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This is a preprint of: Glenn et al., “Analysis of bird wing airfoil aerodynamic efficiency,” AIAA SciTech
2024 Forum. The published article may differ from this preprint.
Analysis of bird wing airfoil aerodynamic
efficiency
Rowan Glenn1, Lucas B. Dahlke1, Andrew Engilis, Jr.2, Christina
Harvey3
University of California Davis, Davis, CA, 95616, USA
Historically, aviation has benefited from the study of avian flight. Effective biologically informed
design requires knowledge of quantifiable biological principles that researchers can integrate into
the development of future aircraft. The study of avian flight is especially applicable to the design
of uncrewed aerial vehicles (UAVs) due to their similarity in size, speed, and flight environments.
However, extracting relevant biological principles is challenging due to the number and variety
of bird species, complicating the selection of a species that would best inspire a specific design
objective. Proper selection requires information on both overall wing shape and airfoil
properties. Additionally, each bird species experiences different natural selective pressures that
constrain the evolution of their morphology over time depending on their flight style, life history,
and ecological niche. To study the aerodynamic traits of various birds, we developed a systematic
method to scan bird wings, extract their airfoils, and quantify their aerodynamic performance.
This tool allowed us to test our hypothesis that birds that preferentially perform gliding and
soaring flight have airfoil aerodynamic properties that are unique from flapping species. To test
this hypothesis, we scanned prepared bird wings from multiple species. We adapted a slicer
algorithm from 3D printing software to extract the airfoil shape at known locations along the
span. Next, we used XFOIL to estimate the aerodynamic properties at a Reynolds number of
1.5×105. We found a slight, but statistically insignificant, increase in the aerodynamic efficiency
of airfoils from gliding species compared to airfoils from flapping species. Our results suggest
that the morphology of avian airfoils may account for species’ flight styles, although future work
is required to build a larger dataset for a more robust model. Moreover, we found our highest-
performing avian airfoils achieved a similar aerodynamic efficiency, if not higher, than that of
human-engineered airfoils (FX63-137, S1223, and NACA 4415) at the analyzed Reynolds
number. In all, our results show promise in bio-inspired airfoil design and ultimately advance the
fundamental understanding of bird airfoil aerodynamic characteristics.
I. Introduction
By studying bird morphology, we can identify the most advantageous flight strategies that birds have
developed to drive the development of novel bio-informed aircraft [1]. Early studies of bird wing morphology used
prepared specimens to establish how properties like camber and wing twist affect wings’ lift and drag coefficients [2].
Studies on bird wing morphology have also identified how barn owls and eagles adjust to turbulent conditions [3, 4],
how gulls use their elbow angle to negotiate between flight efficiency and stability [5], and have found that the majority
of bird species can shift between more maneuverable and more stable configurations by morphing their wings [6].
Such studies have also expanded our understanding of how birds cope with rapid changes in the angle of attack [7],
which has led engineers to successfully implement flexible flaps on the surface of aircraft wings to improve
This is a preprint of: Glenn et al., “Analysis of bird wing airfoil aerodynamic efficiency,” AIAA SciTech
2024 Forum. The published article may differ from this preprint.
aerodynamic performance [8]. Additionally, a 2023 study scanned over 1,000 bird wings and found evidence that the
bird wing is composed of two modular units: the handwing and the armwing. [9]
Bird wings vary along their span because their skeletal structure extends only partially into the wingspan,
and near the tip, the airfoil is composed of only feathers (Fig. 1). It has been established that the interior of bird wings
have a more cambered airfoil than the wing tip [10]. Understanding the distribution of airfoils along a bird wing and
how this varies between species will be critical to establishing generalized models of bird flight. Due to the complexity
of bird wings and the lack of data on avian airfoils, previous studies have relied on assuming a “typical” wing profile
[11] or have used historical data that has been acquired for a few individuals of a few species [2,6,9]. However, the
aerodynamic role of each wing section has not yet been quantified. Often researchers must select bird airfoils based
on estimations and limited empirical data. Our method for analyzing bird wing morphology introduces a systematic
way to scan and analyze airfoil data from bird wings. This approach, and others like it [9], builds a more
comprehensive dataset of avian airfoil shapes.
