ARCHIVES
MASSACHUSETTS INSTITUTE
OF TECHNOLOGY
NOV 10 2015
LIBRARIES
Study of the Microstructure and Mechanical Properties
of Hummingbird Wing-Bones
By
Tatiana Marie Kish
Submitted to the
Department of Materials Science and Engineering
in Partial Fulfillment of the Requirements for the Degree of
Bachelor of Science
at the
Massachusetts Institute of Technology
June 2011
C 2011 Tatiana Kish
All rights reserved
The author hereby grants to MIT permission to reproduce and to
distribute publicly paper and electronic copies of this thesis document in whole or in part in any
medium now known or hereafter created.
Signature redacted
Signature of Author
Department of Materials Scienr:e and Engineering
Certified by
Accepted by
...............................
.....................
Signature redacted
. 6 20 1 1
Loma Gibson
Matoula S Salapatas Professor of Materials Science and Engineering
upervisor
Tis
Signature redacted
Lionel C. Kimerling
Thomas Lord Professor of Materials Science and Engineering
Chair, Undergraduate Committee
1
ABSTRACT
A study of the microstructural and mechanical properties of wing bones of an Anna's
hummingbird (Calypte Anna) and a tree swallow (Tachycineta bicolor) was conducted to
determine whether the hummingbird bones exhibited unique features due to the high wing
loading of the bird. It was hypothesized that the hummingbird's ability to hover, flapping its
wings at an incredible rate, would create higher principal stresses that would require an internal
bone structure notably different from that of the swallow. Micro-computed tomography,
scanning electron microscopy, and nano-indentation experiments were conducted to determine if
such anomalies existed. Additional macroscale measurements were takcn to compare relative
proportions of each of the bones of interest, which included the humerus, radius, and ulna. Upon
examining the images produced via micro-computed tomography and scanning electron
microscopy, it was found that trabecular bone was present, suggesting the mechanical
advantages of the trabeculae were required. Nano-indentation results proved to be relatively
inconclusive, but generally provided results reasonably close to expected literature values.
Further experimentation would be required to determine if the deviation from expected values
were meaningful.
ACKNOWLEDGEMENTS
Professor Lorna Gibson (advisor)
Professor Douglas Altshuler, University of California, Riverside (providing Anna's
Hummingbird)
Dr. Kimberly Bostwick, Cornell University Museum of Vertebrates (providing tree swallow)
Dr. Scott Malstrom (Micro-CT training and experimentation assistance)
Alan Schwartzman (Nano-indentation training and experimentation assistance)
Donald Galler (SEM training and troubleshooting)
Matthew Humbert (training on metallographic techniques for mounting and polishing samples)
Dr. David Bono (assisting with sample sectioning using an abrasive saw)
Lina Garcia (assisting with sample preparation and data analysis software)
2
TABLE OF CONTENTS
4
Introduction
Bird Flight
4
Bone Structure
7
Materials and Methods
9
Wing Removal Procedure
9
Micro-Computed Tomography Procedure
11
Nano-indentation Procedure
12
Scanning Electron Microscopy Procedure
15
Results
17
Discussion
23
Conclusion
27
References
29
3
INTRODUCTION
Hummingbird flight has been a topic of research and discussion for decades. These
amazing little birds, averaging in size from about 2 grams to 20 grams (1), can hover in place or
move in any direction, changing direction almost instantaneously. They flap their wings at
extremely high rates, averaging at about 70 times per second though many are capable of
flapping up to 200 times per second during high-speed dives. (1) Compare this to the abilities of
a swift, which is in the same order as the hummingbird (Apodiformes), which averages 10-20
beats per second. (2) Hummingbirds are also among those birds that are capable of producing an
appreciable amount of power and lift both in the up-stroke and down-stroke of a wing flap. As a
result, it is expected that the bones in a hummingbird's wings are designed to withstand much
higher forces multi-directionally than other birds. In this study, wing bones from Anna's
hummingbird (Calypte Anna) will be compared to those of a tree swallow (Tachycineta bicolor).
Bird Flight
Before specifically considering the hummingbird bones, one should understand the
motivation behind this research. In terms of aerodynamics, hummingbirds are quite unique.
