A large number of bat fatalities have been reported in
wind energy facilities in different regions globally. Wind farm operators
are required to monitor bat fatalities by conducting carcass surveys at wind
farms. A previous study implemented the ballistics model to characterize the
carcass fall zone distributions after a bat is struck by turbine blades. The ballistics
model considers the aerodynamic drag force term, which is dependent upon
the carcass drag coefficient. The bat carcass drag coefficient is highly
uncertain; no measurement of it is available. This paper
introduces a methodology for bat carcass drag coefficient estimation. Field
investigation at Macksburg wind farm resulted in the discovery of three bat
species: the hoary bat (

Carbon emissions and subsequent climate change have motivated nations across
the globe to develop energy sources and alternatives to fossil fuels, including
wind energy. As a result, global wind energy production is continuously
increasing with an average growth rate of 25 % yr

Several studies have applied different methods to estimate the number of
bats killed at wind energy facilities in the United States. Using model and survey data, Kunz et al. (2007) estimated there to be
33 000–111 000 annual bat fatalities at wind energy facilities.
Cryan (2011) estimated annual bat fatalities to be 450 000 in North America
based on a bat fatality rate of 11.60 bats MW

The USFWS requires wind farm operators to perform carcass surveys within a specified radius around wind turbines to estimate bat take. However, guidance for the prescribed search radius around turbines is based on limited data. This could result in surveys conducted where bats are unlikely to be found, or limited search areas could cause bat carcasses that land outside the survey area to be missed. Turbine operators need a reliable method to guide survey efforts and determine the appropriate extent of surveys, targeting only areas where bat carcasses are likely to be found around the turbines. A technically defensible survey is critical to help operators determine whether wind turbines adversely affect listed species and to evaluate project impacts.

Figure 1 shows a schematic of the three-blade horizontal axis turbine with associated components including the tower, hub, rotor blades, and rotor-swept area. The vertical distance from the ground to the turbine hub is called the hub height. In Fig. 1, three rotor blades are denoted in gray and the dotted red periphery indicates the rotor-swept area.

Schematic of the typical utility-scale, three-blade, horizontal axis wind turbine.

Only a few studies, including Arnett (2005) and Smallwood and Thelander (2005), have estimated the fall zone for birds and bats to guide carcass search area. Osborn et al. (2000) quantified the search area by dropping carcasses from the nacelle and the upper and lower bounds of the rotor-swept area on days with brisk wind. However, this method did not consider the effect of impact with rotating blades on the carcass fall trajectory. Gauthreaux (1996) suggested that the search area should be circular, with a minimum radius proportional to the height of the turbine. He suggested the search area to be within 70 m of a wind turbine. Thelander and Rugge (2000) found the average fall distance of birds to be 20.20 m, with 75 % of birds falling less than 30 m away from the tower. It is not clear whether some of these studies have bias in search radius estimates due to insufficient search zones. Smallwood (2007) mentioned that an inadequate search radius could cause bias in the carcass survey data.

Huso and Dalthorp (2014) proposed polynomial logistic regression models of relative carcass density as a function of distance from the nearest turbine. The study considered the carcass search locations at several turbine sites in Philadelphia: 15 turbines at Locust Ridge in 2010 and 22 and 15 turbines at Casselman in 2008 and 2011, respectively. The best-fit logistic model of carcass densities was found to be cubic for Casselman and linear for Locust Ridge. This study limited the search area for bat carcasses to 80 m. If the bat carcasses landed beyond the 80 m distance, the surveyor missed those bat carcasses.

Additionally, investigators have applied physics-based models for estimating the trajectory of objects thrown from turbine blades, including ice fragments and parts of broken blades. Biswas et al. (2011) used a ballistics model to estimate the trajectories and landing zones of ice fragments thrown from wind turbine blades. They considered a turbine with 45 m long blades and a hub height of 100 m and found ice fragments could travel up to 350 m from the base of the turbine. Sarlak and Sørensen (2015) investigated the trajectories of thrown objects from a 2.3 MW horizontal axis wind turbine upon blade failure. They found that under normal operating conditions, the blade fragments can land between 100 and 500 m, depending on their size. Both studies solved the equations describing the physics of ballistics using the fourth-order Runge–Kutta (RK4) numerical scheme.

