000

2000

1000

800 700 600 500 400

300

200

100Y 80 70 60 50 40

30

20

10

8 7 6 5

4

3

2

1 1 2 3 4 567810 20 30 4050 70 100

(b) x

length the bill of the godwit shows positive allometry The

term isometry describes growth in which the proportions remain constant and neither positive nor negati ve allomeshytry occurs The cubes shown in figure 4 6 exemplify iso meshytry as do the salamanders illustrated in figure 413


DArcy Thompson popularized a system of transformation grids that express overa ll changes in shape The technique compares a reference structure to a de rived structure For instance if the skull of a human fetu s is taken as a reference structure a rectilinear transformation grid can be used [0

define reference points at the intersections of the horizontal and vertical grid lines (figure 414) These referen ce points

132 Chapter Four

600 shy500 400

300

200

150

100

E 70 s 60 r 50 ~ 40

~ 30 o I 20

15

10

7 6 5 4

3

300 400 600 1000 Basilar length of skull (mm)

FIGURE 4 I 2 Allometric trends in phylogeny The

skull and horn lengths of titanotheres an extinct family of

mammals are plotted The horn length increases allometrically

with increasing size of the skull of each species

A~er McNlOhon and Bonner

o

FIGURE 4 I 3 Isometry These six species of

sectalamanders differ in size yet the smallest is almost the same J 5 ape as the largest because body proportions within this genus

(Desmognothus) remain almost constant from species to species

Fetal skull

FIGURE 4 I 4 Transformation grids in ontogeny

Shape changes in the human skull can be visualized more easily

with correlated transformation grids Horizontal and vertical lines

spaced at regular intervals can be laid over a fetal skull The

intersections of these lines define points of reference on the fetal

skull that can be relocated on the adult skull (bottom) and used

to redraw the grid Because the adult skull has a different shape

the reference points from the fetal skull must be reoriented A

reconstructed grid helps to emphasize this shape change

After Thompson

on the fetal skull are then relocated on the adult skull Next these reference points are connected again to redraw the grid but becluse the shape of the skull has changed with growth the redrawn grid too is differently shaped Thus the grid graphically depic shape changes Similarly transforshymation grids can be used [0 emphasize graphically phylogeshynetic differences in shape between species such 8S the fishes shown in figure 415

Transformation grids and allometric equations do not explain changes in shape they only describe them Howshyever in describing changes in proportions they focus our

attention on how tightly shape couples with size

Biological Design

1

133

c

d

b

a

6 5 4 3 2 0 o6 5 4 3 2 e

65432 10

6

FIGURE 4 I S Transformation grids in phylogeny Changes in shape between (WO or more species usually closely

rela(ed can also be visualized with (ransforma(ion grids One

species is (aken as (he reference (Ief() and (he reference poims

are reloca(ed in (he derived species (righ() co reconstruct (he

(ransformed grid

Modi(Jed (rom Th ompson

On the Consequences of Being the Right Size

Animals large or small enjoy different advamages because of their sizes The lalger an animal the fewer are the predamrs that pose a serious threat Adult rhinoceroses lind elephants are simply tOO big for most would-be predarors to hand le Large size is also advantageous in species in whi ch physical aggression between competing males is part of reproductive behavior On the other hand sma ll size has its advantages as well In fluctuating environments struck by tempora ry drought the sparse grass or seeds that remain may sustain a few small rodents Because they are small th ey require only a few handfuls of Food to see them through When the drought slackens and food resources return the surviving rodems with th eir shorr reprod uctive and generation times respond in short order and their population recove rs In contrast a lalge animal needs large quantities of Food on a regular basis During a drought a large animal must migrate or perish Typshyica lly large animals also have long generation times and proshylonged juvenile periods Thus populat ions of large animals ma y take years ro recover after a severe drought or other devshyas tating envi ron mental trauma

The large r an an imal the more its design must be modified to carry its relatively greater weight a consequence of the in creasing effects of gravity It is no coincidence that the blue wha le the larges t ani mal on Earth evo lved in an aqua tic en vironmem in which its gre at weight rece ived sup shyPOrt from th e buo ya ncy of the surrounding water For telTesshytrial vertebrates an upper size limit occurs when supportive limbs become so massive that loco motion becomes impracshytica l The mov ie creatO rs of God zilla were certainly una ware of the impracti cal ity of their design as thi s great beast crashed abo ut stOmping buildings For lots of reasons not the least of which is his size Godzilla is an impossibility

Body pans used for disp lay or defens e often show allometry as the ad ul t ram horns in figure 416 illustrate As a male lobster grows its defens i ve claw grows (00 but much more rap idl y than the rest of its body W hen the lobster attains a respectable size its claw has grown in to a formid ashyble weapon (figure 417 ) The claw exhibits geometric growth that is its length is multiplied by a constant in each time interval The rest of the body shows arithmetic growth because a co nstant is added to its length in eac h time inter shyval To be effec tive in defense the claw must be larg e but a yo ung lobster ca nnot yet wield so heavy a weapon because of its small size Only after attaining substantial hody size can

FI( geo sub

such a claw be effectively depioyed in defense The lCcelershy amr

ated growth of the claw brings it in later life up to fighting are

siz e Before that th e small lobsters major defensive tac tic is to dash for cove r under a rock

This example sh ows that size and shape are sO l11e times link ed beca use of bi olog ica l funct ion as with the lobs ter and its claw More often however design is concerned with the consequ ences of geometry Changes in the rela tionship among length surface and volu me as an object inCleases in si ze (figure 46) are the maj or reason why change in size is necessar ily accompanied by change in shape As we see time and again through out the book size itself is a fact or in vershytebrate design and perfmmance

Biomechanics

Physical forces are a permanent part of an anima ls environshyment Much of the design of an animal ser ves (0 catch prey elude predators process food and meet up with mates But biologica l design must also address the ph ys ica l demands placed upon the organism In part ana lys is of bio logical design requires an understanding of the physica l forces all animal expe riences Those in the fi eld of bioengineering or biomechanics borrow concepts from engineering mechanics to address these questions

Mechanics is the oldes t of the physica l sciences with FIG defensa successful history dating back at leas t 5000 years (0 the leng(hancient pyramid builders of Egy pt It continues up to the body i

present with rhe eng ineers who send spaceships to the plan shydrama

ets Through the course of its history engineers of this diSCIshy line in pline have developed principles that describe the phys ical allorne

134 Chapter Four

Q Q (5 (5 o (5 (5

Lamb Yearling Yearling 25 35-6 6-8 -16 Age in years 05 15 15

FIGURE 4 I 6 Changes in horn shape These species and subspecies of Asiatic sheep show changes in horn shape across their geographic distribution (top)The first in the lineup is the Barbary sheep (Ammocrogus) from North AfricaThe others belong to species or subspecies of Ovis Asiatic sheep of the argali group that extend into central Asia The last sheep on the right is the Siberian argali (Ovis ammon ammon) As a young male bighorn grows in size (bottom illustration) its horns change shape as well In the adult ram these horns are used in social displays and in combat with male rivals

Modiled (rom Geist 1971

It

Is

n ) r

S

Lobster allometry Although the h defensive claw is small at first it grows geometrically while body le length increases only arithmetically Because of this when the

le bddy is large enough to use the claw the claw has increased

nshy dramatically in size to become an effective weapon The dashed 1shy cates the size the claw would reach if it did not show al flIlII()rtH~trv that is if it grew arithmetically instead of geometrically

prope rti es o f objects fro m bodies to buildings Ironically enginee rs and biologists usually work in re ve rse directions

An enginee r starts w ith a problem for instance a rive r to

span and then designs a product a bridge to so lve the pro bshy

lem A biologist however starts with the product fo r

instance a bird wing and works back to th e physica l probshylem it so lves namely flight N o netheless reducing animals

to enginee ring analogies simplifies our task of understanding

animal designs


Certainly anima ls are more than just mac hi nes But the per shy

spective of biomechanics gives a clarity to bio log ical design that we might not otherwise expect An introduc ti on to a

few basic biomechanical princ iples fo llows


Mos t of the ph ysical concepts we deal with in biomechanics

are famili a r Length is a concept of distance time is a conshy

cept of th e flow of events and mass is a concept o f inertia Length and time come to us easily But when it comes

to the concept of mass however o ur intuition not only fails bu t actual ly inte rfe res because wh at most people cali weight is not equiva lent to mass Mass is a property of

matter weigh [ a measure of force One way (0 chink of che

difference is to consider two objects in outer space say a pen

Biological Design

11

135

FIGURE 4 I 8 Units of reference We use familiar

objects as references of size If denied familiar references such as

fellow humans (top) we can easily overes ti ma te the true size of

the cathedral (bottom) Units of measurement such as inches feet

and pounds are conventions attached to quantities in order for us

to set standard references for expressing distances and weight

lt1 nd lt1 rerrigerlt1 ror Bm h would be weightless and neither wo~ld exert a rorce on a scale Howeve r bo th scill have mass alchough [he mass or eac h is dirrercm To ross che pen co a companion asrro nau[ would require hule erfor[ bu c ro move tile massi ve DU[ weighdess refrigeraror would req uire a mighty heave even in che weighrlessness or space Comrary (0 imuicion cherefore we ighc and mass are nm rhe same conceprs

Units

Unics are noc conceprs buc convemions They are scanshydards or measuremem char when anached [0 lengrh cime and mass give rhem concrece values A phocograph of a building alone gives no necessa ry indication of it s size (figshyure 41 8) chere fore a fri end is often pressed l1 to se rvice to

srand in che pic cure (0 give a sense of sca le [0 che building Similarl y unirs se rve as a familiar scale Buc d ifferenc sys shy[ems of unics have grown up in engi neering so a choice musc be mJde

In a fe w Engli sh-speaking countries mainly che Un iced Scaces che English sys rem of measuremem-pollnds feec seconds-has been preferred Inicially chese uni cs grew up fro m famil iar objecrs such as body pans The inch was origshyinally associaced with rhe thumbs width che palm was che breadth )f che hand abouc J inches che foot equaled 4 pa lms and so on

TABLE 41 Common Fundamental Units of Measurement

Systeme English Physical Internationale System Quantity (51)

Slug or Mass Kilogram (kg) pound mass

Foot (ft) Length Meter (m)

Second (s) Time Second (s )

Feetsecond Velocity Meterssecond (fps) (m s-)

Feetsecond2

(ft sec1)

Acceleration M~terssecond2 (m s-2)

Pound (Ib) Fo rce Newtons (N or kg m s-)

Foot-pound Moment (wrque) Newwns meters (ft-Ib) (Nm)

Although pue[lC the English syscem can be cumbershysome when convening unl[s For instance to change miles [0 yards requ ires mu lcip lying by 1760 To convcn yards [0

fee t we musc mulciply by J dnd (0 conven feet to inches we mulriply by 12 During the French Revolurion a simpler sysshytem based on [he mecer was introduced Changing kilomeshycers (0 meters meEers [0 ce ntimecers or centime[ers ru mil limecers requi res only moving che decimal poinL T he Systeme Inrernationale or SI is an ex cended wrsion of the older metric syscem Primary uni ts of che SI include mecer (01) kilogram (kg) and second (s) for dimensions of length mass and cime respeccively In this book as throughout phys ics and biologv Sf units are used Tab le 41 hsts the common uni ts of measurement in both the English dnd che SI systems

Derived Quantities-Velocity Acceleration Force and Relatives

Velocity and acc eleration desc ribe the motion of bodies Velocity is [he rate of change in an objeers pos iLio n and acceleration in turn IS the rare of change in it s velociry In pan our intu ition helps our underscanding of these two concepts When tra veling east by car on an ilHe rs t8 te highshyway we may change our pos iti on ac the ra te of 88 km per hour (ve loc icy) (8 houc 55 mph if you are SClI I chinking in the English sys tem) Step on che gas and we accelerace hit the brake and we dece lerate o r beccer scated we expe rience nega tive accelerarilln ith mathematical calcula tions negari ve acceleration IS c1 bener term to use th ein decelerashyci on beca use we can keep posi rive and negacive signs in a more stra ightforward way The sensati on of accelera ti on is famili ar CO mosc buc in common conve rsa tion unics are seldom mentioned When they are proper ly applied unn may sound strange For inswnce sudde nly braking a car may producG a negarive acce leration of - 290 km h shy

l36 Chapter Four

2

(about - 180 mph h- I ) The units may be unfamiliar but

the experience of acceleration like that of ve loc ity is an everyday event

Force describes the effects of one body acting on another through their respecti ve mass and acceleration Density is mass div ided by vo lume Water has a density of 1000 kilograms per cubic meter (kgm m- 3) Pressure is force divided by the area over which it acts-pounds ft- 2 or N m- for instance Work is the force appl ied to an obJeer times the distance the object moves in the direction of the force wi th a joule (after] ames Joule 1818- 1889) as the u ni t Oddly if the obieer does not move much force may be applied but no work is accomplished A chain holding a chandelier exertS a force keeping the object in place but if the chandelier remains in position no displacement occurs so no work occurs Power is the rate at which work ge ts done therefore power equa ls work di vided by the time it takes The unit is the watt (after Jam es Watt 1736-1 819) and one wa tt is a joule per sec (J s-I)

Common conversation has allowed these terms to

drift in meaning which we need to avoid when we use them in a physical sense I have already mentioned the misuse of weignt (a result of gravity) and of mass (a result of the objects own prope rties independent of gravity) We might speak of a strong arm squeeze as a lot of force when our d isshycomfort may in faer result from force per concentrated area- pressure Vie might express admiration for a person lifting a weight by say ing he or she exerts a lot of power when in fac t we are not talking about the rate of do ing work but the force ge nerated to lift the leight In physical terms we might speak ambiguously If we say something is hewy we could mean either it is massive or that it is very dense Even units nave slipped The Calorie listed on food packaging is actually a kilocalorie but calorie sounds leaner

Reference Systems When preparing to record events a convent ional frame of reference is selected that can be overlaid on an animal and its range of activity But be prepared A reference system can be defined relative to the tClsk at hand For instance when you wal k back to the restroom in the ta il section o f an ai rshyplane you use the plane for reference and ignore the fau that you are really walking forward with respect to the Earth below A bird cant get its wi feathers ruffled by flying with atail wind-it just goes that much faster with respect to the Earth below For our purposes ~md for most engineering applications as we ll the coordinate system is usually defined

ns relative to the surface of the Earth

ra- For reference systems there are several choices includshy

n a ing the polar and cylindrical systems The most common II is however is the rectangular Cartesian reference system (figshy

are ure 419) For an animal movi ng in three-dimensional space

ni tS its position at any moment can be described exactly on three

car axes at right angles to each other The horizontal axis is x the vertical axis is y and the axis at nght angles to these is zmiddot

y

14

Pigeon

8 z~------------------------~

FIGURE 4 I 9 A three-axis Cartesian coordinate reference system defines the position of any object Customarily the horizontal vertica l and axis at right angle to

these two are identified as x y and z respectively The three intersect at the origin (0) The direct projection line of an object

to each axis defines its position at that instant along each axfs

Thus the three projections fix an objects position in space-I

24S for the hawk and 21 148 for the pigeon The white dot

graphically Iepresents the center of mass of each bird

Once defined the orientation of these reference systems canshynot be changed at least not during the episode during which we are taking a serie of measurements

Center of Mass If we are interested in the motion of a whole organism rather than the separate motion of its parts we can think of the mass of the animal as being concentrated at a single point called its center of mass The center of mass in laypersons terms the center of gravity is the point about which an anishyma l is evenly balanced As a mov ing an imal changes the configuration of its parts the pos ition of its center of mass changes from one instant to the next (figu re 420)

Vectors

Vectors describe l1ieasurements of variables with a magnishytude and a direction Force and veloc ity are examples of such va riables hecause they have magnitude (N in the SI mph in the English system) and di rection (eg northwesterly direcshytion) A measurement with on ly magnitude and no direcshytion is a scalar quantity Time duration and temperature have magnitude but no direction so they are scalar not vecshytor quantities A force applied to an object can also be

