A versatile modeling package for drone performance in various weather environments.
Project description
DroneAWE: Drone Applications in Weather Environments
This repository is being developed to advance the state of the art of drone performance predictions under a wide range of weather and battery conditions with mission planning in mind. An interactive GUI is available at http://droneecon.com. This README will explain general usage as well as the underlying theory for the models used, as currently implemented. Note that DroneAWE is a work in progress (see Future Work). This document will explain general usage for the latter, as well as the engineering theory at work behind the scenes.
Installation
DroneAWE may be used in two ways: using the GUI available at http://droneecon.com, or by using the source code directly. To use the source code directly, install using
pip install drone_awe
Usage
Basic Usage
Base functionality is achieved by running the following:
import drone_awe m = drone_awe.model(args) m.simulate()
where args
is a dictionary containing simulation parameters. Note that for every parameter not specified in args
, a default value is used. It is possible to run the default simulation by passing an empty dictionary into the drone_awe.model()
method:
import drone_awe m = drone_awe.model({}) m.simulate()
Settable dictionary keys with example values for args
include the following:
{ "validation":False, "validationcase":"DiFranco2016", "dronename":"djiMavic2", "batterytechnology":"nearfuture", "stateofhealth":90.0, "startstateofcharge":100.0, "rain":False, "dropsize":1.0, "liquidwatercontent":1.0, "temperature":15.0, "wind":False, "windspeed":10.0, "winddirection":0.0, "relativehumidity":0.0, "mission": { "missionspeed": 10.0, "altitude":100.0, "heading":0.0, "payload:0.0 }, "timestep":1, "plot":True, "xlabel":"missionspeed", "ylabel":"power", "title":"First_test", "simulationtype":"simple", "model":"abdilla", "xvals":[0,1,2,3,4,5], "weathereffect":"temperature", "weathervals":[10,20,30,40] }
These are explained further in Settings. After a drone_awe.model
object is instantiated, settings can be changed by modifying the input
class variable as:
m.input['xlabel'] = 'payload' m.input['validationcase'] = 'Stolaroff2018'
The simulation must then be rerun using:
m.simulate()
Plotting
An optional boolean may be set to produce a plot on runtime by running:
m = drone_awe.model({},plot=True)
when a drone_awe.model
is instantiated. Alternatively, the drone_awe.model
's plot
variable may be set at any time:
m.plot = True
Settings
The following subsections explain the use of various settings of a drone_awe.model
object.
'dronename'
'dronename'
must be set to a string that is defined in the drone database. To access a dictionary containing all supported drones, use the following methods:
droneDictionary = drone_awe.drones
If a drone or validation case does not exist in the drone database, it may still be used by setting a custom dictionary:
m.drone = droneDictionary
where droneDictionary
is a dictionary with the same keys as the following:
{ 'id': 'djiMavic2', 'wingtype': 'rotary', 'diagonal': 0.354, 'takeoffweight': 0.907, 'speedmax': 20, 'altitudemax': 6000, 'endurancemax': 31, 'endurancemaxspeed': 6.944, 'endurancemaxhover': 29, 'rangemax': 18000, 'rangemaxspeed': 13.889, 'temperaturemin': 10, 'chargerpowerrating': 60, 'batterytype': 'LiPo', 'batterycapacity': 3850, 'batteryvoltage': 15.4, 'batterycells': 4, 'batteryenergy': 59.29, 'batterymass': 0.297, 'waterproof': 'no', 'windspeedmax': 10.8, 'batteryrechargetime': 90, 'rotorquantity': 4, 'rotordiameter': 0.2, 'cruisespeed': 6.94, 'payload': 0.0, 'length': 0.322, 'width': 0.242, 'height': 0.084 }
Note that not all parameters need be specified, but if a simulation is run that requires unspecified parameters, the model will not run.
'validation'
and 'validationcase'
To view validation cases for drone_awe
models, set 'validation'=True
and 'validationcase'
to a string contained in the validation case database. To access a dictionary containing all supported validation cases, run the following:
validationDictionary = drone_awe.validationdata()
Additionally, validationCaseDictionary
is a dictionary with the following format:
{ 'id': 'Stolaroff2018', 'xvalid': [1.358974359,1.7179487179,1.6923076923,1.7692307692,1.7692307692,1.8205128205,1.8717948718,1.8974358974,1.9230769231,1.9743589744,2.0512820513,2.1025641026,2.1025641026,2.1794871795,2.2820512821,2.3076923077,2.3333333333,2.4358974359,2.5384615385,2.5384615385,2.6666666667,2.7948717949,2.9487179487,3.1025641026,3.2564102564,3.358974359,3.4615384615,3.641025641,3.7435897436,3.8717948718,4.0512820513,4.2564102564,4.358974359,4.641025641,4.8974358974,5.8461538462,6,6.2820512821,6.5384615385,7.1538461538,7.4871794872,7.8205128205,8.4871794872,9.1794871795,9.7692307692,10.2564102564,10.6923076923,11.1282051282,11.5897435897], 'yvalid': [133.7510729614,149.2375075128,142.6477385276,144.5897859156,140.9450186657,141.7583868756,142.3874173587,140.4340604922,139.3656195241,139.5335348046,140.2321151941,139.9589946754,136.1689649626,138.3618186589,141.3711557508,139.4001574523,136.7492021569,136.5131929807,137.712167001,133.136399421,135.7755034665,136.58240428,141.8694500174,143.7278953027,145.8751386173,144.4503136349,143.5492800366,144.4966689523,140.8944307591,139.7885398414,140.0842115956,140.6905892611,140.7593265104,140.4412051028,148.3297356325,161.0751453894,160.7738527567,158.8079335653,157.0439596719,161.2248774665,165.1381601781,164.7032531681,177.1408013138,175.6982333173,190.095233258,197.4485952036,209.0736216573,203.7684942987,215.7551870381], 'drone': { 'validationcase':'Stolaroff2018', 'wingtype': 'rotary', 'rotorquantity': 4, 'takeoffweight': 1.3, 'batterytype': 'LiPo', 'batteryvoltage': 11.1, 'batterymass': 0.262, 'props': '10x4.7', 'endurancemaxhover': 16, 'payloadmax': 0.4, 'batterycapacity': 5500, 'payload': 0.0, 'rotordiameter': 0.254, 'batterycells': 3, 'length': 0.280, 'width': 0.140, 'height': 0.100, 'waterproof': 'no' }, 'settings': { 'dronename': 'drone', 'stateofhealth': 100.0, 'startstateofcharge': 100.0, 'altitude': 100.0, 'temperaturesealevel': 15.0, 'rain': False, 'dropsize': 0.0, 'liquidwatercontent': 1.0, 'temperature': 15.0, 'wind': False, 'windspeed': 0.0, 'winddirection': 0.0, 'relativehumidity': 85.0, 'icing': False, "mission": { "missionspeed": 10.0 }, 'timestep': 1, 'xlabel': 'missionspeed', 'ylabel': 'alpha', 'title': 'Stolaroff', 'simulationtype': 'simple', 'model': 'abdilla', 'xvals': [0.0,1.0,2.0,3.0,4.0,5.0,6.0,7.0,8.0,9.0,10.0,11.0,12.0,13.0,14.0,15.0], 'validation': False, 'validationcase': 'Stolaroff2018', 'batterytechnology': 'current' } }
Data used for validation cases can be found in [2,610].
Assumed Specs
Some specifications are not explicitly available, or require some adaptation at runtime. Note that the 'altitude'
setting of validation cases is not always known and is set by default to '0'
. 'length'
, 'width'
, and 'height'
parameters are not necessarily set to geometrically accurate values; rather, they are set so that 'length'
times 'width'
results in the top area and that 'width'
times 'height'
results in the drone's frontal area.
'L/D'
and 'propulsiveefficiency'
When simulating a fixedwing drone, the current model requires input parameters for the lifttodrag ratio ('L/D'
) and the efficiency of the propulsive system ('propulsiveefficiency'
). Ballpark estimates for small UAVs are on the order of 10 and 30%, respectively, although these values heavily depend on the specific geometries and propulsive systems of the drones.
These parameters need to be edited for each specific fixedwing drone in drones.py.
Battery parameters
'batterytechnology'
'batterytechnology'
must be set to one of the following options: 'current'
, 'nearfuture'
, or 'farfuture'
. 'current'
will use the current battery capacity as specified in drone.params
. 'nearfuture'
projects a future capacity in five years based on an increase of 3.5% of battery capacity each year. 'farfuture'
projects battery capacity for lithiumair batteries, about ten times the capacity of current LiPo batteries.
'stateofhealth'
and 'stateofcharge'
'stateofhealth'
refers to the amount of capacity contained within the battery relative to its initial capacity at first use. 100% would be a new battery. LiPo batteries (most commonly used battery for drones) are typically retired when their state of health falls to 8085%. At lower states of health, the battery capacity is decreased and cycles through a full charge more quickly.
'stateofcharge'
refers to the current capacity level of the battery, where 100% is fully charged (regardless of how much the battery has been used before), and 0% is a dead battery.
Weather parameters
'dropsize'
, 'liquidwatercontent'
and 'rainfallrate'
These parameters specifiy rain characteristics. If there is no rain in the simulation, set these to 0.0.
'dropsize'
refers to the diameter of a raindrop (assuming a spherical shape), with units of meters. 'liquidwatercontent'
refers to the amount of water in a given volume of air, with units of kg/m^3. 'rainfallrate'
is the rate of rainfall in units of mm/hr, which translates to litres per cubic meter per hour.
Only one of 'liquidatercontent'
and 'rainfallrate'
needs to be specified.
'temperature'
Units of temperature are given in degrees Celcius.
'relativehumidity'
'relativehumidity'
refers to water content in the air, ranging from 0% to 100%.
Mission parameters
'mission'
is a dictionary with the following keys:

'missionspeed'
— the cruise velocity of the drone, with units of m/s. 
'altitude'
— in units of meters. 
'heading'
— the heading angle of the drone, in units of ___________. 
'payload'
— the mass of any exra payload attached to the drone (e.g., camera), in units of kg.
Plotting parameters
'xlabel'
and 'ylabel'
not only specify axis labels of the plot, but also tell the simulation what to solve for ('ylabel'
) and what parameter to loop through ('xlabel'
). 'ylabel'
can be range
, endurance
, or power
. 'xlabel'
can be any variable from the following list:
"startstateofcharge",
"altitude",
"temperature",
"dropsize",
"liquidwatercontent",
"newtemperature",
"windspeed",
"winddirection",
"relativehumidity",
"payload",
"missionspeed"
'xvals'
is a list containing all the values of x the simulation will loop through and produce a single data point for.
'zlabel'
can be specified to any of the variables used for the 'xlabel'
parameter (see list above) to loop through. This will produce a curve for each of the values in 'zvals'
and plot them on the same figure. This is useful for looping through a weather effect, such as temperature or relative humidity, to see their effects on a plot of range vs payload.
'title'
is the title displayed on the top of the plot, followed by the current date. Currently, the title needs to be one word. A title of multiple words can have each word separated by an underscore en lieu of a space.
Theory
Drone AWE
is intended to predict performance parameters of rotary and fixedwing drones based on readilyavailable specifications. To accomplish this, the power requirements for a given flight maneuver is calculated and used to predict battery drain behavior. Then, parameters such as range and endurance can be calculated. Comprehensive state data is collected at each step of a simulation, providing a versatile data set as output for study.
Power
Rotary Drones
For rotary drones, power consumption is predicted in two steps. First, model parameters are calibrated based on known specifications, like maximum hover time and rotor diameter. Then, momentum theory is used to predict the power consumption.
Calibration
Momentum Theory
According to rotor momentum theory, five equations govern the flight of a rotorcraft:
 $T = \sqrt{W^2 + D^2}$
 $tan(\alpha) = \frac{D}{W}$
 $D = \frac{1}{2} \rho V_\infty^2 C_D A_{\bot}$
 $v_i = \frac{T}{2 A_{rotor} N_{rotor} \rho \sqrt{V_\infty^2 cos^2(\alpha) + (V_\infty sin(\alpha) + v_i^2)}}$
 $A_{\bot} = A_{front} cos(\alpha) + A_{top} sin(\alpha)$
A modified set of these equations were applied to rotary drones by Stolaroff, Samaras, O'Neill et. al. in [1]. Drone AWE
predicts the power consumption of a rotary drone by solving this system. GEKKO, a software package introduced in [2], is used to solve for:
 $T$  thrust per rotor
 $\alpha$  angle of attack
 $D$  drag
 $v_i$  rotor induced velocity
 $A_{\bot}$  planform area of the drone perpendicular to its velocity
given the following:
 $W$  effective weight
 $V_\infty$  drone speed
 $C_D$  drag coefficient
 $A_{rotor}$  rotor area
 $N_{rotor}$  number of rotors
 $\rho$  air density
 $A_{front}$  frontal drone area
 $A_{top}$  drone top area
Note that the model currently assumes that the drag coefficient does not change with velocity and/or angle of attack.
The power requirement for the hover case is calculated according to another equation from [1]:
 $P_{hover} = \frac{W^{3/2}}{\eta \sqrt{2N_{rotor} A_{rotor} \rho}}$
where $\eta$ is the propulsive efficiency calculated as:
 $\eta = \frac{P_{hover}}{P_{hover, actual}}
where $P_{hover, actual}$ is predicted using:
 $P_{hover, actual} = \frac{CV_{battery}}{E_{hover}}$
where $C$ is the battery capacity, $V_{battery}$ is the battery voltage, and $t_{hover}$ is the hover endurance of the drone. Ideally, each parameter is available as published specifications for the drone to be modeled. Next, $\eta$ is used to predict power consumption for the nonhover case as:
 $P = \eta T(V_\infty sin(\alpha) + v_i)$
FixedWing Drones
The power requirement for fixedwing drones is found in [11] and is as follows:
$P = \frac{1}{2} \rho U^3 S C_{D_0} + \frac{2W^2 k}{\rho U S}$
$k = \frac{1}{\pi \times b^2/S \times e}$
where $P$ is power required for steadylevel flight, $\rho$ is air density, $U$ is the drone velocity, $S$ is the wing area, $C_{D_0}$ is the nolift drag coefficient, $W$ is the weight of the drone, $k$ is a coefficient relating to pressure drag, $b$ is the wing span, and $e$ is the spanwise efficiency, estimated to be 0.8 in this model.
Spanwise efficiency and the nolift drag coefficient are assumed parameters, so this model has much room for improvement. It is also difficult to update from rain effects other than momentum, as the model is not easily manipulated by editing a lifttodrag ratio.
Range and Endurance
Endurance is defined as the length of time a drone can remain airborne. Range is the physical distance traveled by the drone. Endurance is calculated by dividing the battery energy (capacity multiplied by voltage) by the power required:
$t = \frac{C\times V}{P}$
where $t$ is the endurance, $C$ is the battery capacity, and $V$ is the average battery voltage. Range is then simply calculated by multiplying the endurance by the average velocity of the drone:
$R = t\times U$
where $R$ is the range in meters and $U$ is the average drone velocity.
