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Drone flight data reveal energy and greenhouse gas emissions savings for small package delivery

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Abstract

The adoption of Uncrewed Aerial Vehicles (UAVs) for last-mile deliveries will affect the energy productivity of package delivery and require new methods to understand the associated energy consumption and greenhouse gas (GHG) emissions. Here we combine empirical testing of 187 quadcopter flights with first principles analysis to develop a usable energy model for drone package delivery. We develop a machine-learning algorithm to assess energy use across three different flight regimes: takeoff, cruise, and landing. Our model shows that, in the US, a small electric quadcopter drone with a payload of 1 kg would consume approximately 0.05 MJ/km and result in 41 g of CO$_{2}$e per package. The energy per package delivered by drones (0.19 MJ/package) can be up to 96\% lower than conventional transportation modes. Our open model and generalizable coefficients can assist stakeholders in understanding and improving the energy use of drone package delivery.
Drone flight data reveal energy and greenhouse gas emissions savings
for small package delivery
Thiago A. Rodrigues1,2
, Jay Patrikar3
, Natalia L. Oliveira4,5
,
H. Scott Matthews1
, Sebastian Scherer3
, Constantine Samaras 1, 2
Summary
The adoption of Uncrewed Aerial Vehicles (UAVs) for last-mile deliveries will affect the energy produc-
tivity of package delivery and require new methods to understand the associated energy consumption and
greenhouse gas (GHG) emissions. Here we combine empirical testing of 187 quadcopter flights with first
principles analysis to develop a usable energy model for drone package delivery. We develop a machine
learning algorithm to assess energy use across three different flight regimes: takeoff, cruise, and landing.
Our model shows that, in the US, a small electric quadcopter drone with a payload of 1 kg would consume
approximately 0.05 MJ/km and result in 41 g of CO2e per package. The energy per package delivered
by drones (0.19 MJ/package) can be up to 96% lower than conventional transportation modes. Our open
model and generalizable coefficients can assist stakeholders in understanding and improving the energy use
of drone package delivery.
Key words: quad-copter drone, last-mile delivery, energy consumption, greenhouse gas emissions, robot
delivery, autonomous delivery.
1 Introduction
Achieving large improvements in the energy productivity of the freight transportation sector is challenging,
especially in the overwhelmingly petroleum-powered transport sector where medium and heavy trucks in the
US comprises 24% of transportation energy use. This sector is responsible for 37% of transportation-related
greenhouse gas (GHG) emissions while light-duty vehicles comprise 57% of transportation GHG emissions and
64% of transportation energy use. In addition, transportation remains a large source of nitrogen oxides (NOx)
and other air pollutants [1]. However, the way that consumers are obtaining goods in the U.S. is changing
rapidly [2].
Even before COVID-19, the growing demand for fast, contactless deliveries has been driving firms to experi-
ment with automated package delivery vehicles, such as Uncrewed Aerial Vehicles (UAVs) that can avoid traffic
in urban centers and rapidly reach rural areas that would not be served otherwise [3, 4]. Initial survey data of
483 customers in Portland, Oregon by Pani et al. [5] show that COVID-19 is contributing to an environment
where more than 60% of online customers are willing to pay extra to receive their packages using autonomous
delivery robots. Nevertheless, along with technology and policy challenges, increasing shipping costs is one of
the main limitation for the adoption of autonomous delivery vehicles [6].
The appeal of delivery robots also reflects new physical distancing demands to avoid the spread of coronavirus
in product deliveries [7]. As autonomous delivery technologies advance, new companies emerge to compete for
this market niche [8, 9, 10, 11, 12]. At the same time, alternative transport modes, such as electric cargo
bicycles, are becoming cost-effective alternatives to delivery trucks for short-distance deliveries [13], drastically
reducing the CO2emissions of last-mile delivery in highly dense metropolitan areas [14]. With the increased
electrification of delivery vehicles, the energy consumption and environmental impacts of the transportation
sector are expected to change drastically over the coming years [15, 16], and both technology and demand
are primary drivers. Widespread adoption of UAVs to replace a portion of first/last-mile truck pickups and
deliveries could reshape this sector by changing demand patterns and shifting fuel demands from fossil fuels to
electricity. Autonomous Delivery Robots are coming to the transportation sector, but how these vehicles and
systems could be designed to maximize energy productivity is less clear.
