Introduction
Airborne wind energy is the conversion of wind energy into electrical or
mechanical power by means of flying devices. Some of the pursued concepts use
tethered airplanes or gliders, while others use flexible membrane wings that
are derived from surf kites or parafoils . The present paper
focuses on an airborne wind energy system (AWES) with an inflatable membrane wing that
is controlled by a suspended cable robot . Compared to rigid-wing aircraft, the aerodynamics of
tethered membrane wings are not so well understood and kite development still
relies heavily on subjective personal experience and trial and error
processes . One reason for this is the
aeroelastic two-way coupling of wing deformation and airflow, which can cause
complex multi-scale phenomena. Another reason is a lack of accurate
quantitative measurement data to support the design process. Soft kites such
as leading edge inflatable (LEI) tube kites are highly flexible and have no
rigid structure to mount sensors for precise quantification of the relative
flow in the vicinity of the wing. This is why many experiments rely on
ground-based force measurements and position tracking of the kite. In these
experiments the environmental wind velocity introduces substantial
uncertainties .
Experimental methods for determining the lift-to-drag ratio of soft
kites. Size refers here to total wing surface area.
Method
Kite
Size
Limitations
Wing loading
va
Relative power
L/D (-)
Reference
type
(m2)
(N m-2)
(m s-1)
setting up (-)
Rotating arm
C-Quad
3.2
kite size, forces
100
11
low
4.9
Towing test
C-Quad
3.2
unknown wind
–
–
low
4.6–5.6
Wind tunnel
ram air
6
kite size
25
8
low–high
6
Wind tunnel
ram air
6
kite size
60
12
low–high
6.7–5.7
Wind tunnel
ram air
6
kite size
120
16
low–high
8–5.5
Crosswind
ram air
6
kite size, forces
300
24
high
6.1
Towing test
ram air
3
kite size, forces
30
8
–
6
Towing test
LEI
15.3
force and speed limited
40
14
–
4.5–5.5
Crosswind
LEI
14
wind data unknown
140
–
high
6
Towing test
LEI
14
force and speed limited
40
11.3
low–high
4–10
Crosswind
LEI
5
kite size
300
20
high
4.6
Crosswind
LEI
14, 25
wind data unknown
215, 123
–
high
4, 3.6
With dimensions of the order of several meters, large surf kites or even
larger kites for power generation exceed the size capacity of most wind
tunnels. Downscaling a physical model, as is customary for rigid-wing
aircraft, would require a synchronous scaling of the aerodynamic and
structural problems, which for a fabric membrane structure with seams,
wrinkles, multiple functional layers and integrated reinforcements is
practically very difficult, if not unfeasible. For example, scaled models of
large gliding parachutes have been analyzed in the wind tunnel at NASA Ames
Research Center , while a 25 % model of the FASTWing
parachute was tested in the European DNW-LLF wind tunnel
. A first full-scale experiment to determine the shape
of a kite in controlled flow conditions was performed by .
Using photogrammetry as well as laser light scanning the three-dimensional
surface geometry of a small ram-air surf kite was measured in two larger wind
tunnels. This geometry was used as a boundary condition for computational fluid
dynamic (CFD) analysis of the exterior flow. The results show a substantial
deformation of the membrane wing by the aerodynamic loading. Due to the
difficulty of scaling, these results cannot be transferred to larger kites
that fly at higher speeds for the purpose of wind energy conversion.
In general, the numerical simulation of strongly coupled fluid–structure
interaction (FSI) problems is computationally expensive. If the flow is fully
attached, standard panel methods with viscous boundary layer models can be
used for efficient calculation of the aerodynamic load distribution. While
this approach works, for example, for ram-air wings at a lower angle of attack,
it is not feasible for LEI tube kites because of the inevitable flow
separation region behind the leading edge tube. and
develop multibody and finite-element models of LEI tube
kites and use an empirical correlation framework to describe the aerodynamic
load distribution on the membrane wing as a function of shape parameters.
performs CFD analysis using the deformed shape of the
kite measured by ; however, these results cannot be
extrapolated to different kites. We conclude that without accounting for the
aeroelasticity of the membrane wing an accurate aerodynamic characterization
does not seem feasible. We further conclude that presently experiments
seem to be the most viable option to determine the global aerodynamic
characteristics of a kite.
In Table we list experiments described in the literature
to determine the lift-to-drag ratio of kites.
The relative flow velocity at the wing is denoted as va and the power
setting up describes the symmetric actuation of the rear suspension
lines of the kite. A high value of up means that the wing is powered,
while a low value of up means that the wing is depowered (see Eq. ). The variety of methods, test conditions and kites as well
as generated results makes it difficult to derive a clear trend.
conducted a performance study of different single-line kite
designs used for wind anemometry. A first quantitative aerodynamic assessment
method for power kites was presented by ,
, and . The test procedure involves
flying kites on a circular trajectory indoors as well as outdoor towing
tests.
A similar manual test procedure for determining the lift-to-drag ratio of a
surf kite was proposed by . The kite is flown in horizontal
crosswind sweeps just above the ground, measuring the achievable maximum
crosswind flight speed vk,τ of the kite at a downwind position
together with the wind speed vw. Assuming that the measured wind
speed is identical to the wind speed at the kite, the lift-to-drag ratio
can be calculated from :
vk,τ=LDvw.
The method can be generalized to characterize the aerodynamics of kites
flying complex maneuvers by either measuring or estimating the unperturbed
relative flow velocity va in the vicinity of the wing.
Figure shows a self-aligning Pitot tube setup mounted in the
bridle line system between the kite and its control unit.