Most birds only generate lift during the down-stroke when flapping, but when hummingbirds
hover, they generate lift in the upstroke, as well. (3) This fact is not completely surprising given
that many insects generate lift in both the up-stroke and down-stroke when flapping their wings,
but the fact that a bird is capable of the same type of flight despite extreme physiological
differences is quite interesting. The aerodynamics is not exactly the same, as insects produce
about the same amount of lift in the up-stroke as the down-stroke, while hummingbirds produce
70 - 75 percent of the total lift on the downstroke and only 25 - 30 percent on the upstroke. (4)
This is made possible by the soft and flexible structure of the insect wings. The flexible wing
4
allows easy manipulation of the leading edge of the wing to adjust the camber, or the degree of
the difference in curvature of the top of the wing to the underside of the wing, which allows the
insect to minimize negative lift on the up-stroke. The shape therefore prevents excessive
decrease in air pressure under the wing. The upstroke of the hummingbird is significantly less
efficient compared to insects, but other birds are unable to produce any appreciable amount of
lift in the up-stroke, leading many birds to simply tuck their wings back to minimize drag as they
prepare for another down-stroke of the wing. (3) The hummingbird drastically and rapidly
changes the shape of its wings to adjust the camber like an insect would, except that, because it is
a vertebrate, its skeletal structure limits the extent that the wing's shape may change, accounting
for the decrease in efficiency. (5) Nevertheless, the shape deformation of the trailing edge of the
wing still causes high degrees of twisting and rotation from joint to joint along the length of the
wing. (5)
Because two birds are being compared for analysis, it should also be noted that variations
in the weight of the bird, the wingspan, and other relative dimensions of the bird affect speed of
flight. Based on the "Great Flight Diagram," found in Figure 1, there is a common
proportionality between the wing loading, measured in Newtons per square-meter of surface area
of one face of a wing, the weight of the flying object, and the cruising speed of the object. (3)
Wing loading data provides a normalized relationship between the wing size and mass of a bird,
bat, insect, or man-made flying object as a greater wingspan is obviously required to produce
more lift for a heavier object.
5
wing loading INS (newtons per meter squared)
1
10
102
I
I
I
10,
103
747
le6
DO=, 727
F-
Foker
Seeui Awbr
s~eei konenae
Lseo" 3
Seeaxwam
Seech Son
-
10*
F* *P-14
SChexh*rASW220
SchleteA
SohWIC*Wr
aK23
*unwon
human-powered eIeneOe
a
oue
.
Man-made aircraft
POanoW1n e
*
mft am"
wmwwb" wout 0b
*
Cnada goose
wuele pean
geGnemesee e
Wenne
0
*
grown pes"
102
I
t' k-
no
paeerit
*UOV 0b tro"
wtne
II
Birds
dgua pj* e puesga
Frs
Cp
pIgeon ___e
ornwnIernJ
**" '~i
pArpl meen
io
aw
I
100
h erme sUvin C
gqa.wn
C Enlleianow
0w
0
bu* ewdiow e e
eenp
n
Y4whese
ume
i"LV* 00 Ma__ w
se
10'
pdeihowk e
iue imdsng e
*
*
10-2
d cew
e ae msig b"ee
4 comn~n sen1owid1 0 -nw ceiw
e baiseae
oil
wule
gen agoneyCe
ecabbege
an bn e
scorpion say
deu
v
hoe-bee
lie.fy I
a e'*
'
102
Insects
ehowey
104
* ho'Vr
e nedge
104
1
2
C
3
II
my
4
5
7
cruising
Figure
I
i
10
20
30
speed V (meters per second)
I I I II
50 70
100
1. The "(Great Flight Diagram." (3) Arrows added to the diagram show the location of the tree sw alows and the
ruby-throated hummingbird, which is of similar weight to the Anna's hummingbird studied in this project
6
Looking at the diagram in further detail, one finds that the ruby-throated hummingbird and the
tree swallow fall on opposite sides of the line that defines the average relationship between the
mass of the bird and its wing loading. (The ruby-throated hummingbird and Anna's
hummingbird, the species being used for this study, are about the same weight and therefore it
can be assumed that Anna's hummingbird would fall in the same location on the diagram) Those
birds or objects that fall to the right of the line have a higher wing loading relative to their mass
than those that fall to the left of the line. This therefore means that a hummingbird's wings
experience moreforce per unit area than a swallow's wings.
Bone Structure
While all bone is composed of calcified collagen, bone can take on many different
structural forms depending on the purpose of the particular bone or section of bone. Bone can be
divided into two main categories when considering
mechanical significance; cancellous bone and cortical
bone. (6) Cancellous bone, also often referred to as
1i trabecular bone, makes up the foam-like framework of
trabeculae that is typically found in the ends of long'bones
S
such as the femur. The length of individual
trabeculae has been found to be nearly independent of
wl
Figure 2. Trabecular bone and cortical bone shown in a
human femur. D2002-2004 arttoday.com
the size of the animal. In other words, if one was to
examine the cancellous bone at the top of the femur
in a dog and compare it to that of a whale, one
would find that the trabeculae would be about the same length and thickness in both instances.
7
(7) As can be seen in Figure 1, there is not uniformity in the orientation of the trabeculae in any
one direction that remains constant through the bone. The orientation of the trabeculae depends
on the direction of the principal stresses, aligning parallel to the direction of principal stresses.
Compact bone has a much denser composition and is typically found through the narrow
middle region of long-bones and along the outermost surface of the bones. In mammals, any
noticeable porosity is due to the incorporation of osteons throughout the bone, as can be seen in
Figure 3. Osteons serve as a means to
transport blood and nutrients to bone that
is too thick to absorb them strictly
through diffusion. Structurally, they're
characterized by narrow pores, or
Haversian canals, that run through the
length of the bone surrounded by lamellar
Figure 3. Example of Osteons. Note the large, central canal
surrounded by concentric rings of lamellae that are then riddled with
sheets of bone with radial symmetry. (8)
tiny pores. These pores mark the location of osteocytes.