1Department of Civil and Environmental Engineering. Carnegie Mellon University. 5000 Forbes Avenue, Pittsburgh, 15213,
PA USA
2Corresponding authors: tarodrig@andrew.cmu.edu and csamaras@cmu.edu
3Robotics Institute, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, 15213, USA
4Department of Statistics and Data Science, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, 15213, USA
5Machine Learning Department, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, 15213, USA
1
arXiv:2111.11463v1 [eess.SY] 22 Nov 2021
So far, a few studies have estimated the energy consumption of quadcopter vehicles and the energy esti-
mations vary considerably among the different methods used [17]. Some studies have created models based on
theoretical principles [18, 19, 20, 21, 22, 23, 24, 25, 26], while others have developed models based on regression
models built on small flight samples [20, 27, 28, 24]. Finally, a comparison of the energy consumption and
greenhouse gas (GHG) emissions between package delivery UAVs and different transportation modes have been
estimated by a few studies [23, 29, 30, 31], but alternative emerging delivery modes, such as electric cargo
bicycles are not included.
Here we help stakeholders and researchers understand the energy use of uncrewed aerial package delivery
drones. We provide an energy model based on extensive empirical data from 187 flights of a quadcopter
drone DJI Matrice 100, from which we developed a novel and high-resolution dataset [32] of package delivery
drone energy use. We also develop an algorithm that automatically identifies the flight regime across takeoff,
cruise and landing. We show the impact of the cruise speed and payload mass on the drone’s range, provide
generalizable energy use coefficients, and we compare the energy consumption and GHG emissions of a small
quadcotper drone to other last-mile transportation modes on a energy per package basis.
2 Results and Discussion
We collected data on 187 flights to assess the power profile of a package delivery drone given a set of operational
parameters (payload, altitude, and speed during cruise). The data, available at [32], and a data descriptor [33],
provide the details of the experiment. In addition, we have developed an algorithm that separates the data into
three different flight regimes: takeoff, cruise, and landing, in order to better understand the energy consumption
profile during flight, see Supplementary Figures S1 to S4.
Then, we conducted a first principles analysis and developed a model to estimate the energy required to
power a quadcopter. Each of the flight regimes were modeled separately, that is, each energy model was treated
as a model class and three different optimal models from that class were selected, one per regime. In order to
fairly compare the model classes’ performance and avoid overfitting, we split the data into train and test folds
following a stratification strategy by flight ID number. With 120 flights, the training fold was used to estimate
the parameters of each model, which were then applied to the remaining 67 flights from the test fold in order
to evaluate the performance of the energy models on unseen data.
2.1 Energy Model
Our energy (E) model uses the Induced Power (Pi), which is the power required to overcome gravity in a
hover-no-wind situation, as a parameter estimator of the average power observed throughout the flight.
E= (b1Pi+b0)t(1)
where, tis the flight duration, and b1and b0are coefficients that linearly correlate Piand the average power
throughout the flight. The induced power, used in eq. 1, is calculated as
Pi=(mg)1.5
2ρA (2)
where, mis the total mass of the drone (including the payload), gis the acceleration of gravity, ρis the air
density, and Ais the total area under the propellers.
The estimated coefficients and their standard errors are shown in Table 1.
Table 1: Estimated coefficient ±bootstrap standard error
Coef. Take off Cruise Landing
b11.97 ±0.08 1.69 ±0.06 1.62 ±0.14
b013.8 ±0.01 16.8 ±0.01 -4.7 ±0.01
The coefficients shown in Table 1 were obtained by performing a linear regression between Piand the average
power observed throughout each of the 120 flights. The results were then applied to the remaining flights and
the absolute relative error was 3% on average, proving the accuracy of the energy model in terms of estimation
of energy consumption.
