Long-Range Path Planning Using an Aircraft Performance Model for Battery-Powered sUAS Equipped With Icing Protection System

Abstract

Earlier studies demonstrate that en-route atmospheric parameters, such as winds and icing conditions, significantly affect the safety and in-flight performance of unmanned aerial systems. Nowadays, the inclusion of meteorological factors is not a common practice in determining the optimal flight path. This study aims to contribute with a practical method that includes meteorological forecast information in order to obtain the most energy efficient path of a fixed-wing aircraft. The Particle Swarm Optimization based algorithm takes into consideration the aircraft performance, including the effects of en-route winds and the power required for active electro-thermal icing protection systems to mitigate the effects of icing. As a result, the algorithm selects a path that will use the least energy to complete the given mission. In the scenario evaluated with real meteorological data and real aerodynamic parameters, the battery consumption of the optimized path was 52% lower than the standard straight path.

Full text

IEEE JOURNAL ON MINIATURIZATION FOR AIR AND SPACE SYSTEMS 1
Long range path planning using an aircraft
performance model for battery powered sUAS
equipped with icing protection system
Anthony Reinier Hovenburg, Student Member, IEEE, Fabio Augusto de Alcantara Andrade, Member, IEEE,
Richard Hann, Christopher Dahlin Rodin, Student Member, IEEE, Tor Arne Johansen, Senior Member, IEEE,
and Rune Storvold, Member, IEEE
Abstract—Earlier studies demonstrate that en-route atmospheric parameters, such as winds and icing conditions, significantly affect
the safety and in-flight performance of unmanned aerial systems. Nowadays, the inclusion of meteorological factors is not a common
practice in determining the optimal flight path. This study aims to contribute with a practical method that includes meteorological
forecast information in order to obtain the most energy efficient path of a fixed-wing aircraft. The Particle Swarm Optimization
based algorithm takes into consideration the aircraft performance, including the effects of en-route winds and the power required
for active electro-thermal icing protection systems to mitigate the effects of icing. As a result, the algorithm selects a path that will
use the least energy to complete the given mission. In the scenario evaluated with real meteorological data and real aerodynamic
parameters, the battery consumption of the optimized path was 52% lower than the standard straight path.
Keywords—Path-planning, icing protection systems, unmanned aerial systems, particle swarm optimization.
I. INTRODUCTION
SMALL Unmanned Aerial Systems (sUAS) have become
versatile tools that can be used in a broad spectrum of
missions. The rapid growth of the use of sUAS is justified
by their endurance, reduced cost, rapid deployment and flex-
ibility. This flexibility is mainly due to the many types of
sensors that can be mounted on sUAS, enabling them to
be used in many different applications, such as surveillance,
reconnaissance, search and rescue, delivery, photogrammetry,
inspection, among others. In addition, they offer reduced risk
for humans and impact on the environment, when compared
to manned aircraft.
A next and necessary step for the continuous evolution
of sUAS technology is to enable safe autonomous missions
also in adverse weather conditions. For this to be possible,
effects of wind and icing on the aircraft performance must
be addressed, controlled and taken into consideration by the
path planning algorithm to decide if it is worth it to face the
adverse weather conditions or to take a detour in order to avoid
exposing the sUAS to this.
Scientific literature on path planning of sUAS is abundant.
In [1] a comparative analysis of four three dimensional path
planning algorithms based on geometry search was done.
The algorithms compared were Dijkstra, Floyd, A* and Ant
Colony. Run time and path length were the two analyzed
aspects. In [2], the author used the Voronoi diagram to produce
routes minimizing their detection by radar, while in [3] the
A. R. Hovenburg, F. A. A. Andrade, R. Hann, C. D. Rodin, T. A. Johansen
and R. Storvold are with the Department of Engineering Cybernetics, Norwe-
gian University of Science and Technology, Trondheim, Norway (e-mail: hov-
enburg@ieee.org; fabio@ieee.org; richard.hann@ntnu.no; cdahlin@ieee.org;
tor.arne.johansen@ntnu.no; rust@norceresearch.no).
F. A. A. Andrade and R. Storvold are with the Drones and Autonomous
Systems, NORCE Norwegian Research Centre, Tromso, Norway.
F. A. A. Andrade is with the Graduate Program in Electrical Engineering,
Federal Center of Technological Education of Rio de Janeiro, Rio de Janeiro,
Brazil.
Rapidly Exploring Trees (RTTs) were used with a smoothing
algorithm based on cubic spiral curves for collision-free path
planning. Optimization techniques are also adopted, as Genetic
Algorithms [4], MILP [5] and Particle Swarm Optimization
[6], where the author used the method to minimize the UAS
path’s length and danger based on the proximity of threats.
Atmospheric wind usually constitute 20-50% of the airspeed
of sUAS [7]. Therefore, it affects the aircraft’s in-flight per-
formance significantly. In [8], a sophisticated method was de-
scribed where Model Predictive Control (MPC) was employed
for path planning optimization including the effects of uniform
wind. In [9], the author used Markov Decision Process to
optimize the unmanned aerial vehicle’s path, integrating the
uncertainty of the wind field into the wind model. The goal
of the algorithm was to minimize the energy consumption and
time-to-goal. A similar approach was chosen in [10], where
the Ant Colony Optimization (ACO) technique was used to
optimize the path by minimizing the travel time considering
the effects of an uniform wind.
Most of the works about path planning of sUAS that takes
the wind into consideration use an uniform wind distribution.
This information is often used in a simplified model when
calculating the effects of the wind on the energy consump-
tion. However, in [11], aircraft performance was successfully
included, with the assumption of a constant wind field. In
recent literature a nonuniform wind distribution in addition to
an aircraft performance model was used. That is the case in
[12], where the flight path was optimized so that sUAS was
guaranteed to be able to reach a pre-designated safe landing
stop. This was done by continuously calculating the remaining
range considering the remaining battery capacity in case of
an engine failure. In that study a wind map with nonuniform
wind distribution was used in the calculations of the maximum
range of the sUAS. Also using a nonuniform wind distribution,
[13] proposed a two-dimensional optimization algorithm to