<http://education.vetmed.vt.edu>
The Haversian canals are then connected transversely by Volkmann canals, which are
considerably shorter and narrower than the large passageways through osteons. Throughout the
lamellae are smaller pits called lacuna that house the osteocytes. These cells are part of the
complex rebuilding system of bones and are sister cells to osteoblasts and osteoclasts, which
deposit new bone and resorb old bone, respectively. (9)
Recognizing that hummingbirds have a relatively high wing-loading relative for their
mass, further experimentation was conducted to understand how the structural and mechanical
properties of hummingbird bones vary compared to those in a swallow. Micro-computed
8
tomography and scanning electron microscopy were used to characterize the overall dimension
and the microstructure. Nano-indentation test were performed on the bone from both birds to
measure the Young's Modulus.
EXPERIMENTAL METHODS
Two Anna's hummingbirds (male; Calypte Anna) that were previously sacrificed were
shipped to the lab on ice from the University of California, Riverside. A tree swallow (sex
unknown; Tachycineta bicolor) that was previously sacrificed was also shipped to the lab on ice
from Cornell University. The birds were stored in the freezer of a standard Kenmore Kitchenstyle refrigerator/freezer on the coldest setting (-5'F). The swallow and the hummingbird used
for examination weighed 12.120 grams and 3.895 grams, respectively, and were weighed on a
Symmetry-Cole ParmerECII-120 digital scale with maximum capacity of 120 grams and
resolution up to 0.005 grams. To examine the wing bones using pL-CT, the wings had to be
removed from the bird to fit on the stage of the machine and to more easily focus on the region
of interest when analyzing the images. The wings were further dissected after this to isolate only
the bones so that cross-sections could be taken to view under the scanning electron microscope
and samples could be polished according to nano-indentation procedures.
Wing Removal Procedure
In preparing the bones for examination, the wings of the birds had to be removed. The
first hummingbird was thawed by placing it on a table and was left at room temperature for one
hour. It was then determined that the bird would thaw more evenly and controllably in the
refrigerator for approximately 48 hours. Once thawed, the bird was laid prone and the wing was
9
extended to locate the humerus and coracoid. Using a pointed scalpel, the wing was removed
between the humerus and coracoid, located using the bird-skeleton diagram in Figure 4. This
process was repeated for the opposite wing, but included the removal of the coracoid, as well.
The feathers were then carefully removed to expose the skin, though not all feathers could be
removed safely, without the risk of breaking the bones. The wings and bird were then
individually wrapped in damp paper towels and returned to the freezer until they were used for
experimentation.
socket
Metacarpal
__-
-
Carpal
Eye
Skull
Phalanges
Radius
mandrible -
Ulna
H um eru s'_
Scapula
BIrd
-
BidS keleton
Coracold
Lower
mandible'm
Iu
Caudal (tail)
vertebrae
F rcula
Cervical
(wishbone)
Pygostyle
(neck)
y
vertebrae
Keeled
sternum
Patella
(knee)
Toes -
.
Tibia
--
Fibula
Femur
Tarsometatarsus
@EnchantedLearnin g.com
Claws
Figure 4. General
schemalic
Ribs
of a bird skeleton.
Lichaniedl
arning.com
The swallow wings were removed following a similar procedure. The swallow was
placed in the refrigerator for 48 hours to thaw and was then laid prone with one wing extended to
locate the humerus and coracoid. For ease of removal, incisions were made between the scapula
and the vertebrae, thus including the scapula in the removed wing. This was then repeated with
10
the opposite wing, again, wrapping them in damp paper towels and then placing back in the
freezer.
Micro-Computed Tomography Procedure
Micro-Computed Tomography was used to qualitatively compare the structure of the
entire bone relative to other bones in the wing. Imaging was done using a GeneralElectric
eXplore Locus Micro-CT scanner, typically used for small-animal analysis.
All samples were thawed in the refrigerator for 48 hours so that they could be removed
from the damp paper towels. Once thawed, the wing was placed on the stage in the micro-CT
scanner. The scan parameters were set for a 27 micron resolution scan lasting 88 minutes and
were adjusted such that the x-ray tube voltage was 80 kV, the x-ray tube current was 450 ptA,
numbers of views was 400, exposure time was 2000 ms, detector bin mode was lxI, and the
effective pixel size was 0.021 nm. An additional low-resolution scan was also taken of the left
hummingbird wing to quickly get a working 3-dimensional image to better identify each bone in
the wing. The scan parameters were the same as the high-resolution scan with the exception that
the exposure time was only 400 ms, the detector bin mode was 2x2, and the effective pixel size
was 0.047 nm.
Measurements of the length and diameter of each bone were made using the "Line" tool
that allows the user to specify the endpoints of a line through a three-dimensional rendering of
the computed tomography image and gives the length of the line in millimeters.