Fig. 1 Approximate wing anatomy demonstrating the expected structural differences between proximal
(inboard) airfoils and distal (outboard) airfoils. Adapted from [1].
To build the airfoil database, we scanned 18 prepared bird wings, adapted a 3D printing slicer algorithm, and
normalized the data to extract the airfoil shape along each specimen’s wing. This standardized approach allows for
quick and accurate analysis of wing airfoil shapes across various individuals and species. Furthermore, by analyzing
our extracted airfoils in XFOIL [13], we quantified the aerodynamic characteristics of bird airfoils and determined
their maximum lift-to-drag ratio.
This dataset enabled us to compare the aerodynamic characteristics of various bird species based on their
primary flight style. We hypothesized that gliding and soaring birds face similar selective pressures that constrain their
airfoil shape and resulting aerodynamic properties. Despite different evolutionary histories, we predicted that if gliding
This is a preprint of: Glenn et al., “Analysis of bird wing airfoil aerodynamic efficiency,” AIAA SciTech
2024 Forum. The published article may differ from this preprint.
birds had similar maximum lift-to-drag ratios and geometries, there may exist some empirical ideal airfoil shapes for
efficient gliding flight. We expected these properties to differ compared to the wings of flapping birds. Flapping birds
regularly encounter highly unsteady aerodynamic forces, which may lead to different evolutionary pressures for their
airfoil shape and wing size. Indeed, recent work has found evidence that flapping flight aerodynamics drove the
evolution of the avian wing geometry [10].
II. Methodology
A. Wing Selection
Our method adapts existing structured-light 3D scanning technology to extract information about the airfoils
of various bird wings at a series of standardized locations. For this study, we scanned the geometry of prepared wing
specimens from nine species of birds. The species include prairie falcon (Falco mexicanus), turkey vulture (Cathartes
aura), red-tailed hawk (Buteo jamaicensis), red-shouldered hawk (Buteo lineatus), band-tailed pigeon (Patagioenas
fasciata), Laysan albatross (Phoebastria immutabilis), western gull (Larus occidentalis), yellow-billed magpie (Pica
nuttalli), and black scoter (Melanitta americana). These species were selected to cover a broad range of the avian
phylogeny and account for different flying styles in different clades of birds. We selected specimens from species that
either flap or glide as their modus operandi. Gliding species include prairie falcons, turkey vulture, both hawk species,
western gull, and Laysan albatross, and the flapping species include band-tailed pigeon, yellow-billed magpie, and
black scoter. These selected species span a wide range of avian mass. The smallest bird, the magpie, weighs
approximately 0.16 kg, whereas the largest bird, the Laysan albatross, weighs approximately 3.3 kg.
We collaborated with the UC Davis Museum of Wildlife and Fish Biology to obtain the wing specimens to
scan. All wings were previously prepared and follow a standardized style where the wing is preserved, flattened from
the elbow out, with the elbow joint, arm, phalanges, and flight feathers outstretched, similar to shapes observed by
birds in soaring flight. Our initial round of data collection involved scanning multiple wings for each of our nine
species, resulting in a total of 18 wing models. Three wing scans were not usable due to low scanning resolution and
precision, reducing our final total to 15 models.
B. Wing Scanning
We anchored the wings to a flat surface with a clamp to prevent wing movement during the scan. The wings
were clamped and scanned in two configurations. In the first configuration, we positioned the wings with the wing tip
pointing directly upwards and the wing root anchored. In the second configuration, we clamped the wing's leading
edge at the wrist, with the primary feathers pointing upwards. We covered the wings with infrared markers at a density
of approximately one marker per in2. The wings were scanned using a 3D infrared scanner (Revopoint POP2) with a
precision of 0.05 mm (0.002 in). Each wing was scanned up to six times to ensure that the complete geometry was
captured with the maximum possible resolution. These included scans to capture the geometry and details of the
leading and trailing edges of each wing, as well as detailed images of the dorsal and ventral wing faces.
C. Importing and Processing 3D Files
We used RevoScan 5’s point cloud editing capabilities to align these scans using common morphological
features as a reference. This allowed us to crop the clamps out of the scan while maintaining the accuracy of the scan.