Pitot tube during calibration in the wind tunnel (a)
and suspended in the bridle line system of a remote-controlled 25 m2 LEI V2 kite during a flight test (b).
The placement of the Pitot tube in the bridle line system was chosen to avoid
a perturbation of the relative flow by the wing and the control unit.
However, concluded that the quality of the measurement
data of this setup was insufficient and thus estimated the wind speed at the
kite from other available data. In the absence of reliable velocity measurements,
describe an approach to estimate the lift-to-drag ratio of
the airborne system components from measured force and position data.
have mounted a Pitot tube directly on the center strut of
a small surf kite to measure the relative flow speed. Together with data
from other onboard sensors, this has been used to feed an extended Kalman
filter to get an optimal estimate of the aerodynamic force and torque
generated by the kite as well as the relative flow velocity vector and other
kite state variables.
and used towing test setups to generate a
variable relative flow at the wing. Operating on days with calm wind allows
for measurements at well-defined relative flow conditions.
developed a similar trailer-mounted towing test setup to measure the
lift-to-drag ratio and aerodynamic coefficients of surf kites. The test
procedure includes active depowering, which in general aerospace engineering
terminology is denoted as a change in the trim of the wing and measuring line
angles at the test rig. For future experiments,
recommends the use of an airborne flow sensor to avoid the uncertainties
caused by the wind environment and by the sagging of the tether.
describe a setup to measure the aerodynamic performance of
kites for ship traction applications. Using a three-dimensional load cell to
record the traction force vector and a wind profiler to determine the wind
velocity at the kite, the technique is applied to determine the lift-to-drag
ratio of kites during crosswind maneuvers.
The companies Kitepower B.V. , a startup of Delft University of
Technology, Kite Power Systems (KPS) and Skysails Power
are currently developing and testing AWES with soft kites
that are operated on a single tether and controlled by a suspended cable
robot. These prototypes have reached considerable sizes (see, for example,
Fig. ) and for this reason the use of measurement data
acquired during flight operation is the only viable option for characterizing
the aerodynamics of the complete airborne system.
LEI V5.40 kite with 40 m2 wing surface area controlled by a
suspended cable robot. This prototype temporarily reached a tether force of
15 kN and a mechanical power of 100 kW during a test flight in May 2018
.
None of the other experimental setups presented in
Table allow us to execute dynamic flight maneuvers and
handle kites with a wingspan of 10 m or larger at flight speeds above 20 m s-1 while withstanding tensile forces of several kN or more. It is the
objective of the present study to develop an experimental method for
aerodynamic characterization of large deformable membrane kites that are used
for energy conversion. At the core of this method is a novel setup for the
accurate measurement of the relative flow conditions at the kite during
energy generation in pumping cycles. Since the setup is additional equipment
for tests of a commercial prototype the mounting of the setup has to consume
as little time as possible.
The paper is organized as follows. In Sect. we
describe the airborne components of the kite power system, the measurement
setup and the data acquisition procedure. In Sect.
we describe how the power setting is related to the angle of attack of the
wing and how the aerodynamic properties are derived from the measured data.
In Sect. the results are presented and discussed.
System description and data acquisition
The experimental study is based on the AWES
prototype developed and operated by the company Kitepower as a test platform
within the EU Horizon 2020 “Fast Track to Innovation” project
REACH . The prototype can be classified as a
ground-generation AWES operating a remote-controlled soft kite on a single
tether. This general setup is illustrated schematically in
Fig. c.
Basic components of the kite power system (c) and wing with suspended
control unit, together denoted as the kite (b); measurement frame
attached to the power lines (a). Sensor positions: tether force Ft
and tether reel-out speed vt are recorded at the ground station (1), GPS and
IMU modules are mounted on the center strut of the kite (2), and the kite control unit (3)
actuates the wing for steering and changing its power state, also measuring the instantaneous lengths
of steering and depower tapes; the relative flow sensors for inflow angles αm, βs
and apparent wind speed va are mounted on a rigid frame (4) that is attached to
the two power lines connecting to the inflatable leading edge tube of the wing. The depicted
velocity va* is the component of the apparent wind velocity va projected into the drawing plane.
The main system components are the ground station for converting the linear
traction motion of the kite into electricity, the main tether and the
C-shaped, bridled wing with the suspended kite control unit (KCU). In the
following, we will denote the assembly of the wing, bridle line system and KCU as
the “kite”. To generate power the kite is operated in cyclic flight patterns
with alternating traction and retraction phases. During the traction phase
the kite performs crosswind maneuvers, such as figure-eight or circular
flight patterns, while the tether is reeled off a drum that is connected to a
generator. In this phase the AWES generates electricity. For the subsequent
retraction phase the crosswind maneuvers are stopped and the generator is
operated as a motor to reel in the tether. This phase consumes some of the
generated electricity. To maximize the net gain of energy per cycle the wing
is depowered during retraction. Both steering lines are released
symmetrically such that the entire wing pitches down to a lower angle of
attack, which significantly reduces the aerodynamic lift force.
Just below the KCU the main tether splits into two power lines of constant
length that run along the sides of the KCU and support the inflatable leading edge tube and also partially the strut tubes of the wing. This is depicted
schematically in Fig. a and b and in more detail in
Fig. a without the measurement setup. A short line
segment connects the KCU to the end point of the main tether, while steering
and depower tapes connect the KCU to the steering lines and eventually, via a
fan of bridle lines, to the wing tips and trailing edge. Details on this
specific layout will be described in the following section. The KCU can
actuate the two steering lines either symmetrically to power and depower the
kite or asymmetrically to steer the kite.