11
Nano-indentationProcedure
Nano-indentation tests were performed to measure the hardness and Young's modulus of
the cortical bone in the humerus and ulna in each bird. A Hysitron TriboIndenter with a
pyramid-shaped Berkovich tip with a tip radius of 100 nm - 150 nm was used. The tip was
nearly a year old, however, and becomes duller over repeated uses, so it was assumed to have an
actual radius of 200 nm. Because the experiment is operated at the nano-scale, extreme care had
to be taken to ensure a completely flat and smooth surface free of external contaminants. To
accomplish this, the samples needed to be well polished. Various locations along the outer
cortical bone were then chosen for indentation. At each location, a 5x5 grid was made to provide
a statistical average of the data. The machine then applied a prescribed maximum amount of
force in micro-Newtons, increasing the force up to this maximum at a prescribed rate, and
measured the depth of penetration of the tip in the material. The softer the material, the deeper
the indentation in the material will be.
A series of points was then generated and plotted on a load vs. indentation depth curve.
An example of this can be found in Figure 5. The plot represents both the loading and
Load vs. Indentation Depth of Swallow Humerus at
One Indentation Site
600
500
400
300
Oliver-Pharr
Reeime
I-HPrtzian Regime
200
100
0
-20
20
4100
Figure 5. Nano-indentation
60
40
indentation Depth (nm)
data
80
for a single indentation point
12
100
120
unloading of the sample where the measurements follow the upper curve upon loading until the
maximum load is achieved and the lower curve upon unloading, as shown by the directional
notation on the graph.
During loading, the material experienced both elastic and plastic deformation, as can be
seen graphically by the change in slope at the tick-mark on the plot. The material only
experienced elastic deformation during unloading, however, as plastic deformation, by
definition, is permanent and will thus not change upon the removal of the load. Further
considering the plot, one can find the elastic regions known as the Hertzian regime and the
Oliver-Pharr regime. Both of these regimes could be used to find the Young's Modulus of the
material. The Oliver-Pharr regime is more often used as the data tends to be more consistent
throughout the regime and was therefore used for this analysis.
The nano-indentation tests in the Hysitron Tribolndenter required dry specimens.
Therefore, the bones needed to be completely removed from the fleshy wings, which proved to
be a challenge. Various methods to clean the bones manually, using forceps and a scalpel, were
attempted but with little success as the hummingbird bones were so small and delicate. Upon
further research, it was discovered that in taxidermy, carcasses are typically left outdoors to
naturally decompose, leaving the bones completely intact without the use of chemicals that could
alter the mechanical integrity of the bones. This process can be accelerated by placing the
carcass in still, tepid water. The latter technique was followed by first removing all of the
feathers from the wings, then placing the wings in beakers filled with 100 mL and 500 mL of
deionized water for the hummingbird and swallow wings, respectively. The beakers were
covered with Parafilm and left to stand at room temperature for 18 hrs. The wings were then
removed from the now soiled water and rinsed briefly with clean, deionized water. The wings
13
were then cleaned manually with forceps and a scalpel. The flesh was loosened considerably.
After some time, it was found that there were still regions where the flesh was difficult to remove
so the bones were sonicated twice for 10 minutes, then again placed in beakers of deionized
water and left for another 24 hours. The above manual procedure was carried out again until
nearly all of the flesh was removed. There were a few regions near joints where the flesh could
not be completely removed but this was deemed acceptable as the regions of interest for the
nano-indentation were near the center of each bone. The humerus was separated at the "elbow"
joint, but the radius and ulna were left attached to each other. The bones were then left to air-dry
at room temperature for 48 hours.
Nano-indentation requires a smooth, polished surface due to the sensitivity of the
instrument. Because the samples were so small, they could not be safely sanded and polished
immediately upon drying and were therefore prepared following typical procedures used for
metallographic analysis. Each bone or bone-set (radius and ulna) was suspended normal to the
table surface in thermo-set epoxy and left at room temperature to harden overnight. Upon
solidification, samples were sectioned transversally to provide cross-sections using a Buehler
ISOMET 11-1180 Low Speed diamond/abrasive saw set at between 5 and 8 on the speed setting.
A Struers Cut-off wheel (HQ) with 125mm diameter blade made of Aluminum Oxide (used
typically for cutting hard ferrous materials, but found effective in cutting epoxy and bone, as
well) was used for sectioning. The discs were polished following Struehr's guidelines for
polishing bone using a Struehr's TegraForce-5 and TegraPol-21 system. They were sanded
using 500, 800, and 1200 grit sandpaper for 2 minutes each under 20 Newtons of force and then
were polished using OPS 0.02 micron Colloidal Silica, and the appropriate polishing wheel.
Smoothness was verified by observing the surfaces under an optical microscope.
14
The polished samples were then super-glued onto square metallic disks required for the
stage set-up in the Hysitron TriboIndenter. Using the optical microscope included in the set-up
of the Tribolndenter, 3 to 5 locations per bone were chosen throughout the circumference of the
bone, centering the indentation field such that all indentations were performed as far from the
edge of the bone as possible to minimize edge-related abnormalities.