Biological Design [37

h-2

FIGURE 420 Center of mass The single point at

which the mass of a body can be thought to be concentrated is

the center of mass As the con figuration of this iumper s body

parts changes from takeoff (left) to midair (right) the

instantaneous location of the center of mass (white dot) changes

as well In fact note that the center of mass lies momentarily

outside the body A high-iumper or pole-vaulter can pass over the

bar even though his or her center of gravity moves under the bar

represemed along a rectangular Cartesian reference sys tem Vhen we use such a reference sys tem trigonometry helps us to calculate vector values for example we can measure the force applied ro a dragged objeer (F in figure 421) but the ponion of that force acting horizon[(111y against surface fricshycion (FJ is more difficult to measure directly Howeve r given the force (F) and angle (8) we can calculate both horshyizontal and ve rtical components (Fx and FJ And of course conversely if we know the componem for~es (F x and FJ we can calculate the combined resultam force (F)

Basic Force Laws Much of engineering is based on laws rhat were formulated by Isaac Newton 0642-1727) Three of his laws are fundamental

1 First law of inertia Because of its inertia eve ry body continues in a state of rest or in a uniform path of motion umil a new force acts on it to set it in motion or change its d irec tion Inertia is the tendency of a body to res ist a change in its st8te of morion If the body is at reSt it will resist being moved and if it is in motion it will resist being divened or ~topped

2 Second law of motion Simply stated the change in an obj ects morion is proportional to the force acting on it (figure 422) Or a force (F) is equell to the mass (m) of an object times its experienced acceleration (a)

F = rna

Units of thi s force in newtons (N) kg m 5-2

are the force needed to accelerate 1 kg mass ar 1 meter per secondshy

~ ) F - -----bull ---F I )

~ ~ ~~j Fx

FIGURE 42 I Vectors When dragging the seal the

polar bear produces a resultant force (F) that can be represented

by tWO small component forces acting vertically (Fy) and

horizontally (F)The horizontal force acts against surfa ce friction

If we know the resultant force (F) and its angle (8) with the

surface we can calculate the component forces using graphic or

trigonometric techniques

3 Third law of action reaction Between twO objec ts in contact there is for each ac tion an opposite and equal reaction Applying a force automat ica lly gene rates an equa l and opposite force-push on the ground and it pushes back on you

Alben Einstei n s (1879-1954) theories of relativity placed limits on these Newtonian laws But these limitations become mathemat icaily significan t on ly when the speed of an obj ect approaches the speed of light (186000 miless) Newtonian laws serve space trave l well enough (() get ve hishycles to the moon and back and so the y wLlI se rve LI S here on Eanh as well

In biomechanics Newtons second law or its modifishycations are most often used because the separate quantities can be measured dlrecdy In addition knowing th e forces experienced by an cll1imal often gives us the bes t undershystandi ng of its particul ar design

Free Bodies and Forces To calcu late forces it often helps [0 isolate each part from the rest in order [0 look at the forces acting on tl13t part A free-body diagram graphically depicts the isolated pa rt with its forces (figure 423ab)

When you ~al k across a noo r yo u exen a force upon it The noor gives ever so slighdy and llnpetceptibly until it recums a force equal to yours which exemplifi es the action and reaction principle described by New[Oos third law If the noor did not push back equally you would fall through Think of a di ver perched at the eod of 3 diving board Tht~

board bends until it pushes back with a force equal [0 the force exerted on it by the diwr Diver and board are sepashyrated in the free- body di3gram and the forces 00 each are shown in figure 423a If both forces are equal and opposite they cancel and the twO 3re in equilibrium If not motion is produced (figure 423b)

138 C hapte r Four

3N 5N(a)

[7d 4N

C2J 4N 5N 3N

(b) Ground force Reaction force

FIGURE 422 Forces of motion (a) The force a frog produces at liftoff is the resul( of its mass and acceleration at that instant (F = mol (b) Forces produced collectively by both feet of a hefty frog and (he ground are opposite but equalThe vector parallelograms represent the components of each force If a frog of SO g ( 05 kg) accelerates 100 m s - 2 a force of 5 N = (100 X

05) is generated along the line of travel By using trigonometric relations we can calculate the component forces If liftoff is at 37deg then (hese component forces are 4 N = (cos 37deg X 5 N) and 3 N = (sin 3r X 5 N)

II

As a practical matter mechanics is di vided be tween these two conditions Where all forces acting on an objec t balance we are dea ling with that part of mechanics known

1- as statics Where acting forces are unbalanced we are dea lshyn ing with dynamics

[- Torques and Levers $ In the vertebrates muscles generate forc es and skelew l eleshy

ments apply these forces There are several ways to represent this mechanica lly Perhaps rhe most intuiti ve representat ion is with to rques and levers The mechani cs of torques and levers arc fami liar because mos t persons have firsthand expeshyrience ith a simple leve r S5tem the teeter-totter or seesaw

n of childhood Ac tion of the seesaw de pends on the oppos ing weights seated on oppos ite ends and on the distances of h these eights from rhe pi vot pa ine or fulcrum This d isshy

tance from we ight to fulcrum is the lever arm The leve r arm n is measured as the r erpendicular d is tance from force to fulshyit crum Shorten the leve r arm and more weight must be added n to keep the board in balance (figure 424a) Lengthen it sufshyIf fi cientiy and a little sister can keep several big broth ers balshy1 anced on theo rrosite end t A fo rce acting at a distance (the lever arm) from the e fulcrum te nds to turn the seesaw about this roint of rotation

b r more formally it is said to produce torgue (1hen leve rs are used to perform a task we also recognize an in-torque and out-torque If more output force is requ ired shorteni ng

IS the out and lengthening the in lever arms increases the out-torque Converse ly if out-torque speed ( = veloc ity) or

6W t

II (a)

(b)

FIGURE 423 Free-body diagrams (a) Two phySical bodies the board and the diver each exert a force on the other If the forces of the two bodies are equal opposite and in line with each other then no linear or rotational motion re sults Although the forces are present the two bodies are in equilibrium (left) To depict these forces (right) the two bodies are separated in freeshybody diagrams and the forces acting on each body are represented by vectors (arrows) (b ) If force s are unequal motion is imparted The diver has by sudden impact pushed the board down farther than it would go under his weight alone So it then pushes upward with a force greater than (he weight of the diver and the diver is accelerated upward

travel d is tance is requ ired then lengthening th e out and shortening the in leve r arms fa vo r green er ve loc ity and disshytance Ln the out-torque (figure 4 24c) Of co urse th is increased sreed and distance are achieved ltit the expense of fo rce in the out- torque In engineering terms torque is more co mmonly described as the moment about a po int and the leve r arm as the moment arm

The mechanics of levers mean that output (orce and output speed are opposites Long output lever arms favo r speed whereas short ones favor force Regardless of how des irabl e it would be to have both in the des ign of say an animals limb simple mechanics do not re rmit it S imi shyla rl y long ourput lever arms sweep through a grea ter disshytance whereas short ones move through a shorter distance For a given input both output force and output speed can shynot be max imized Compromises and trade -offs in des ign must be made


~

~

--~=- ~

~--------~-------~ Lever arm () Lever arm (I)

(a) (b)

8 - Digger

V I ~ J~ I I I I I

I 1 I(a)

FIGURE 42 S Strength versus speed The forearms

of a digger (a) and a runner (b) are drawn to the same overall

length Input forces (F) and input velocities (V) are the same but

output forces (Fo) and velocities (Vo) differ The differences result

from the differences between the lever arm ratios of the two forearms Output force is greater in the digger than in the runner

but output velocity of the digger is less Formally these

differences can be expressed as differences in mechanical

advantages and in velocity ratios

FIGURE 424 Principles of lever

systems (a) The balance of forces about a

point of pivot (fulcrum) depends on the forces

times their distances to the point of pivot their

lever arms (0 (b) To get more output force the

point of pivot is moved closer to the output

an d farther from the input force In this

diagram the short output lever arm (10) and

long input lever arm () work in favor of more

output force (c) To produce high output speed

the pivot point is moved closer to the input

force (I) Other things be ing equal speed is

achieved at the expense of output force

Consid er [he fore li mbs of cwo mammals v ne a runner ~pec ia lized fo r speed [he ocher d digger spec ialied [ el ge nerate

large outpUt force In figure 425a [he relative ly lung elbolV process and sho n forearm of [he digger fJvur la rge fo rce out shy

put In [he runner (figure 4 25 b) [he e lbow is shore th e foreshya rm long Leve r arms are less favorable [0 force lJU[PU [ m [he fo refooc o f [he runner bue more favo rabl e [0 speed The speed of the elbo lV is magnlfied by [he relati vely greater outpU[ lever

arm but [his is accomplished a[ [he expense of output fvrce

More formally we can cxpress [he mech lt1l1lcs of inpu t and o utput forc es ilt differe nt ve loc i[i es wi th ~ imple ra tios

The ratio of F)F [he o utput [0 in put force is the mechanshyical advantage (or force advantage) The ra tio of the output

[0 input le ver ar ms U Ii is the velocity ratio (or speed or

distance advantage)

As we might ex pec t digge rs enj oy a grea[cr mechanishy

ca l ad va ntage in [hei r forearm but runners e nJoy a greater veloc ity ad vantclge in [heir forearm There are of course

o ther ways o f producing o utput fo rce o r speed Increilsed size

il nd h enc e force o f input muscles and emphis of fast shycon tracting muscle cell s both affect o utpu[ The le ver sysshy[e ms o f an animal in rum set [he re lationsh ips hetwee n

force and speed (or distance ) Arc iodactyl s such as deer have limbs des igned for

bmh force and speed (figure 426) Two ll1u scl e~ [he medial glu[ells dna [he sem imembranos lls wit h different mec han ishyca l advantages make different contributio n w foc e o r [l

speed ouepu[ The medial gluteus enj o ys a h igher veloc j[Y

rat io (1) = 44 compa red With Uti = II for the sentimem

140 Chapter Four

ler lte

JW

utshyreshy

ehe ced

ceo tput ios lanshytput dor

High and low gear muscles Both the cater gluteus and the semimembranosus muscles turn the limb urse same direction but they possess different mechanical I size in doing so A muscles lever arm is the perpendicular

fastshy to the point of rotation or pivot point (black dot) from ine of muscle action (dotted line)The velocity ratio is higherr sysshy

medial gluteus which can move the limb faster But the mimmhranosus moves the limb with greater output force

of its longer lever arm Lever arms in both the muscles the common lever arm out (10) are indicated

branosus) a leverage that favors speed Lf we compare these muscles With the gears of a car the medial gluteus would be a high gear muscle On the other hand the semimembrashynosus has a mechanical advantage favoring force and would be a low gear muscle During rapid locomotion both are active but the low gear muscle is most effective mechctnishycally during acceleration and the high gear musde is more effective in sustaining the velocity of the limb

The two muscles of the deer limb swing it in the same direction But each muscle acts with a different lever advantage One is specializedfor large forces the other for speed This represents one way biological design may incmpomtc the mechanics of torques and levers to provide the limb of a running animal with some degree of both force and speed output Just as a seesaw does not have a sinshygle fulcrum that can maximize output fmce and output speed simulraneously similarly one muscle cannot maxishymize both A single muscle has leverage that can maximize either its force output or its speed output but not both a limitation that arises from the nature of mechanics not from any necessity of biology To work around this two or more muscles may divide the various mechanical chores amlngst them and impart to the limb favorable force speed or distance during limb rotation Biological design must abide by the laws and limits of mechanics when mechanical problems of animal function (fise

Land and Fluid For terrestrial vertebrates most external forces they experishyence arise ultimately from the effects of gravity Vertebrates in fluids such as fishes in water or birds in flight experience additional forces from the water or air around them Because the forces are different the designs that address them differ as well


Gravity acts on an obiect to accelerate it On the surface of the Earth the average acceleration of gravity is about 981 m 5-

2

acting toward the Earths center Newtons second law (F = mal tells us that an animal with 8 m8SS of 90 kg produces a total force of 8829 N (90 kg X 981 m s-2) against the Earth upon which it stands An object held in your

hand exerts a force 8gainst your hand which results from the objects mass and gmvitys pull Release the object and the acceleration from gravitys effects becomes apparent as the object picks up speed as it falls to Earth (figure 427) Gravitys persistent attempt to accelerate a terrestrial animal downwmd constitute rhe animals weight In tetrapods this is resisted by the limbs

The weight of a qUildrupedal animal is distributed among its four legs The force borne by fore- ilnd hind limbs depends on the distance of each from the center of the anishymals milS Thus a large Diplodocus might have distributed

its 18 metric tons (39600 pounds) with a ratio of 4 tons to its forelimbs and 14 to its hindlimbs (figure 428)


FIGURE 427 Gravity The clam released by the seagull accelerates under gravitys pull and picks up speed as it falls to

the rocks With equal intervals of time designated by each of the

six arrows note the accelerating positions of the clam

When we explored the consequences of size and mass at the beginning of this chapter we noted that large an imals have relati ve ly more mass w com end widi diem srnall anishyrnals A srnall lizard scampers safel y across uee limbs and vertica l walls a large li zard is earthbound Grav ity like O[her forces is a pltlIT of an animal s environrnem and affens per shyfonnance in proportion to body size Size is also a facwr for animals that live in nuicis a ldilt)ugh forces O[her than gravshyity tend to be predorninanr

Life in Fluids

Dynamic Fluids W~He r and air are nuids Cen ainly air is th inner and less viscous than water but It is a fluid nonetheshyless The physical phenomena that au on fi shes in water genshyerally apply [U birds in air Air and wa ter differ in viscosity but they place sirnilar ph ys ical clerncmds on animal designs

(a) (b)

FIGURE 428 Weight distribution (a) The estimated

cen ter of mass of this dinosaur lies closer to the hindlimbs than

to its forelimbs so the hindlimbs bear most of the an imals

weight For Diplodocus its J 8 metric tons (39600 pounds) might

have been carried by a ratio of 4 tonnes to its forelimbs and 14

tonnes to its hindlimbs (b) If Diplodocus lifted its head and

forefeet up to reach high vegetation then all 18 tonnes would

have been carried by hindlimbs and ta il which forming three

points of suppOrt give each limb and the tail 6 tonnes to carry

When a body mOles through ltI nuid the tluid exerts a res istshying force in the opposite di rection w the bodys motion This resisting force termed drag may arise from va rious physica l phenomena but forces caused by friction drag (or ski n fricshytion) and by pressure drag are usually the most importanr As an animal moves through a nuid the nuid nows along the sides of its bod y As nuid and bJdy surface move past each O[her the fluid exerts a resist ing force (drag) on the surface of the animal where they make contact Th is force creates fr iction drag and depends among other thing~ on the visshycosity of the nuid the area of the surface the surface tex ture and the relati ve speecl of fluid and surface

Indi vidual particles in a nuid trave ling in 8 fl oll desc ribe indi vidual paths If the ave rage di recti on of these panicles is planed and po ints co nnec ted along ~he line of overall fl ow nonoverl8pPll1g streamlines that represent [he general layered panem of fluid now can be prod uc ed The derived strea mlines therefore express [he st ~l[ i st lcClI sumshymary of laye red flows slipping smoothl y across one another within a moving fluid Specia l and often complex event OCCLlr withll1 the boundary layer the thin fluid laye r clmshyest to the surface of the body Generally it is a th m grad ient slowing from the veloc ity of the general now down [0 zero on the surface of the obj ec t across which the fl uid fl ows In a Boeing 747 the boundary layer is about 1 in (hick at the trailing edge of the wi ng Natural instabilities in the bou ndmiddot dry layer may cause the fluid to become chaot ic and the nolV is spoken of as turbulent This inc reases drag dramaticallv W here the flow is nonchao tic it is described as laminar

If the pa rticles in the bou ndmy laye r pass ing around an object are unab le w make the sha rp turn smoot hly behind the obj ec t then the layers within the flow tend to part th is is termed flow separation (figure 429a) The fluid behind the obj ec( moves fa ster and pressure drops b hing to preshysure drag wh ich may be seen as a wake of el i rbed fluiJ

C hapter Four 142

(a) Fast Separation

(b)

FIGURE 429 Streamlining_ (a) Particles in the boundary layer are unable co make the sharp change in direction and velocity co negotiate the turn around the cylinder-shaped object and now separation occurs behind the object (b) Extension and capering of the object inco the area of disturbance helps prevent separation and resul ts in a streamline shape

beh ind a boat Physical ly the fl ow separation results from a substantial pressure different ial (pressure drag) betwee n the front and the back of the animal An ex tended taper ing body fills in the area of potential separation encourages streamlines to close smoothly behind it and thereby reduces pressure drag (figure 4290) The result is a streamlined shape common to all bod ies that must ass rapidl y and effishyciently through a fluid An active fish a fast- fly ing bird and a supersonic aircraft are all stream lined for much the same reason-to reduce pressure drag (figure 430a-d)

v A golf ball in fli ght meets the same prob lems but is engineerld differently to add ress drag forces The dimpled surface cf a golf ball helps hold the houndary layer longe r