Weather
Temperature
From the ideal gas law, $PV=nRT$ (which applies to standard air conditions), temperature is inversely proportional to air density:
$T \propto \frac{1}{\rho}$
In this model the increase or decrease in temperature is taken from 15 °C, and is used to calculate an associated change in air density. In turn, density directly influences power required for drones.
Humidity
Humidity also has a direct impact on air density, which directly affects power requirements for drones. This model uses empirical data obtained from [3], where the effects of varying levels of humidity and temperature on air density were recorded.
Rain
Rain has many effects on the flight performance of drones; however, there is little to no information or validation experiments that test the effects of rain on rotarywing drones. Thus, for rotary drones in this model, only the effects of downward momentum imparted by the rain to the drone is considered. It is not meant to be comprehensive and, with the aid of more empirical data, could be refined and/or altered significantly to better represent the effects of rain.
For fixedwing drones, in addition to the momentum exchange, rain has been shown to both decrease lift and increase drag at all practical angles of attack. In this model, a slight reduction in the lifttodrag ratio is performed, based on averages taken from plots from [4] and [5] (the lift coefficient is reduced by 6% and the drag coefficient increases by 0.01).
Force from downward momentum was calculated from the droplet size and liquid water content, as specified by the user. If a rainfall rate was instead given, the following conversion is performed taken from [4]:
$Drizzle:\ LWC = \frac{30000\pi10^{3}}{5.7^4R^{0.84}}$
$Widespread:\ LWC = \frac{7000\pi10^{3}}{4.1^4R^{0.84}}$
$Thunderstorm:\ LWC = \frac{1400\pi10^{3}}{5.7^4R^{0.84}}$
where $LWC$ is the liquid water content in $g/m^3$ and $R$ is the rainfall rate in mm/hr. Drizzle, widespread, and thunderstorm rain conditions were determined based on the value of $R$.
The force from a single droplet is found by multiplying the droplet mass by the change in velocity of the droplet upon impact ($\Delta V$). Assuming each drop is a sphere of diameter 'dropsize'
, the terminal velocity can be calculated as:
$Terminal\ velocity\ V_t = \sqrt{\frac{2mg}{C_d\rho A}}$
where $m$ is the droplet mass, $g$ is accelleration due to gravity, $C_d$ is the coefficient of drag (in this case assumed to be 0.5), $\rho$ is the density of air, and $A$ is the crosssectional area of the droplet. This equation can be derived from setting equal the forces of gravity and drag on the raindrop. Upon impact with a drone's surface, some or all of the drop can stick to the surface or splash back. Criteron given in [4] determines this outcome based on the droplet's weber number:
$We = \frac{\rho_{air} V_t^2 d}{\sigma}$
where $d$ is the droplet diameter, $V_t$ is the drop's velocity, and $\sigma$ is the water surface tension (this is taken from empirical values based on the current temperature).
The result of the drop's impact is assumed to be:
$We < 5$: drop sticks; $\Delta V = V_t$
$5 < We < 10$: drop rebounds; $\Delta V = 2V_t$
$10 < We < 18.0^2 D_p(\rho_{drop}/\sigma)^{1/2}V_t^{1/4}f^{3/4}$: drop spreads; $\Delta V = V_t$
$18.0^2 D_p(\rho_{drop}/\sigma)^{1/2}V_t^{1/4}f^{3/4} < We$: drop splashes; $\Delta V = V_t(1+2/\pi)$
The number of raindrops incident on the drone per second ($f$) can be determined by dividing the liquid water content (with units of kg/m^3) by the droplet mass, and then multiplying by the drone area and the velocity of the drops:
$#\ of\ drops\ incident\ per\ second\ f = \frac{LWC A_{drone} U_{drop}}{m_{drop}}$
Putting all of this together, the force imparted by all incident raindrops per second on a drone is the number of incident drops multiplied by the change in momentum, the average droplet mass multiplied by the average change in velocity:
$F = f * (m_{drop} \times \Delta V)$
This force acts in the opposite direction of lift, which requires more power to overcome. It effectively increases the "weight" of the drone as far as power generation is concerned.
Wind
Icing
Ice accretion has many adverse effects on a drone's flight performance, including significant losses in lift and increases in drag. In addition, ice adds more weight to the system, which is especially significant for drones, whose weights are small to begin with. Icing effects can even lead to premature stall conditions. Despite these dangerous risks, icing is also very difficult to predict without using computational fluid dynamics (CFD), which is outside the current scope of this project.
In this model, we do not attempt to predict the effects of icing; however, at certain conditions we do issue a warning to the user that icing could occur at those operating conditions, specifically when temperature is low and humidity is high. We encourage users to refer to the icing sections in our literature reviews of weather effects on drone flight performance for more information.
Units
Properties and their respective units are converted within the simulation to SI units, and then converted back. Those units are:
Electricity
 Capacity: milliamphours [mAh]
 Voltage: volts [V]
 Current: amperes [A]
 Resistance: ohms [Ω]
Mechanics