Scanning Electron Microscopy Procedure
The cross sectioned samples were observed under a scanning electron microscope after
sectioning, but before polishing as polishing made for a less clean surface for viewing due to
bone residue accumulation in the pores of the bone. Samples were mounted on the stage of the
LEO 438 VP (Variable Pressure) scanning electron microscope and were viewed under variable
pressure conditions between 10 Pa and 20 Pa as neither the bone nor the epoxy was particularly
conductive and thus typically quickly became charged under "High Vacuum" Pressure
conditions. The Iprobe was set to 250pA, the collector bias was set to 350 V, the gun brightness
was adjusted between 2.3 A and 2.7 A, depending on the sample, and the working distance
remained between 10 mm and 20 mm from the viewing source. Each bone was then viewed at
progressively higher magnifications from 30x to 2000x to search for any unique microstructural
features.
RESULTS
Micro CT images of the wing bones in the Anna's hummingbird and tree swallow are
shown in Figures 6 through 8.
15
Figure 6. Three dimensional micro-CT rendering of the entire hummingbird and swallow wings
16
Below, in Table 1, one can see that the dimensions of the various bones in the wing are quite
different from the hummingbird to the swallow. For comparison, the ratio of the dimensions of
the humerus to those of the radius and ulna were each taken and listed in Table 2. These various
ratios can then be compared between the hummingbird and swallow. The relative size of the
bones can also be seen in the three dimensional rendering of the bones shown in Figure 6. It
should be noted that the diameters measured and listed on the table were taken using the dynamic
Micro-CT software that made it possible to measure the diameter at the center of the bone.
Bones are not, however, perfectly cylindrical so the diameter varies along the length of the bone.
The midpoint along the length of the bone was chosen for measurements because the region was
closest to uniform in all perspectives, although the diameters of the bones listed in the table
varied by about 0.2 millimeters, depending on the perspective from which the measurement was
taken.
Hummingbird
Swallow
'Table
1.
Humerus
Length
Humerus
Diameter
(mm)
(mm)
4
13.7
Measurements of the
length
Humerus
Aspect
Ratio
4.49438
Hummingbird
7.21033
Swallow
Ulna
Radius Radius
Ulna Diameter
Length
Length Diameter
(mm)
(mm)
(mm)
(mm)
0.7
4.2
0.35
.89
3.7
22.8
1.7
21.5
0.6
1.9
and diameter of
th
Ulna
Aspect
Ratio
5.99988
13.41202
L(h):L(u)
0.95238
0.60088
hu merus, radius, and
ulna
D(h):D(u)
1.27142
1.11764
D(h):D(r)
2.54285
3.16667
D(r):D(u)
0.5
0.35294
Table 2. Aspect Ratio (diameter/length) of the humerus and ulna and %arious length (L) and diameter (D) ratios of the
humerus (h), radius (r), anid ulna (u)
Looking at various cross-sectional slices of the bone, one can see that there are notable
differences between the structures of the bones. Looking at the hummingbird humerus, shown in
Figure 7, there are two distinct regions - the dense outer edge of the bone and the hollow center.
Throughout the bone, there also appears to be several narrow bridges connecting opposite walls
17
of the bone, presumably trabeculae. These only extend across the width of the bone and do not
extend along the length of the bone. The swallow, shown in Figure 8, appears to have three
different regions through the cross-section of the bone - the dense out edge of bone, a foamy
middle region, and a hollow center. Note that in Micro-CT images in Figures 7 and 8, the
images appear a bit ambiguous, so the relative length scale should be considered. The
hummingbird humerus length is about 4mm and its diameter is about 0.9 mm. The swallow
humerus length is about 13.7mm and the diameter is about 1.9mm. Additionally, the
perspectives of the hummingbird and swallow bones are not identical due to size constraints of
the imaging software. The hummingbird slices are very near parallel to the long edge of the
bone, but the swallow slices show sections closer to a 45 degree angle from the plane parallel to
the length of the bone. While not ideal, the image clarity is good enough to see structural
differences between the bones.
Figure 7. Length-wise slices of hummingbird humerus produced via Micro-CT and a 3-dimensional rendering of the same
bone to demonstrate the perspective from which the images were taken.
18
Figure 8. Length-wise slices swallow humerus produced via Micro-CT and a 3-dimensional rendering of the same bone to
demonstrate the perspective from which the images were taken.
Several images were taken with the scanning electron microscope to not only look at the
cross-section of each bone as a whole, but also to observe various regions of cortical or
trabecular bone. Entire cross sections are shown in Figures 9 and 10, though it should be noted
Figure 9. Cross sections of the hummingbird humerus (left) and swallow humerus (right) with included diameter measurements for the
particular cross section
that the hummingbird cross section is much closer to the end of the humerus than cross section of
the swallow as sectioning and polishing the bone removed up to a millimeter of material. This
19
view is therefore likely closer to one-quarter of the length down the bone, contributing to the less
circular cross-section.