IEEE JOURNAL ON MINIATURIZATION FOR AIR AND SPACE SYSTEMS 2
find the path between two points with the minimum energy
consumption. By being aware of the wind map valid for a
given altitude, it was possible to choose a path where the wind
was used favorably for energy savings for that flight level.
One of the most important meteorological constraints for
sUAS mission planning is atmospheric icing. This hazard is
also called in-cloud icing and occurs when an airframe travels
through a cloud containing supercooled liquid droplets. When
these droplets collide with the airframe they freeze and result
in surface icing that grow over time into ice horns that can
significantly alter the wing shape. Even small ice accretions
have been shown to be able to decrease the aerodynamic
performance of a wing dramatically [14] [15].
The icing hazard is a well-researched topic for general avi-
ation, but little attention has been given to this topic until the
recent years for sUAS – although the issue has already been
identified during the 1990s [16]. UAS icing is in many ways
similar to icing on large aircrafts, but also exhibits significant
differences when it comes to flight velocities, airframe size,
mission profiles, and weight restrictions. In particular, sUAS
typically operate at Reynolds numbers an order of magnitude
lower compared to general aviation which causes differences
in the flow regime [17].
Modeling of icing effects on sUAS have shown that icing
results in a degradation of aerodynamic performance. Ice
accretions on the leading edge of the lifting surfaces can
decrease lift, increase drag, and initiate earlier stall [18].
The degree of the degradation seems strongly linked to the
prevailing meteorological conditions. In addition, icing has
also shown to have detrimental effects on static and dynamic
stability. In summary, icing is a severe hazard, especially for
sUAS, and it is common practice to avoid flying in icing at
all costs.
An icing protection system (IPS) can be used to mitigate
this restriction of the flight envelope. In the scope of this work,
an electro-thermal system will be investigated [19] [20]. This
system consists of heating zones on the leading edge of the
lifting surfaces that are activated when the aircraft enters an
icing cloud. The IPS can run in two different modes. In anti-
icing mode, the system will continuously heat the leading edge
to inhibit the build-up of any ice. In de-icing mode, the systems
operates in a cyclic way, allowing for the accumulation of
a small amount of ice over a time of 90 s, followed by
the removal of the ice by activating the heating zones for
30 s. Typically, the de-icing mode will require lower power
requirements compared to anti-icing, but will also results in
performance degradation during the ice accumulation cycles
[21].
As weather conditions often varies for geographic location
and altitude, it is important that the path planning algorithm is
able to allow altitude changes during the flight. Consequently,
the terrain profile must be taken into consideration and treated
as an obstacle by the algorithm. This was previously imple-
mented by [22], where the PSO and Parallel GA optimiza-
tion techniques were compared when used to find the best
trajectory by minimizing a cost function based on the path
length and average altitude, including a penalization in the
cases when the path has parts under the terrain.
In this study, a path planning algorithm is proposed to
find an optimal path between a chosen origin and destination
allowing both changes in course and altitude. It is important
to stress to the reader that this work does not present in-
novation on the path planning method itself neither on the
optimization technique, but rather contributes by integrating
several elements in the cost function, some of which are
novel and others that are normally studied individually in the
literature. These factors include: the icing protection system
usage, which is a very novel solution that enables sUAS to fly
under icing conditions; nonuniform horizontal wind, that is a
major issue on sUAS operations and has only recently been
studied; terrain elevation profile, that is a fundamental factor
that has already been included in many studies; the aircraft
performance model, which brings more realistic and accurate
calculations of the propulsion required power according to the
aircraft platform and environmental parameters; and battery
discharge properties, which is a relevant factor as sUAS are
typically powered by electric batteries and the discharge rates
vary according to the remaining capacity.
Therefore, this work contributes to the field by proposing a
tool that can be used to plan the sUAS mission and to evaluate
different possible scenarios, in order to assist the decision
making. The highlights of the contributions are summarized
as the following:
•Integration of different models such as aircraft perfor-
mance, terrain elevation, nonuniform wind and battery
potential in the cost function;
•Inclusion of the effects of performance degradation dur-
ing the ice accumulation cycles on the aircraft perfor-
mance;
•Inclusion of the icing protection system model and its
effects on the energy consumption in the cost function;
and
•Simulations for a scenario with real weather and elevation
data, as well as real aircraft, battery and icing protection
system parameters.
The work is organized as follows: after the introduction,
Section II contains the aircraft performance model and the
battery performance model is described in Section III. The
meteorological and elevation data are described in Section IV.
The path planning algorithm and its cost function are described
in Section V. The case study, including the aircraft and icing
protection system parameters are presented in Section VI. The
results are discussed in Section VII and conclusions are given
in Section VIII.
II. AIRCRAFT PERFORMANCE MODEL
In this chapter the aircraft performance model is presented
with all the equations that are needed for the calculation of
the required power to propel the aircraft in given atmospheric
conditions and for a desired maneuver.
A. Pressure
The pressure (pin [Pa]) is calculated from the aircraft
altitude by using the barometric formula with subscript 0, that

IEEE JOURNAL ON MINIATURIZATION FOR AIR AND SPACE SYSTEMS 3
is valid from sea level up to 11000 m of altitude:
p(h) = p0T0
T0+L0(h−h0)
g0M
RL0(1)
where his the altitude in [m], p0is the standard pressure at
sea level of 101325 Pa, T0is the standard temperature at sea
level of 288.15 K, L0is the standard temperature lapse rate
for subscript 0 of -0.0065 K/m, h0is the altitude at sea level
of 0 m, Ris the molar gas constant of 8.314472 Jmol-1K-1 ,M
is the molar mass of Earth’s air of 0.0289644 kg/mol and g0
is the gravitational acceleration at sea level of 9.80665 m/s2.
The values of the constants are taken from the International
Standard Atmosphere (ISA) mean sea level conditions [23].
B. Air Density
The density of air (ρin [kgm-3]) is an atmospheric property
which significantly affects the aerodynamic forces.
To calculate the air density, the ideal gas law is used:
ρ(p, T ) = p
RdT,(2)
where pis the pressure in [Pa] given by Eq. 1, Tis the air
temperature in [K] and Rdis the specific gas constant for dry
air of 287.058 Jkg-1K-1 .
C. Power Required
Assuming that the lift (Fig. 1) is high enough to compensate
its opposite weight component to keep the aircraft in the air,
it is necessary to provide a power high enough to: provide a
thrust to overcome the drag force and the weight’s component
tangent to the aircraft’s trajectory; and to move the aircraft
forward in its trajectory with an excess thrust. Therefore, the
required propulsive power is given by multiplying the required
thrust by the desired airspeed:
Preq (Treq , va) = Treq va(3)
where Preq is the required propulsive power in [W] given by
Eq. 3, vais the airspeed in [m/s] and Treq is the required
thrust in [N], which is given by:
Treq (D, θ) = D+W sin(θ)(4)
where Dis the drag force in [N] given by Eq. 5, Wis the
aircraft weight in [N] and θis the climb angle in [rad].
Fig. 1. 2-D representation of an aircraft in a straight flight.
Hence, when the aircraft is cruising (θis equal to zero), this
results in sin(θ)being equal to zero. In this case, the weight
is normal to the drag force and tangent to the lift.
As the drag force is dependent on the body’s size (e.g. the
wing surface), the air density and the airspeed, the equation
for drag force Dis derived by dimensional analysis following
the Buckingham’s π-Theorem:
D(ρ, va, CD)=0.5ρv2
aSCD(5)
where ρis the air density in [kgm-3] given by Eq. 2, vais the
airspeed in [m/s], Sis the wing surface area in [m2] and CD
is the drag coefficient, given by Eq. 8.
For an aircraft equipped with propellers, the engine’s re-
quired power (Pshaft ) is obtained dividing the propulsive
required power (Preq in W, given by Eq. 3) by the propeller
efficiency (ηp):
Pshaft(Preq ) = Preq
ηp
.(6)
From the descent slope which no propulsion power is
required, the aircraft’s motor is assumed to be completely shut
off and the on-board systems, except for the icing protection
systems, are assumed to use insignificant amounts of energy.
Therefore, the energy consumption in this case is assumed to
be equal to the energy consumption of the icing protection
requirements. This is possible for an electric powered aircraft
that does not need to keep an engine running during the entire
mission. However, the maximum descent angle needs to be
chosen so that sufficient lift is provided for airspeed values that
are in the range of predefined accepted values of the desired
airspeed.
1) Aerodynamic Coefficients: To be able to calculate the
drag force, which characterizes the power required to propel
the sUAS, it is necessary to first calculate the drag and lift
coefficients (CDand CLrespectively).
In common A-to-B missions the aircraft is expected to
primarily be flying in a horizontal straight flight, and performs
a limited amount of turns. These turns depend on the path
optimization, however the turns denote on a relatively small
part of the entire path. Therefore, the effects of turns (circling
flights) are not considered in the following calculations. This
holds valid for ”A-to-B” missions, and not for other mission
types, such as loitering.
In addition, and with respect to the mission profile, the
aircraft is assumed to follow a steady motion flight path, trust
angle is zero, and the angle of attack is small, typically ranging
between -4 and 10 deg.
The lift coefficient for straight flight is given by [24] as:
CL(θ, ρ, va) = 2Wcos(θ)
ρSv2
a
,(7)
where vais the airspeed in [m/s], Wis the aircraft weight
in [N], θis the climb angle in [rad], ρis the air density in
[kgm-3] given by Eq. 2 and Sis the wing surface area in [m2].
In this study, the drag coefficient (CD) as a function the lift
coefficient (CL) was derived by a curve fitting process that
aims to find a polynomial equation that represents the true
drag polar, typically acquired from wind tunnel experiments or