An almost fully powered LEI V3 kite (a), a depowered kite (b) and deformation
of the wing by extreme steering input in depowered state (c). Dots indicate the end of the depower tape.
The actuation of the wing as part of the kite is illustrated in
Fig. . The photographic footage from 23 August 2012 documents tests of a
mast-based launch setup. While the left photo is taken during crosswind
maneuvers during power generation, the two right photos are taken during a
flight maneuver close to the launch mast.
The sensors on the ground station (1), the kite (2) and the KCU
(3) provide data that are required for the autopilot of the kite power
system (see Fig. ). The experiments described in this paper
have been performed with a LEI V3 kite with a wing surface area of 25 m2,
a battery-powered KCU for 2–3 h of continuous operation and a ground
station with 20 kW of nominal traction power. These components have been
developed by the kite power research group of Delft University of Technology
and reflect the technology status in 2012 .
Because the membrane wing is continuously deforming during operation it is
not as straightforward as for a rigid-wing aircraft to define the orientation
of the kite relative to the flow. One option is to use the inflated center
strut as a reference component to mount the flow measurement equipment
. Mounting the equipment directly on the
suspended KCU is not considered to be an option because this relatively heavy
component is deflected substantially when flying sharp turns
and can also exhibit transverse vibrations. Another
option is to mount the measurement equipment on the two power lines. These
lines transfer the major part of the aerodynamic force from the wing to the
tether and for this reason are generally well tensioned and span a plane that
characterizes the orientation of the kite (wing and suspended KCU).
Considering the deformation of the membrane wing by asymmetric and symmetric
actuation as well as aeroelasticity, we consider this plane to be the most
suitable reference geometry.
Figure a illustrates how the three relative flow sensors
(4) are mounted on a rigid frame that is attached to the two power
lines about 8.5 m below the wing. In Appendix we use a
simple lifting-line model of the wing to show that the assumption of free-stream conditions at this distance from the kite is justified. The Pitot tube
can rotate freely around its pitch and yaw axis to align with the relative
flow, measuring the barometric pressure, the differential pressure and the
temperature from which the apparent wind velocity va can be
calculated. The two flow vanes are used to determine the inflow angles
αm and βs, which are measured from the normal vector
of the plane spanned by the two power lines. The two angles are measured by
total magnetic encoders with a resolution of 0.35∘. The data are
recorded at a frequency of 20 Hz, converted to a digital signal by a
Pixhawk® microcomputer, transmitted to the KCU via antenna and from
there to the ground station to be logged simultaneously with all other
acquired sensor data. It is important to note that the relative flow sensors
are add-on measurement equipment for the present study and are not essential
for the operation of the kite power system. More information on the sensors
and the measurement setup can be found in .
The new setup addresses two shortcomings of earlier attempts to determine
the relative flow conditions at a kite, as illustrated in Fig. .
Firstly, a self-aligning Pitot tube alone can measure only the magnitude of
the relative flow velocity but not its direction. The orientation of the wing
relative to the flow, however, is important information for the aerodynamic
characterization. Secondly, the tensile suspension of the Pitot tube in the
bridle system of the kite was not sufficiently robust against perturbations,
which negatively affected the quality of the measurement results.
describe a similar setup for gliding parachutes, mounted in
the bridle lines between payload and wing, to measure the angle of attack and
relative flow speed. By choosing a setup that flies with the kite we are
able to acquire the relative flow conditions in situ during operation of the
full-scale system and are not constrained by the traction force limit of a
particular ground testing rig. This allows us to also characterize the
aerodynamics of power kites that produce much more lift force than usual surf
kites.
Front view (a) and side view (b) of the LEI V3 kite with reference
frames, geometric parameters, mass distribution and definition of the reference
chord cref. The total wing surface area is denoted as S, while the
projected value is denoted as A. The mass of the bridle lines is part of the wing mass.
The side view distinguishes between the physical (real) kite and bridle line system,
displayed in the background, and the overlaid simplified geometric depower model. The
explicit dimensions describe the unloaded design shape of the wing.
Data processing
The raw data from the rotary encoders and the pressure sensor can have
missing data points and can also fluctuate due to variations in the supply
voltage. To address these issues we apply a moving-average filter using the
MATLAB® function “smooth” with a span of seven measurement points
(0.3 s). This operation returns a smooth signal while still being able to
capture systematic oscillations that occur at frequencies of up to 1.2 Hz
. In the following, we describe how the relative flow data
are used together with the data from the other sensors to determine the
aerodynamic properties of the kite.
Geometry and reference frames
The geometry of the wing and the layout of the tensile support system,
comprising bridle lines, steering and depower lines, as well as steering and
depower tapes, are illustrated in Fig. .
The two pulleys are attached to the two branches of the rear bridle line
systems and allow the steering lines to slip freely to adjust the line
geometry to the actuation state. The instantaneous length of the depower tape
is denoted as ld. Both renderings show a depowered kite, as
illustrated by the photo in Fig. b, using the design
shape (CAD geometry) of the wing and thus not accounting for additional
deformation.
As shown in Fig. b, we define two different reference
frames to describe the orientation of the tether and the kite. The tether
reference frame (xt,yt,zt) is attached to the kite end
of the tether with its origin at the bridle point B where the tether
splits into the two power lines. The zt axis is tangential to the
tether, while the xt axis is located in the plane spanned by the
zt axis and the normal vector of the plane spanned by the two
tensioned power lines. This definition is identical to the “kite reference
frame” used by as a basis for a point mass model. The
measurement reference frame (xm,ym,zm) is attached to
the rigid frame on which the relative flow sensors are mounted. As depicted
in Fig. a, the zm axis is aligned with the two
upright members of the frame, while the ym axis is aligned with the
transverse member. Because the measurement frame is attached to the two
tensioned power lines the xm axis defines the heading of the kite.