He smoothes the streamlines reduces the size of the d istu rbed wake and hence reduces pressure drag As a result a gol f e

nshy ball with dimples travels other things be ing equal about twice as far as one with a smooth surface er

I t S Together fri ct ion and pressure drag contribu te to proshy

file drag which is related to the profile or shape an object presents to the moving fluid If you plltlce your cupped hand out the window of a fast-mov ing car yo u can fee l the differshyence when presented edge-on or pa lm-on to the onrushing air A change in profile changes the drltlg A thin broad wing ofa bird meeting the ai r edge-on presems a small profile But as the wing tips up changing the angle of attack the broltld profile of the wing meets the air increasing drag Fish fi ns or seal flip pers when used to make sharp turns are moved with the broadest profile to the water much Iike the power stroke an of a boat oar taking advantage of profil e drag to help genershylind ate cornering force s(hi s

Engineers examine the phys ical problems associated hind wi th motion through fluids within the disc iplines of hydro shydynamics (water) or aerodynamics (a ir ) Applied to animal

designs that move through fluids these disciplines revertl how size and shape affect the way the physica l forces of a fluid act on a moving body

In general fou r physicrtl ch arrtc te ri sti cs affect how th e flu id ltlnd body dynrtm ically inte rac t One of these is the density or mass pelmiddot unit vo lum e of the fluid A secshyond is th e size and shape of the body as it me ets th e flUid The resistance rt rowboat oa r expe riences when the blade is pull ed broads id e-on is of course quite different than when it is rulled edge-on The third ph ys ica l charactershyisti c of a fluid is it s velOCity Finally the viscos ity of a flu id refers to its resista nce to fl ow These four charac teristics are brough t toge ther in a rat io known as the Rey nolds number

pLURe = shy

fL

where p is the densi ty of the fluid and i-L is a measure of its viscosity I is an expression of the bod ys characteris tic shape and size and U is its veloc ity through the fluid

Perhaps because we ourse lves are large land ve rteshybrates we have so me intuition about the importance of grav ity but no special feeling for a ll th8t the Re yno lds number has to tell us about life in flu ids The units of all variables of the ratio c8nce l each other leaving the Reynolds number withoLit units- no feet per second no kilograms per meter nothing It is d im ensionless a furthe r factor obscuring its message ye t it is one of the most important express ions that summarizes the physica l demands placed upon 8 body in a fluid The Reynolds number was developed dU ri ng the nineteenth cen tury to

describe the natu re of fluid fl ow in particular how differshyent circumstances migh t resul t in fluid fl ows that arc dynamically simil ar The Reyno lds numbe r tells us how properties of an animal affect fluid flow around it In ge n shyera l at low Re yno lds numbers skin fricti on is of great im portance at high Reyno lds numbers pressure drag might predo minate Pe rhaps most importantl y at leas t for a bio logist the Reynolds number tells us how changes in size and shape might affect the phys ical pe rformance of an animal traveling in a fluid It draws our attention to the fe atures of the fl uid (v iscos ity) and the fea tures of the body (size shape eloci ty) that are most likely to affect performance

For sc ientists performing experiments th e Reyno ld s number helps them to build a scale model that is dynami shycally similar to the original For example seve ral biologists wished to examine air ventilation through prairie dog bur shyrows but lacked the convenient space to build a life-siLed tunnel system in the laboratory Instead the y bu ilt a tunnel system ten times smaller but compensated by running winds ten times faster through it The biologists we re confident that the scale model duplicated condit ions in the full- sized origina l because a simil ltH Reynolds number for each tunnel verified that they we re dynamically similar even though their sizes differed


FIGURE 430 Life in fluids (a) The airplane wing shown in cross section encourages smooth flow of the passing airmiddotstream (b) As its angle of attack to the direction of flow increases separation of flow(a) from the upper wing sunace suddenly forms and lift is lost (c) Birds such as this falcon have a small tuft of feathers (a lula) that can be lifted to smooth the airflow at high angles of attack (d) When separation begins this small ai noil can be lifted to form a slot that acce lerates air over the top of the wing preventing separation and thus stalling-a sudden drop in lift

(d)

Static Fluids FlUids even thin low-density fluid s such as air exert a pressure lln objects within them The unit of presshysure Pascal (Pa) is equivalent [Q 1 new[Qn aC[ing over 1 square meter The expression as light as a ir betrays the common misconception that ai r has almos t no physica l presshyellce In fa C[ air exe rts a pressure in all directions ( Ibou t 101000 Pa (I 4 7 psi or pounds per square inch) at sea level which is eq uivalem [Q 1 atmosphere (atm) of pressu re The envelope of air su rro unding Earth extends up to sevmiddot~ hUllshydred kilometers Although not dense [he column of air bllVe the surface of Earth is quite h ih so the add itive veight ~t its base rroduces a substant ial pressure CIt Earchs surface YJe and other terrestrial animltlb are unaware of this pressure since it comes from all directions and is l~c1[erba lshyancel by an eq ual outward pressu re from our bodies Thus all forces on ou r bodies balance inside with our Respira[ory sys tems need only produce rela tive ly small changes in presshysure to move air in and out of the lungs

If we drive fro m low eleva tion to high elevLllivn in a short period of time we might notice the unbalanced p resshysure that builds uncomfortably in our ears umil d yaw n or stretch of our jaw pops and equilibrates [he rnside and outshyside pressures to relieve the mismatch Mos[ of us ha ve expeshyrienced increas ing pressure as we dive deeper in water At a glvlOn depth the press ure surrounding an animal in water is the same from all sides The deeper the animal [he greater is [he pressure In fresh water with each me ter of depth a tmospheric pressure increases by about 98 X 101 Pa A[ 5 meters atmospheric pressure would be about 49 X 103 Pa Scaled for a human that would be like trying to breache With a 90-kg slab placed upon the chest A fully submerged sauroshypod would experience 49 X IOJ N on each square meter of its entire chest (figure 431) Ie i~ nor likely thar even the massive chest muscles of this dinosaur could overcome so 111uI-h pressure when i[ drew in a breath Therefore Brashychiosauru s and other long-necked an ima ls probabl y d id not live aquatic lives with their bodies deeply submerged and cheir heads reaching far above to the su rface to sno rkel air

Modred ro m McMahon and Bonner

FIGt incr-eaSnorkeling wo rks only fo r small creatures close LO rhe waters from csurface such as mosquito larvae ll r a blow-hole-equipped pressu

cetacean breaching the surface sauro~

Buoyancy describes the tendency of a submerged pressu object in a fluid to sink or to rise Long ago Archimedes too ml (287-212 BCE) figured out that buoyancy was re lated to Breach the volume an object disp laces compared to its own weigh t shown If the density of [he submerged object is less than that of water then buoyancy will be a pos itive upward force if its density IS greater than wa ter then the buoyancy is negclti ve and i[ is forc ed down S ince denSity IS re lated to volu me an

of a IIIchange in vo lu me wdl affect the tendency of [he obJeer to the tra rrse or sink Many bony fish possess a flexible gas bladder are mil(sw im bladd er) that can be filled with various gases As the for tral fis h dives deepe r pressure increases compress ing the air tons tr reduci ng vo lume and thereby effew vely making th t fish the co denser The negative buoyancy now pushes the fish dow n cranks l and I[ scar[s to sink As we will see rn chapter 11 SU Cil a fi sh wheelscan add more gas into the gas bladder to increase its volume from tIand return it ove rall to neutral buoyanc y forces (

Machines a mach force bWhen we are interested in the motions of pa rts of the same the Ja animal it is customary to represent each movable part with a force plrnk A Joined se ries of links is a kinematic chain representing mandltthe main elements of an aninlal If these linkages are fl oppy (figure middot and without control then [he chain is said to be unconshy

strained A kinema tic chain resniered in motion is conshystrained and form ally constitutes a mechanism The motion Stren~

of one link will impart a definite and predictable mOtion in all A we ig other links of the same mechan is m (figure 432a) applied

A kinematic mechanrsm simula tes the relative mUlions general of the parts of [he animal i[ represents so it helps identify the pact It a role of each elemen[ For example seve ral bony elements on sile fore both sides of a lizard s skull are involved when i[ lifts its snoU[ (figure during fe eding These elements can be represented by a kineshy able to matic chain that constitutes the jaw mechanism of [he lizard equally (figure 432bc) sustains

Chapter Four 144

I

e

It5m~~ lve t- --- -~--~d

lt ----c~~-ir

FIGURE 43 I Water pressure Water pressure

increases with depth but at any given depth pressure is equal~rJs

from all directions For each meter below the surface the leo pressure in fresh water increases by about 9800 Pa A large

sauropod submerged up to its chin would experience water ed pressure of about 49000 Pa (5 m X 9800 Pal around its chest 1eS too much pressure to allow chest expansion against this force co Breathing would be impossible Sauropods such as Brachiosaurus

hr shown here were probably not completely aquatic

of irs

Often we are interested in more rhan just the motion ny of a mechanism We might want to know something about

to the transfer of actual forces Such devices that transfer forces Ier are machines Formally defined a machine is a mechanism he for transferring or applying forces In a cars engine the pisshytons transfer the explosive forces of gaso line combustion to the connecting rod the rod to the crankshaft and the crankshaft in turn (0 the gears ax les and wheels Pistons to

wheels collectively form a m8chine th n transfers energy ne from the ignited gasoline to the road Le ve rs that transfer forces qua lify as machines (00 The inpur force brought into a machine by a le ve r arm is 8ppli ed elsewhere as 8n output force by the oposite lever arm In this engineering senseIe the jaws of a herbivore are a mach ine whereby the input

a force produced by the Jaw muscles is transferred along the mandible as m output force to the c ushing molar teeth (figure 433)

1shy

)11 Strength of Materials A weight-bearing stru ctu re carries or resists the forces appl ied to it These fo rces may be exper ienced in ri1ree

IS general ways Forces pressing down on an object to comshyIe pact itare compressive forc es those th C t stretch it are tenshyn sile forces and those that slide its sec tions are shear forces 1t (figure 434a-c) Su rprisingl y the sa me structure is not

able to withstand the three types of force applications d equally For any structure the maximum force a structure

sustains in compression before breaking is its compressive

7-~ __

---~=====~~---- ----- --- 2 ------ 1 1 I --- I ~

I I I I I I I

3 I I

I

(a) 4

(b)

(e)

FIGURE 432 Kinematic chain (a) This four-linkage

mechanism is joined by pin connections so that the motion of link

3 imparts a specific motion to the three other links (b) The fourshylinkage chain of a lizard skull (ignoring the lower jaw) is

constrained (c) Again motion of link 3 imparts a specific motion

to each of the other links

strength il1 tension is its tensile strength and in shear is its shear strength_ Table 42 lists the st rengths of several materia ls hen the y are exposed to compress ive tensil e and shear forces

Notice from this table that most materials are stronges t in resisting compress ive forces and weakest in their ab ility to withstand tension or shear This is very significant in design Ordinarily supportive columns of buildings bear the load in 8 compressive fashion their s[[ongest weightshybearing orientation However if the column bends slightl y tensile force s to wh ich they are more susceptible appear

W hen any objeer bends compressive forces build up on the inside of the be nd and tensil e forces on the outside Opposite sides experi ence different force applications The column may be strong enough to withstltl nd compressive forces but the appea rance of tensile forces introduces forces it is intrinsically weaker in resisting If bend ing persists breaks may origina te on the side exper iencing tension propshyagate through the material and cause the column to fail Flying bumesses side braces On the main support piers (columns) of Gothic cathedrals were used to prevent the

Biologicltll Design

III

145

FIGURE 433 Jaws as machines A machine transfers

forces Here the lower jaw of a herbivore transfers the force of the

tempolalis muscle (open arrow) co the cooth row (so lid arrow)

where food is chewed Rotation occurs about the condyle

pi ers from bending thus keeping them in compression and allowing them to be tte r carry the we ight of the cathedra ls mc hed roof (fIgure 435)

Loaes

Howa load is pos itioned upon a supportive column affects its tendency to bend (figu re 436a-c) When the load is arranged evenly above the columns mai n axis no buckli ng is ind uced dnd the co lumn primarily experiences the load as compressive fo rce (figu re 436b) The same 10aJ pbced asymmetrlcally o ff center causes the column to bend (figure 436c) Tensile (a nd shear) fo rces now appear Tensile and compressive forces are greatest at the surfaces of the column least at its center Development of surface te nsile forces is espec ially ominous

because of the intrinsic susceptibility of supportive elements to such forces-what we notice as cracks


Fatigue Fracture With prolonged or heavy use bones

like machines can fa t ig ue and break When mit ially deSigned the working parts of a machine are built wit h materials strong enough to wit hst and the calculated

stresses they will experience H oweve r with use o ver time these parts oft en fltlil a conditi on kn own to eng ineers as fatigue fractur e N ot long after the Industrial Revo lution engineers noticed tha t moving parts o f machinery occa shysionally broke at loads within safe limits Axb of tr a im in use for some time suddenly broke for no apparent reashy

so n Cranks or cams that had withstood peak loads many

1shy(a) Compress ion (b) Tension (c) Shear

FIGURE 434 Direction of force application The

susceptibility of a material co breaking depends on the direction

in which the force is applied (almiddotrows) Most materials withstand

compression best (a) and are wea ker when p laced in tension (b) or shear (c)

thrusc fr

After Gordo

FIGlJ cathedrTABLE 42 Strength of Different Materials Exposed how th

to Compressive Tensile and Shear Forces simples Compressive Tensile Shear pinnaclE Strength Strength Strength the inte

Material (Pa) (Pa) (Pa) prodUC E

pressurtBone 165 X la 110 X la tends cc

Cartilage 276 X 10 30 X la opposi t Concrete 414 X 10 40 X la

Cast iron 6205 X 10 117 X la 124 X la

Granite 103 X la 10 X la 13 8 x 10

Uhimoce suenglhs shown

Source Adopted rom J E Gordon 1978 StruCl ues or why things don farr down DoCopo Press NY Other sources have 0150 been used

times before sometimes suddenly broke under ro utine operat ion Even ru 1 11y eng inee rs apprecia ted that one of the factors leading to these failures was fatigue fracture Although a mov ing part 111lght be strong enough inicia lh to bear up eail y to peak loads over time tin y microfracmiddot

tures fo rm in the mater ial These are insig nificant indio v idually but cu mula t ive ly they can add up [0 a lT18j Or

fr ac ture tha t exceeds the strength of the ma terial and

breakage follows

Load Fracture [n vertebrates bones are loaded ~yrnrnetr i

cally o r where tha t is not poss ible muscles and tendons aCl

as braces to reduce the cendency for a load to ind uce bend

lllg of a bone (figu re 437) The greatest stresses de ve lop ar the surface of bone wh ile fo rces are a lmost neglioible at ilS center Consequently the core of a bone can be hollow with out much loss of its effective strength Probably for the sa me

reason catta il reeds bamboos bicycle frames and fi shing poles are h o llow a~ well This econom izes on materi 1 withmiddot out a great loss in strength

Most fractures likel y begin on the side of the bone experiencing tensi Ie fo rces A fracture propagates through the bone ma trix causing failure Bone howeve r is a com

(a)

FIGUR under a Ie concave si

(b) When

weight cer compressi

represemJ

down arro

within this

same mass

compressi Both comp and least tc

posite mal ent mechi the propag alone (figl

gives fibel

146 C hapter Four

n

I b)

n

w re ia lty (racshy

mdi-

Interior pier

Exterior pier

Gothic cathedral The right side of the cathedral shows its structural elements The left side illustrates how these structures carry the thrust lines of forces At its simplest the cathedral includes the exterior pier topped by a pinnacle the main interior pier and the nying buttresses between the interior and exterior piers The weight of the vault (roof) produces an oblique thrust against the interior piers Wind pressure or snow load accentuates this lateral pressure which rends to bend the main inter ior piers Flying buttresses act in an opposite direction to resist this bending and help carry latera l thrust from the roof to the ground (small arrows)

A~er Gordon

(a) (b) (c)

Loading (a) When a material bends under a load compressive forces (solid arrows) develop along the concave side tensile forces (open arrows) along the convex side (Ii)When a supportive column is loaded symmetrically (with the