With the energy model validated, we estimated the energy consumption of a package delivered by a small
quadcopter drone. Figure 1a shows the total Energy Consumption for a two-way delivery trip (delivery and
return) according to the delivery distance and the total weight of the drone (with payload) operating at a cruise
speed of 4 and 12 m/s and altitude of 100 m. Our analysis also shows that variations in the cruise speed have
2
great impact on the total energy consumption per trip and consequently range of the drone (Figure 1a). The
total time of flight is reduced as the speed increases, which results in longer distances for the same amount of
energy. In addition, we calculated the GHG emissions per package delivered based on the US electricity grid,
upstream electricity generation, and battery life-cycle emissions according to the delivery distance (Figure 1b)
Figure 1: (a) Total energy consumption by distance of delivery varying payload mass and cruise speed. (b)
CO2e emissions according to the delivery distance varying according grid emission factor and battery life cycle
emissions. The total energy and CO2e correspond to takeoff, cruise from the origin to destination and landing
loaded, and takeoff, cruise from destination to origin and landing empty. As an energy limitation, the nominal
capacity of LiPO TB48D battery is 130 Wh [34]. Altitude during cruise of 100 m, takeoff speed 2.5 m/s and
landing speed 2 m/s.
2.2 Comparison between different transportation modes
We compared the energy consumption of quadcopter drones against diesel and electric medium-duty trucks and
small vans, and electric cargo bicycles.
Figure 2: Energy Consumption for different transportation modes. Error bars represent variations in (a) driving
styles and vehicle characteristics, and (b) number of packages delivered per distance.
Total energy consumption per distance of small quadcopter drones is among the lowest across transportation
modes, as the vehicle is small, light, and has lower payload capacity (Figure 2a). However Figure 2b shows
the energy consumption per package of drone-equivalent deliveries, i.e., assuming that all packages delivered
by the other modes are within the payload and space capacity of a small quadcopter drone [35]. On an energy
consumption per package basis, small quadcopter drones are also among the most efficient methods of delivery.
The number of stops per kilometer and the number of packages delivered per stop varies according to the
transportation mode and delivery density (highly dense areas are more likely to have more stops and packages
delivered per kilometer).
Similarly, an analysis of the greenhouse gas (GHG) emissions of the fuel of each transportation mode
shows that quadcopter drones are among the most efficient vehicles in grams of CO2e per km (Figure 3a)
and a competitive alternative in terms of GHG emissions per package (Figure 3b). On the other hand, it is
important to note that small drones are considerably limited in terms of weight and volume of the packages
transported. Therefore, an analysis of the energy consumption and GHG emissions on a per metric ton-km
basis (Supplementary Figure S5) shows that small drones are the most energy-intensive vehicles. Also, local
airspace regulations that require longer delivery routes, not considered in this study, can potentially increase
the energy consumption and GHG emissions of drones [36]. Finally, alternative methods, such as the concept
3
of mobile warehouses [37] can be an effective alternative to incorporate drones and mitigate current limitations
by combining drones and delivery trucks.
Figure 3: Greenhouse gas (GHG) emissions for different transportation modes. Error bars represent uncertain-
ties due to variations on fuel carbon intensity, battery life cycle emissions, and number of packages delivered
per distance.
We compared our results to values provided by the United Parcel Service, Inc. (UPS). In 2019, UPS
reported the energy intensity for U.S. Domestic Package operations was 28 MJ/package, from which ground
vehicles represented approximately 9.5 MJ/Package or 34% (airline fuel, facility heating fuel and indirect energy
correspond to 60%, 3% and 3%, respectively), with GHG emissions (CO2e) intensity of 1 kg/package [38]. It is
important to note that these values encompass the entire ground fleet, rather than only last mile delivery.
We estimate a small quadcopter drone, with a payload of 1 kg operating at a cruise speed of 12 m/s and
cruise altitude of 100 m, consumes approximately 0.05 MJ/km and is generates 41 g of CO2e per package when
charged on average U.S. electricity. Our energy model has simple, generalizable, and accurate coefficients that
can provide stakeholders and researchers an energy consumption estimation for speed ranges below 12 m/s.
However, at greater speeds or using drones with more surface area, a more comprehensive energy profile method
could provide more accurate predictions.