Velocity/Speed: meters per second [m/s]

Power: watts [W]

Endurance or Flight time: minutes [min]

Altitude: meters [m]

mass: kilograms [kg]
 note that "takeoff weight" is measured in mass units
Miscellaneous

Temperature: degrees Celcius [°C]

Wind Resistance: meters per second [m/s]
*refers to the maximum wind speed rating for the drone

Battery recharge time: minutes [min]
functions.py — Commonly used functions
getparams
reads in a .txt or .csv file and outputs a dictionary with keys from a specified list and values from the specified parameter file.getXandY()
reads in data from a validation case and saves the contents to lists for x and y. This function assumes the first row contains labels and ignores them.interpolate()
does a simple linear interpolation with inputs of 2 xvalues, 2 yvalues, and the xvalue of the interpolated value.
Testing
 test_power.py
 test_drone.py
 test_plotter.py
Future Work
This section is to be used to record ideas for future development that cannot be immediately implemented due to time constraints.
 calculate propulsive efficiency at max range and max endurance and interpolate between the two
 go weather by weather and determine the appropriate model to be used
 validate the fixedwing power model
 implement a more comprehensive model for power that could include lifting line theory
 Revisit after having recorded wind tunnel data
Classes
This section contains a detailed description of each class, all contained in Classes.py.

the
Drone
class
class variables contain:

data sheet specifications of specific drone models (e.g., the Mavic 2 Pro), including
 battery size
 battery type
 range under specified conditions
 fixed wing or rotary wing
 etc.


methods calculate certain characteristics based on available information


the
Battery
class
class variables describe:

properties of specific batteries used to model their discharge characteristics, including
 battery type
 number of cells
 low, nominal, and charged cell voltages