IEEE JOURNAL ON MINIATURIZATION FOR AIR AND SPACE SYSTEMS 4
Computational Fluid Dynamics (CFD) simulations. AOA data
ranging from -4 to 8 deg was used in the curve fitting process.
To derive a valid polynomial equation, it is necessary to first
define the range of the lift coefficient where the equation will
be valid. This domain can be calculated by finding the lowest
and highest lift coefficient (CLmin and CLmax), respectively,
for the mission and aircraft constraints, such as minimum and
maximum accepted airspeed (va), minimum and maximum
accepted climb angle (θ) and minimum and maximum air
density (ρ). CDis therefore a function of CL:
CD(CL) = f(CL),(8)
where fis the fitted function.
D. Ground speed
The airspeed is the speed of the aircraft with relation to
the mass of air in which it is flying. Therefore, when the
aircraft climbs or descends, it is possible to calculate the
projection of the airspeed on the horizontal axis (Fig. 2), with
the assumption of the absence of vertical wind, by:
vh(vhx, vhy) = qv2
hx+v2
hy,(9)
with xand ycomponents of the horizontal airspeed (vh) given
by:
vhx(va, ψ, θ) = vasin(ψ) cos(θ),
vhy(va, ψ, θ) = vacos(ψ) cos(θ)(10)
where vais the airspeed in [m/s], ψis the heading in [rad]
(Eq. 12) and θis the climb angle in [rad].
Fig. 2. Representation of side view of the aircraft.
The presence of wind affects the aircraft’s travelled trajec-
tory (Fig. 3). The travelled trajectory is subject to the aircraft’s
ground speed (vgs in [m/s]), which is the aircraft’s speed
relative to the ground and calculated by:
vgs(vhx, vhy, vw indx, vwindy) =
q(vhx+vwindx)2+ (vhy+vwindy)2,(11)
where vhis the horizontal airspeed in [m/s] and vwind the
wind speed in [m/s].
Fig. 3. Wind triangle.
The heading angle (ψ) is the direction where the aircraft is
pointing to. Its angle starts at the North direction (ψ= 0) and
increases towards East. It is, therefore, given by:
ψ(χ, vwind, va, ψw ind) = χ−arcsin vwind
vasin(ψwind −χ)!,
(12)
where the course angle (χin [rad]) is the travel direction
relative to the ground, with the wind speed (vwind in [m/s])
given by:
vwind(vw indx, vwindy) = qv2
windx+v2
windy,(13)
and with the wind heading angle (ψwind in [rad]) given by:
ψwind(vw indx, vwindy) = arctan2(vwindx, vwindy).(14)
III. BATTERY PER FO RM AN CE M OD EL
Modern electric batteries have become dominant power
sources within sUAS, mainly because of their simplicity, and
relatively high peak power output. Common battery types,
such as lithium-based cells, are rechargeable and durable,
which makes them suitable for sUAS operations.
Electric batteries have variable potential according to the
remaining capacity. [25] presented a simple model for open-
circuit potential determination. With this model, it is possible
to calculate the battery potential with respect to the current
being drawn. Lately, [26] derived the model equations to
calculate the rate of discharge for a constant-power. [24]
modelled the battery potential (Voc in [V]) based on [25] as
(Fig. 4):
Voc(C, Vo) = Vo− κCcut
Ccut −C!+Ae−BC ,(15)
where Ccut is the capacity discharged at cut-off in [Ah], C
is the capacity discharged in [Ah], A=Vfull −Vexp and
B= 3/Cexp where Vfull is the fully charged potential in [V].
Additionally, Vexp is the potential at the end of the exponential
range in [V], and Cexp is the capacity discharged at the end