These scans were converted into a mesh (.stl), a format commonly used in additive manufacturing. To prepare these
point clouds for aerodynamic analysis, we edited our scans to linearly interpolate across gaps in the scan, such as those
left by the infrared markers (Fig. 2). Additionally, we removed background objects that were picked up by the scanner.
This is a preprint of: Glenn et al., “Analysis of bird wing airfoil aerodynamic efficiency,” AIAA SciTech
2024 Forum. The published article may differ from this preprint.
Fig. 2 Revopoint editing process. a) Initial point cloud, b) mesh conversion, and c) final edited scan of the albatross
specimen, WFB-17490.
Finally, we corrected minor meshing errors and standardized the orientation of all scans using the .stl editing
tool PrusaSlicer [14]. The total number of mesh triangles corrected by PrusaSlicer was minor, comprising less than
1% of the total triangle count of each wing. They resulted from computational artifacts generated during the conversion
of our models from point clouds to meshes. The wing meshes were oriented with the leading edge pointing vertically
upwards. The primary flight feathers, which roughly form a flat plane near the shoulder joint for all specimens, were
aligned horizontally. PrusaSlicer’s internal angle measurement capabilities provided angle guidelines every 5° while
scan orientation was taking place. By visually aligning the leading edge with these markers, we could ensure that the
scan was accurately aligned within 2.5°.
Fig. 3 Slicer algorithm results for the Laysan Albatross wing, specimen WFB-17490. a) With the wing
model and b) without the wing model.
This is a preprint of: Glenn et al., “Analysis of bird wing airfoil aerodynamic efficiency,” AIAA SciTech
2024 Forum. The published article may differ from this preprint.
D. Slicer Algorithm Adaptation
We then imported our scans to a function adapted from an open-source slicing function [15] intended for
generating G-Code used in 3D printing. The function divides the .stl file into evenly spaced slices, determined by user
input. It does this by detecting mesh triangles that intersect with each given slicing plane and outputting these points
as a set of comma-separated values. The points can be graphed as a series of slices for user visualization (Fig. 3), and
the x-y coordinates for each airfoil are saved to an individual spreadsheet for future input into XFOIL. By adjusting
the distribution and number of slices, this function outputs data about the 2D airfoil shape at any specified location.
We sliced each wing at ten evenly spaced locations along the span between the root and top, creating sections that
were each 1/11th of the wingspan.
In the process of creating the final three-dimensional models of each wing, multiple scans from various angles
were combined to capture as much detail as possible. Inaccuracies in the alignment occasionally resulted in duplicate
surfaces within the interior of the wing model. As a result, we occasionally observed incidental points in the center of
the sliced airfoils, as demonstrated in Fig. 4. Because these points do not affect the wing's aerodynamic properties but
would cause errors in our XFOIL analysis, we removed all interior points. Additionally, noise was intermittently
present along the perimeter of the airfoils generated; these came in three varieties, as demonstrated in Fig. 5 below.
Fig. 4 Incidental points in airfoil interior. a) Before and b) after editing.
Fig. 5 No-Go Scenarios. a) Splits down trailing or leading edges, b) irregular airfoils,
or c) secondary bodies along the airfoil perimeter.
This is a preprint of: Glenn et al., “Analysis of bird wing airfoil aerodynamic efficiency,” AIAA SciTech
2024 Forum. The published article may differ from this preprint.
In cases like Fig. 5a) and c), the noise along the leading edge made it impossible to determine an airfoil shape
that accurately represented bird wing geometry, so these airfoils were discarded. In cases like Fig. 5b), the slicer
generated a continuous geometry, but the airfoil was too irregular or jagged to be analyzed in XFOIL. These, along
with any cases where several geometries were created during slicing, were discarded, although future work should
explore these unique shapes.
E. Curve Fitting
We conducted the initial pass to clean up the data with a custom R code that read in the input airfoil
coordinates, aligned the airfoils, and normalized their chord length to one. The data was split at the leading and trailing
edges to extract the points that form the top and bottom surfaces. Then, a fourth-degree B-spline was fitted separately
to the top and bottom surfaces using knots at 1%, 5%, 25%, 50%, 75%, and 90% of the chord. To account for the large
shape change at the airfoil nose, a third constrained B-spline was fit to the front 2.5% of the chord, requiring the end
points to align with the top and bottom B-spline at 2.5% of the chord. To smooth the predicted data, we performed a
second fit on the predicted nose data, expanding to a constrained B-spline with endpoints at 5% of the chord. An
example of the output from this process can be seen in Fig. 6.