In the full cross-section images, there are two notable feature differences. First, the
hummingbird humerus has a clearly defined edge along the inner-surface of the bone walls,
distinguishing where the bone starts radially. The swallow humerus, on the other hand, appears
to have a region of dense bone along the outer portion of the bone encapsulating a more porous
region on the inside before it becomes completely devoid of bone in the center. Additionally,
one can see that while the swallow bone has a relatively uniform radial profile, there does not
appear to be uniform radial symmetry through the hummingbird bone as there appears to be a
bridge of bone structure connecting opposite bone walls.
Upon closer examination, there are also some interesting features in the microstructure of
these bones. The hummingbird bones appear to have significant pitting throughout all visible
bone, both along the outer edge and through the segment the runs through the cross-section. The
Figure 10. Higher magnification of the humerus cross section of the hummingbird (left) and swallow (right) with bone-wall thickness
measurements included
swallow bone, however, lacks these surface anomalies. In both cases, the bone appears to be
lacking osteons through the length of the bone.
20
In analyzing the nano-indentation data, the Oliver-Pharr regime was used to find the
Young's Modulus and hardness. While computer software was used to calculate Modulus, it is
useful to consider the process by which the value was determined computationally. The OliverPharr regime was fitted to an equation of the form,
P = A(h -h)
m
(1)
where P is the applied load at a given time, h is the variable depth, hf is the final depth reached
at maximum loading, and A and m are additional constants that mathematically define the curve.
Taking the derivative of the equation with respect to the variable hardness, where S is the
stiffness of the material,
(2)
= S =m * A(h - hf)m-1
dh
one can then calculate the reduced Young's Modulus, Er , defined in Equation 3 where A, is the
contact area of the indenter tip. The reduced Modulus actual Young's Modulus, E, by the
relationship between E and E, given in Equation 4.
Er =
s
1-V 2
Er
E
(3)
--*
1-v
diamond
tip
E
2
sample
While the TriboIndenter calculated the Poisson's ratio of the sample internally, it is known that
cortical bone typically has a Poisson's ratio around 0.3, which does not appear to deviate greatly
between species. (10) The diamond Berkovich tip has a Poisson's ratio of 0.07 and a Young's
Modulus 1141 GPa. Substituting values, one finds the Young's modulus of the various bones,
21
consistent with the plots shown in Figure 11. The Young's modulus averaged between 30 and
45 GPa for the swallow and between 10 and 40 GPa for the hummingbird, excluding the linear
region of the plot of the humerus indentations as those values were consistent with the Young's
modulus of the epoxy in which the bone was set.
Young's Modulus of Hummingbird
Humerus and Ulna
50
40
U
30
0
*
20
*
*~
10
U
U
~ \'* ~
-1%
::
19
0
U
*
.'.
________
qu
U
*
*+ Humerus
Humerus
**
Ulna
** Ulna
0
-15
0
150
100
50
Trial Number
Young's Modulus of Swallow
Humerus and Ulna
IA
0
C
70
60
50
40
30
* Humerus
20
10
0
* Ulna
0
20
40
60
80
100
120
Trial number
Figure 11. Young's modulus calculated at each of the indentation sites for the hummingbird and
swallow where "Trial Number" refers to the nth indentation site in the series
22
The hardness, H, of the bone was also measured using data from the plot and applying it
to equation (5), with Pmax as the maximum applied force and Ac as the contact area of the
indenter.
H=
Pmax
(5)
Taking the contact area at the maximum load gives a hardness of between 0.22 GPa and 0.9 GPa
for the hummingbird and between 1.3 GPa and 1.9 GPa when excluding far-outlying data points.
DISCUSSION
Various aspects of the bone were considered in the analysis. Starting from the most
macroscale comparison, there were some notable differences between the overall dimensions of
the hummingbird and swallow. An especially unexpected difference was found when comparing
the length of the humerus relative to the length of the ulna and resulting overall proportions of
the bones in the wing. As the data shows, the humerus is nearly the same length as the ulna in
the hummingbird but only slightly more than half the size of the ulna in the swallow. It is also
interesting to consider the aspect ratio of the humerus and ulna in both cases. The humerus has
an aspect ratio, length/diameter, of 4.4944 and 7.2103 and the ulna has an aspect ratio of 5.9999
and 13.4120 in the hummingbird and swallow, respectively. This is counterintuitive as skeletal
lengths, L, tend to decrease as mass, m, increases, following the allometric scaling where mass is
proportional to length cubed, m ~ L. This is because as mass increases, a wider cross-sectional
area is required to safely support the animal's weight. It would therefore be expected that the
bones of the hummingbird would have been relatively longer and thinner than those of the
swallow, resulting in a higher aspect ratio. Upon examination, however, it was discovered that
the opposite was true. This would make sense, assuming the hummingbird experiences much
23
higher stresses due to the greater amount of wing loading. A longer, narrower bone would be
inappropriate as it would be more prone to fracture, especially considering the hardness and
rigidity of bone.