Realtime discharge characteristics for simulation, including
 instantaneous voltage
 instantaneous current
 instantaneous state of charge
 current state of health


methods are used to update class variables using information from the
params/
directory


the
Power
class
class variables describe
 baseline power consumption
 an array of 'correction' objects used to modify the power consumption class variable due to weather or other effects (these could be the weather effect classes, actually)
 total power consumption

methods are used to
 update the total power consumption class variable
 append
PowerCorrection
objects toPower
objects using theaddCorrection
method  throw an error if
addCorrection
attempts to append a timevariantPowerCorrection
object to a timeinvariantPower
object  the
PowerCorrection
method adjustments to the baseline power requirements of the drone
 whether the simulation is timevariant or timeinvariant
 methods perform miscellaneous bookkeeping functions


the
Weather
class
class variables describe
 an instance of each weather effect to be modeled
 droplet size (rain)
 Liquid Water Content (LWC) (rain)
 rainfall rate (rain)

the
__updateRain
method For all drone types, this calculates the momentum imparted to the drone from falling rain droplets based on their size and liquid water content.

the
__getWebernumber
method Calculates weber number based on rain density, velocity, diameter, and frequency. This is used to obtain momentum in the __updateRain method.

the
updateLD
method Refers to a predetermined value for loss in lift and increase in drag based on validation data as noted in the theory section. Only for fixedwing drones.

the
__getSurfaceTension
method empirically interpolates surfaces tension based on current temperature

the
updateDensityTemperature
method 
the
updateDensityHumidity
class 
the
Wind
class 
class variables describe
* wind speed * wind direction * amount of turbulence? * variation in speed and/or direction?

the
Gust
class
class variables describe
 frequency
 amplitude


the
Ice
class Because of modeling difficulty, this class does not attempt yet to model icing effects. It may in the future be used to identify if icing conditions are present.


the
Mission
class
class variables describe
 mission speed


the
Simulation
class class variables describe
 start time
 end time
 timestep
 current timestep index
 current time
 methods are used to run and store simulation information, including procedures to get range and endurance
 class variables describe
NOTE: the model is based on power consumption to accomodate future development. The Power
class is designed to receive an indefinite number of modifications based on weather effects

the
Plotter
class plots results according to labels and titles specified by the user in the
settings.txt
file. Methods can plot a line or scatter plots. The validation method plots results on top of specified validation data.
 plots results according to labels and titles specified by the user in the
References
 Beal, L.D.R., Hill, D., Martin, R.A., and Hedengren, J. D., GEKKO Optimization Suite, Processes, Volume 6, Number 8, 2018, doi: 10.3390/pr6080106.
 Stolaroff, J. K., Samaras, C., O’Neill, E. R., Lubers, A., Mitchell, A. S., & Ceperley, D. (2018). Energy use and life cycle greenhouse gas emissions of drones for commercial package delivery. Nature Communications, 9(1), 1–13. https://doi.org/10.1038/s41467017024115
 Yue, W., Xue, Y., & Liu, Y. (2017). High Humidity Aerodynamic Effects Study on Offshore Wind Turbine Airfoil/Blade Performance through CFD Analysis. International Journal of Rotating Machinery, 2017, 1–15. https://doi.org/10.1155/2017/7570519
 Cao, Y., Wu, Z., & Xu, Z. (2014). Effects of rainfall on aircraft aerodynamics. Progress in Aerospace Sciences, 71, 85–127. https://doi.org/10.1016/j.paerosci.2014.07.003
 Ismail, M., Yihua, C., Wu, Z., & Sohail, M. A. (2014). Numerical Study of Aerodynamic Efficiency of a Wing in Simulated Rain Environment. Journal of Aircraft, 51(6), 2015–2023. https://doi.org/10.2514/1.c032594
 Abdilla, A., Richards, A., & Burrow, S. (2015). Power and endurance modelling of batterypowered rotorcraft. In 2015 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) (pp. 675–680). IEEE. https://doi.org/10.1109/IROS.2015.7353445
 Chang, K., Rammos, P., Wilkerson, S. A., Bundy, M., & Gadsden, S. A. (2016). LiPo battery energy studies for improved flight performance of unmanned aerial systems. In R. E. Karlsen, D. W. Gage, C. M. Shoemaker, & G. R. Gerhart (Eds.) (Vol. 9837, p. 98370W). International Society for Optics and Photonics. https://doi.org/10.1117/12.2223352
 Di Franco, C., & Buttazzo, G. (2016). Coverage Path Planning for UAVs Photogrammetry with Energy and Resolution Constraints. Journal of Intelligent and Robotic Systems: Theory and Applications, 83(3–4), 445–462. https://doi.org/10.1007/s108460160348x
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