~ wPllght centered) the only type of force experienced is force The distribution of the I OO-kg mass within a

section is depicted graphically The lengths of the arrows show equal distribution of compressive forces this representative section (c) Asymmetrical loading of the

mass causes the column to bendThe column experiences ~(1igmpressive forces (down arrows) and tensile forces (up arrows)

compressive and tensile forces are greatest near the surface toward the center of the colum n

~tR9sit material consisting of seve ra l su bstances with differshyanical properties Together these substances resis t

tion of a fractu re better than Clny one constituent

figure 4J8a-c) Th is same prinCiple of composites

its resistance to breaking Fiberglass consists

Tensor fascia lalae muscle

Iliotibial tract

Head of femur

FIGURE 4] 7 Braces The weight of the upper body is carried on the heads of the femurs (left) This means that during the striding gait (right) the head of one femur carries all the upper body weight Consequently the long shaft of the femur is loaded asymmetrically increasing its tendency to bend The iliotibial tract the long tendon of the tensor fasciae latae muscle that runs laterally across the femur partially counteracts this tendency to bend and thereby reduces the tensile forces that would otherwise develop within the femur

o f glass fibe rs em bedded in a plastic resin Glass is brittle

resin weak but (Ogether [hey are st rong because they blunt small cracks and prevent their spread As 8 crack appro8ches

the bound8ry between the two fibergl8ss materials the resin g ives slightly That spreads out the forc e Cl nd thus reduces

the stress at the tip of [he crack that makes it advance A

space in the mate rial can do the sa me job thus hard foams resist cracking Bone makes lise o f both stress relief and small voids o r spaces to reduce prop8gation

Collagen fibers and hydroxyapa tite crystals a re the

main materials of bone matrix They 8re thought to 8ct in a

manner analogous (0 the glass 8nd resin offibe rglass (0 bl unt sm8 fractures Further the o rientation of collagen fibers

alternates in successive laye rs so that they better receive tenshy

s ile and compressive forces

Bone structure (p 179)

Tissue Response to Mechanical Stress Tissues ca n change in response to mechanical s tress If livshy

ing tissu e is unstressed it tends to decrease in prom inence

a conditi o n termed atrophy (figure 4398) If it experishy

ences increased stress tissue tends to inc re ase in promishyne nce a condition termed hypertrophy (figure 43 9b)

Cell division and proliferation under stress a re termed

hyperplasia Thus in response to exercise the muscles of


(a) (b) (e)

FIGURE 4] 8 Fracture propagation (a) Failure of a stlucture begins with the appearance of a microfracture that spreads rapidly (b) In composite materials such as bone the advancing fracture is preceded by stress waves that may cause the concemrated force (0 spread at the boundary between the composite materials where they give slightly (c) As the fracture line meets this boundary its sharp tip is blunted and its fJrogress curtailed

an athlete will increase in s ize This overall inc rease is prishy

maril y due co an increase 111 the size o f ex isting muscle cells noc co an increase in cell number (h ypertrophy but

no t much hyperplasia ) During pregn (l ncy smooch musshy

cles of the uterus increase bo th in size and number (hypershytrophy and hyperplasia)

Muscle response to chronic exercise (p 375)

Tissues can under so me circumstances change from

one type to anocher (l transfo rm a ti on called metaplasia

Metapl(lstic transformati ons are o ften p8tho logic(ll For

example the normal cilia ted pseudos rratified columnar

epitheliumof the trachea may become stratified squamous

epithelium in cobacco smoke rs But some metaplastic

changes seem to be pa rt o f no rmal growth and repair processes as well Fo r exam ple re ptiles ex hi bit metaplastic

bone formation during growth of lo ng bo nes Cho ndrocytes

become os teoblasts and ca rtilag ino us m8tr ix becomes

OSSlUUS as cartilage undergoes direct tr8nsform8tion inco ossi fied bone During bone repa ir in reptiles amphibians

and fishes the cartilaginous ca llus a ppea rs co arise from conshy

nective tissue through metapl aS ia

Tissue types (p 174)

All tissues retain some physio logica l ability to adjust

to new demands even after embryonic deve lopment is comshy

plete Weight training causes an athle tes existing muscles to

increase and his or her tendons to strengthen Regular longshy

distance running enhances circula tion increases blood vo lshy

ume improves oxygen deltve ry to tissues and metaboli zes

stored lip ids more effiC ie ntly Altho ugh the number of nerve

cells does not usuall y increase in respo nse to the phys iolog ishy

cal stress o f exercise coordina tio n o f muscle pe rformance

often does Ti ssues co ntinue to adapt phys io logically to

changes in demand throughout the life of the individual

One of the best examples is bone because it illustrates the complexity of tissue response

Responsiveness of Bone While pe rfo rming in a pro tective or supportive ro le bone

cannoc significamly d eform o r change shape Leg bon es

that telescope o r be nd like reeds would certainly be ine fshy

fective as suPPOrtS fo r th e body Bones must be firm But

because living bo n e is dynamic and responsive it gradu shy

ally ch anges during the life of an individual The genetic

program o f a person se ts fo rth the basic form a bone takes

but immedi a te e nvironm emal factors also contribute to ultimate bone fo rm S ome peo ples of the New lo rld

developed the practice o f wrapping a babys head against a

cradle boa rd (fi gure 440a left) A s a result the no rma l

sku II shape o f the ba by was a Itered so that the side pressed

to the boa rd was fl a ttened In parts of Africa and Pe ru

prolo nged band aging of the bac k of the skull caused e lonshy

gatio n o f the cra nium (figure 440a right) Until recent

times young Chinese g irls who looked forward ro a leisured life had the ir feet permanently folded and tightly

bound to produce tin y fe e t in adulthood The toes we re crowded and the a rch exagge rated (figure 440b right) The n o rma I and by comparison large foot was considered

ugly in wo men (figure 440b left) Because foot-binding impaired bi o mecha nica l performance this also had what

was considered the prope r social consequence of keep ing

women lite ra lly in the ir pl ace

Environmental Influences Four types of en vironmental

influences a lter o r enhance the basic shape of bo ne se t

down by the gene tic program One is infectious disease A

pathoge nic o rga nism can act directly to alter the patte rn of

bone depos itio n and cha nge its o verall appearance Or the

pathoge n ca n phys ica lly des troy regio ns of a bone A second

enviro nmental influence is nutriti on With adequate dict normal bone fo rma tion is usua lly taken for granted If the

diet is de fi c ient bo nes can suffer considerable abnormalishy

ties Rickets for exa mple caused by a deficiency of calcium (b)

in humans results in buckling of weight-bearing bones (fig shyure 440c) Ultravio let radiation transforms dehydrocho lesshy

terol into vitamin D which the human body needs to

incorporate ca lcium 1I1to bones Sunshine and supple ments en II i r l of mtlk are usua ll y enough to prevent rickets Hormon es a re bone the third fac to r tha t can a ffect bone fo rm Bone is a calc ium bone ( reserv o ir which is perhaps its o ldest functio n When it bec( demand ed some ca lcium is remo ved from bone matri x fo r tell Calcium dra ins occur during lac tation when the fem a le proshy own t

duces calcium-rich milk durin g pregnancy-when the fc ta l G eo me skeleton beg ins to oss ify during egg la ying when hard shell grea ter is added and during antle r gro wth when the bony rack of its bod antlers is deve lop ing 1I1tenti

stimul8 Endocrine control of bone calcium (p 589) ity Co

The fourth environmental influence on bone form is activity mechanica l stress (figure 440bc) Each weight-bearing bone this che experiences gravity and muscles tug on most bones Fo rces injury ( produced by gravity and muscle contraction place bone in an e ty o f re

148 Chap re r Four

FIGURE 439 Loss (atrophy) and increase (hypertrophy) of bone (a) Cross

section of a normal foot bone from a

dog is illustrated on the left Cross section of the same bone from the

opposite foot (right) that was

immobilized in a cast for 40 weeksMedullar

reveals significant atrophy (b) Crosscavity section of a normal femur from a pig is depicted on the left Cross section

of a femur from a pig that had been

vigorously exercised on a regular basis for over a year shows increased bone mass (right) Hypertrophy is

evident from the thickening and middotNormal Hypertrophy

environmem of stresses thm determ ine the fin a l shape of

bone Throughout an ind iv iduals life these stresses uron bone change As a young animal gains its footing and daring it becomes more active As an ad ult it might migrate ba trle

for territOry or increase its foragi ng to support offspring of its

own As the animal grows bigge r scal ing becomes a facto r Geometric increase in the mass of a growing animal places greater mechanical demands upo n the supportive e lements of its body Human athletes o n a continuous training progmm intentiona lly increase the ir loads on bones and musc les to

stimulate physio logica l adaptation to the heightened ac tivshyity Conversely age o r inclination can lead to declining act ivi ty and reduced stress on bones Teeth might decay and

this changes the stress pat te rn experie nced by the jaws An injury can lead to favoring one limb over another Fo r a va ri shyety of reasons then the forces experienced by bones change

greater density of the bone cortex

Atrophy and Hypertrophy The response of bone to mechanshy

ica l stresses depends upon force duratio n If bone experishyences continuous pressure bone tiss ue is lost and atrophy occurs Continuous pressure aga inst bone arises occasionally

with abnormal growths such as brain tum ors that bulge from

the surface of the brain cmd press on the underside of the bony skulL If this continuous pressure is prolonged the bone erodes forming a shallow depressi on along the surface of comact Aneurysms ba ll oonings of blood vessels at weak spo ts in the vessel wall can exert continuous pressure against nearby bone and cause it to atrophy Orthodon tic braces c inc hed to tee th by a dentist forc e tee th up agai nst the sides of the bony socke ts in which the y sit Resorption of

continuously stressed bone ope ns the way fo r teeth to migra te slowly but steadily into new and rresumably bener rositions within the jaws


(a)

(b) Normal foot

(e)

FIGURE 440 Responsiveness of bone to mechanical stress (a) The continuous mechanical pressure of a cradle board flattened the back of the Navajo Indian skull (left)

and wrapping of the Peruvian native skull (right) caused it to elongate (b) Historically many Chinese followed the practice of binding the feet of young girls with tight wrappings The small deformed foot shown on the right was considered socially attractive (c) A nutritional calcium deficiency during infancy led to rickets which weakened this womans skeleton shown here at age 70 Her bones bent under the normal load of her body

A(ter Halsted and Middleton

l50 Chapter Four

Thus bone that experiences a continuous force atroshyphies however so does bone that expeliences no force When fo rces are absent bone density actua lly th ins People restricted to prolonged bed res t without exercise show signs of osteoporos is This has been studied experimentally in

dogs on whom a cast has been applied to one leg The immoshybilizing cast e liminates or considerably reduces th e no rmal loads carried on a leg bone Bones so immo bilized exh iblf significant signs of resorption which can occur rather quickly Experiments with immobilized wings of roosters show that within a few weeks wing bones become extenshy

sively osteoporetic Rarificatio n of bone matrix occurs in

as tronauts during ex tended pe ri ods of weightl ess ness Calshycium salts leave bones circulate in the blood and th is excess

i- actually excreted When as tronauts return to Eanhs gravshyitationa l forces their skeletons graduall y recove r their forshymer density Eve n ove r long voyages the ossified ske leton is

not likely to disappear altogerhe r but it may fall to a ge netshyically determlI1ed minimum And of course muscle COI1shy

tractions maintail1 some regime of fo rces o n bone But

during deep space trave l lasting many months bone atrophy can progress far enough to make return to Earrhs gravity hazardous Prevention of bone atroph y il1 space trave l remail1s an ul1So lved problem

Between continuously stressed and ul1stressed bone is

the th ird type of fo rce application intermittem stress Intershymittent stress stimulates bone deposition o r hvpenrophy The impo rral1ce of intermi ttent force s on bone growth anJ

form has long been suspected from the fact that bone atroshyphies when intermittent forces are removed Conversely when rabbit bones were intermitten tly stressed by a spec ial mechanical apparatus hypertrophy occurred Ivlore recently bones of the rooster wing were stressed once daily wllh comshypressive loads but o therwise left immobilized After a month the artificially stressed bones did nO( ex hibit osteoshyporosis but did show growth of new bone clearly an approshypriate ph ys io logica l response to the anificial ly induced

intermittent stresses

Internal Design The overa ll shape of a bone retlects its ro le

as pan of the skeletal system Internal bone tissue consists of areas of compact and spongy bone Distribution of compact and spongy bone is also thought to be directed by mechanishycal factors although there is little hard evidence to suppmt this correlation According to an engineering theory called

the rrajectorial theo ry when a load is placed on an object the material within the object carries the resulting internal stress along stress trajectories or paths that pass these forces from molecule to molecule within the object (figure 441a) Ashybeam embedded at its base in the wall will bend und er its own weight The lower surface of the beam experiences compresshysive forces as the mate ria l is pushed together ltmd the up pe r surface of the beam experiences tension as material here is pulled apart The resulting compressive and tensile stresses are carried along stress trajectories that cross at right angles

to each other and bunch under the beams surface

--

J e s

n

n

~r

is s ~s

along the wall within the shaft of the femur

lotlicework model kindly supplied by P Dullemeiler ofter Kummer

u

FIGURE 44 I Stress trajectories (a) A beam projecting from

a wall tends to bend under its own weight placing internal stresses on

the material from which it is made Engineers visualize these internal

stresses as being carried along lines called stress trajectories Compressive forces become concentrated along the bottom of the

beam tensile forces along the tOp Both forces are greatest at the surface

of the beam (b) Stress trajectories in living bone When this theory is

applied to living bone the matr ix of bone appears to be arranged along

the lines of internal stress The result is an economical latticework of

bone with material concentrated at the surface of a tubular bone A

cross section through the proximal end of a femur reveals the lattice of

bone spicules within the head that become concentrated and compacted

Culmann and Meyer nineteenth-century engineers applied this trajectorial engineering theory to the internal rchitecture of bone Because the femur carries the load or

weight of the upper body they reasoned that similar stress trajectories must arise within this bone In order for the body to build a strong structure and yet be economical with mateshyrial bony tissue should be laid down along these stress tra shy

tories the lines along which the load is actually carried ~fter looki ng at sections of bone Culmann suggested that nature arranged bone spicules (trabeculae) into a lattice of spongy bone at the ends of long bones (figure 441 b) Because these hnes of stress move to the surface near the middle of the

the trabeculae follow suit and the overall result is a

(a)

tubular bone If the trabeculae of bone follow internal lines of stress these trabeculae might be expected to form a lattice of spongy bone after birth when functional loads are first experienced This is borne out Trabeculae of young fetuses display ra ndom honeycomb architecture O nly later do they become arranged along presumed lines of internal stress

Wolffs Law As applied mechanical forces change bone responds dynamically to adapt physiologically to changing stresses Wo lffs Law named for a nineteenth-century scienshytist who emphaSized the relationship between bone form and function states that remodeling of bone occurs in proshyportion to the mechanical demands placed upon it

Biological Design

Vertical wall

-- Tension

- Compression ____

Stress trajectory

151

New mechanical stress

(e)

(b)

FIGURE 442 Bone remodeling When tubular bone

experiences a new and more distorting stress (a) it undergoes a

physiological response that both thickens and straightens it New

bone forms along the concave sUliace (b) remodeling the bone and the straight shape is restored (c) Further remodeling returns

the bone to its original shape (top) although the walls would now

be thicker to withstand the new increased load

When bone ex periences new IClads the resu lt is often a greater tendency to buckle When buc kli ng occurs tens ile forces appea r Bones are less able to withstand tensi le forces than they can compressive forces In orde r to compensa te bone undergoes a physiological remode ling to better adap t to the new load (figure 442a~c) Initially adapti ve remodshyeling entails thickening a long the wall exper ienc ing comshypression Eve ntua lly overall re model ing restores the eve n tubular shape of the bone H ow a rc cells along the compresshysive side selectively stimulated to deposit new bone Nerves pene trate thlOughout bone so they mlght be one way of proshymoting and coo rdinat ing the physio logica l response of osteocy tes to changes in load ing Howeve r bones to which nerves have been cut still ab ide by Wolffs LalV and adjust to

changes in mecha nical de mand Muscles pulling on bone affect the shape of vascular

channels nea r the ir points of attachment to bone wh ich a lters the blood pressure in vessels su pp lying hone cells

Increased muscle ac tivi ty accompany ing incrcased load might via such blood pressure changes stimulate bone ce lls to remode l However muscle action on bone even if suffishycient to change blood pressure seems toO globa I a mechashynism to lead to the specific remodelll1g responses ac tua lly observed in bone