Looking at the bone on the next smaller scale through micro-CT images, one notices that
any trabecular bone found through the structure is very localized in the swallow bones and looks
more like a foamy material due to the fact that trabeculae attach not only to the outer wall of the
bone, but also to other trabeculae. In the hummingbird, however, the trabeculae were found to
span the entire diameter of the bone and appear less foamy as trabeculae only attached to the
outer wall of the bone. While interesting, this is more likely due to the sheer size of the animal
as opposed to a structural feature arising from the function of the bone, as was the case for the
overall dimensions of the bone. It has been well documented that in very small animals,
individual trabeculae tend to only connect directly to the cortical bone in the bone wall and do
not connect to other trabeculae to form more foam-like structures as they do in larger animals.(7)
The appearance of these trabeculae in both cases provides insight into the mechanical
design of the bone. In the hummingbird humerus, the existence of trabeculae through the cross
section of the bone suggests that principal stresses are experienced through thickness of the bone.
Likewise, the swallow bone appears to have a similar anisotropy. This is consistent with the
forces experienced during wing loading and thus still follows the same directional trend as found
in weight-bearing joints of larger land animals.
Continuing in magnification using the scanning electron microscope, there are a few
additional observations that can be made about the material of the bone, itself. It is readily
apparent that there is limited trabecular bone through the humerus of the hummingbird and what
24
is observed under higher magnification verifies the fact that any existing trabeculae only
transverse from one section of cortical bone to another section of cortical bone. In both the
swallow and hummingbird cortical bone, there is a noted lack of osteons. While surprising at
first, when one considers that an osteon is typically around 100 microns in diameter, one realizes
that an osteon simply will not fit in the thin cortical bone of either sample as the bone is, at most,
about 200 microns through the thickness of the cortical bone. It is known that osteons actually
help minimize the growth of fractures through bone by acting to diffuse strain energy when a
micro-crack encounters a Haversian canal and the surrounding lamellae. When the crack
encounters the canal, several small cracks develop through the circumferences of the lamellac,
thus minimizing damage from a single crack propagating transversely through the bone. There is
evidence in the literature that the presence of these canals causes a "higher local stress
concentration and lower strength," as is the case in most structural materials. (12) If osteons
were present, it is possible that given the size of the bones and the small distances through which
cracks could propagate, osteons would therefore actually decrease the fracture resistance of the
bone.
There are also apparent pits in the hummingbird sample that are not apparent in the
swallow sample. These pits are likely lacunae that are the site for osteocytes, though the reason
for fewer pits in the swallow bone is uncertain.
Nano-indentation results were fairly inconclusive due to inconsistencies in the data, but
some observations were still made. Cortical bone is known to have a Young's modulus typically
between 18 GPa and 21 GPa. (11) Results of this experiment, however, revealed values of, on
average, between 30 GPa and 40GPa for the cortical bone found in the swallow's ulna and
between 35 GPa and 45 GPa in the swallow's humerus, making experimental values one and a
25
half to two times higher than expected. Similar, though slightly more expected results were
found in the hummingbird with the Young's modulus of humerus falling between 10 GPa and 25
GPa and the modulus of the ulna falling between 15 GPa and 35 GPa. These values are not
representative of the entire data-set, however, as the first 75 data points for the humerus gave
values consistent with those expected for the epoxy and were thus not included in the average.
Additionally, because the ulna was so much smaller, and therefore the cortical bone so much
thinner, it was difficult to find regions along the outer circumference of the bone that were thick
enough to accurately retrieve results from. Only the final location chosen for the experiment,
corresponding to the final 25 data points on the plot in Figure 11, was visibly thick enough to
completely avoid edge effects of the bone and therefore is the only set considered in this average.
It is possible that avian bone might have a higher modulus than published values as
mammalian bone is more often studied and therefore referenced in the literature, but it would be
unlikely that the difference would be as great as those found in this experiment. Without
additional data to demonstrate a statistical average, as only one swallow was studied, it is
impossible to make a conclusive statement about implications of these results. It is instead more
likely that errors in sample preparation contributed to these values. Indentations were intended
to be made exactly normal to the longitudinal axis, but no steps were taken to ensure that this
was the case beyond simply looking at it with the naked eye. It is anomalous that the Young's
modulus was measured to be higher than expected values, however, as discrepancies were
expected to occur do to possible wetness in the bone. Since wet bone is known to have a lower
Young's modulus than dry bone, it was expected that the opposite trend would have occurred.
Hardness values fell within the expected range in the hummingbird bone with values
between 0.22 GPa and 0.99 GPa. The swallow bone had values much higher than expected with
26
hardness values between 1.3 GPa and 1.9 GPa. Literature values suggested that cortical bone
should have a hardness value between 0.23 GPa and 0.76 GPa. (13) It is again uncertain why
these values were higher than those expected as the most likely cause of error would be
interactions between neighboring indentation sites. Further experiments would need to be
conducted on additional samples to have statistically conclusive results.