The energy consumption of small quadcopter drones is comparable to the most energy efficient modes of
last-delivery when the total mass of delivery is not the main feature considered. For example, in delivery
situations where small and light items with high added value, such as small electronics and medicines, drones
might became a competitive tool to reduce transportation emissions in large urban centers [39]. In these
scenarios, we found that drones can reduce the energy consumption by 96% and 60% and GHG emissions by
91% and 59% per package delivered by replacing diesel trucks and electric vans, respectively. We also found
that the delivery intensity, i.e. the number of packages delivered per km, and the fuel carbon intensity are the
main factors contributing to the drone’s energy and environmental performances. It is also important to note
that the drone used to collect the data was not optimized to minimize energy consumption, which could further
improve the its efficiency.
3 Methods
3.1 Experiment
We performed a series of flights to empirically measure the energy consumption of a quadcopter UAV. An
experimental protocol was created and followed to ensure a reliable approach for data acquisition [33].
A DJI®Matrice 100 (M100) quadcopter was equipped with an anemometer, current and voltage monitor,
GPS, and accelerometer collecting data on wind speed and direction, battery current and voltage demand,
and position, orientation, velocity and acceleration. The flights were performed in a pre-established route
with varying altitude (25 m, 50 m, 75 m and 100 m), speed (4 m/s, 6 m/s, 8 m/s, 10 m/s and 12 m/s) and
payload mass (no payload, 250g and 500g). Each combination was repeated at least three times, totaling 187
flights. The data provided by each sensor were synchronized to a frequency of approximately 5Hz using the
ApproximateTime [40] message filter policy of Robot Operating System (ROS).
For a better understanding of the energy consumption profile of each flight we created an algorithm to
automatically divide the data into three different flight regimes: takeoff, cruise, and landing (see Supplementary
Figures S1 to S4).
3.2 First Principles Analysis
The energy required to power a UAV can be estimated using a first principle analysis based on helicopter
aerodynamics [41]. First, we defined the working coordinate frames for a quadcopter drone (see Supplementary
4
Figures S6 to S8). Then, the we assessed the power required to maintain the drone at a steady hover condition.
Finally, we expanded the power analysis to include other power demands.
The main power demand of a drone is in the form of induced power (Pi). The induced power represents the
power required to overcome the force of gravity in order to keep the aircraft in the air, and it can vary according
to the flight maneuver [41]. The most basic way to estimate Piis considering a hover condition without wind
(Figure 4).
Figure 4: Hover condition without wind.
In that case, the thrust (T) equals the only force acting on the drone, its weight (W=mg) [41], and Pican
be estimated as
Pi=T vi(3)
where viis the induced velocity.
During hover, vican be simplified as
vi=sT
2ρA (4)
where ρis the air density and Ais the total area covered by the all four propellers.
Combining Eq. 4 and 3
Pi=(T)3/2
2ρA =(mg)1.5
2ρA (5)
where mis the total mass of the drone, gis the gravitational acceleration.
More details of the first principles analysis and an expanded first-principles energy model is available in the
supplementary information (see supplementary Figures S9 to S11).
3.3 Energy Model
Our energy model inquires how effectively Pican be used as an estimator for the energy consumed during a
package delivery flight. In such a case, the average power ( ¯
P) throughout the flight is modeled as a linear
regression of the induced power ¯
P=b1Pi+b0(6)
where b1and b0are the slope and intercept of the linear regression, respectively.
Eq. 6 is expanded to account for the sum of the three flight regimes (Figure 5) and the total energy
consumption (E) is estimated as
E=X
r∈R, l∈L
(b(r, l)
1P(l)
i+b(r, l)
0)t(r, l)(7)
for R={takeof f, cruise, landing }and L={loaded, unloaded}.
5
Figure 5: Linear regression of flights separated by flight regime.
3.4 Machine Learning Approach
However, evaluating if the model’s performance is good given the available measurements cannot be inferred
from its performance alone. Therefore, we compare the predictive power of the energy model to a flexible
nonlinear algorithm [42], XGBoost, available in the programming environment R. This boosted tree algorithm
prioritizes predictive power against interpretability, and it is appropriate for predictive performance given the
available features. If our energy model presents similar accuracy to XGBoost, it indicates that the parametric
and functional restrictions we have made for the energy model development are suitable.