Bone ce lls occu py small lacunae spaces with in [he calcium ma tr ix of a bone Slight co nfiguratio nct changes in the lacunae occ upied by bone cel ls o ffer a mOle promiSing mechanism Under compressio n lacunae tend to fl at ten under tension they tend to become round If these co nfigu shy

rational changes produced under load could be read by the bone cells occ upying the lacunae then bone cells might inishyt iate a remodel ing matched to the type of stress experie nced

Another mechanism might involve piezoelectricity or low-le vel e lec tric charges These are surface cha rges that arise within any crystalline material und e r stress-nega tive charges appea r on the surface under compression and pos ishytive charges on th e surface in tension Bone wi th its struCshy

ture of hydroxyapatite cryswls experiences piezoelec triC charges when it is loaded It can be eas ily imagi ned that under a new load a new environ ment of piezoelec tri c cha rges would appea r within [he tissue of stressed bone If ind ividual bone cells could key off th ese loca hzed p iezoelectric charges then a specific re model ing response might fo ll ow

A lthough plomlsing each of these proposed mechashynisms by itself seems insufficient to account for the phys ioshylogica lly adaptive remodeling that occurs during bone response to the functional demands placed upon it T hls is a challenging area for further research

Biophysics and Other Physical Processes

Biophysics is concerned with pri nc iples of energy exchange and the sign ifica nce of these princ iples for li ving urganisms The use of light the exchange of heat and the diffus io n of

molecules are fundamenta l to the surviva l of an o rganism Biolog ica l design and its limits a re determined by the physishyca l principles govern ing energy exchange between an organ shyism and its environment and internal ly between active tissues within the organism One of the most important of these phys ical principles app lies to the exchange of gases

Diffusion and Exchange

Pressures and Partial Pressures Air pressure varies slightl y with wea ther condlt ions suc h as lo w- and hig h-pressure fronts and wah tempera shyture When animals ascend in a ltitude a ir pressure d ro ps significantly as the a ir th ins (beco mes less de nse ) and

brea thing becomes more labored This drop in pressure of the gases espec ia lly oxygen crea tes th e difficul tv A ir is a mi x ture of nitrogen (about 78 by vo lume) oxygen (about 21 by volu me) ca rbon dioxide and trace ele shy

ments Each gas in air J c ts mdependentl y to prod uce ilS own press ure ir res pective of the other gases in the ml xw re Of the to ta l 101000 Pa (pressure of air) a t sea level oxyshyge n contributes 21 210 Pa (101000 Pa X 21) to the w tal nitrogen 78 780 Pa (1 0 1000 Pa X 78 ) and (he remaining gases 1010 Pa Because each gas comributes

l5 2 Chapter Four

only a part of the total pressure its contribution is its parshytial pressure The rate at which oxygen can be inhaled depends on it5 partial pressure At 5300 m (18000 ft) air pressure drops to about 05 atm or 50500 Pa Oxygen still composes about 21 of the air but because the air is thinshyner (here is less total oxygen present I tS partial pressure falls to 10605 Pa (50500 Pa X 21 ) With a drop in the partial pressure of oxygen the respi ratory system picks up less and breathing becomes more 18bored Animals living in the high mountains and especially high-flying birds must be designed to 8ddress this change in 8tmospheric pressure

Bcc8use w8ter weighs much more than air per unit of volume an animal descending through water experiences pressure changes much more quickly than one descending through air With each descent of abo ut 103 m 038 ft) water pressure increases by about 1 atm (atmosphere) Thus aseal at a depth of206 m experiences almost twO addition8l atmospheres of pressure more than it experiences IVhen basking on the beach The effec t of this pressure change on body nuids and solids is probabl y inconsequentia l but g8s in the lungs or in the gas bladders of fishes is compressed sigshynificantlmiddot Each I-meter descent in wate r adds 9800 Pa of pressure or about 15 lb of pressure per square inch of chest wall Compressing the lungs or the gas bladder reduces their volume and thus affects buoyancy The movement of gases into and Out of the bloodstream is affected by the difference in the partial pressu re of oxygen breathed in 8t the surface and its partial pressure when it is diffused into the blood once the animal is submerged We look specifically a t these properties of gases and the way in which the vertebrate body is designed to accommodate them when we examine the res shypira to rv and circulatory systems in chapters 11 and 12 respectilmiddotely

Countercurrent Concurrent and Crosscurrent Exchange

Exchange is a large part of life Oxygen and ca rbon dioxide pass from the environment into the organism or from the mgamsm into the environment Chilled anim81s bask to pick up heat from their surroundings large active 8nimals lose heat to their su rroundings to prevenr overheating Ions a re exchanged between the organism and its environmenr This process of exchange whether it involves gases or heat or ions is sometimes supplemenred by a ir or w8ter currenrs passshying one another Efficiency of exchange depends on whether the currents pass in opposite or equi valent directions

Imagine two parallel but separate idemica l tu bes through which streams of water flow at the same speed Water entering one tube is hot md water entering the other is cold if the tubes are made of conducting material and contact each mher heat will pass from one to the othe r (figshylire 443ab) Water flow may be in the same direct ion as in concurrent exchange or in oppos ite directions as in counshytercurrent exchange The efficiency of heat exchange between the tubes is affec ted by the directions of flow

If rhe streams are concurrem as the two tubes come in contact the temperature difference will e at its maximum but will drop as hear is transferred from rhe hotter to rhe colder tube The cold stream of water will warm the hot stream will coo so at their point of departure both streams of wltlter approach the average of their two initial temperashytures (figure 443 a) If we take the same tubes and same startshying temperatures but run the currents in oppos ite directions we have a coumercurrem exchange heat transfer becomes much more efficient than ifboth currents flowed in the same direction (figure 443b) A counte rcurrent flow keeps a difshyferentia l between the tlVO passing streams throughout their emire course nm JUSt at the initial poim of contact The result is ( much more complete transfer of heat from the hot stream to the cold stream When the tubes are separated rhe cold stream is nearly as warm as the adjacent hot stream Conversely the hot stream gives up most of ItS heat in this countercurrem exchange so that its temper8ture has fallen to almost rhat of the entering cold stream

This physical principle of coumercurrent exchange can be incorporated imo the design of many living organshyisms For example endothermic birds that wade in co ld water could lose much of their critical body heat to the icy water if warm blood circulated through their feet was exposed to the cold water Replacing this lost heat could be expensive A coumercurrent heat exchange between outgoshying warm blood in the arteries supplying the feet and returnshying cold blood in the veins prevents heat loss in ~8ding birds In the upper legs of such birds small arte ries come in contact with small veins forming a rete a network of intershytwining vessels Because arterial blood in these vessels passes in oppmite directions to venous blood ltI coumercurrent sysshytem of heat exchange is established By the time the blood in the arter ies reaches the feet it has given up almost 811 of its he8 t to the blood in the veins returning to the body Thus there is little heat lost th rough the foot into the cold water The countercurrent system of the rete forms a heat block preve ming the loss of body heat to the surroundings Estimates indicate that the rete is so efficient in heat transshyfer that if boiling water were poured through a wading bi rds arter ies at one end ltlnd ice water through its veins at the othe r end blood vessels in the feet would lose less than 110000 of a degree in temperature

Respiration in many fishes is characterized by a counshytercurrent exchange also Water high in oxygen flows across the gills which contain blood capillaries low in oxygen flowing in the oppos ite direction Because water and blood P8SS in opposite directions gas exchange between the two flllids is Iery efficient

In bird lungs 8nd perhaps in othe r animals as well gas exchange is based on another type of fl ow a stepwise crossshycurrent exchange between blood and air capillaries Because blood capillaries cross at nearly right angles to the air capi lshylaries in which gas exchltlnge occurs a crosscurrent is created (figure 443c) Blood capillaries run sequentially from an arteriole to supply e8ch air capillary When blood capillaries


----------------

(a) Distance

Crosscurrent

=gtIL-__---~ Blood flow

c Q

e c QJ ltl c o ltl c QJ

~ gtlt o

(c) Distance

(b)

Airflow

Air lt

capillary

cross an air capi tlary oxyge n passes imo the bloodsrream and CO2 is given up [0 the air Each blood capillary comributes stepwise [0 the rising level of oxygen in the venule it JOins Partial pressures vary along the length of an air capillary but th e add itive effect of these blood capillaries in series is [0

build up efficiem levels of oxygen in venous blood as it leaves the lungs

Concurrent Countercurrent

Tube 1

Tube 2

30degC30degC

QJ~ J s OJ 200C OJ a a E E ~ ~

1aoc10degC

Tube 1

Tube 2

Distance

FIGURE 443 Systems of exchange Direction and design of exchange tubes affect the efficiency of transfer regardless

of whether the exchange involves heat gases ions or other

substances The first two examples (a and b) illustrate heat transfer

The third example (c) depicts gas exchange (a) Concurrent

exchange describes the condition in which separated fiuids fiow in

the same direction Because the temperature gradient between the fiuids is high when they enter the tubes and rather low when they

exit the average difference in heat exchanged between the two

fiuids is relatively high The fiuid in tube 2 is at 10deg when it enters

and at 20deg when it exits (b) In countercurrent exchange the fluids

pass in opposite directions within the two tubes so that the temperature difference between them remains relatively low all

along their lengths The fluid in tube 2 is at 10deg when it enters and

at 28deg when it exits Thus more heat is transferred with countercurrent exchange than with concurrent exchange (c) In a

stepwise crosscurrent exchanger each blood capillary branch

passes across an air capillary at about right angles to it and picks up

oxygen The levels of oxygen rise serially in the departing blood

Arrows indicate the direction of flow

OptiCS Light carries information about the environment Color brightness and direction all arrive coded in light Decoding this information is the business of light-sensitive organs However the ab ility to take advantage of this infonnation is affected by whether the animal sees in water or in air and it is affected by how much the twO eyes share overlapping fields of view

154 Chapter Four

Stereoscopic vision Where the conical fields of the deer overlap they produce stereoscopic vision

~4~ (slladE~d area)

The position of the eyes on the head represe nts a trade -off

lgtetween panoramic vision and depth rerception If the eyes

are posi tioned laterally each sca ns serarate halves of the surshy

[Q nding world and the total field o f view at any moment is

enensi ve Where visual fields do no t overlap an an imal has

lIDonocuJar vision It is common in animals preyed upon and

gives the individual a large visual sweep of its environment

middotr to detect the approach of potential threats from most surshying directions Strict monocular vision in which the

I fi elds of the two eyes are totally se parate is relatively

Cyclostomes some sharks salamanders penguins and 01 have strict monocular v ision

Where visua l fields overlap vision is binocular vision

nsive ove rlap of visual fields characterizes humans We

as much as 140deg of binocular vision with 30deg of

lar vision on a side Binocular vision is important in

(up to 70deg) reptil es (up to 45deg) and some fishes (as

~llC[l as 40deg) Within the area of overlap the two visual

~e-~8~I~~~ merge into a single stereoscopic image (figure 444) advantage of stereoscopic vision is that it gives a se nse

perception Closing one eye and maneuvering

a room demonstrates how much sense of depth is lost

the visual field of only one eye is used Depth perception resu Its from how the brain processes information With binocular vision the visual field

by each eye is divided in the brain In most mamma ls

lo r naJllgOeS to the same side and the o ther half crosses v ia the

his ~llla la to the oppos ite side of the brain Fo r a given

ver of the visua l field inputs from both eyes are brought

I by on the same side of the brain Within the brain the

Iby of the two images is compared Parallax is the

different views one ge ts of a distant object when it is

Viewed from two different points Look at a distant lamppos t

from one positio n and the n step a few feet laterally and look

at it aga in from this new position Slightly more of one side

of the lamppost can be seen less of the opposite side and the

posit ion of the post re lative to background reference points changes as well The nervous sys tem takes advantage of parshy

allax resulting from eye position Each visu(ll image gathered

by each eye is slightly offset from the o ther because o f the

distance between the eyes Although this distance is slight

it is enough for th e nervous system to produce a sense of

depth resulting from the differences in parallax

Depth perception and stereoscopic vision (p679)

Accommodation

Sharp focusing of a visual image upon the retina is termed accommodation (figure 445a) Light rays fro m a distant

object strike the eye at a slightly different angle than r8Ys from a nearby object As a vertebrate alters its gaze from

close to distant objects of interest the eye must adjust or accommodate to keep the image focu sed If the image falls behind th e retina hyperopia or farSightedness results An

image focused in front of the retina produces myopia or

nearSightedness (figure 445bc) The lens and the cornea are especially Important in

focusing entering light Their Job is conSiderably affected by the refractive index of the media through which light passes

a measure of the bending effects on light passing frorr one medium to another The refractive index of water is si milar to

the refractive index of the cornea therefore when light passes

through water to the cornea in aquatic vertebrates there is litshy

tle change in the amount it bends as it converges on the retma But when light passes through air to the liquid medium

of the cornea in terrestrial ver tebrates it bends considerably

Similarl y aquatic animals viewing an object in air must comshypensate for the distortion produced by differences in the refrac ti ve indexes of air and water (figure 446) As a conseshy

quence of these basic optical differences eyes are designed to

work either in water or in air Underwater vision is not n ecesshy

sari ly out of focus It ju~t looks that wa y to our a ir-adapted eyes

when we jump into a clea r stream and attempt to focus our

eyes If we place a pocket o f air in front of our eyes (eg a divshy

ing face mask) the refractive index our eyes are designed to

accommoclate returns and things become clear Accommodation can be accomplished by mechanisms

that change the lens or the cornea Cyclostomes have a corneal

muscle that changes the shape of the cornea to focu s on entershying light In e lasmobranchs a special protractor muscle changes the position of the lens within the eye The elasmobranch eye is focused for distant vision For near obJectS the protractor

muscle moves the lens forward In most amni otes the curvature

of the lens changes to accommodate the eyes focus on objects

near or far Ciliary muscles ac t on the lens to change its shape and thus al ter itS abili ty to focus passing light (which by the

way have nothing to do with microscopic cilia)

Eyes and mechanisms of accommodation (chapter 17)


(a) Accommodation

(b) Farsighted (c) Nearsighted (hyperopia) (myopia)

FIGURE 44S Accommodation (a) Normal vision in

which (he image solid lines is in sharp focus on (he retina of (he

eye (b) Farsigh(ed condition (hyperopia) in which (he lens brings

(he ligh( rays (0 focus behind (he retina (c) Nearsigh(ed

condition (myopia) in which (he sharpest focus falls in front

of (he retina

~t~I I

I I I I

I I I

I I

I

I I

I

FIGURE 446 Refraction Differences in (he refractive

indexes of water and air bend ligh( rays (ha( enter (he water

from (he insect The resul( makes (he insect seem (0 be in a

different position (han i( really is indicated by (he dashed li nes

The archer fish must compensate in order (0 shoot a squirt of

water accura(ely and hit (he real not (he imaginary image

Overview

Size matters so does shape Like any O[her characteristic of an organism size and shape have survival consequences Large organis ms have fewer serious enernies Small organisms find strength in numbers But size and shape have physical conseshyquences in and of themselves For a small animal gravity presents a lmost no dangers Small lizards migh t scamper up walls and across ceilings But for large animals gravity may be more of a threa t than predators As] B S Haldct ne reminds

Chapter Four

us because of differences in scal ing a change in size inevitab ly requires a change in form This is nO[ for reasons of biology but is instead a necessa ry consequence of geometry Surface area increases rap idly with increase in size sca ling in proporshytion to the square of the linear dimensions volume (mass) is even more affected increasing by the cube of linear dimenshysions Inevitably larger organisms have relative ly greacer mass with which to contend and conseq uently the supportive and locomotor systems must be built differently and stronge r to meet the accompanying physical demands

Shape changes in proportion to SIze termed allometry are common during the growth of a young organism lOto the larger adult These can be illustrated with graphs or transforshymation grids The result relati ve to body size is often to accelerate the development of a body part bringing it to full size late r in life when th e adult is large enough and mct cure enough to use it Shape is important for animals that move 3[

significant speeds through fluids A thin shape presented to the fluid flow he lps reduce drag that wou ld otherw ise retard progress Turned broctdside a fin or flipper uses profile drag to generate forces A favorable shape sumiddotch as streamlinlOg encourages smooth nonseparating fl ow The Reyno lds numshyber tells us how changes in size and shape might affect pershyformance of an animal in fluid and emphasizes the importance of both in meeting physical demands of the fluid environment