CONCLUSION
Throughout this study, the architecture and mechanical properties of the wing bones of an
Anna's hummingbird (Calypte Anna) were studied and compared to those of a tree swallow
(Tachycineta bicolor). It was found conclusively that the hummingbird has a lower aspect ratio
of its humerus and ulna than the swallow, which was unexpected due to the allometric scaling of
length with respect to mass. When considered in light of the fact that the wing loading of the
hummingbird is higher than that of a swallow, the deviation from allometric scaling is justified.
Additionally, limited trabecular architecture was found in the hummingbird humerus, but was not
unexpected due to the size of the bones. Directional anisotropy in the hummingbird bone that
was less pronounced in the swallow bone provides further evidence of higher principal stresses
due to increased wing loading.
Both the hummingbird and the swallow lacked osteons through the length of the cortical
bone, most likely due to the fact that osteons can measure up to 200 microns in diameter, proving
to be too wide to fit in the 50 micron to 200 micron-thick cortical bone. Some literature
evidence suggests that the lack in osteons could minimize stress concentration sites, which could
be crucial that this scale. Finally, Young's modulus and hardness values were higher than
expected which could possibly suggest that avian bone possesses unique structural composition,
27
but further analysis would need to be made with additional samples to make this assumption
statistically conclusive.
Given the opportunity, it would be interesting to repeat the nano-indentation experiment
on more samples to determine if there is a statistical trend in avian bones to have a higher
Young's modulus. It would also be useful to conduct these experiments under wet conditions as
wet bone is known to have significantly different properties to dry bone to include a lower
Young's Modulus and greater elastic response. Density analysis and mineral content of various
bones would also provide useful data that would shed additional light on the whether the
Young's modulus and hardness values found in this study are meaningful.
28
REFERENCES
(1) "Migratory Bird Center: Hummingbirds." Smithsonian NationalZoologicalPark.
Smithsonian Institution, n.d. Web. 1 Apr 2011.
<http://nationalzoo.si.edu/scbi/migratorybirds/webcam/hummingbirds.cfm>.
(2) Moore, A. D. The Auk. 63, Number 1. Lancaster, PA: The American Ornithologists'
Union, 1946. 70-72. eBook.
(3) Tennekes, Henk. The Simple Science of Flight: From Insects to Jumbo Jets. 2nd Edition.
Cambridge, MA: The MIT Press, 2009. 29
(4) Warrick, Douglas R., Bret W. Tobalske, and Donald R. Powers. "Aerodynamics of the
Hovering Hummingbird." Nature. 435.23 June (2005): 1094-1097.
(5) Ho, Steven, Hany Nassef, Nick Pornsinsirirak, Yu-Chong Tai, and Chih-Ming Ho.
"Unsteady aerodynamics and flow control for flapping wing flyers." Progressin
Aerospace Sciences. 39. (2003): 635-681
(6) Currey, John D. Bones: Structure and Mechanics. 2nd Edition. Princeton, NJ: Princeton
University Press, 2002. 20-30.
(7) Swartz, Sharon M., Antigone Parker, and Christine Huo. "Theoretical and Empirical
Scaling Patterns and Topological Homology in Bon Trabeculae." Journalof
ExperimentalBiology. 201. (Feb 1998): 573 - 590.
(8) "Osteon." EncyclopaediaBritannica. EncyclopaediaBritannica Online. Encyclopedia
Britannica, 2011. Web. 28 Apr. 2011.
<http://www.britannica.com/EBchecked/topic/434325/osteon>.
(9) "Osteocyte." Encyclopcedia Britannica. EncyclopcediaBritannicaOnline. Encyclopwdia
Britannica, 2011. Web. 29 Apr. 2011.
<http://www.britannica.com/EBchecked/topic/434280/osteocyte>.
Ricos, Vicente, Douglas R. Pedersen, Thomas D. Brown, Richard B. Ashman,
(10)
Clinton T. Rubin, and Richard A. Brand. "Effects of Anisotropy and Material Axis
Registration on Computed Stress and Strain Distributions in the Turkey Ulna." Journalof
Biomechanics. 29.2 (February 1996): 261-267.
Rho, JY, RB Ashman, and CH Turner. "Young's Modulus of Trabecular and
(11)
Cortical Bone Material: Ultrasonic and Microtensile Measurements." Journalof
Biomechanics. 26.2 (February 1993): 111-119.
Ebacher, Vincent, and Rizhi Wang. "A Unique Microcracking Process Associated
(12)
with the Inelastic Deformation of Haversian Bone." Advanced FunctionalMaterials. 19.
(2009): 57-66.
(13)
Zysset, Philippe K., X. Edward Guo, C. Edward Hoffler, Kristen E. Moore, and
Steven A. Goldstein. "Elastic Modulus and Hardness of Cortical and Trabecular Bone
Lamellae Measured by Nanoindentation in the Human Femur." JournalofBiomechanics.
32. (1999): 1005-1012
29