The rotation of the xt axis into the xm axis is described by
the angle λ0, which is not constant and cannot be controlled
actively. The angle depends on the aerodynamic load distribution acting on
the wing, the kite design and the bridle layout. The inflow angles
βs and αm are determined in the measurement
reference frame. Because the zm axis can be regarded as the yaw axis
of the kite, the inflow angle βs is equivalent to the sideslip
angle. Similarly, the ym axis can be regarded as the pitch axis of
the kite and the inflow angle αm is a measure for its pitch
orientation with respect to the relative flow.
To transform αm into a meaningful angle of attack of the wing we
define a reference chord cref, which describes the pitch orientation
of the wing within the kite system as a function of the symmetric actuation
of the steering lines.
This two-dimensional, simplified geometric depower model is illustrated in
Fig. b. For the fully powered kite, the reference chord
is defined to be perpendicular to the plane spanned by the power lines.
Depowering the kite is modeled as a pitching of the reference chord around
the front suspension point, while the real wing additionally deforms by
spanwise twisting and bending. The specific bridle layout of the LEI V3 kite
shifts the front suspension point about 0.5 m backwards from the leading
edge.
The rotation is described by the depower angle αd and by
definition the fully powered state is given by αd=0. A reference
chord that is perpendicular to the power line plane is a reasonable
approximation of the fully powered wing, which is designed for optimal
transfer of the aerodynamic load from the membrane wing to the bridle line
system. These structural requirements are generally best met if the front
bridle lines, which transmit most of the forces, connect perpendicularly to
the wing. It is in principle straightforward to account for a constant offset
angle α0 ; however, for the investigated kite
design this offset angle is rather small. For this reason we set
α0=0.
The geometrical dimensions are extracted from the CAD geometry of the kite.
The distance of the front suspension point from the bridle point is d=11.0
m. For the fully powered kite, the distance to the rear suspension point
from the bridle point is l0=11.22 m. The length of the reference chord can
be determined as cref=2.2 m. The kite is depowered by extending the
rear suspension of the wing by Δl. In the following section, we
relate this length extension to the deployed length ld of the depower
tape and the relative power setting up. The angle of attack of the
relative flow with respect to the reference chord is calculated from the
measured inflow angle and the depower angle as
α=αm-αd,
while the angle of attack of the relative flow with respect to the tether
reference frame is calculated as
αt=αm+λ0.
Figure illustrates how the azimuth angle ϕ, the
elevation angle β and the radial distance r are used to specify the
position of the bridle point B relative to the ground attachment
point O.
Ground reference frame (xw,yw,zw),
tether reference frame (xt,yt,zt), heading
angle ψ and spherical coordinates (β,ϕ,r). Only in the case of a
straight tether does the zt axis point in the radial direction to the
ground attachment point O.
The heading angle ψ specifies the orientation of the kite in the local
tangential plane τ. The angle is measured between the local upward
direction (dotted line) and the projection of the xt axis onto the
tangential plane. Similarly, the course angle χ (not displayed)
specifies the direction of the tangential kite velocity vk,τ
in the local tangential plane. Combining Eqs. () and () to eliminate the measured inflow angle αm we
can differentiate three distinct contributions to the angle of attack:
α=αt-λ0-αd.
The contribution of the tether angle of attack αt is due to the
flight motion of the kite, represented by the bridle point B, through
the wind environment. The contribution of the line angle λ0 is due
to the pitch of the entire kite, represented by the plane spanned by the
power lines, with respect to the tether. The contribution of the depower
angle αd is due to the pitch of the wing with respect to the
plane spanned by the power lines.
Kinematics of depowering
Instead of assuming a linear correlation between the relative power setting
up and the depower angle αd, as proposed by
, we use the geometric depower model illustrated in
Fig. b to calculate an analytic equation for the
depower angle αd by applying the law of cosines:
cos(90∘+αd)=d2+cref2-(l0+Δl)22dcref.
Considering the specific layout of the actuation system depicted in
Fig. a, the extension of the rear suspension of the
reference chord is approximated as
Δl=12ld=1-up2ld,max,
where ld is the deployed length of the depower tape with the maximum
value ld,max=1.7 m. Because we employ a pulley system to decrease the
required forces in the actuation system, only half of the length of the
depower tape is translated into lengthening or shortening the rear suspension
of the reference chord. Equation () shows that a full
depowering of the wing with up=0 leads to a maximum extension Δlmax=1/2ld,max, from which a maximum depower angle of
αd,max=24∘ can be calculated on the basis of
Eq. ().
Aside from a general increase in the aerodynamic load, an increasing angle of
attack also leads to a gradual backwards shift of the load distribution
towards the rear of the wing. To balance this load shift, the entire kite has
to pitch down around the bridle point, which increases the angle
λ0. This aerodynamic characteristic of LEI tube kites has been
observed experimentally by and . Because
the chordwise location of the center of pressure controls how the total
aerodynamic load is distributed on the front and rear bridle line systems,
measuring the line forces is a way to quantify the load shift. To describe
how much of the total load is transferred through the front bridle lines, we
define the force ratios Ft,f/Ft,r and
Ft,f/(Ft,f+Ft,r), where Ft,f and Ft,r are
the magnitudes of the resultant forces transferred through the front and rear
bridle line systems, respectively (see also Fig. ).
Distribution of tensile forces in the bridle line system from low to high
power setting (red, green, blue, black) measured for a commercially available LEI Hydra
V5 kite with 14 m2 wing surface area by Genetrix Kiteboarding adapted from.