IEEE JOURNAL ON MINIATURIZATION FOR AIR AND SPACE SYSTEMS 5
of the exponential range in [Ah], with the Polarization Voltage
(κin [V]):
κ=(Vfull −Vnom +A(e−BCnom −1))(Ccut −Cnom)
Cnom
,
(16)
where Vnom is the potential at the end of the nominal range in
[V], Cnom is the capacity discharged at the end of the nominal
range in [Ah], and with battery constant potential (Voin [V]):
Vo(Ief f , Voc) = Vfull +κ+ (RCIeff )−A, (17)
where RCis the internal resistance in [Ohms] and Ieff is the
effective discharge current in [A].
Fig. 4. Battery discharge curve. (From [25])
In this study, the power is considered constant during the
discretization step, and, therefore, the effective discharge cur-
rent is the variable to be calculated. As a result, the Trembley’s
equations were manipulated to accommodate obtaining the
effective discharge current for a given power. From Ohm’s
law, the effective current (Ieff in [A]) is given by:
Ief f (Voc) = Peff
Voc
,(18)
with the potential (Voc in [V]) being obtained by solving the
nonlinear equation:
Vn+1
oc − Vfull +κ−A−κCcut
Ccut −C+Ae−BC !Vn
oc−
RCI1−n
ratedPn
eff = 0,
(19)
where nis the battery-specific Peukert’s constant and Irated
is the maximum battery rated current in A.
Note that to obtain the potential (Voc), it is necessary to
solve the nonlinear Eq. 19. The valid solution will be in the
range from the cut-off potential (Vcut) to the fully charged
potential (Vfull).
IV. MET EO ROLOGICAL AND ELEVATION DATA
This work aims to allow sUAS operations in adverse
weather conditions. Therefore, meteorological forecast data
needs to be considered. This data is used in the calculation of
the total aircraft energy consumption, as it affects the aircraft’s
in-flight performance. Additionally, the meteorological condi-
tions define when the icing protection systems are to be used,
and how much power is required to mitigate the adverse effects
of aircraft icing. Finally, the elevation data is of importance
as the path planning algorithm optimizes the sUAS’ altitude,
and therefore it is vital to ensure a minimum terrain clearance
in the aircraft’s planned path.
A. Meteorological parameters
In Table I the downloaded parameters are shown. The wind
and air temperature parameters are implemented directly in
the form that they were supplied in. Other parameters were
modified due to unit compatibility for usage in the calculation
of other parameters, as described in the following sub-sections.
TABLE I
LIS T OF DOWNL OAD ED PAR AME TE RS.
Parameter Description Units
vwindxMeridional wind in x direction m/s
vwindyMeridional wind in y direction m/s
TAir temperature K
qSpecific humidity kg/kg
LW C Atmospheric cloud condensed water content kg/kg
(Liquid Water Content)
1) Relative Humidity: The specific humidity parameter can
be downloaded from the meteorological service. However, in
this work, the parameter used in the calculations is not the
specific humidity but the relative humidity. This is because the
aircraft is assumed to be in icing conditions and turn on the
icing protection system when the temperature is below 0 °C
and the relative humidity is over 0.99. Therefore, the relative
humidity (H) needs to be calculated and it is given by [27]:
H(ea, esat) = ea
esat
(20)
with the vapour pressure (eain [Pa]):
ea(p, q) = qp
0.622 + 0.378q(21)
where qis the specific humidity, pis the pressure in [Pa] given
by Eq. 1 and with the saturated water vapour pressure (esat
in [Pa]):
esat(T) = 10 0.7859+0.03477(T−273.16)
(1+0.00412(T−273.16)) + 2 (22)
where Tis the temperature in [K].
2) LWC and MVD: The ”mass fraction of cloud condensed
water in air” can be also referred as ”liquid water content
(LW C)”. In the icing protection system regression model,
the LW C is one of the input parameters to estimate how
much power is required by the system. The regression model
uses the LW C concentration in [gm-3] but the downloaded
parameter is the LW C mixing ratio in [kg/kg]. Therefore,
to convert LW C mixing ratio (LW Cmin [kg/kg]) to LW C
concentration (LW Ccin [gm-3]), the gas law for dry air is
used:
LW Cc(p, LW Cm, T ) = LW Cmp
RdT×103,(23)

IEEE JOURNAL ON MINIATURIZATION FOR AIR AND SPACE SYSTEMS 6
where Tis the temperature in [K], Rdis the specific gas
constant for dry air of 287.058 Jkg-1K-1 . and pis the pressure
in [Pa] given by Eq. 1.
The Water Droplet Median Volume Diameter (MV D in
[µm]) is another parameter used to calculate the power re-
quired by the icing protection system. It is approximated by
following [28] and given by:
MV D(λ) = 3.672 + µ
λ,(24)
with the shape parameter (µ) given by:
µ=min 1000
Nc
+ 2,15!,(25)
where Ncis the pre-specified droplet number of 100 cm-3 and
with:
λ(LW Cc) = "π
6
ρwNc
LW Cc
Γ(µ+ 4)
Γ(µ+ 1)#1
3
,(26)
where Γis the gamma function, ρwis the density of water of
1 gm-3 and Ncis equal to 100x10-6 m-3.
3) Meteorological data download: The Norwegian Mete-
orological Institute hosts a webapp called THREDDS Data
Server, where it is possible to have access to weather forecasts
of several meteorological parameters. One of the services is
the MetCoOp Ensemble Prediction System (MEPS) [29], from
where the parameters used in this work were downloaded.
This service provides data for the Scandinavian region with
horizontal resolution of 2.5 km and from around 0.00986
to 0.99851 atm pressure levels (that can be converted to
altitude) divided into 65 not equally spaced values. In the
MEPS service, raw and post processed data are available for
10 ensemble members (set of forecast simulations) and for up
to 66 hours of forecast. The models are run every 6 hours
(00,06,12,18 UTC) and the first data file (00) is the most
complete one and the only file containing all the necessary
parameters for the development of this work. Therefore, the
00 file was downloaded for the esemble member 0 (mbr0)
and the data from the forecast time slot 0 was used in the
simulations. The time slot 0 reflects the instant information
of the chosen date/time while the other time slots are hourly
forecast.
The files are available in the Network Common Data Form
(NetCFD) format and each file is up to 200 GB. However, it is
possible to select which parts to download by using the Open-
source Project for a Network Data Access Protocol (OPeN-
DAP). Therefore, the selected parameters can be downloaded
only for the region of interest and for the desired pressure
levels (altitudes).
B. Elevation data
The elevation data was downloaded from the Norwegian
national website for map data (geonorge.no). Geonorge pro-
vides a catalog with a wide variety of map products, including
elevation maps. These elevation maps are in the form of Digital
Terrain Model (DTM) or Digital Surface Model (DSM) and
can be visualized in the website or downloaded via WCS or
WMS services. In this work, the DTM was used, which is
available with 1 m and 15 m of vertical resolution for the
regions correspondent to UTM32, UTM33 and UTM35.
1) Elevation data download: To download the data with
the WCS service, the web browser can be used as the WCS
client. Therefore, the data is requested via HTTP through URL
parameters. The commands to be used are: GetCapabilities;
DescribeCoverage; and GetCoverage. The first one returns all
service-level metadata and a brief description, the second one
returns the full description and the third one returns the data
itself. The URL parameters varies according to the product
and are usually described in the information obtained by the
GetCapabilities and DescribeCoverage commands. One of the
parameters is regarding horizontal resolution, which in this
work, was chosen to be 50 m.
V. PATH PLANNING
The goal of this work is to find a three dimensions path that
minimizes the energy consumption of a long range sUAS flight
from an origin to a destination in adverse weather conditions.
To solve this problem, an optimization technique is used to
minimize the given cost function by finding a sub-optimal set
of waypoints and airspeed changes.
A. Optimization technique
Since the main goal of this work is to investigate the benefits
of integrating the previously described models in the cost
function, an optimization technique of simple implementation
that is also able to minimize non-convex and discontinuous
functions was chosen. Particle Swarm Optimization (PSO)
[30] technique is a meta-heuristic optimization method where
the particles (solutions) are updated every iteration based on
the best global and local solutions. In this study, the standard
PSO was used with a modification to reduce the maximum
absolute particle velocity by an factor. This was implemented
to keep the search more local, and thereby avoiding too large
movements in the solution domain per iteration, as it may be
expected that the optimum solution is relatively close to the
straight line path.
The parameters that must be defined in the PSO algorithm
are: the number of iterations, which was chosen as 400; the
cognitive and social parameter (c1and c2, respectively) which
were chosen both as 2.0; and the velocity constraint factor (),
which was chosen as 0.1.
In addition, the boundaries of the variables (minimum and
maximum airspeed and climb angle) must also be defined
according to the aircraft platform, as well as to the mission
envelope, in order to limit the search to the region where the
solution is certain to be.
It is important to address that other meta-heuristic optimiza-
tion techniques may also be applied to this problem, achieving
similar results.
B. Optimization algorithm
The algorithm’s block diagram is shown in Fig. 5. The
orange blocks scenario-based input parameters, such as the