Hull and Muir (2010) (referred to as HM10) utilized ballistics theory to
propose a model to estimate the fall zone of different-sized bird and bat
carcasses struck by different-sized turbines. The two-dimensional (2-D) ballistics model describes the trajectory of bat carcasses within the
rotor plane by relating the variation in fall velocity to the net resultant
forces on a carcass, which include gravitational and aerodynamic drag
forces. HM10 also employed the RK4 method to numerically integrate the
ballistics model and determine the position and velocity of the carcass
relative to the turbine base at each time step. They assumed bats are
incapacitated after being struck by a blade and therefore unable to affect their fall
trajectory. They also assumed carcasses would be stationary in the rotor
plane before being hit by the blade and therefore did not account for any
initial precollision velocity. They also assumed calm conditions with no
turbulence, resulting in no wind drift effects on the carcasses' fall
trajectory, and they assumed an equal likelihood of strike anywhere in the
rotor-swept area. They modeled a carcass as a tumbling object, allowing
the projected area and drag coefficient (

Given the lack of available measurements of

The following sections are organized as follows: the experimental
methodology presents the research design for estimation of the carcass drag
coefficient, the description of the ballistics model, the experimental setup,
data acquisition, limitations of the measured data, and the

The following methodology was employed to determine drag coefficients for
bat carcasses:

Collect fresh bat carcasses representing a range of species, and perform carcass drop experiments to acquire the time vs. position data during each fall.

Evaluate whether the carcasses attain terminal velocity during the fall. If a carcass attains terminal velocity, calculate the drag coefficient by equating the drag force to the carcass weight.

If carcasses do not attain terminal velocity, estimate the carcass drag coefficient by fitting the ballistics model to the measured velocity.

Motion of falling bodies can be described physically based on projectile and
ballistics models. The projectile motion of an inertial particle only
considers the influence of gravity on the fall trajectory and neglects
aerodynamic drag. An analytical solution of projectile motion can easily be
obtained and applied to evaluate trajectories. However, drag can
significantly alter the particle trajectory, and therefore, a more realistic
description of motion follows the ballistics model, which incorporates the
quadratic drag model to account for the effect of fluid resistance. A
simplified, 2-D version of the ballistics model was employed by HM10,
solving the following set of equations describing the ballistics motion for
velocity and acceleration of a bat carcass:

Figure 2a represents the time vs. velocity plot obtained from the
analytical solution of the ballistics model (Eq. 3) by considering the
mean values of

A common approach for measuring the drag coefficient of an object is to drop
the object, allow it to achieve terminal velocity, and then obtain the
result by balancing drag force with gravitational force. Figure 2b shows
the velocity variation with position for the initial drop height (

The ballistics model would be useful for guiding carcass surveys if it can
accurately predict carcass fall trajectories. This can only be done if the
aerodynamics of the carcasses are known. Given the lack of available

Illustration of the simplified geometric representation of bats for the ballistics model. The image (WEST, Inc., 2016) is of a northern long-eared myotis.

Firstly, the irregularly shaped carcass was approximated as an ellipsoid
(Fig. 3). The symbols

Table 1 lists the mass, body dimensions, equivalent diameter, and projected area of bat carcasses discovered on the day of the experiments. The range of bat carcass mass and size is represented by a large, medium, and small bat. The hoary bat was the largest with, a significantly larger mass and area than the others, whereas the evening bat was the lightest and smallest bat.

Physical properties of freshly discovered bat carcasses.

Composite image illustrating an example carcass drop experiment (drop test 1 for the hoary bat).

Figure 4 shows an annotated composite image of the bat carcass drop
experiment, showing a carcass at four instances. Freshly collected carcasses were dropped in front of a 6.30 m high wall on the leeward side
of a building to achieve approximately quiescent or no wind conditions. For
each species, two experiments were performed and recorded using a high-speed camera to extract the time series of carcass position. The wall was
marked using horizontal strips of tape over a total distance of 4.50 m. A
schematic of the side view of the experimental setup is shown in Fig. 5.
The figure includes an illustration of various experiment components, including
the location of the wall with markings, the location of the camera and its
field of view, and the position of the dropping platform. The carcass drop
tests were performed from a dropping platform located 1 m in front of the
wall (

Schematic of the side view of the carcass drop experimental setup.

The images obtained from the high-speed video recording were used to
determine the vertical position (

The time vs. position data obtained from high-speed imaging were used to
calculate the fall velocity (

Measurements and modeled time vs. fall velocity for drop test 1 of the hoary bat.

Drag coefficient computed from the terminal velocity assumption.