We fitted a gradient boosted tree algorithm, XBGoost [42]. The algorithm was separately trained for each
flight regime with a quadratic loss function and for all regimes, we used 75% as a subsample ratio of both
features and observations for each tree. For hyperparameter tuning, we varied learning rate, maximum tree
depth, and regularization parameter γin a grid search approach. 5-fold CV was used for error estimation; for
tuning only, we compared Absolute Relative Error (ARE, Equation 8) instead of quadratic error. After tuning,
the model was trained with the optimal hyperparameters on the entire training set and AREs were computed
for the flights on the test set.
Standard errors To obtain standard errors of the estimated coefficients, we used a nonparametric bootstrap
approach [43]. 1000 bootstrap replications were used to resample with replacement the 120 training flights,
and the two energy models for the three flight regimes were refitted for each bootstrap sample. At the end,
standard error of the coefficients were obtained from their sampling distribution.
Model predictive power To evaluate the model’s predictive power, the regime-specific fitted models were
then applied to the testing flights of the test set and were compared by Absolute Relative Error (ARE), computed
at flight resolution. That is, for each flight from the test set, we computed their Emeasured integrating power
over time, and the Em
estimated as the sum of the integral of the estimated power over time for the three flight
regimes via method m:
ARE(m) =
Emeasured Em
estimated
Emeasured
(8)
for m∈ {Energy Model,XBGoost}.
3.5 Drone’s range
Our analysis also shows the impact of varying operational parameters (speed, altitude and payload) on the
range of the drone. The two-way drone range (d) can be calculated considering the cruise speed
E=X(b1Pi+b0)t=XEtakeof f +XElanding +X(b1Pi+b0)d
Vcr
(9)
Expanding for a two-way trip and solving for d
d=hEmax El
takeof f +Eu
takeof f +El
landing +Eu
landingiVcr
b1Pl
i+Pu
i+ 2b0
(10)
6
where, Emax is the energy available in the battery; Etakeof f and Elanding are the energy consumed during
takeoff and landing for delivery (loaded = l) and returning (unloaded = u), respectively; Piis the induced
power, calculated using Eq. 5, for delivery (loaded = l) and return (unloaded = u); b1and b0the coefficients
from Table 1 for cruise and Vcr is the average inertial cruise speed.
The energy during takeoff and landing can be calculated as
E= (b1Pi+b0)h
V(11)
where h is the cruise altitude, V is the average speed during takeoff and landing.
For instance, a small quadcopter operating at Vcr = 12 m/s, payload = 1000 g, h = 100 m, takeoff average
speed (Vtk ) = 2.5 m/s, landing average speed Vld = 2.0 m/s has a range of approximately 11 km (5.7 km of
delivery range), consuming approximately 120 Wh (per round trip delivery). Therefore, a quadcopter drone
flying under these conditions would consume approximately 0.039 MJ/km, not considering charging and trans-
mission losses. The energy consumption during takeoff and landing for this trip corresponds to approximately
17% of the total energy consumption (19.4 Wh per trip). This share of energy could be reduced by 95% in a
5-m takeoff (from 19.4 to Y 0.97 Wh per trip), which could be achieved, for instance, if the drone would depart
from the top of a building. This would reduce total trip energy by 15% (120 to 102 Wh), or increase the range
from 5.7 to 6.7 km.
3.6 Transport mode comparison
We compare the small quadcopter drone to different transportation modes in terms of energy consumption and
CO2e emissions and validate it against top-down sustainability reports from the United Parcel Service, Inc.
(UPS)’s 2019 . The energy consumption of a medium-duty diesel truck is considered as 11 MJ/km [44]. Whereas
a Medium-duty electric truck has energy consumption of 1.4 kWh/mile[44], or 3.13 MJ/km. Diesel Vans operate
at 18.4 MPG on average[45], or 4.9 MJ/km, (conversion factors: 1 gallon of diesel = 137,381 Btu[46], 1 MJ =
947.817 Btu, 1 mile = 1.60934 km). On the other hand, electric vans operate with energy consumption of 0.38
kWh/km[47], or 1.36 MJ/km. Finally, an electric cargo bicycle operates at 0.023 kWh/km[48], or 0.08 MJ/km
(conversion factors: 1 kWh = 3.6 MJ). In addition, variations in driving style can vary energy consumption by
40%[49]. Based on our energy model, a small quadcopter drone consumes approximately 120 Wh in a 5.5 km
delivery distance (11 km total distance), or 0.039 MJ/km, when delivering at maximum capacity (1 kg payload
with unloaded return) and cruise speed of 12 m/s. Transmission losses of 6.5% and a charging efficiency of
88% [50, 51, 52, 53] were included to the energy consumption of the electric vehicles (Table 2). Supplementary
Table S1 summarizes the nominal energy consumption and also provides the payload capacity of each mode.