IEEE JOURNAL ON MINIATURIZATION FOR AIR AND SPACE SYSTEMS 7
meteorological and elevation data, the origin and destination,
the number of decision variables and the PSO parameters. The
other boxes outside the blue box are part of the pre-processing
phase when the model is created and the initial solutions are
generated.
The blue box contains the optimization loop. First the
candidate solutions are evaluated with respect to the terrain.
If part of the path is under terrain, the solution is discarded
(cost =∞). If not, the optimization will evaluate the icing
conditions for each discretization step i.
If icing conditions are present in the step i(Hi>99% and
Ti<0 °C), the deice and anti-ice required power are cal-
culated (Pdeiceiand Panti−icei, respectively). For the deicing
operations the engine’s required power is calculated with an
updated drag coefficient (C∗
Di), which constitutes the average
icing penalty, and therefore an updated required propulsive
power P∗
shafti. For the anti-ice operations the aircraft’s wings
are kept clear from icing. Therefore the engine’s required
power is the same as without ice (Pshafti). However, the anti-
icing system does require thermal energy. In this study the
anti-icing system uses the main battery as power source (i.e.
does not have a separate power source), and therefore induces
a performance penalty during usage. The total power required
by the deice and anti-ice systems, including the respective
engine’s required power, are compared and the solution that
requires the least total power is chosen. If there are no icing
conditions present the total required propulsion power remains
unchanged (Pshafti).
The next step is to calculate the battery energy consumption
in the step itaking into consideration the battery model and
how much battery capacity is left. Finally, the total battery
energy consumption is calculated by summing the battery
energy consumption times the flight time of all steps. The total
battery energy consumption is, therefore, used to update the
particles’ position in the domain. The new solutions are then
evaluated. This process repeats for the chosen total number of
iterations.
C. Cost Function
The aim of the optimization algorithm is to minimize a cost
function (Eq. 27), which represents the total energy consump-
tion and is calculated by the sum of the battery discharge rate
(˙
Cin [Ah/s]) in each discretization step, multiplied by the
time in each discretization step:
minimize Ctot (˙
C,t) =
N
X
i=1
˙
Citi(27)
where ˙
Cand tare the vectors with all ˙
Ciand ti, respectively.
Ctot is the total discharged capacity in [Ah], iis the index of
the discretization step, Nis the number of discretization steps
in the path, tiis the time in [s] at the i-th step given by:
ti(Lstep, vgsi) = Lstep /vgsi,(28)
where vgsiis the ground speed in the discretization step iin
[m/s] given by Eq. 11, with the step’s length (Lstep in [m])
given by:
Lstep(L) = L
N,(29)
and with the total length of the path (Lin [m]) given by:
L(x,y) =
N
X
i=1 p(xi+1 −xi)2+ (yi+1 −yi)2(30)
where xiand yiare east and north positions in the ENU frame
and iis the index of the discretization step.
The the rate of discharge ( ˙
Cin [Ah/s]) given by:
˙
Ci(Itoti) = Itoti
3600,(31)
with the total current (Itot in [A]) given by:
Itoti(Ptoti, Voci) = Ptoti
Voci
,(32)
where Voc is the battery’s potential in [V] (Eq. 19) and with
the total required power (Ptot in [W]) given by:
Ptot(Pshaf t) = Pshaft ,(33)
if there are not icing conditions occurring, or
Ptot(P∗
shaft, Pdeice) = P∗
shaft +Pdeice,(34)
when there are icing conditions occuring, and the deice
solution is the one requiring the least power, or
Ptot(Pshaf t, Panti−ice) = Pshaf t +Panti−ice (35)
if there are icing conditions, while the anti-ice solution re-
quires the least power. Here, Pshaf t is the engine’s required
power in [W] (Eq. 6), P∗
shaft is the engine’s required power
when using the deice solution in [W] (Eq. 40), Panti−ice is
the anti-ice solution required power in [W] and Pdeice is the
deice solution required power in [W].
Finally, Ciis the total capacity discharged in [Ah] until
instant iand given by:
Ci(˙
Ci,ti) =
i
X
i=0
˙
Citi,(36)
where ˙
Ciis the vector of ˙
Cfrom ˙
C0to ˙
Ciand tiis the vector
of tfrom t0to ti.C0is the initial discharged capacity.
Note that when parts of the path are not above the terrain,
or if the total energy consumption is higher than the battery’s
capacity, this candidate solution receives an infinite penalty to
ensure it is disregarded as a candidate solution.
D. Decision variables
The required decision variables are horizontal plane way-
points (x,y), airspeeds (va) and climb angles (θ). The number
of waypoints (O) and airspeeds/climb angles (K) are chosen
by the user when defining the scenario. Note that the airspeed
and climb angle changes were chosen to occur at the same
time for algorithm simplicity.