The force ratios measured for an LEI Hydra V5 kite are illustrated in
Fig. , indicating that the aerodynamic load gradually shifts
towards the rear bridle lines for an increasing power setting up. At the
highest power setting the loads transferred through the front and rear bridle
line systems are about equal.
Since we did not measure the bridle line forces of the LEI V3 kite we assume
a constant position of the center of pressure, derived as an average of
several different types of kites by . Measuring the bridle
line force ratio for the LEI V3 kite in flight would help increase the
accuracy of this study but would require additional instrumentation and is
recommended for future tests.
However, it is not only the shifting center of pressure that affects the
orientation of the kite with respect to the tether. Another important factor
is the gravitational and inertial force of the KCU, which contributes almost
40 % of the kite system mass and is suspended below at considerable distance
from the wing (see Fig. ). When the kite is flying upwards,
the gravitational force pulls the suspended KCU down, increasing
λ0, while when it is flying downwards, the effect is inverted and
λ0 is decreased. When the kite is flying sideways, the mass of the
KCU affects the roll orientation of the kite with respect to the tether. In
general, the gravitational effect of the KCU increases towards lower
elevation angles and lower tension in the tether.
The competing effects of kite aerodynamics and KCU mass are illustrated in
Fig. for two extreme load cases.
Side view of a kite partially depowered during a landing maneuver (a)
and fully powered during a crosswind flight maneuver (b). The photo on the right
was taken during a flight test in which the KCU was replaced by a ring that collected the joined
power lines and the two steering lines and redirected them as a triplet of parallel lines to
the pilot on the ground. The position of this ring is indicated by an overlaid transparent image of the KCU.
The partially depowered kite on the left is flying statically and is thus
only lightly loaded. For this reason, the rear bridle lines are sagging and
the wing membrane is not taut. From the photo we can measure a depower angle
αd=5.6∘ and a line angle λ0=14.7∘.
The relatively large line angle indicates that the gravitational effect of
the KCU mass by far outweighs the aerodynamic effect. On the other hand, the
fully powered kite on the right is flying fast crosswind maneuvers and is
thus heavily loaded. As a result, the wing membrane and bridle lines are
taut. In this particular test, the wing is operated without the KCU and
λ0 thus depends solely on the aerodynamic load distribution on the
wing. From the photo we can measure a line angle λ0=5.1∘
and can further recognize that the concept of a reference chord
perpendicular to the front bridle lines is a good representation of the
actual center chord of the wing.
In this work, the wing is idealized as a lifting surface with fixed geometry.
The proposed geometric depower model is a simplified two-dimensional
approximation of the complex three-dimensional aeroelastic response of the
bridled membrane wing.
The photographic footage depicted in Fig. illustrates how the
wing shape changes when transitioning from a depowered to powered state.
Depowered kite (a) and powered kite (b) from a video
camera mounted on the KCU and looking into the wing. The video sequence
of the entire maneuver is available from .
The GoPro® video camera with an ultrawide angle “fisheye” lens
captures the entire wing and bridle line system, from which we can make
several qualitative comparisons. It is obvious that the powering of the wing
tensions the entire bridle line system such that the two pulleys (marked by
circles) move forward towards the leading edge. The increasing projected
center chord indicates that the wing pitches into the projection plane. The
slightly increasing projected span indicates that the entire wing straightens
under the substantially increased aerodynamic loading when being powered.
This effect is also described by p. 61. The
curvature (sweep) of the leading edge tube also slightly decreases. It is clear
that these effects cannot be described by a geometric model without
accounting for the fluid–structure interaction problem, including membrane
wing, bridle line system and steering actuation.
Determining the Lift-to-drag ratio
A common method to estimate the lift-to-drag ratio of a kite is to measure
the elevation angle β of the tether with the horizontal during static
flight . Disadvantages of this method are the
uncertainties arising from the tether sag and the usually unknown wind
conditions at the position of the kite. introduces the
tether angle of attack αt to account for all forces acting on
the kite system above the bridle point, in our case the KCU, the bridle line
system and the wing. This angle, which is related to the measured inflow
angle αm by Eq. (), can thus be used to
characterize the aerodynamics of the entire kite. However, the value of
αt also depends on the gravitational and inertial forces acting
on the kite components. These vary with the specific flight situation such as
flying upwards, downwards, sideways or turning maneuvers, as outlined in the
previous section.
To understand how the aerodynamic characteristics of the kite are related to
the kite design and measured properties we first neglect the effect of
gravity. For steady flight, the resultant aerodynamic force Fa
is in equilibrium with the tether force Ft. Because the
flexible tether can only support a tensile force but no bending moment, the
two forces are tangential to the tether at the bridle point, pointing in
opposite directions. The aerodynamic force can be further decomposed into
lift and drag components L and D, respectively. By
definition, the drag force is aligned with the apparent wind velocity vector
va and because Fa is aligned with zt, the
lift-to-drag ratio L/D is related to the tether angle of attack
αt by
LD=cotαt.
When flying on a curved path, as, for example, during figure-eight
maneuvers, the centrifugal force perpendicular to the tether needs to be
balanced by an additional lateral component of the aerodynamic force vector.
How this side force Fa,s in the yt direction is generated depends
on the specific type of wing and the implemented steering mechanism.
Classical rigid-wing concepts with aerodynamic control surfaces
and the Skysails ram-air wing roll
the wing such that the lift vector tilts towards the center of turn. Most
flexible membrane wing concepts, on the other hand, yaw and twist the wing
using the vertical surface of the wing tips to generate a side force and
turning moment. This mechanism is depicted in Fig. and
described in more detail in Sect. 17.3.1 and
Sect. 15.2.2.