Next, we compare the

The analysis of the high-speed video of the carcass drop
experiments showed that horizontal carcasses movement is negligible except
for in the case of the evening bat carcass, which experienced oscillating lateral
translation with an amplitude on the order of 10 cm, or about 2.5
body lengths. Based on our observations, carcasses are assumed to
fall along the vertical line at a distance

Mann et al. (1999) and Ott and Mann (2000) proposed a refined methodology for determining the position of the particles occupying more than 1 pixel in the image, similar to the bat carcasses in the present study. This procedure demonstrated position estimation of particles in images with enhanced precision of 0.10–0.02 pixels by fitting a Gaussian function to the particle image based on grayscale intensity. This analysis methodology is recommended for high-precision position measurements from images. This approach was demonstrated for images of the first hoary bat drop experiment. The carcass position measurements obtained from the refined methodology were found to be similar to the measurements from the carcass' top and bottom pixel coordinates, with the difference being of the order of 1.50 pixels. The detailed procedure and results of fitting the Gaussian distribution to pixel coordinate and intensity measurements of the first hoary bat drop experiment images are presented in the Supplement.

The ballistics model defined by Eq. (1) is an initial value problem, where
the initial condition for position (

The proposed

Optimal filtering window, initial position, drag coefficient, and terminal velocity.

Comparison of position

The accuracy of optimal

The sensitivity of

Drag coefficient sensitivity with respect to initial position.

It is evident that for the hoary and eastern red bat, even a small error of
1 % in initial drop position can cause 6 %–14 % difference in

The range of

Sampled range of drag coefficients and terminal velocities for three species of bat carcasses.

Carcass fall distributions for

The sensitivity of bat fall zone distributions in the rotor plane
(according to the modeling approach of HM10) was tested with respect to carcass mass and
its drag coefficient. The hoary and evening bat were selected for
this exercise because they are the heaviest and lightest bats, respectively.
Figure 9 shows fall zone distributions for the hoary bat (upper row) and evening
bat (lower row) for the highest and lowest values of

It is evident from Fig. 9 that for the same mass (represented by species),
the maximum in-plane fall distance (

The goal of this research was to make the first measurements of the drag
coefficient of bat carcasses. This data will allow for robust modeling of
carcass fall distributions around wind turbines to guide carcass surveys.
Fresh bat carcasses (hoary bat, eastern red bat, and evening bat) were
discovered at the Macksburg wind farm, and carcass drop experiments were
performed. Carcass fall trajectories were measured with high-speed video.
Due to the complex fall dynamics of carcasses and limited drop height, the
irregularly shaped carcasses did not reach terminal velocity. Therefore,

The range of the maximum fall zone for the hoary bat (heaviest) and evening
bat (lightest) was investigated with a ballistics model, and the
sensitivity of the bat carcass fall zone distributions based on the measured
carcass mass and range of drag coefficient was determined. The hoary bat,
assuming the smallest

The ballistics model framework proposed by HM10 generates a 1-D carcass fall zone distribution in the reference frame of the wind turbine rotor. In the future, the modeling framework can be extended by incorporating meteorological conditions such as wind speed and direction, resulting in a 2-D fall zone distribution to provide more realistic representation of the distribution of carcasses falling around the base of the turbine. The resulting distributions would provide useful information that can be compared to the carcass surveys to validate the ballistics model and guide search efforts. The model can also be used to generate results useful for correcting survey data for limited or unsearched areas, for example when carcass surveys are conducted only on highly visible gravel surfaces of access roads and turbine pads.

Data and code can be made available upon request from the corresponding author.

The supplement related to this article is available online at:

SP conducted the study as part of his doctoral research supervised by CDM. CDM conceptualized the research and acquired financial support and access to the equipment and facilities. SP conducted data analysis and produced final results, figures, and the original draft of this paper. SP and CDM collected the data, interpreted the analysis results, and reviewed and revised the final version of the manuscript.

The authors declare that they have no conflict of interest. The funders had no role in the study design, analysis of the data, decision to publish, or preparation of the manuscript.

The study was conducted with financial support from MidAmerican Energy Company (MEC) and with input from scientists at the United States Fish & Wildlife Service (USFWS) in support of the development of a Habitat Conservation Plan for wind energy facilities in Iowa. The authors are grateful to Jesse Leckband, Senior Environmental Analyst at MEC, for providing access to the wind farm facility and for procuring fresh bat carcasses for the experiments. We also thank Pablo Carrica, PhD, Professor of Mechanical Engineering and Research Engineer at IIHR – Hydroscience & Engineering, for help in collecting the data.

This research has been supported by the MidAmerican Energy Company.

This paper was edited by Jakob Mann and reviewed by Jakob Mann and one anonymous referee.