IEEE JOURNAL ON MINIATURIZATION FOR AIR AND SPACE SYSTEMS 8
Fig. 5. Algorithm block diagram.
E. Model and Mission Parameters
1) ENU frame: The ENU frame was chosen as the co-
ordinate system of the optimization algorithm. Therefore, all
information in World Geodetic System 1984 (WGS84), which
is in the format of latitude, longitude and altitude, must be
converted to the ENU frame. Also, the resulting waypoints of
the optimized solution must be converted to WGS84 in order
to be fed into the sUAS’ flight control system.
In this work, when using the ENU frame, the xaxis points
east, the yaxis points north and the zaxis points up.
It is also necessary to define the origin (0,0,0) of the ENU
frame. As the region around the origin is less affected by the
frame conversion error, the origin was chosen to be in the
geographical midpoint between origin and destination at sea
level.
2) Domain: The candidate solutions’ waypoints are limited
to be away from the straight path up to a maximum distance.
This maximum distance was defined as one third of the
length of the straight path between the origin and destination.
Therefore, the optimization algorithm can only find candidate
solutions containing waypoints within this domain region.
The boundaries of airspeed (va) and climbing angle (θ) must
also be defined according to the aircraft platform’s constraints.
In addition, these boundaries should be fine tuned for values
around the expected optimization resulting values, in order to
achieve faster convergence.
3) Discretization strategy: The cost function (Eq. 27) is
evaluated for each discretization step of the path and the
total cost is the sum of the energy consumption in each step.
Therefore the number of steps will affect the resolution of the
optimization algorithm, and the processing time. The number
of discretization steps (N) is defined by the multiplication
factor (F) and the number of airspeed and climb angle changes
(K):
N=KF −1(37)
These parameters are presented for a scenario example in
Fig. 6. In this example, A is the origin and B is the destination.
There is one waypoint between origin and destination (O= 1).
There are three airspeed and climb angle changes (K= 3),
and three of multiplication factor (F= 3). Therefore there are
eight discretization steps (N).
Increasing the number of discretization steps makes the
optimization more accurate. However, the computation time is
increased accordingly. The lower limit of the distance between
discretization steps that could affect the results is the lowest
resolution step of the data used. In the case of this work, that
is the resolution of 50 m of terrain elevation.
It is also relevant to note that after the optimization and
before the flight, it is important to make an evaluation of the
path regarding the terrain elevation with a low resolution step,
in order to make sure that the entire length of the path is above
the terrain.
Additionally, the first particle in the PSO algorithm has to
be initiated with a candidate solution. A good candidate initial
solution for the first particle is a straight path from origin to
destination, climbing with constant climb angle to the altitude
a few meters above the highest peak, then cruising close to
the destination, and finally descending with constant negative
climb rate to the destination.
Also, the other particles (candidate solutions) of the pop-
ulation must be initiated. To not distract the optimization
algorithm from the region around the first candidate solution,
which is expected to contain an optimal solution, the particles

IEEE JOURNAL ON MINIATURIZATION FOR AIR AND SPACE SYSTEMS 9
Fig. 6. Example of a path and its division.
are chosen to be variations of the first particle following the
exponential probability distribution. Therefore, the values of
the set of variables of the other particles are close to the values
of the first initial solution set of variables.
VI. CA SE S TU DY
In this section, the chosen mission case and operational
profiles that were evaluated are described, and the aircraft
and battery parameters used in the optimization algorithm are
explained.
A. Aircraft platform
The P31016 (Fig. 7) is a small battery-powered aircraft that
is powered by a 6.0 kilowatt brushless motor. The propulsion
efficiency (ηp) is assumed constant at 50% with an ideal
electrical discharge pattern. This value lies in range of typical
typical propulsion efficiency of a small UAS, as described in
[31] The aircraft has a wing surface (S) of 0.81 m2and has
a typical mission-ready weight of 171.5 N (W).
Fig. 7. P31016 concept battery-powered fixed-wing unmanned aircraft
Due to factory specification, the climb angle (θ) was set
ranging from -10 to 10 degrees. Regarding the airspeed (va), it
was set ranging from 20 m/s to 30 m/s. This choice was made
to avoid the optimization algorithm explores too high airspeed,
considering the aircraft performance and mission envelope.
The aircraft performance data was generated with the flow
solving module FENSAP, which is part of FENSAP-ICE [32].
Three-dimensional CFD simulations were performed on the
P31016 (Fig. 7) at Reynolds number (Re) of 1.2×106with
angles of attack (AOA) corresponding to the set envelope
limitations and using a numerical setup described in Table
III. The results for drag and lift of the P31016 are presented
in Fig. 8. The simulations indicate that the flow separation
starts from the trailing-edge at AOA of 8 deg. Drag forces
increase unproportionally after the onset of stall, whereas lift
is decreased as the separation intensifies with higher AOAs.
Fig. 8. AOA (Angle-Of-Attack) vs CDand CLfrom CFD simulations
This data was used to fit the drag polar curve (Fig. 9). The
curve was fitted for a lift coefficient range calculated based on
the aircraft and mission constrains. These constrains are: min-
imum and maximum airspeed (va), minimum and maximum
climb angle (θ) and minimum and maximum air density (ρ).
The air density was calculated according to the minimum and
maximum expected relative humidity (H), temperature (T)
and pressure (p) in the meteorological data. The minimum and
maximum resulting lift coefficient for these constrains were
0.3436 and 1.0371 respectively. The fitted curve of the drag
polar for this range is given as:
CD(CL)=0.1407C2
L−0.07989CL+ 0.02496,(38)
where CLis the lift coefficient and CDis the drag coefficient.
B. Icing protection System model
The power requirements for de-icing and anti-icing, as well
as the performance penalties during de-icing are generated
using numerical simulation methods. Two icing codes are used
for this. LEWICE is an icing code that has been developed
by NASA over several decades for general aviation [33].
It is a widely validated code [34], but it has been shown
that there may be limitations for the application of sUAS
[35] [36]. The code is based on a panel-method, that can
simulate ice accumulation, anti-icing, and de-icing with very
low computational resources. ANSYS FENSAP-ICE is an
icing code using modern computational fluid dynamics (CFD)