In a similar way, the effect of gravity needs to be balanced by an additional
component of the aerodynamic force vector. This is formally expressed by the
force equilibrium at the bridle point for steady flight:
Fa+mg+Ft=0.
However, in difference to the centrifugal acceleration during turning
maneuvers, the resultant gravitational force mg acts not only
sideways but also depending on the orientation of the kite in all three
directions, xt, yt and zt. To derive the required
balancing components of Fa we express the resultant
gravitational force of all kite components in the tether reference frame:
mg=-cosβcosψcosβsinψsinβmg.
This representation is based on the assumption of a straight tether such
that the angle between the horizontal and the zt axis is identical to
the elevation angle β of the kite (see Fig. ).
The force equilibrium given by Eq. () is illustrated
in Fig. for the special case of an upwards-oriented kite
(ψ=0∘).
Force equilibrium of a kite in steady-state flight for the special
case of the kite oriented upwards with ψ=0∘, flying in the plane spanned
by the wind velocity vector and the vertical, described by ϕ=0∘. The
forces acting on the kite components are lumped to the bridle point. See Fig. 2.11
for an illustration of the force equilibrium extended to the general case of kite flight in three dimensions.
The vector diagram shows how the gravitational force is compensated for by an
upwards rotation of the aerodynamic force by an angle Δα. For
arbitrary orientation of the kite, the aerodynamic force components that are
required to compensate for the gravitational force are given by the inverse of
Eq. (). Considering the compensation in the
xt–zt plane only, we can derive the following relation between
tether force, gravitational force and the compensation angle Δα:
tanΔα=mgcosβcosψFt+mgsinβ,
which is illustrated by the shaded right triangle in Fig. for
the special case ψ=0∘. Using the tether angle of attack
αt defined by Eq. (), the lift-to-drag ratio can
be determined from
LD=cot(αt-Δα).
The gravitational force in the yt direction is compensated for by a steering
force
Fa,s=-mgcosβsinψ,
which for the investigated type of kite is generated by a sideslip angle
βs . When flying figure-eight maneuvers,
the angles β and ψ continuously vary and the gravity
compensation accordingly alternates through the xt, yt and
zt directions. Neglecting this effect would have the consequence that
the measured aerodynamic characteristics seemingly vary along the flight
maneuver.
For orientations with an upward component (-90∘<ψ<90∘),
we obtain positive values for Δα. For orientations with a downward
component, gravity opposes the aerodynamic drag of the wing, resulting in
negative values for Δα. The elevation angle β of the kite
is determined by the position of the kite with respect to the ground station
(see Fig. ) and only in the case of a straight tether identical to
the inclination of the tether force (see Fig. ). One of the
key advantages of the described measurement method is that sagging of the
tether does not directly affect the measurement of L/D. We use the
elevation angle β only to correct for the effect of gravity in
Eq. (). This correction is also affected by the ratio of
gravitational force to tether force. In contrast to this, sagging has a
direct effect for methods that are based on ground-based measurements of the
tether angle of attack, as proposed, for example, by .
The tether angle of attack αt can be calculated from
Eq. () using the measured inflow angle αm and
the line angle λ0. The latter is determined numerically by solving
for the quasi-steady force equilibrium of the simplified mechanical model
illustrated in Fig. .
Fully powered kite (a) and simplified mechanical model of the kite
system (b), including the wing, measurement setup and KCU, showing external forces
(black: gravitational forces and tether force at the bridle point, blue: aerodynamic forces)
and internal forces (red: bridle line forces) to calculate the bridle line angles
λ1 and λ2. Depicted is the special case of an upwards-oriented kite
with apparent flow velocity and all model forces in the drawing plane. Force vectors are not to scale.
In this framework, the individual components of the kite are idealized as
point masses that are exposed to external forces (gravity, aerodynamic lift
and drag, tether force at the bridle point) and internal bridle line forces.
The drag and the mass of the bridle line system are assigned to the wing. The
total resultant aerodynamic force and the gravitational force acting on the
kite components are thus decomposed as
Fa=Lwing+Dwing+DKCU+Dsensor,mg=mwing+mKCU+msensorg.
In a first step, we calculate the resultant aerodynamic force
Fa,wing=La,wing+Da,wing that is
required to balance the given tether force Ft and the
aerodynamic and gravitational forces acting on the kite components.
Approximating the KCU and the measurement setup as blunt bodies with an
aerodynamic drag coefficient of CD=1.0, we calculate a drag
contribution of the KCU of about 10 % of the wing drag and a contribution of
the measurement setup of about 1 %.
In a second step, we use a shooting method to iteratively adjust the bridle
line angles until the two-dimensional model geometry for the known external
forces and bridle line lengths is in quasi-steady equilibrium. For this we
assume that a bridle line force is always in line with the connection line of
the two attachment points. We further assume that the center of pressure and
the center of mass of the wing are both at 25 % of the reference chord (see
Fig. ). This is in line with the mass distribution used by
and the average ratio of 3:1 for the forces in front and
rear bridle lines measured by for different kites at
various power settings. Starting from an initial guess for the line angle
λ1, we calculate the angle λ2 and the respective angles for
the steering lines. Based on the resulting geometry, we then compute the
distance between the front and rear bridle attachments on the chord line of
the wing. If this distance is larger than cref, the value of
λ1 is reduced and the calculation repeated. The iteration loop is
terminated when the target distance cref of the bridle attachment
points is reached. The algorithm generally converges within four iterations
using a termination criterion of 0.01 m or 0.5 %.