Forces produced by musc les are conveyed through le ve rs the skeleta l system The Newtonian laws of motion identify the physical forces an dnimal meets arising hmiddotom inertia motton and action reac tion When initiating motion th e bone-muscle system overcomes inenia accel shyerates 11mbs or bodv into motion and the contdcted fluid or ground returns reac tion forces Muscles put a force into a leve r system and the lever sys tem outputS that force as part of a task The output to input ratio represents the mechanIcal advantage a way of expressing whether a musshycle has a leverage that incre3ses either force output or speed output Linked chains of jOi nted bones wo rk as machines to transfer input forces from one part of the mechanism to another

When conveyll1g or receivi ng forces the bone-muscle system itself is exposed to stresses that may be experienced as compression tension or shear forces Failure level under each is different with bones generally strongest in compresshysion and most suscep tible to brea kage in shear Further the resulting stresses are carried unevenl y within the skeletal elemen t Wolffs Law notices that bone remodels interna lly in proportion to the level and distribution of these stresses We also meet the fund amentals for gas diffusion clOd op tics which we will appl y more full y in several of the later chapshyters In this chapter we recognize that organisms face physshyical demands that endanger their survival Consequently we turn to the discipline thar studies such a physical relationshyship between design and demands namely engineering From this we usefully app ly its illsights from biomechanics and biophysics to understand more of the adaptive basis of animal architecture

156

SELECTED REFERENCES

Alexander R McN 1981 Facrors of safe ty in the s([uctu re of anim3 ls Sci Prog (Oxford) 67109-30

---1983 An imal mechanics London Blackwell Sc ientific Pub Iications

exander R M 2003 Principles of animal locomotion Prince ron Princeron University Press

Benjamin M andJ R Ralphs 1998 Fibrocartilage in tendons and ligamenrs-An adaptation ro compressive load] AnaL 193481-94

ltlJalder W A 1984 Size fncclon and life history Cambridge Hanard University Press

Frost H M 1990 Skeletal strucrural adaptations ro mechanical usage (SATMU) 1 Redefining Wolffs Law The bond modeling problem Anat Rec 226403-13

-- 1990 Skeletal Structural adaptations ro mechanical usage (SATMU) 2 Redefining Wolffs Law The remodeling problem AnaL Rec 226414-22

-- 1990 Ske letal strucrura l adapta tions ro mechanica l usage (SATMU) 3 The hya line cartilage mode ling problem AnaL Rec 226423-32

- -- 1990 Skeletal structural adaptati ons ro mechanical usage (SATMU) 4 Mechanical innuences on inract fibrous tissues Anac Rec 226433-39

Gordon J E 1968 The new science of strong macerials London Penguin Books

---1978Scruccuresorwhythingsdontfalldown New

York DaCapo Press Gould S J 1977 Ever since Darwin Reflections in natural

history New York W Y Norron Haldane JB S 1928 On being the right size Nell York

Harper --- 1956 On being the right size In Th e world of

mathematics edired by James R N ewman New York Simon and Schuster

Schmidt-Nielsen K 1984 Scaling Why is animal size so important Cambridge Cambridge University Press

Thompson DA W 1942 On gTOwth and form 2d ed Cambridge Camhridge University Press

Vogel S 1994 Life in movingfluids 2d ed Pnnceton Princeton University Press

--- 2003 Comparative biomechanics Lifes physical tvorld Princeron Princeton University Press

WEB LINKS

Visit this books website at wVmiddotmhhecomKlfdong4 (click Architectural Pattern and Diversity of Animals on this books title ) ro find Web links for further reading on

this topic


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FIGURE 4 I Animal sizes range over many orders of magnitude The largest animal is the blue whale the smallest adult vertebrate a tropical frogAII organisms are drawn to the same scale and are numbered as follows (I) the pterosaur Quetzalcoatlus is the largest aerial reptile (2) the albatross is the largest flying bird (3) Baluchitherium is the largest extinct land mammal (4) Aepyornis is the largest extinct bird (5) ostrich (6) a human figure represented by this scale is 6 feet tall (7) sheep (8) horse (9) this line designates the length of the largest tapeworm found in humans (10) the giraffe is the tallest living land animal (I I) Diplodocus (12) Tyrannosaurus (13) the blue whale is the largest known living animal (14) African elephant (15) the Komodo dragon is the largest living lizard (16) the saltwater crocodile is the largest living reptile (17) the largest terrestrial lizard (extinct) (18) Palaeophis is the largest extinct snake (19) the reticulated python is the longest living snake (20) Architheuthis a deep-water squid is the largest living mollusc (21) the whale shark is the largest fish (22) an arthrodire is the largest placoderm (23) large tarpon (24) Trimmatom nanus is one of the smallest fishes (25) housefly (26) medium-sized ant (27) this tropical frog is the smallest tetrapod (28) cheese mite (29) smallest land snail (30) Daphnia is a common water flea (31) a common brown hydraThe lower section of a giant sequoia is shown in the background on the left of the figure with a I OO-foot larch superimposed

Ncer H G Wells j S Huxley and G P Wells

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(e)









Biologicltll Design

III

145






Loaes













thrusc fr

After Gordo













breakage follows







(a)


(b) When


represemJ

down arro

within this

same mass



gives fibel

146 C hapter Four

n

I b)

n

w re ia lty (racshy

mdi-

Interior pier

Exterior pier


A~er Gordon

(a) (b) (c)











Iliotibial tract

Head of femur




















(a) (b) (e)


































































148 Chap re r Four























(a)

(b) Normal foot

(e)




l50 Chapter Four

















--

J e s

n

n

~r

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u
















(a)



Biological Design

Vertical wall

-- Tension

- Compression ____

Stress trajectory

151


(e)

(b)























l5 2 Chapter Four











----------------

(a) Distance

Crosscurrent


c Q


~ gtlt o

(c) Distance

(b)

Airflow

Air lt

capillary




Tube 1

Tube 2

30degC30degC


1aoc10degC

Tube 1

Tube 2

Distance


















154 Chapter Four


~4~ (slladE~d area)







































Accommodation




























(a) Accommodation







of (he retina

~t~I I

I I I I

I I I

I I

I

I I

I







Overview


Chapter Four






156

SELECTED REFERENCES




















WEB LINKS


this topic


108Blue whale

106Rhinoceros

102Squirrel

101Lizard


Large amoeba 10-4



Bacterial flagella














Middle C

l f




























Size


(a) (b)















ChCl

fau Ch8

reb desi size

all p

mcn sion~

the c

128 Chapter Four

V

V V V

L

Vy

V V VV

V V




L

V

V

(b) Surface area






ss






her per



V (X [3













130 Chapter Fou r

10 White mousec


squirrel

I Kangaroo ratQ


001




one hour (h) sh a r






AI Volume and Mass





51

~~f~1i~~~~








Shape


Allometry






y = bx


Years 042 075 275 675 1275 2575








A

x y


(a)

















10000

8000

6000 5000 4000

3000

2000

1000

800 700 600 500 400

300

200

100Y 80 70 60 50 40

30

20

10

8 7 6 5

4

3

2

1 1 2 3 4 567810 20 30 4050 70 100

(b) x






132 Chapter Four

600 shy500 400

300

200

150

100

E 70 s 60 r 50 ~ 40

~ 30 o I 20

15

10

7 6 5 4

3







o




Fetal skull










After Thompson




Biological Design

1

133

c

d

b

a

6 5 4 3 2 0 o6 5 4 3 2 e

65432 10

6





(ransformed grid






FI( geo sub





Biomechanics





134 Chapter Four

Q Q (5 (5 o (5 (5




It

Is

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S










animal designs












Biological Design

11

135








Units










Feetsecond2

(ft sec1)








l36 Chapter Four

2













y

14

Pigeon

8 z~------------------------~









Vectors



h-2













F = rna



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138 C hapte r Four

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II









6W t

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~

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distance advantage)









140 Chapter Four

ler lte

JW

utshyreshy

ehe ced











2










Life in Fluids


(a) (b)













C hapter Four 142

(a) Fast Separation

(b)











pLURe = shy

fL







(d)












Chapter Four 144

I

e

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lt ----c~~-ir






of irs





1shy





7-~ __

---~=====~~---- ----- --- 2 ------ 1 1 I --- I ~

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3 I I

I

(a) 4

(b)

(e)









Biologicltll Design

III

145






Loaes













thrusc fr

After Gordo













breakage follows







(a)


(b) When


represemJ

down arro

within this

same mass



gives fibel

146 C hapter Four

n

I b)

n

w re ia lty (racshy

mdi-

Interior pier

Exterior pier


A~er Gordon

(a) (b) (c)











Iliotibial tract

Head of femur




















(a) (b) (e)


































































148 Chap re r Four























(a)

(b) Normal foot

(e)




l50 Chapter Four

















--

J e s

n

n

~r

is s ~s



u
















(a)



Biological Design

Vertical wall

-- Tension

- Compression ____

Stress trajectory

151


(e)

(b)























l5 2 Chapter Four











----------------

(a) Distance

Crosscurrent


c Q


~ gtlt o

(c) Distance

(b)

Airflow

Air lt

capillary




Tube 1

Tube 2

30degC30degC


1aoc10degC

Tube 1

Tube 2

Distance


















154 Chapter Four


~4~ (slladE~d area)







































Accommodation




























(a) Accommodation







of (he retina

~t~I I

I I I I

I I I

I I

I

I I

I







Overview


Chapter Four






156

SELECTED REFERENCES




















WEB LINKS


this topic










Size


(a) (b)















ChCl

fau Ch8

reb desi size

all p

mcn sion~

the c

128 Chapter Four

V

V V V

L

Vy

V V VV

V V




L

V

V

(b) Surface area






ss






her per



V (X [3













130 Chapter Fou r

10 White mousec


squirrel

I Kangaroo ratQ


001




one hour (h) sh a r






AI Volume and Mass





51

~~f~1i~~~~








Shape


Allometry






y = bx


Years 042 075 275 675 1275 2575








A

x y


(a)

















10000

8000

6000 5000 4000

3000

2000

1000

800 700 600 500 400

300

200

100Y 80 70 60 50 40

30

20

10

8 7 6 5

4

3

2

1 1 2 3 4 567810 20 30 4050 70 100

(b) x






132 Chapter Four

600 shy500 400

300

200

150

100

E 70 s 60 r 50 ~ 40

~ 30 o I 20

15

10

7 6 5 4

3







o




Fetal skull










After Thompson




Biological Design

1

133

c

d

b

a

6 5 4 3 2 0 o6 5 4 3 2 e

65432 10

6





(ransformed grid






FI( geo sub





Biomechanics





134 Chapter Four

Q Q (5 (5 o (5 (5




It

Is

n ) r

S










animal designs












Biological Design

11

135








Units










Feetsecond2

(ft sec1)








l36 Chapter Four

2













y

14

Pigeon

8 z~------------------------~









Vectors



h-2













F = rna



~ ) F - -----bull ---F I )

~ ~ ~~j Fx














138 C hapte r Four

3N 5N(a)

[7d 4N

C2J 4N 5N 3N




II









6W t

II (a)

(b)





~

~

--~=- ~


(a) (b)

8 - Digger

V I ~ J~ I I I I I

I 1 I(a)





























distance advantage)









140 Chapter Four

ler lte

JW

utshyreshy

ehe ced











2










Life in Fluids


(a) (b)













C hapter Four 142

(a) Fast Separation

(b)











pLURe = shy

fL







(d)












Chapter Four 144

I

e

It5m~~ lve t- --- -~--~d

lt ----c~~-ir






of irs





1shy





7-~ __

---~=====~~---- ----- --- 2 ------ 1 1 I --- I ~

I I I I I I I

3 I I

I

(a) 4

(b)

(e)









Biologicltll Design

III

145






Loaes













thrusc fr

After Gordo













breakage follows







(a)


(b) When


represemJ

down arro

within this

same mass



gives fibel

146 C hapter Four

n

I b)

n

w re ia lty (racshy

mdi-

Interior pier

Exterior pier


A~er Gordon

(a) (b) (c)











Iliotibial tract

Head of femur




















(a) (b) (e)


































































148 Chap re r Four























(a)

(b) Normal foot

(e)




l50 Chapter Four

















--

J e s

n

n

~r

is s ~s



u
















(a)



Biological Design

Vertical wall

-- Tension

- Compression ____

Stress trajectory

151


(e)

(b)























l5 2 Chapter Four











----------------

(a) Distance

Crosscurrent


c Q


~ gtlt o

(c) Distance

(b)

Airflow

Air lt

capillary




Tube 1

Tube 2

30degC30degC


1aoc10degC

Tube 1

Tube 2

Distance


















154 Chapter Four


~4~ (slladE~d area)







































Accommodation




























(a) Accommodation







of (he retina

~t~I I

I I I I

I I I

I I

I

I I

I







Overview


Chapter Four






156

SELECTED REFERENCES




















WEB LINKS


this topic


V

V V V

L

Vy

V V VV

V V




L

V

V

(b) Surface area






ss






her per



V (X [3













130 Chapter Fou r

10 White mousec


squirrel

I Kangaroo ratQ


001




one hour (h) sh a r






AI Volume and Mass





51

~~f~1i~~~~








Shape


Allometry






y = bx


Years 042 075 275 675 1275 2575








A

x y


(a)

















10000

8000

6000 5000 4000

3000

2000

1000

800 700 600 500 400

300

200

100Y 80 70 60 50 40

30

20

10

8 7 6 5

4

3

2

1 1 2 3 4 567810 20 30 4050 70 100

(b) x






132 Chapter Four

600 shy500 400

300

200

150

100

E 70 s 60 r 50 ~ 40

~ 30 o I 20

15

10

7 6 5 4

3







o




Fetal skull










After Thompson




Biological Design

1

133

c

d

b

a

6 5 4 3 2 0 o6 5 4 3 2 e

65432 10

6





(ransformed grid






FI( geo sub





Biomechanics





134 Chapter Four

Q Q (5 (5 o (5 (5




It

Is

n ) r

S










animal designs












Biological Design

11

135








Units










Feetsecond2

(ft sec1)








l36 Chapter Four

2













y

14

Pigeon

8 z~------------------------~









Vectors



h-2













F = rna



~ ) F - -----bull ---F I )

~ ~ ~~j Fx














138 C hapte r Four

3N 5N(a)

[7d 4N

C2J 4N 5N 3N




II









6W t

II (a)

(b)





~

~

--~=- ~


(a) (b)

8 - Digger

V I ~ J~ I I I I I

I 1 I(a)





























distance advantage)









140 Chapter Four

ler lte

JW

utshyreshy

ehe ced











2










Life in Fluids


(a) (b)













C hapter Four 142

(a) Fast Separation

(b)











pLURe = shy

fL







(d)












Chapter Four 144

I

e

It5m~~ lve t- --- -~--~d

lt ----c~~-ir






of irs





1shy





7-~ __

---~=====~~---- ----- --- 2 ------ 1 1 I --- I ~

I I I I I I I

3 I I

I

(a) 4

(b)

(e)









Biologicltll Design

III

145






Loaes













thrusc fr

After Gordo













breakage follows







(a)


(b) When


represemJ

down arro

within this

same mass



gives fibel

146 C hapter Four

n

I b)

n

w re ia lty (racshy

mdi-

Interior pier

Exterior pier


A~er Gordon

(a) (b) (c)











Iliotibial tract

Head of femur




















(a) (b) (e)


































































148 Chap re r Four























(a)

(b) Normal foot

(e)




l50 Chapter Four

















--

J e s

n

n

~r

is s ~s



u
















(a)



Biological Design

Vertical wall

-- Tension

- Compression ____

Stress trajectory

151


(e)

(b)























l5 2 Chapter Four











----------------

(a) Distance

Crosscurrent


c Q


~ gtlt o

(c) Distance

(b)

Airflow

Air lt

capillary




Tube 1

Tube 2

30degC30degC


1aoc10degC

Tube 1

Tube 2

Distance


















154 Chapter Four


~4~ (slladE~d area)







































Accommodation




























(a) Accommodation







of (he retina

~t~I I

I I I I

I I I

I I

I

I I

I







Overview


Chapter Four






156

SELECTED REFERENCES




















WEB LINKS


this topic








130 Chapter Fou r

10 White mousec


squirrel

I Kangaroo ratQ


001




one hour (h) sh a r






AI Volume and Mass





51

~~f~1i~~~~








Shape


Allometry






y = bx


Years 042 075 275 675 1275 2575








A

x y


(a)

