IEEE JOURNAL ON MINIATURIZATION FOR AIR AND SPACE SYSTEMS 10
Fig. 9. Drag polar fitted curve
methods [37]. The code is very flexible and has in the past
been used for UAS applications [38] but still lacks a dedicated
validation for icing at small Reynolds numbers [39].
In this work, the LEWICE is used to generate a model for
the anti-icing and de-icing loads, whereas FENSAP-ICE is
used for the de-icing performance penalties. The low compu-
tational requirements of the panel-method of LEWICE allow
to simulate a large number of different meteorological icing
conditions in short time, in the order of minutes on a typical
desktop computer. The same computations would take several
days on a high-performance computing (HPC) cluster with
FENSAP-ICE.
A total of 112 different icing cases have been simulated with
LEWICE to generate a dataset for anti-icing with LEWICE.
The boundary conditions of the meteorological cases are
based on the icing envelope of 14 CFR Part 25, App. C
[40] used for the airworthiness certification of commercial
aircrafts. The simulation cases cover the intermittent maximum
(IM) icing and continuous maximum (CM) icing envelope.
The range of values for each icing parameter is shown in
Table II. Simulations were performed in 2D using the mean
aerodynamic chord (MAC = 0.275 m) of the wing. For all
simulation it was assumed that only 20% of the leading-edge
area of the lifting surfaces was protected (surface temperature
of +5 °C). Runback icing, generated by the refreezing of
melted ice from the heated zones, was not included in this
study. This was done for reasons of simplification and lack of
dedicated studies of runback icing on sUAS. Runback icing
itself may be a significant source of aerodynamic performance
degradation of any IPS [41].
TABLE II
RAN GE OF VAL UES F OR E ACH I CIN G PARA ME TER
Parameter Range of values
Airspeed [20, 30, 40, 50] m/s
Angle of attack AOA [0] deg
Chord c [0.275] m
Temperature TC[-2, -5, -10, -30] °C
Median (droplet) volume diameter MVD [15, 20, 30, 40] µm
Liquid water content LWC concentration [0.04 ... 2.82] gm-3
The de-icing power requirements have been assumed to be
60% lower than the anti-icing loads. In contrast to the anti-
icing, the minimum power requirement for de-icing can not be
directly simulated with a steady-state assumption. This means
that transient simulations that prescribe a power supply to
the leading-edge is required. Such simulations were carried
out with LEWICE and confirmed that the aforementioned
assumption provides sufficient power for successful de-icing.
It should be noted however, that this assumption is a gross
simplification, but is deemed sufficient for the purpose of this
work.
The 112 simulation cases from LEWICE for the anti-
icing and de-icing power requirements (Panti−ice and Pdeice,
respectively) were used to generate linear models that are
used for the path-planning optimization. Forth order linear
regression models were used and have been found to be able
to predict the power loads depending on airspeed (vain [m/s]),
temperature (TCin [°C]), Liquid Water Content concentration
(LW Ccin gm-3) and Median Volume Diameter (M V D in
[µm]) with good accuracy (R2= 0.977).
The data for the de-icing performance degradation was
obtained with FENSAP-ICE in 2D and then extrapolated for
the entire aircraft. First, 90 s of ice accretion were simulated
with FENSAP-ICE with the numerical parameters specified in
Table III. The degradation of lift and drag was then averaged
over a full de-icing cycle of 120 s. Again the 14 CFR Part 25,
App. C icing envelopes (CM & IM) were applied. In order to
reduce the number of simulations, only the cruise velocity of
25 m/s and a single MVD of 20 µm was considered.
TABLE III
NUMERICAL PARAMETERS SETUP
Parameter Setup
Flow conditions Steady-state, fully turbulent
Turbulence model Spalart-Allmaras
Droplet distribution Monodisperse
Artificial
Viscosity
Second order
Streamline upwind
The aerodynamic degradation occurring during de-icing is
presented in Fig. 10 and 11. A linear model (Eq. 39) was
selected for the drag (R2= 0.81).
C∗
D(CD, LW Cc) = CD+CD(0.0785LW Cc+0.4973).(39)
Therefore, the required power to propel the aircraft when
the de-icing solution is used (P∗
pshaft in [W]) needs to be
calculated using the degraded drag coefficient (C∗
D):
P∗
pshaft(ρ, va, C ∗
D, θ) = (0.5ρv2
aSC ∗
D+W sin(θ))va
ηp
.(40)
1) Battery parameters: The P31016 is assumed to be
equipped with a commercial 10-cells LiPo battery with 26.4
Ah capacity (Ccut). Following Tremblay’s model, the potential
parameters of a 10-cells LiPo battery are approximately: 41.8,
39.67 and 37.67 ampere-hour of fully charged (Vfull ), end of
exponential range (Vexp) and end of nominal range (Vnom )
respectively. The capacity parameters are approximately: 2.64
and 20.4 ampere-hour of end of exponential range (Cexp) and

IEEE JOURNAL ON MINIATURIZATION FOR AIR AND SPACE SYSTEMS 11
Fig. 10. LWC [gm-3] vs ∆CL[%] degradation
Fig. 11. LWC [gm-3] vs ∆CD[%] degradation
end of nominal range (Cnom), respectively. In addition, from
the battery’s manual it is found that the internal resistance
(Rc) is 0.015 Ohms and the maximum rated discharge current
(Irated) to be 660 ampere. The potential curve of this battery
with respect to the capacity discharged for 10 ampere of
constant current is shown in Fig. 12.
Fig. 12. Battery potential times capacity discharged
Note that for all cases, the battery was assumed to be fully
charged in the beginning of the mission. Therefore, C0(the
initial capacity discharged of the battery) was assumed to be
equal to 0 Ah.
C. Mission Case
The region of Northern Norway was chosen for the eval-
uation of the proposed solution. The meteorological and ele-
vation data were obtained for the area of the white rectangle
of Fig. 14. In this area, one mission case was defined to be
investigated and the weather of the date of 20th of January
of 2019 was chosen as the reference weather. For this area
and date, the parameters of liquid water content concentration
(LW Ccin [gm-3]) and temperature in °C are related as shown
in Fig. 13 if icing conditions are met.
Fig. 13. LW Ccand temperature distribution.
Fig. 14. Mission case.
1) Operational Profiles: For the mission case, twelve dif-
ferent operational profiles (OP) were evaluated as described
below.
Note that all the operational profiles start at 250 m of alti-
tude, regardless of the altitude of the take off spot. Therefore,
it is assumed that before starting the autopilot, the aircraft will
be taken by the pilot to 250 m of altitude. Also, when reaching
the destination, the aircraft must be landed by the pilot. Take
off and landing maneuvers are not considered in this work.