Compared to ground-based methods, for example, with angular sensors at the
ground attachment point of the tether, the sagging of the tether does not
affect the measurement significantly. Also, the effect of gravity on the
measurement setup was found to be negligible. This is because the measurement
setup is a lightweight construction compared to the KCU and because the power
lines are generally well tensioned. We have observed that the line angles
λ1 and λ2 in general differ only by 0.1∘ to
0.2∘ such that the power lines can practically be considered
straight. We thus use the mean value of λ1 and λ2 as line
angle λ0. The KCU, on the other hand, has a considerable effect,
especially during reel-in maneuvers when the force in the rear suspension
lines is of the order of the gravitational force of the KCU.
The calculated values vary over 0∘<λ0<2∘ for
flying downward. For upward flight and during reel-in we find values of
3∘<λ0<7∘. For low tether tension and upward flight
values of 10∘<λ0<12∘ occur. These computed ranges
agree well with photographic evidence, such as the snapshots shown in
Fig. . The highest values occur when both tether tension and
elevation angle are low, which is the case during launch and landing.
When all lines are well tensioned and straight, the pitching of the kite
around the bridle point does not affect the bridle geometry. However, the
rear bridle lines are not always well tensioned, as can clearly be seen for
the landing maneuver shown in Fig. a. When flying
upwards during power production (see Fig ), the effects of
drag and gravity are both in a downward direction, which can cause a
measurable sag of the rear bridle lines. This effective shortening of the
bridle lines increases the powering of the kite and can be modeled as a
reduction of the depower angle αd.
Determining the lift coefficient
The lift coefficient CL is a dimensionless number,
L=12ρCLva2A,
characterizing the lift force as a function of the air density ρ,
relative flow velocity va and projected wing surface area A.
Density and relative flow velocity are measured directly, while a constant
value for the projected wing surface area is used (see the table included in
Fig. ). Using the lift-to-drag ratio L/D we can compute the
lift force generated by the kite as
L=FaLD21+LD2.
We resolve Eq. () in the horizontal and vertical
directions to relate the force magnitudes as
Fa=(Ftcosβ)2+(Ftsinβ+mg)2,
again making use of the idealization that the tether force is aligned with
the radial direction from the ground attachment point. The special case of an
upwards-oriented kite with all forces in the drawing plane is illustrated in
Fig. .
Results
The data for this study were acquired during a 1 h test flight of the
prototype described in Sects. and on 24 March 2017 at the former naval air base
Valkenburg, close to Leiden, the Netherlands. A video camera mounted on the
measurement setup documented that all sensors were moving freely in the
airflow and did not exhibit any visible faulty behavior. This is illustrated
in Fig. , with the diagram showing 27 s at the beginning
of a representative traction phase.
Video still of the relative measurement setup taken from the right power line (a), raw values
of apparent flow velocity va,
and inflow angles αm and βs recorded over time at
the beginning of a representative traction phase (b).
The first 180 s of the 1 h test flight are available as video
footage from . The maximum apparent flow velocity occurs
during the first 2 s of the depicted time window, when the kite
transitions from the retraction to the traction phase. Because the kite flies
downwards during this maneuver, it is additionally accelerated by the effect
of gravity, which leads to a temporary increase in the apparent flow
velocity.
Our measurements contradict the earlier study of , who
reported considerable variations in the angle of attack (up to 30∘
during the traction phase) and sideslip angle (-20∘<βs<20∘). In our study, the angle of attack is limited to a narrow range
of 6∘<α<16∘ during the traction phase. The measured
sideslip angle deviates from its mean value by a maximum of
Δβs=10∘ only during very sharp turns, which is
indicative for the high aerodynamic side force produced by a moderate sideslip angle. We conclude that an accurate determination of the relative flow
at the kite is not feasible without in situ measurements at the kite. Using
only GPS and IMU data and ground-based measurements, as proposed by
, leads to a substantial degradation of the achievable
accuracy. The apparent flow speed is around va=18 m s-1 during the
traction phase and va<15 m s-1 during the retraction phase. In the
analyzed data set, the mean value of the sideslip angle was not zero, which
we would have expected for a symmetric kite. This offset resulted from an
asymmetric layout of the bridle lines, causing the kite to fly in an
asymmetric pattern during the traction phase. We recommend investigating the
effect of the sideslip angle on the kite aerodynamics in a future study
using alternative data for a verified symmetric layout of the bridle line
system.
A common technique to analyze measurement data from wind turbines or other
rotating machinery is phase averaging. In contrast to we
did not use this technique because of the difficulty to determine a clear
phase location of the data. Harvesting wind energy with tethered flying
devices operated in pumping cycles has many more degrees of freedom than
conventional wind turbines and even though the operation in a variable wind
environment requires these to be actively controlled, the location of the
lightweight devices along the flight path is tightly coupled to the evolution
of the wind field along this path. For a wind turbine with rotor blades that
are mechanically linked and have a comparatively large rotational inertia,
the determination of a phase location is comparatively straightforward.
Instead of using rigorous phase averaging, we only differentiate between
traction and retraction phases, subdividing the crosswind maneuvers further
into flying upwards (against gravity) and flying downwards (with gravity).
This can be regarded as a low-resolution phase averaging tailored to the
specific physics of tethered flight in pumping cycles. However, the available
data covered only five separate cycles, which is by far not sufficient for a
meaningful statistical analysis.