10000

8000

6000 5000 4000

3000

2000

1000

800 700 600 500 400

300

200

100Y 80 70 60 50 40

30

20

10

8 7 6 5

4

3

2

1 1 2 3 4 567810 20 30 4050 70 100

(b) x






132 Chapter Four

600 shy500 400

300

200

150

100

E 70 s 60 r 50 ~ 40

~ 30 o I 20

15

10

7 6 5 4

3







o




Fetal skull










After Thompson




Biological Design

1

133

c

d

b

a

6 5 4 3 2 0 o6 5 4 3 2 e

65432 10

6





(ransformed grid






FI( geo sub





Biomechanics





134 Chapter Four

Q Q (5 (5 o (5 (5




It

Is

n ) r

S










animal designs












Biological Design

11

135








Units










Feetsecond2

(ft sec1)








l36 Chapter Four

2













y

14

Pigeon

8 z~------------------------~









Vectors



h-2













F = rna



~ ) F - -----bull ---F I )

~ ~ ~~j Fx














138 C hapte r Four

3N 5N(a)

[7d 4N

C2J 4N 5N 3N




II









6W t

II (a)

(b)





~

~

--~=- ~


(a) (b)

8 - Digger

V I ~ J~ I I I I I

I 1 I(a)





























distance advantage)









140 Chapter Four

ler lte

JW

utshyreshy

ehe ced











2










Life in Fluids


(a) (b)













C hapter Four 142

(a) Fast Separation

(b)











pLURe = shy

fL







(d)












Chapter Four 144

I

e

It5m~~ lve t- --- -~--~d

lt ----c~~-ir






of irs





1shy





7-~ __

---~=====~~---- ----- --- 2 ------ 1 1 I --- I ~

I I I I I I I

3 I I

I

(a) 4

(b)

(e)









Biologicltll Design

III

145






Loaes













thrusc fr

After Gordo













breakage follows







(a)


(b) When


represemJ

down arro

within this

same mass



gives fibel

146 C hapter Four

n

I b)

n

w re ia lty (racshy

mdi-

Interior pier

Exterior pier


A~er Gordon

(a) (b) (c)











Iliotibial tract

Head of femur




















(a) (b) (e)


































































148 Chap re r Four























(a)

(b) Normal foot

(e)




l50 Chapter Four

















--

J e s

n

n

~r

is s ~s



u
















(a)



Biological Design

Vertical wall

-- Tension

- Compression ____

Stress trajectory

151


(e)

(b)























l5 2 Chapter Four











----------------

(a) Distance

Crosscurrent


c Q


~ gtlt o

(c) Distance

(b)

Airflow

Air lt

capillary




Tube 1

Tube 2

30degC30degC


1aoc10degC

Tube 1

Tube 2

Distance


















154 Chapter Four


~4~ (slladE~d area)







































Accommodation




























(a) Accommodation







of (he retina

~t~I I

I I I I

I I I

I I

I

I I

I







Overview


Chapter Four






156

SELECTED REFERENCES




















WEB LINKS


this topic


~~f~1i~~~~








Shape


Allometry






y = bx


Years 042 075 275 675 1275 2575








A

x y


(a)

















10000

8000

6000 5000 4000

3000

2000

1000

800 700 600 500 400

300

200

100Y 80 70 60 50 40

30

20

10

8 7 6 5

4

3

2

1 1 2 3 4 567810 20 30 4050 70 100

(b) x






132 Chapter Four

600 shy500 400

300

200

150

100

E 70 s 60 r 50 ~ 40

~ 30 o I 20

15

10

7 6 5 4

3







o




Fetal skull










After Thompson




Biological Design

1

133

c

d

b

a

6 5 4 3 2 0 o6 5 4 3 2 e

65432 10

6





(ransformed grid






FI( geo sub





Biomechanics





134 Chapter Four

Q Q (5 (5 o (5 (5




It

Is

n ) r

S










animal designs












Biological Design

11

135








Units










Feetsecond2

(ft sec1)








l36 Chapter Four

2













y

14

Pigeon

8 z~------------------------~









Vectors



h-2













F = rna



~ ) F - -----bull ---F I )

~ ~ ~~j Fx














138 C hapte r Four

3N 5N(a)

[7d 4N

C2J 4N 5N 3N




II









6W t

II (a)

(b)





~

~

--~=- ~


(a) (b)

8 - Digger

V I ~ J~ I I I I I

I 1 I(a)





























distance advantage)









140 Chapter Four

ler lte

JW

utshyreshy

ehe ced











2










Life in Fluids


(a) (b)













C hapter Four 142

(a) Fast Separation

(b)











pLURe = shy

fL







(d)












Chapter Four 144

I

e

It5m~~ lve t- --- -~--~d

lt ----c~~-ir






of irs





1shy





7-~ __

---~=====~~---- ----- --- 2 ------ 1 1 I --- I ~

I I I I I I I

3 I I

I

(a) 4

(b)

(e)









Biologicltll Design

III

145






Loaes













thrusc fr

After Gordo













breakage follows







(a)


(b) When


represemJ

down arro

within this

same mass



gives fibel

146 C hapter Four

n

I b)

n

w re ia lty (racshy

mdi-

Interior pier

Exterior pier


A~er Gordon

(a) (b) (c)











Iliotibial tract

Head of femur




















(a) (b) (e)


































































148 Chap re r Four























(a)

(b) Normal foot

(e)




l50 Chapter Four

















--

J e s

n

n

~r

is s ~s



u
















(a)



Biological Design

Vertical wall

-- Tension

- Compression ____

Stress trajectory

151


(e)

(b)























l5 2 Chapter Four











----------------

(a) Distance

Crosscurrent


c Q


~ gtlt o

(c) Distance

(b)

Airflow

Air lt

capillary




Tube 1

Tube 2

30degC30degC


1aoc10degC

Tube 1

Tube 2

Distance


















154 Chapter Four


~4~ (slladE~d area)







































Accommodation




























(a) Accommodation







of (he retina

~t~I I

I I I I

I I I

I I

I

I I

I







Overview


Chapter Four






156

SELECTED REFERENCES




















WEB LINKS


this topic



A

x y


(a)

















10000

8000

6000 5000 4000

3000

2000

1000

800 700 600 500 400

300

200

100Y 80 70 60 50 40

30

20

10

8 7 6 5

4

3

2

1 1 2 3 4 567810 20 30 4050 70 100

(b) x






132 Chapter Four

600 shy500 400

300

200

150

100

E 70 s 60 r 50 ~ 40

~ 30 o I 20

15

10

7 6 5 4

3







o




Fetal skull










After Thompson




Biological Design

1

133

c

d

b

a

6 5 4 3 2 0 o6 5 4 3 2 e

65432 10

6





(ransformed grid






FI( geo sub





Biomechanics





134 Chapter Four

Q Q (5 (5 o (5 (5




It

Is

n ) r

S










animal designs












Biological Design

11

135








Units










Feetsecond2

(ft sec1)








l36 Chapter Four

2













y

14

Pigeon

8 z~------------------------~









Vectors



h-2













F = rna



~ ) F - -----bull ---F I )

~ ~ ~~j Fx














138 C hapte r Four

3N 5N(a)

[7d 4N

C2J 4N 5N 3N




II









6W t

II (a)

(b)





~

~

--~=- ~


(a) (b)

8 - Digger

V I ~ J~ I I I I I

I 1 I(a)





























distance advantage)









140 Chapter Four

ler lte

JW

utshyreshy

ehe ced











2










Life in Fluids


(a) (b)













C hapter Four 142

(a) Fast Separation

(b)











pLURe = shy

fL







(d)












Chapter Four 144

I

e

It5m~~ lve t- --- -~--~d

lt ----c~~-ir






of irs





1shy





7-~ __

---~=====~~---- ----- --- 2 ------ 1 1 I --- I ~

I I I I I I I

3 I I

I

(a) 4

(b)

(e)









Biologicltll Design

III

145






Loaes













thrusc fr

After Gordo













breakage follows







(a)


(b) When


represemJ

down arro

within this

same mass



gives fibel

146 C hapter Four

n

I b)

n

w re ia lty (racshy

mdi-

Interior pier

Exterior pier


A~er Gordon

(a) (b) (c)











Iliotibial tract

Head of femur




















(a) (b) (e)


































































148 Chap re r Four























(a)

(b) Normal foot

(e)




l50 Chapter Four

















--

J e s

n

n

~r

is s ~s



u
















(a)



Biological Design

Vertical wall

-- Tension

- Compression ____

Stress trajectory

151


(e)

(b)























l5 2 Chapter Four











----------------

(a) Distance

Crosscurrent


c Q


~ gtlt o

(c) Distance

(b)

Airflow

Air lt

capillary




Tube 1

Tube 2

30degC30degC


1aoc10degC

Tube 1

Tube 2

Distance


















154 Chapter Four


~4~ (slladE~d area)







































Accommodation




























(a) Accommodation







of (he retina

~t~I I

I I I I

I I I

I I

I

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Overview


Chapter Four






156

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WEB LINKS


this topic


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154 Chapter Four


~4~ (slladE~d area)







































Accommodation




























(a) Accommodation







of (he retina

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I I I

I I

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Overview


Chapter Four






156

SELECTED REFERENCES




















WEB LINKS


this topic


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(ransformed grid






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distance advantage)









140 Chapter Four

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Life in Fluids


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Biologicltll Design

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Loaes













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breakage follows







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148 Chap re r Four























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(a)



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154 Chapter Four


~4~ (slladE~d area)







































Accommodation




























(a) Accommodation







of (he retina

~t~I I

I I I I

I I I

I I

I

I I

I







Overview


Chapter Four






156

SELECTED REFERENCES




















WEB LINKS


this topic


Q Q (5 (5 o (5 (5




It

Is

n ) r

S










animal designs












Biological Design

11

135








Units










Feetsecond2

(ft sec1)








l36 Chapter Four

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8 z~------------------------~









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ler lte

JW

utshyreshy

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2










Life in Fluids


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C hapter Four 142

(a) Fast Separation

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pLURe = shy

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Chapter Four 144

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of irs





1shy





7-~ __

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Biologicltll Design

III

145






Loaes













thrusc fr

After Gordo













breakage follows







(a)


(b) When


represemJ

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within this

same mass



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146 C hapter Four

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(a) (b) (e)


































































148 Chap re r Four























(a)

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l50 Chapter Four

















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(a)



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154 Chapter Four


~4~ (slladE~d area)







































Accommodation




























(a) Accommodation







of (he retina

~t~I I

I I I I

I I I

I I

I

I I

I







Overview


Chapter Four






156

SELECTED REFERENCES




















WEB LINKS


this topic









Units










Feetsecond2

(ft sec1)








l36 Chapter Four

2













y

14

Pigeon

8 z~------------------------~









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distance advantage)









140 Chapter Four

ler lte

JW

utshyreshy

ehe ced











2










Life in Fluids


(a) (b)













C hapter Four 142

(a) Fast Separation

(b)











pLURe = shy

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Chapter Four 144

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I I I I I I I

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I

(a) 4

(b)

(e)









Biologicltll Design

III

145






Loaes













thrusc fr

After Gordo













breakage follows







(a)


(b) When


represemJ

down arro

within this

same mass



gives fibel

146 C hapter Four

n

I b)

n

w re ia lty (racshy

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A~er Gordon

(a) (b) (c)











Iliotibial tract

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(a) (b) (e)


































































148 Chap re r Four























(a)

(b) Normal foot

(e)




l50 Chapter Four

















--

J e s

n

n

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(a)



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-- Tension

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151


(e)

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l5 2 Chapter Four











----------------

(a) Distance

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c Q


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(c) Distance

(b)

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Tube 1

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1aoc10degC

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Tube 2

Distance


















154 Chapter Four


~4~ (slladE~d area)







































Accommodation




























(a) Accommodation







of (he retina

~t~I I

I I I I

I I I

I I

I

I I

I







Overview


Chapter Four






156

SELECTED REFERENCES




















WEB LINKS


this topic














y

14

Pigeon

8 z~------------------------~









Vectors



h-2













F = rna



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distance advantage)









140 Chapter Four

ler lte

JW

utshyreshy

ehe ced











2










Life in Fluids


(a) (b)













C hapter Four 142

(a) Fast Separation

(b)











pLURe = shy

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Chapter Four 144

I

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It5m~~ lve t- --- -~--~d

lt ----c~~-ir






of irs





1shy





7-~ __

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I I I I I I I

3 I I

I

(a) 4

(b)

(e)









Biologicltll Design

III

145






Loaes













thrusc fr

After Gordo













breakage follows







(a)


(b) When


represemJ

down arro

within this

same mass



gives fibel

146 C hapter Four

n

I b)

n

w re ia lty (racshy

mdi-

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(a) (b) (e)


































































148 Chap re r Four























(a)

(b) Normal foot

(e)




l50 Chapter Four

















--

J e s

n

n

~r

is s ~s



u
















(a)



Biological Design

Vertical wall

-- Tension

- Compression ____

Stress trajectory

151


(e)

(b)























l5 2 Chapter Four











----------------

(a) Distance

Crosscurrent


c Q


~ gtlt o

(c) Distance

(b)

Airflow

Air lt

capillary




Tube 1

Tube 2

30degC30degC


1aoc10degC

Tube 1

Tube 2

Distance


















154 Chapter Four


~4~ (slladE~d area)







































Accommodation




























(a) Accommodation







of (he retina

~t~I I

I I I I

I I I

I I

I

I I

I







Overview


Chapter Four






156

SELECTED REFERENCES




















WEB LINKS


this topic














F = rna



~ ) F - -----bull ---F I )

~ ~ ~~j Fx














138 C hapte r Four

3N 5N(a)

[7d 4N

C2J 4N 5N 3N




II









6W t

II (a)

(b)





~

~

--~=- ~


(a) (b)

8 - Digger

V I ~ J~ I I I I I

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distance advantage)









140 Chapter Four

ler lte

JW

utshyreshy

ehe ced











2










Life in Fluids


(a) (b)













C hapter Four 142

(a) Fast Separation

(b)











pLURe = shy

fL







(d)












Chapter Four 144

I

e

It5m~~ lve t- --- -~--~d

lt ----c~~-ir






of irs





1shy





7-~ __

---~=====~~---- ----- --- 2 ------ 1 1 I --- I ~

I I I I I I I

3 I I

I

(a) 4

(b)

(e)









Biologicltll Design

III

145






Loaes













thrusc fr

After Gordo













breakage follows







(a)


(b) When


represemJ

down arro

within this

same mass



gives fibel

146 C hapter Four

n

I b)

n

w re ia lty (racshy

mdi-

Interior pier

Exterior pier


A~er Gordon

(a) (b) (c)











Iliotibial tract

Head of femur




















(a) (b) (e)


































































148 Chap re r Four























(a)

(b) Normal foot

(e)




l50 Chapter Four

















--

J e s

n

n

~r

is s ~s



u
















(a)



Biological Design

Vertical wall

-- Tension

- Compression ____

Stress trajectory

151


(e)

(b)























l5 2 Chapter Four











----------------

(a) Distance

Crosscurrent


c Q


~ gtlt o

(c) Distance

(b)

Airflow

Air lt

capillary




Tube 1

Tube 2

30degC30degC


1aoc10degC

Tube 1

Tube 2

Distance


















154 Chapter Four


~4~ (slladE~d area)







































Accommodation




























(a) Accommodation







of (he retina

~t~I I

I I I I

I I I

I I

I

I I

I







Overview


Chapter Four






156

SELECTED REFERENCES




















WEB LINKS


this topic


3N 5N(a)

[7d 4N

C2J 4N 5N 3N




II









6W t

II (a)

(b)





~

~

--~=- ~


(a) (b)

8 - Digger

V I ~ J~ I I I I I

I 1 I(a)





























distance advantage)









140 Chapter Four

ler lte

JW

utshyreshy

ehe ced











2










Life in Fluids


(a) (b)













C hapter Four 142

(a) Fast Separation

(b)











pLURe = shy

fL







(d)












Chapter Four 144

I

e

It5m~~ lve t- --- -~--~d

lt ----c~~-ir






of irs





1shy





7-~ __

---~=====~~---- ----- --- 2 ------ 1 1 I --- I ~

I I I I I I I

3 I I

I

(a) 4

(b)

(e)