Fig. 6 The airfoils underwent a smoothing process. a) All ten albatross airfoils smoothed, rotated, and scaled.
b) The rotated and scaled raw data points in gray are overlaid with the final B-spline. This airfoil is the 11% span
airfoil on the albatross, specimen WFB-17490.
F. Aerodynamic Analysis (XFOIL)
XFOIL is a computational solver that predicts the aerodynamic characteristics of input airfoils in various
flight conditions for either viscous or inviscid flow conditions [16]. Prior to analysis, our geometry was further
modified in XFOIL to revise the number of panel nodes to avoid sharp angles that could cause separation bubbles
This is a preprint of: Glenn et al., “Analysis of bird wing airfoil aerodynamic efficiency,” AIAA SciTech
2024 Forum. The published article may differ from this preprint.
(locations where the flow separates and reattaches) and further add points to reduce any lingering sharp angles. We
began our set design routine by fixing the number of panel nodes to 500 in the panel editor. Afterward, in the geometry
editor, the maximum panel corner angle was targeted to 10° with five iterations using the arcline spline parameter
over the full length of the airfoil by specifying the interval [-0.1, 1.1], 10% beyond the chordline. This allowed us to
achieve a smoother leading edge while reducing further irregularities throughout the airfoil to increase our likelihood
of convergence.
For our analysis, we estimated the lift, drag, and pitching moment coefficients of our given airfoils under
viscous conditions for a range of angles of attack and a fixed Reynolds number. We varied the angles of attack from
-5 to 10° with a step size of 1° and fixed the Reynolds number to 1.5 x 105. This Reynolds number was selected as it
is a mid-range value used across bird flight; however, it is not necessarily the true flight condition for each species.
Future work should consider a range of Reynolds numbers. To increase the likelihood of convergence in XFOIL, we
used up to 500 iterations in the solver, but convergence is challenging for high angles of attack and complex
geometries. As applicable, un-converged angles were omitted from the analysis. XFOIL returns the airfoil sectional
lift and drag coefficients at each converged condition.
With the outputs from XFOIL, we estimated the aerodynamic efficiency as the maximum lift-to-drag ratio
(maximum Cl/Cd) predicted for each airfoil. This prediction used R to fit a linear model to the coefficient drag with a
quadratic function for the coefficient of lift to all airfoils that converged for a minimum of five angles of attack. We
verified that the linear models were capturing the shape of the XFOIL predictions by verifying that the adjusted R2
value was above 0.75. If the fit was below this threshold, we first would remove the data points above an 8° angle of
attack as approaching stall causes outliers in the theoretically expected quadratic curve. Two airfoils were eliminated
for converging for less than five angles (the yellow-billed magpie at 64% and the scoter at 9%). Ten airfoils still had
low adjusted R2 values due to non-quadratic curves after this adjustment and thus were removed from our analysis
(This includes: three gulls, two turkey vultures, two Laysan albatrosses, one prairie falcon, one scoter, and one red-
shouldered hawk). Future work is required to develop a methodology to evaluate the performance of these unique
avian-derived airfoils. From the extracted quadratic models with an adjusted R2 value over 0.75, we estimated the
maximum lift-to-drag ratio (maximum Cl/Cd), which we refer to within this paper as the aerodynamic efficiency of
the airfoil. The intercept of the model also provides an estimate of the zero-lift drag coefficient (Cd, L=0). In total, we
obtained results for 39 of the 51 airfoils with a converging result across eight species. Note that the prairie falcon
airfoils converged for too few angles of attack to allow a linear model to be fit effectively. The eliminated airfoils will
be explored in detail in future work.