The electricity CO2e emissions were considered to be the 2019 American average of 182 g/MJ (656 g/kWh),
with the lower of 107 g/MJ (384 g/kWh) from New England and the upper limit of 249 g/MJ (896 g/kWh)
reflecting non-baseload emissions from the central Mid-West[52]. CO2e emissions for Diesel Fuel combustion
was considered as 1.61x104lb/Btu[54], or 69.35 g/MJ. Upstream GHG emissions for diesel and electricity
generation are 15 g/MJ and 22 g/MJ[55], respectively. The drone’s LiPO Battery life cycle emissions were
assumed to be similar to Li-iron phosphate 2 g/MJ (base case), 0.6 g/MJ (low case) and 4 g/MJ (high case)[55].
Similarly, the electric cargo bicycle has battery life cycle emissions of 5.1 g/MJ (base case), 1.1 g/MJ (low case)
and 16.9 g/MJ (high case), for the electric van 18.7 g/MJ (base case), 5.6 g/MJ (low case) and 37.4 g/MJ (high
case), and for the medium duty electric truck 32.5 g/MJ (base case), 9.7 g/MJ (low case) and 65 g/MJ (high
case).
The battery life cycle emissions for the drone (assumed to be similar to Li-iron phosphate) was calculated
as 0.76 g/km (base case), 0.23 g/MJ (low case) and 1.52 g/MJ (high case). Similarly, the electric cargo bicycle
has battery life cycle emissions of 1.3 g/km, considering a Li-ion NMC811 battery. For the electric van and
electric medium duty truck we assumed a battery of Li-ion NMC811, resulting in 14.1 g/km for the van and
24.5 g/km for the truck.[55]
The energy consumption per package (Epack) was calculated as
Epack =Edist
Sfreq ·Pfreq
(12)
where Edist is the energy consumption per distance unit, Sf req is the number of stops to delivery packages per
distance unit, and Pfreq is number of packages delivered per stop on average.
Similary, the greenhouse gas emissions per package (GHGpackage) is calculated as
GHGpack =Edist ·GHGenergy
Sfreq ·Pfreq
(13)
where GHGenergy is the mass of CO2e per energy unit.
7
Table 2 summarizes the values calculated per vehicle.
Table 2: Base-case energy consumption and GHG emissions for different vehicles.
Vehicle Class Energy Consumption
[MJ/km]
Fuel GHG
emissions [g/km]
Upstream GHG
emissions [g/km]
Battery GHG
emissions [g/km]
Energy consumption
[MJ/package]
GHG emission
[g/package]
Medium duty truck 11.00 764.5 168.7 5.24 444.4
Small diesel van 4.90 340.6 75.2 1.41 119.5
Medium duty electric truck 3.74 681.4 82.4 24.5 1.78 375.4
Small electric van 1.63 296.1 35.8 14.1 0.47 99.4
Electric cargo bicycle 0.10 18.1 2.2 1.3 0.10 21.6
Quad-copter drone 0.05 8.5 1.0 0.8 0.19 41.1
Acknowledgments
This work was supported by the U.S. Department of Energy’s Vehicle Technologies Office, Award Number DE-
EE0008463. This article was prepared while C.S. was employed at Carnegie Mellon University, and is currently
on public service leave. The opinions expressed in this article are the authors’ own and do not reflect the view
of the United States government or any other organization.
Data Availability
All drone data is available is at https://doi.org/10.1184/R1/12683453 and the all the modeling code is available
at https://github.com/thiago-a-rod/energy consumption
Author Contributions Statement
The research project was conceived by C.S, H.M. and S.S. The drone data collection experiment was designed
by J.P. The energy model was developed by T.R. The results were analyzed by T.R. and N.O. All authors
contributed to the writing of the manuscript.
Declaration of Interests
The authors declare no competing interests.
Supplementary Information
Supplementary Information is available with this manuscript.
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