Biologicltll Design

III

145






Loaes













thrusc fr

After Gordo













breakage follows







(a)


(b) When


represemJ

down arro

within this

same mass



gives fibel

146 C hapter Four

n

I b)

n

w re ia lty (racshy

mdi-

Interior pier

Exterior pier


A~er Gordon

(a) (b) (c)











Iliotibial tract

Head of femur




















(a) (b) (e)


































































148 Chap re r Four























(a)

(b) Normal foot

(e)




l50 Chapter Four

















--

J e s

n

n

~r

is s ~s



u
















(a)



Biological Design

Vertical wall

-- Tension

- Compression ____

Stress trajectory

151


(e)

(b)























l5 2 Chapter Four











----------------

(a) Distance

Crosscurrent


c Q


~ gtlt o

(c) Distance

(b)

Airflow

Air lt

capillary




Tube 1

Tube 2

30degC30degC


1aoc10degC

Tube 1

Tube 2

Distance


















154 Chapter Four


~4~ (slladE~d area)







































Accommodation




























(a) Accommodation







of (he retina

~t~I I

I I I I

I I I

I I

I

I I

I







Overview


Chapter Four






156

SELECTED REFERENCES




















WEB LINKS


this topic


~

~

--~=- ~


(a) (b)

8 - Digger

V I ~ J~ I I I I I

I 1 I(a)





























distance advantage)









140 Chapter Four

ler lte

JW

utshyreshy

ehe ced











2










Life in Fluids


(a) (b)













C hapter Four 142

(a) Fast Separation

(b)











pLURe = shy

fL







(d)












Chapter Four 144

I

e

It5m~~ lve t- --- -~--~d

lt ----c~~-ir






of irs





1shy





7-~ __

---~=====~~---- ----- --- 2 ------ 1 1 I --- I ~

I I I I I I I

3 I I

I

(a) 4

(b)

(e)









Biologicltll Design

III

145






Loaes













thrusc fr

After Gordo













breakage follows







(a)


(b) When


represemJ

down arro

within this

same mass



gives fibel

146 C hapter Four

n

I b)

n

w re ia lty (racshy

mdi-

Interior pier

Exterior pier


A~er Gordon

(a) (b) (c)











Iliotibial tract

Head of femur




















(a) (b) (e)


































































148 Chap re r Four























(a)

(b) Normal foot

(e)




l50 Chapter Four

















--

J e s

n

n

~r

is s ~s



u
















(a)



Biological Design

Vertical wall

-- Tension

- Compression ____

Stress trajectory

151


(e)

(b)























l5 2 Chapter Four











----------------

(a) Distance

Crosscurrent


c Q


~ gtlt o

(c) Distance

(b)

Airflow

Air lt

capillary




Tube 1

Tube 2

30degC30degC


1aoc10degC

Tube 1

Tube 2

Distance


















154 Chapter Four


~4~ (slladE~d area)







































Accommodation




























(a) Accommodation







of (he retina

~t~I I

I I I I

I I I

I I

I

I I

I







Overview


Chapter Four






156

SELECTED REFERENCES




















WEB LINKS


this topic


ler lte

JW

utshyreshy

ehe ced











2










Life in Fluids


(a) (b)













C hapter Four 142

(a) Fast Separation

(b)











pLURe = shy

fL







(d)












Chapter Four 144

I

e

It5m~~ lve t- --- -~--~d

lt ----c~~-ir






of irs





1shy





7-~ __

---~=====~~---- ----- --- 2 ------ 1 1 I --- I ~

I I I I I I I

3 I I

I

(a) 4

(b)

(e)









Biologicltll Design

III

145






Loaes













thrusc fr

After Gordo













breakage follows







(a)


(b) When


represemJ

down arro

within this

same mass



gives fibel

146 C hapter Four

n

I b)

n

w re ia lty (racshy

mdi-

Interior pier

Exterior pier


A~er Gordon

(a) (b) (c)











Iliotibial tract

Head of femur




















(a) (b) (e)


































































148 Chap re r Four























(a)

(b) Normal foot

(e)




l50 Chapter Four

















--

J e s

n

n

~r

is s ~s



u
















(a)



Biological Design

Vertical wall

-- Tension

- Compression ____

Stress trajectory

151


(e)

(b)























l5 2 Chapter Four











----------------

(a) Distance

Crosscurrent


c Q


~ gtlt o

(c) Distance

(b)

Airflow

Air lt

capillary




Tube 1

Tube 2

30degC30degC


1aoc10degC

Tube 1

Tube 2

Distance


















154 Chapter Four


~4~ (slladE~d area)







































Accommodation




























(a) Accommodation







of (he retina

~t~I I

I I I I

I I I

I I

I

I I

I







Overview


Chapter Four






156

SELECTED REFERENCES




















WEB LINKS


this topic






Life in Fluids


(a) (b)













C hapter Four 142

(a) Fast Separation

(b)











pLURe = shy

fL







(d)












Chapter Four 144

I

e

It5m~~ lve t- --- -~--~d

lt ----c~~-ir






of irs





1shy





7-~ __

---~=====~~---- ----- --- 2 ------ 1 1 I --- I ~

I I I I I I I

3 I I

I

(a) 4

(b)

(e)









Biologicltll Design

III

145






Loaes













thrusc fr

After Gordo













breakage follows







(a)


(b) When


represemJ

down arro

within this

same mass



gives fibel

146 C hapter Four

n

I b)

n

w re ia lty (racshy

mdi-

Interior pier

Exterior pier


A~er Gordon

(a) (b) (c)











Iliotibial tract

Head of femur




















(a) (b) (e)


































































148 Chap re r Four























(a)

(b) Normal foot

(e)




l50 Chapter Four

















--

J e s

n

n

~r

is s ~s



u
















(a)



Biological Design

Vertical wall

-- Tension

- Compression ____

Stress trajectory

151


(e)

(b)























l5 2 Chapter Four











----------------

(a) Distance

Crosscurrent


c Q


~ gtlt o

(c) Distance

(b)

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capillary




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(a) Accommodation







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~t~I I

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Overview


Chapter Four






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(a) Fast Separation

(b)











pLURe = shy

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Chapter Four 144

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Biologicltll Design

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145






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breakage follows







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146 C hapter Four

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(a) (b) (e)


































































148 Chap re r Four























(a)

(b) Normal foot

(e)




l50 Chapter Four

















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(a)



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151


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----------------

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~ gtlt o

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(b)

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154 Chapter Four


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Accommodation




























(a) Accommodation







of (he retina

~t~I I

I I I I

I I I

I I

I

I I

I







Overview


Chapter Four






156

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(d)












Chapter Four 144

I

e

It5m~~ lve t- --- -~--~d

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1shy





7-~ __

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(a) 4

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Biologicltll Design

III

145






Loaes













thrusc fr

After Gordo













breakage follows







(a)


(b) When


represemJ

down arro

within this

same mass



gives fibel

146 C hapter Four

n

I b)

n

w re ia lty (racshy

mdi-

Interior pier

Exterior pier


A~er Gordon

(a) (b) (c)











Iliotibial tract

Head of femur




















(a) (b) (e)


































































148 Chap re r Four























(a)

(b) Normal foot

(e)




l50 Chapter Four

















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J e s

n

n

~r

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u
















(a)



Biological Design

Vertical wall

-- Tension

- Compression ____

Stress trajectory

151


(e)

(b)























l5 2 Chapter Four











----------------

(a) Distance

Crosscurrent


c Q


~ gtlt o

(c) Distance

(b)

Airflow

Air lt

capillary




Tube 1

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Tube 1

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154 Chapter Four


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Accommodation




























(a) Accommodation







of (he retina

~t~I I

I I I I

I I I

I I

I

I I

I







Overview


Chapter Four






156

SELECTED REFERENCES




















WEB LINKS


this topic


e

It5m~~ lve t- --- -~--~d

lt ----c~~-ir






of irs





1shy





7-~ __

---~=====~~---- ----- --- 2 ------ 1 1 I --- I ~

I I I I I I I

3 I I

I

(a) 4

(b)

(e)









Biologicltll Design

III

145






Loaes













thrusc fr

After Gordo













breakage follows







(a)


(b) When


represemJ

down arro

within this

same mass



gives fibel

146 C hapter Four

n

I b)

n

w re ia lty (racshy

mdi-

Interior pier

Exterior pier


A~er Gordon

(a) (b) (c)











Iliotibial tract

Head of femur




















(a) (b) (e)


































































148 Chap re r Four























(a)

(b) Normal foot

(e)




l50 Chapter Four

















--

J e s

n

n

~r

is s ~s



u
















(a)



Biological Design

Vertical wall

-- Tension

- Compression ____

Stress trajectory

151


(e)

(b)























l5 2 Chapter Four











----------------

(a) Distance

Crosscurrent


c Q


~ gtlt o

(c) Distance

(b)

Airflow

Air lt

capillary




Tube 1

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30degC30degC


1aoc10degC

Tube 1

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Distance


















154 Chapter Four


~4~ (slladE~d area)







































Accommodation




























(a) Accommodation







of (he retina

~t~I I

I I I I

I I I

I I

I

I I

I







Overview


Chapter Four






156

SELECTED REFERENCES




















WEB LINKS


this topic







Loaes













thrusc fr

After Gordo













breakage follows







(a)


(b) When


represemJ

down arro

within this

same mass



gives fibel

146 C hapter Four

n

I b)

n

w re ia lty (racshy

mdi-

Interior pier

Exterior pier


A~er Gordon

(a) (b) (c)











Iliotibial tract

Head of femur




















(a) (b) (e)


































































148 Chap re r Four























(a)

(b) Normal foot

(e)




l50 Chapter Four

















--

J e s

n

n

~r

is s ~s



u
















(a)



Biological Design

Vertical wall

-- Tension

- Compression ____

Stress trajectory

151


(e)

(b)























l5 2 Chapter Four











----------------

(a) Distance

Crosscurrent


c Q


~ gtlt o

(c) Distance

(b)

Airflow

Air lt

capillary




Tube 1

Tube 2

30degC30degC


1aoc10degC

Tube 1

Tube 2

Distance


















154 Chapter Four


~4~ (slladE~d area)







































Accommodation




























(a) Accommodation







of (he retina

~t~I I

I I I I

I I I

I I

I

I I

I







Overview


Chapter Four






156

SELECTED REFERENCES




















WEB LINKS


this topic


n

I b)

n

w re ia lty (racshy

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Interior pier

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A~er Gordon

(a) (b) (c)











Iliotibial tract

Head of femur




















(a) (b) (e)


































































148 Chap re r Four























(a)

(b) Normal foot

(e)




l50 Chapter Four

















--

J e s

n

n

~r

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u
















(a)



Biological Design

Vertical wall

-- Tension

- Compression ____

Stress trajectory

151


(e)

(b)























l5 2 Chapter Four











----------------

(a) Distance

Crosscurrent


c Q


~ gtlt o

(c) Distance

(b)

Airflow

Air lt

capillary




Tube 1

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30degC30degC


1aoc10degC

Tube 1

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Distance


















154 Chapter Four


~4~ (slladE~d area)







































Accommodation




























(a) Accommodation







of (he retina

~t~I I

I I I I

I I I

I I

I

I I

I







Overview


Chapter Four






156

SELECTED REFERENCES




















WEB LINKS


this topic


(a) (b) (e)


































































148 Chap re r Four























(a)

(b) Normal foot

(e)




l50 Chapter Four

















--

J e s

n

n

~r

is s ~s



u
















(a)



Biological Design

Vertical wall

-- Tension

- Compression ____

Stress trajectory

151


(e)

(b)























l5 2 Chapter Four











----------------

(a) Distance

Crosscurrent


c Q


~ gtlt o

(c) Distance

(b)

Airflow

Air lt

capillary




Tube 1

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30degC30degC


1aoc10degC

Tube 1

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Distance


















154 Chapter Four


~4~ (slladE~d area)







































Accommodation




























(a) Accommodation







of (he retina

~t~I I

I I I I

I I I

I I

I

I I

I







Overview


Chapter Four






156

SELECTED REFERENCES




















WEB LINKS


this topic
























(a)

(b) Normal foot

(e)




l50 Chapter Four

















--

J e s

n

n

~r

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(a)



Biological Design

Vertical wall

-- Tension

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Stress trajectory

151


(e)

(b)























l5 2 Chapter Four











----------------

(a) Distance

Crosscurrent


c Q


~ gtlt o

(c) Distance

(b)

Airflow

Air lt

capillary




Tube 1

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30degC30degC


1aoc10degC

Tube 1

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Distance


















154 Chapter Four


~4~ (slladE~d area)







































Accommodation




























(a) Accommodation







of (he retina

~t~I I

I I I I

I I I

I I

I

I I

I







Overview


Chapter Four






156

SELECTED REFERENCES




















WEB LINKS


this topic


(a)

(b) Normal foot

(e)




l50 Chapter Four

















--

J e s

n

n

~r

is s ~s



u
















(a)



Biological Design

Vertical wall

-- Tension

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Stress trajectory

151


(e)

(b)























l5 2 Chapter Four











----------------

(a) Distance

Crosscurrent


c Q


~ gtlt o

(c) Distance

(b)

Airflow

Air lt

capillary




Tube 1

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30degC30degC


1aoc10degC

Tube 1

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Distance


















154 Chapter Four


~4~ (slladE~d area)







































Accommodation




























(a) Accommodation







of (he retina

~t~I I

I I I I

I I I

I I

I

I I

I







Overview


Chapter Four






156

SELECTED REFERENCES




















WEB LINKS


this topic


--

J e s

n

n

~r

is s ~s



u
















(a)



Biological Design

Vertical wall

-- Tension

- Compression ____

Stress trajectory

151


(e)

(b)























l5 2 Chapter Four











----------------

(a) Distance

Crosscurrent


c Q


~ gtlt o

(c) Distance

(b)

Airflow

Air lt

capillary




Tube 1

Tube 2

30degC30degC


1aoc10degC

Tube 1

Tube 2

Distance


















154 Chapter Four


~4~ (slladE~d area)







































Accommodation




























(a) Accommodation







of (he retina

~t~I I

I I I I

I I I

I I

I

I I

I







Overview


Chapter Four






156

SELECTED REFERENCES




















WEB LINKS


this topic



(e)

(b)























l5 2 Chapter Four











----------------

(a) Distance

Crosscurrent


c Q


~ gtlt o

(c) Distance

(b)

Airflow

Air lt

capillary




Tube 1

Tube 2

30degC30degC


1aoc10degC

Tube 1

Tube 2

Distance


















154 Chapter Four


~4~ (slladE~d area)







































Accommodation




























(a) Accommodation







of (he retina

~t~I I

I I I I

I I I

I I

I

I I

I







Overview


Chapter Four






156

SELECTED REFERENCES




















WEB LINKS


this topic












----------------

(a) Distance

Crosscurrent


c Q


~ gtlt o

(c) Distance

(b)

Airflow

Air lt

capillary




Tube 1

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30degC30degC


1aoc10degC

Tube 1

Tube 2

Distance


















154 Chapter Four


~4~ (slladE~d area)







































Accommodation




























(a) Accommodation







of (he retina

~t~I I

I I I I

I I I

I I

I

I I

I







Overview


Chapter Four






156

SELECTED REFERENCES




















WEB LINKS


this topic


----------------

(a) Distance

Crosscurrent


c Q


~ gtlt o

(c) Distance

(b)

Airflow

Air lt

capillary




Tube 1

Tube 2

30degC30degC


1aoc10degC

Tube 1

Tube 2

Distance


















154 Chapter Four


~4~ (slladE~d area)







































Accommodation




























(a) Accommodation







of (he retina

~t~I I

I I I I

I I I

I I

I

I I

I







Overview


Chapter Four






156

SELECTED REFERENCES




















WEB LINKS


this topic



~4~ (slladE~d area)







































Accommodation




























(a) Accommodation







of (he retina

~t~I I

I I I I

I I I

I I

I

I I

I







Overview


Chapter Four






156

SELECTED REFERENCES




















WEB LINKS


this topic


(a) Accommodation







of (he retina

~t~I I

I I I I

I I I

I I

I

I I

I







Overview


Chapter Four






156

SELECTED REFERENCES




















WEB LINKS


this topic


SELECTED REFERENCES




















WEB LINKS


this topic


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Biological '.Design - California State University, Bakersfieldkgobalet/files/Bio351/Kardong 2006 Ch 4 Biological... · Biological '.Design ... less suitable for locomotion of larger