III. Results
To quantify the effect of flight style and airfoil position on key aerodynamic performance variables, we fit
two linear models. Both models had flight style and the position of the airfoil as the dependent variables and the
independent variable was either aerodynamic efficiency or zero-lift drag. We found that the aerodynamic efficiency
of the extracted airfoils increased for airfoils from gliding species, although the effect was not statistically significant
(p-value = 0.1). Airfoils from gliding species were estimated to have an average aerodynamic efficiency of 46.3 and
the flapping species had an average of 38.8 which demonstrates a 19.3% increase in the efficiency of the gliding birds
we tested. Note that the statistical significance of this result was highly sensitive to small changes in our sample size,
suggesting that it will be crucial to increase the number of species and overall airfoils to confirm this result. (Fig. 7a).
We found that the position of the airfoil along the span did not have a significant effect on aerodynamic efficiency (p-
value = 0.90).
Next, we fit the second linear model with zero-lift drag as the independent variable. We found that both flight
style and the airfoil position had an insignificant effect on the zero-lift drag for the extracted airfoils (p-value = 0.87
and 0.23, respectively). The insignificant effect of the airfoil span position on both linear models is contradictory to
our expectation that interior airfoils would be more cambered than tip airfoils. However, this shape change may not
be effectively captured through these two aerodynamic parameters alone.
This is a preprint of: Glenn et al., “Analysis of bird wing airfoil aerodynamic efficiency,” AIAA SciTech
2024 Forum. The published article may differ from this preprint.
Fig. 7 Gliding birds (blue) had an insignificantly higher aerodynamic efficiency than flapping birds (pink).
a) Aerodynamic efficiency of flapping vs. gliding birds. b) The sectional lift and drag coefficients for each airfoil.
Both linear models had low adjusted R2 values (0.0217 for the aerodynamic efficiency model and -0.0134
for the zero-lift drag model), suggesting that span position and flight style alone do not effectively capture all the
variance in the data set. We have a relatively low sample size of species (n=8) compared to the diversity of modern
bird species, which has more than 10,000 species. Therefore, caution should be applied when extrapolating these
results to species outside the current data set, though our selected species do broadly span the avian phylogeny.
Fig. 8 Drag polar of top-performing bird and engineered airfoils.
The top two performing airfoils resulted from the red-shouldered hawk between 36 and 45% of its wingspan
and the third highest performer came from the turkey vulture at 45% of its wingspan. The estimated maximum Cl/Cd
values are in the corresponding descending order: 78.8, 64.5, and 60.9 at the investigated Reynolds number of 1.5×105.
The highest aerodynamic efficiency from a flapping bird was 53.5, preceded by 10 gliding birds, for the band-tailed
This is a preprint of: Glenn et al., “Analysis of bird wing airfoil aerodynamic efficiency,” AIAA SciTech
2024 Forum. The published article may differ from this preprint.
pigeon at approximately 45% of the span. These avian results can be contrasted with engineered airfoils such as the
NACA 4415 used on the Shadow-200 UAV [16], which has a maximum Cl/Cd of 62.4 at the investigated Reynolds
number of 1.5×105. The high-lift airfoil, S1223 [17], exhibits similar flight characteristics intermediate to the two
highest-performing hawk airfoils, with a maximum Cl/Cd of 71.9 at the Reynolds number of 1.5×105. Furthermore,
when we compare the top hawk airfoil with an efficient low-speed airfoil suggested by Shunsun and Zhen, we can see
the engineered FX63-137 [16] achieves a higher lift-to-drag ratio of 76.2 at a Reynolds number of 1.5×105. Note that
the top-performing hawk airfoil outperforms all three of these airfoils at the equivalent Reynolds number. Therefore,
the top avian airfoils show promise as a template for novel UAV airfoil design, as we are already seeing a higher
aerodynamic efficiency than top-performing engineered airfoils at the the Reynolds number of 1.5×105. Additionally,
the geometry has not yet undergone any additional streamlining to optimize performance, showing promise for an
even higher aerodynamic efficiency with future work.
IV. Limitations
Several potential sources of error should be addressed before this method is used in future studies. First, the
factory resolution of the POP2 scanner is 0.05 mm. However, bird feathers present a unique challenge to 3D scanning
technology. We expect there will be small variations in the quantified airfoil coordinates due to the accuracy of the
3D scanner and because the leading edge is covered in small, easily deformed feathers (known as coverts). Our method
of scanning bird airfoils and generating models is being developed to be both efficient and highly accurate. As
translucent, dark objects with a near-zero thickness along some edges, they can be extremely challenging for the
scanner to resolve at given angles. As a result, the trailing edge thickness of some wings may have been overpredicted
in the airfoils in this study.