IEEE JOURNAL ON MINIATURIZATION FOR AIR AND SPACE SYSTEMS 12
The straight paths are assumed to have constant airspeed of
28 m/s, which is around the value of the best cruise airspeed
for the P31016.
•OP 01: Horizontal straight path between origin and desti-
nation, climbing to a few meters above the highest peak,
flying at constant altitude until close to the destination,
then descending until the destination. Evaluated under no
icing conditions.
•OP 02: Optimized path without considering icing condi-
tions. Evaluated under no icing conditions.
•OP 03: Optimized path considering icing conditions, us-
ing deice or anti-ice (best option) when needed. Evaluated
under no icing conditions.
•OP 04: Optimized path considering icing conditions,
using only anti-ice when needed. Evaluated under no
icing conditions.
•OP 05: Horizontal straight path between origin and desti-
nation, climbing to a few meters above the highest peak,
flying at constant altitude until close to the destination,
then descending until the destination. Evaluated under
icing conditions, using deice or anti-ice (best option)
when needed.
•OP 06: Optimized path without considering icing con-
ditions. Evaluated under icing conditions, using deice or
anti-ice (best option) when needed.
•OP 07: Optimized path considering icing conditions,
using deice or anti-ice (best option) when needed. Evalu-
ated under icing conditions, using deice or anti-ice (best
option) when needed.
•OP 08: Optimized path without considering icing condi-
tions. Evaluated under icing conditions, using only anti-
ice when needed.
•OP 09: Horizontal straight path between origin and desti-
nation, climbing to a few meters above the highest peak,
flying at constant altitude until close to the destination,
then descending until the destination. Evaluated under
icing conditions, using only anti-ice when needed.
•OP 10: Optimized path considering icing conditions,
using only anti-ice when needed. Evaluated under icing
conditions, using deice or anti-ice (best option) when
needed.
•OP 11: Optimized path considering icing conditions,
using only anti-ice when needed. Evaluated under icing
conditions, using only anti-ice when needed.
•OP 12: Optimized path considering icing conditions, us-
ing deice or anti-ice (best option) when needed. Evaluated
under icing conditions, using only anti-ice when needed.
2) Discretization: The number of waypoints (O) was de-
fined as 5; the number of airspeed and climb angle changes
(K) as 20; and the multiplication factor (F) as 5, giving a
total of 99 discretization steps (N). Since the straight path
has around 90 km, this gives a discretization step length of
around 1 km.
VII. RES ULTS
Table IV show the results for the mission case, where the
sUAS flies from Oldervik to Bursfjord. In icing conditions,
the operational profile seven has the lowest battery energy con-
sumption (7.05 Ah), as expected. Compared to the operational
profile one, which consumes 14.82 Ah of battery, it brings a
reduction of 52.43 % on the battery energy consumption. Also,
in this mission case, if only the anti-ice is used and the sUAS
is flying straight (OP 09), the battery energy consumption is
equal to 20.54 Ah, almost three times more than the optimized
path that both deice and anti-ice are available. This is due to
the absence of path optimization and to the fact that the anti-
ice system requires more power.
In addition, if the path is optimized without taking the ice
into consideration, the expected battery energy consumption is
of 6.28 Ah (OP 02). However, if the sUAS actually experiences
icing conditions during this flight, the battery energy consump-
tion is of 10.74 Ah (OP 06), against 7.05 Ah when the path is
optimized taking into consideration the weather forecast (OP
07). Therefore, this shows the importance of using the weather
information to optimize the path.
All optimized paths were longer than the straight path. Also,
the flight time was slightly longer in all cases. This is due to
the fact the optimization takes the wind into consideration so it
is able to change the path to find a better wind profile and/or to
change the airspeed accordingly. Therefore, the flight duration
is longer but the battery energy consumption is lower.
Figure 15 shows the straight path (OP 05) and Fig. 16 the
optimized path (OP 07) of the mission case. It is possible to
notice that in the optimization, the path is optimized so that the
ice is avoided when possible by placing it under or above the
icing clouds (blue dots). Also, when close to the destination,
the descent maneuver is started as soon as possible, so energy
savings are enhanced.
Fig. 15. Straight path.
Fig. 16. Optimized path.
The two peaks on the battery consumption (Fig. 17) between
5 and 10 minutes and between 35 and 40 minutes are due to
the icing conditions. In the first moment that the sUAS is
flying under icing conditions, the power required by the deice

IEEE JOURNAL ON MINIATURIZATION FOR AIR AND SPACE SYSTEMS 13
TABLE IV
MIS SIO N CA SE OP ERAT ION AL PRO FIL ES RE SU LTS
Straight
Opt.
without
ice
Opt.
with
anti-ice
Opt.
with
deice
Eval.
with
anti-ice
Eval.
with
deice
Battery
Cons.
[Ah]
Length
[km]
Time
[min]
Length
in ice
[km]
Time
in ice
[min]
OP 01 x 8.08 91.47 44.68 0.00 0.00
OP 02 x 6.28 91.82 45.59 0.00 0.00
OP 03 x x 6.52 97.49 49.80 0.00 0.00
OP 04 x 6.65 94.84 50.36 0.00 0.00
OP 05 x x x 14.82 91.47 44.68 49.39 23.32
OP 06 x x x 10.74 91.82 45.59 34.89 16.27
OP 07 x x x x 7.05 97.49 49.80 3.90 1.96
OP 08 x x 14.32 91.82 45.59 34.89 16.27
OP 09 x x 20.54 91.47 44.68 49.39 23.32
OP 10 x x x 7.09 94.84 50.36 3.79 1.71
OP 11 x x 7.46 94.84 50.36 3.79 1.71
OP 12 x x x 7.48 97.49 49.80 3.90 1.96
system is 477 W and the increase on the power required to
propel the aircraft is 184 W, totalizing 661 W. The increase
on the propulsion required power is due to the drag coefficient
penalty brought by the deice system. If the anti-ice solution
was used, where there is no penalty on the drag, the required
power would be around 1150 W. Therefore, the deice solution
requires less power in total (deice system plus propulsion
power). The predominance of the deice solution over the anti-
ice will repeat in almost every case investigated in this work.
This is due to the mission constrains and to the fact that,
according to the deice and anti-ice regression models used
in this work, the anti-ice will only have an advantage in
maneuvers with high drag.
Fig. 17. Battery Consumption.
Finally, Fig. 19 shows the optimized airspeed along the path
(OP 07). It is possible to notice that the airspeed is kept around
the known best cruise airspeed of the aircraft, which is around
28 m/s.
It should be noted that several simplifications have been
applied to some of the simulation input of this study regarding
the icing protection system and icing effects that may have a
significant influence on the overall results:
•No runback icing effects
•Simplified de-icing load calculation
•Simplified simulation of the aerodynamic degradation
during de-icing
Fig. 18. Battery Discharged.
Fig. 19. Airspeed of optimized path.
These simplifications were introduced in order to limit the
amount of expensive computational simulations. Since this
work is focussing mostly on the path-planning method, these
simplifications were considered sufficient for this study. For
future work, a greater level of detail can easily be included to
the required input data.

IEEE JOURNAL ON MINIATURIZATION FOR AIR AND SPACE SYSTEMS 14
VIII. CONCLUSION
This work presented a path-planning algorithm for sUAS
equipped with icing protection systems. An aircraft perfor-
mance model was used to calculate the power required to
propel the aircraft. A battery model was also included in the
calculations to give a more precise battery consumption. The
goal of the algorithm was to find an optimum path that uses
the least energy, taking into consideration the atmospheric
parameters, such as wind, liquid water content, relative hu-
midity and temperature of a given time. Climb/decent angles,
airspeed and waypoints were the optimization variables. The
investigated mission case was to fly between two towns
in Northern Norway in a given date of the winter season.
Twelve operational profiles were compared and the proposed
solution, that takes the icing conditions into consideration
when optimizing the path, achieved 52% of battery savings
when compared to the standard straight path, proving itself to
be a very useful solution for path-planning in icing conditions.
In addition, it was verified that, for the sUAS used in this
work, the deice solution will require less power to protect the
sUAS from icing in the majority of situations, compared to
the anti-ice solution.
ACKNOWLEDGMENT
This work has been carried out at the Centre for Au-
tonomous Marine Operations and Systems (AMOS), supported
by the Research Council of Norway through the Centres of Ex-
cellence funding scheme, project number 223254. This project
has received funding from the European Union’s Horizon
2020 research and innovation programme under the Marie
Sklodowska-Curie grant agreement No 642153. We would
also like to acknowledge Research Council of Norway and
industry partners for funding through projects: CIRFA 237906;
and RFFMN D-ICE 285248. The CFD computations were
performed on resources provided by UNINETT Sigma2 - the
National Infrastructure for High Performance Computing and
Data Storage in Norway. We also want to acknowledge Mr.
Øyvind Byrkjedal from Kjeller Vindteknikk for the help with
LCW and MVD calculations.
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