A major limitation of this methodology is our inability to scan wings in motion. Our 3D scanner requires
complete stability to produce an accurate scan, so out of necessity, we have scanned preserved wings in a series of
standardized positions. However, these taxidermy standards do not necessarily conform to the wing configurations
used by living birds. Because birds can morph their wing shapes during flight, the airfoil shape data collected in this
research cannot capture the variety of airfoils used in flight. In addition, our scans were conducted at atmospheric
pressure in a still room with no significant airflow. Bird wings are not rigid, and in normal flight, we expect the
feathers to deform under aerodynamic loading [18], which could lead to different morphology and aerodynamic
characteristics. Additionally, the aerodynamic analysis software we used, XFOIL, comes with its own limitations.
Foremost, it has a limited ability to model complex shapes and restricts us to a 2D analysis, which ignores the 3D
effects of flight. Furthermore, our work is limited to a steady analysis, which is appropriate for gliding flight, but it
challenges our ability to extend this analysis to flapping flight conditions. In future work, we could investigate the
implementation of unsteady panel codes. As we continue our study, we intend to compile an open-source database of
airfoils from a large selection of bird species and individuals. This work uses a broad grouping for gliding flight,
where both gliding and soaring species have been included in the same group. Future work should investigate the
specific role of these different modes of bird flight. This will allow us to expand our knowledge of how biological
attributes can be used in aircraft design and will allow for direct comparison to engineered airfoils.
V. Conclusions
In this study, we scanned multiple prepared bird wing specimens and adapted a 3D printer slicing algorithm
to extract airfoils along the length of their wings. We focused on species that are known to primarily flap and those
that primarily glide to determine if there were functional differences between the airfoils used within these flight
styles. Using XFOIL to analyze the smoothed airfoil shapes revealed that gliding birds employed airfoils that tended
to have a higher aerodynamic efficiency than flapping species, although the effect was not statistically significant.
Future work is required to expand on and confirm this result, as it was sensitive to the sample size. However, we found
that the top-performing airfoils in this study performed at a similar level, if not higher, than engineered airfoils used
This is a preprint of: Glenn et al., “Analysis of bird wing airfoil aerodynamic efficiency,” AIAA SciTech
2024 Forum. The published article may differ from this preprint.
on modern UAVs, suggesting that future UAVs could benefit from exploring the use of avian-inspired airfoils in low-
speed conditions.
VI. Acknowledgments
The authors would like to thank the Museum of Wildlife and Fish Biology’s Collections Manager, Irene Engilis, for
her support, use of specimens, and contributions to the project. Thank you to Kiran Weston, Kaleb B. Bordner, and
other members of the BIRD lab for their helpful discussions and input on the manuscript.
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This is a preprint of: Glenn et al., “Analysis of bird wing airfoil aerodynamic efficiency,” AIAA SciTech
2024 Forum. The published article may differ from this preprint.
Appendix
Table 1. Wing measurements.
Species
ID
Longest
Primary
(mm)
Shoulder to
Longest
Primary (mm)
Shoulder
Chord Length
(mm)
Wrist Chord
Length
(mm)
Shoulder to
Wrist
(mm)
Turkey Vulture
Cathartes aura
WFB-7375
500
672
283
295
177
EM-20
468
663
250
285
192
Red-Shouldered Hawk
Buteo jamaicensis
WFB-8469
332
389
175
220
125
Laysan Albatross
Phoebastria immutabilis
WFB-17490
509
749
171
154
245
WFB-13973
516
744
162
159
240
Western Gull
Larus occidentalis
FAV016
432
575
198
189
155
JC-07
406
545
181
179
147
Band-tailed Pigeon
Patagioenas fasciata
WFB-13607
214
277
115
133
77
Yellow-billed magpie
Pica nuttalli
WFB-9793
187
230
118
130
65
WFB-6155
199
236
140
140
55
Black Scoter
Melanitta americana
WFB-15829
222
295
102
114
73
WFB-15865
214
262
130
111
68
WFB-15836
213
275
138
109
59
Red-tailed Hawk
Buteo jamaicensis
WFB-6901
402
490
195
235
155