Reeling oscillations
The flight data illustrated in Fig. exhibit strong
fluctuations at a distinct frequency of 1.2 Hz in both va and
αm. These oscillations occur repeatedly for several seconds
during the retraction and traction phases. Other independently measured
variables also exhibit this behavior, for example the tether force
Ft, the tether reeling speed vt, the pitch rate of the kite,
and the forward and downward accelerations measured by the
wing-mounted IMU. To identify the cause of these oscillations we considered
two possible mechanisms in a previous study : a first mode
of radial oscillations of the kite that are commanded by the reeling control
of the ground station and a second flight dynamic mode. These tangential
oscillations in the forward–backward direction are kinematically coupled to pitch
oscillations. Based on a simple model of a driven oscillator, we determined
for the flight dynamic mode a relatively strong damping, with a coefficient
ζk of 0.63, and eigenfrequencies fk of 0.81 Hz for the
traction phase and 0.39 Hz for the retraction phase. Because these values
differ from the frequency of the observed fluctuations we conclude that we
are not observing a flight dynamic mode of the kite system but that the
reeling controller of the ground station is the root cause of the
oscillations. This is supported by the additional observation that the
fluctuations cease when the reeling of the tether stops. It is clear that
this behavior could be suppressed by an adjustment of the ground station
controller; however, this is not part of the study.
To estimate the effect of these forced oscillations with frequency
fGS=1.2 Hz on the kite aerodynamics we determine the reduced
frequency :
k=fπcva.
Using a chord length of c=2.7 m and an apparent flow speed of va=20 m s-1, we calculate a value of kGS=0.5. This means that the flow
around the kite is unsteady, which in turn can cause a phase shift of the
aerodynamic load with respect to the angle of attack. To mitigate the effect
of a possible phase shift, we smoothen the data over an interval of T=2.5 s,
which is equivalent to three oscillation periods. In doing this we
essentially regard the forced oscillations and resulting unsteady
aerodynamics of the kite as a subscale process, which we filter out to retain
the assumption of quasi-steady flight.
To assess the effect of the turning maneuvers during crosswind flight on the
aerodynamics of the kite we determine a characteristic frequency of
fturn=0.1 Hz, which corresponds to a half turn in about 5 s.
The corresponding reduced frequency of kturn=0.042 indicates that the
aerodynamic timescale is more than an order of magnitude smaller than the
turning timescale, which also confirms the assumption of quasi-steady flight
from this perspective.
Lift-to-drag ratio
The lift-to-drag ratio L/D is a key parameter to characterize the
aerodynamic performance of a wing. As described by
Eq. (), this parameter determines how fast a
kite can theoretically fly in a given wind environment and by that also what
tether force can be achieved for a given size of the wing
. In contrast to a conventional aircraft, the
C-shaped flexible membrane wing is used as a single aerodynamic control
surface with the double function of steering and generating a tether force
that can be modulated over a wide range. This is of particular importance for
the considered operation in pumping cycles because the achievable net energy
per cycle crucially depends on the ability of the wing to alternate between a
high lift-to-drag ratio during the traction phase and a low ratio during the
retraction phase.
In Fig. we investigate the influence of the angle of attack
α of the wing and the power setting up of the kite.
Measured lift-to-drag ratio L/D of the kite plotted over
the angle of attack α of the wing (a) and relative power setting up of the kite (b). No filtering or smoothing is applied to the data.
The lift-to-drag ratio of the entire kite (all components from bridle point
outwards) is derived on the basis of Eq. () using
Eq. () to account for the measured flow angle αm
and the estimated line angle λ0 and Eq. () to
account for the effect of gravity, expressed as compensation angle
Δα.
No further filtering or smoothing is applied to the data. Although the effect
of gravity on all kite components is taken into account as is the
aerodynamic drag on the KCU and measurement setup, the data are still scattered
considerably. In the following we will show that this is to a considerable
degree due to occasional dips in the tether tension, steering actuation and
the associated sideslip angle.
In Fig. a we can distinguish a distinct region of lower
angle of attack, -7∘<α<3∘, indicating the retraction
phases and a distinct region of higher angle of attack, 7∘<α<15∘, indicating the traction phases. In Fig. b the retraction
phases are indicated by power settings
up<0.55, while the traction phases are indicated by power settings
up≈1. Values between these regions are typical for the
transition between the retraction and traction phases. During the traction
phases we measure an average lift-to-drag ratio of about L/D=4, and during
the retraction phases we measure an average ratio of about L/D=3, which is
desired to reduce the tether force and thus also the energy consumption
during retraction of the kite.
In the next step we filter the data as outlined in Table ,
reducing the spreading and removing outliers.
Three filtering procedures applied to the measured lift-to-drag ratio.
Filter
Description
Reason
Visible effect
1
moving average
forced oscillations with fGS;
reduces spread
over T=2.5 s
remove subscale dynamics
during retraction
2
Ft>400 N
model limitation
eliminate outliers
3
exclude steering
strong deformation
eliminate outliers
The correlated effect of the angle of attack and the relative power setting
on the lift-to-drag ratio is illustrated in Fig. , for which we
have also applied the moving-average smoothing described in
Sect. (filter no. 1).
Measured lift-to-drag ratio L/D of the kite plotted over the angle of
attack α and colored by the relative power setting up. The
coloring ranges from blue, for lower values of up when retracting
the kite, up to dark red, for the fully powered kite with up=1 during
the traction phase. Table filters no. 1 and no. 2 have been applied.
To identify the cause of the high L/D values, we further exclude data
points with a tether force Ft<400 N (filter no. 2). For such low tether
tensions the assumptions of a straight tether and quasi-steady flight state
are no longer valid, which can lead to substantial measurement errors.
Excluding data points with Ft<400 N in fact eliminates many of the
unphysically high L/D values.
The diagrams in Figs. and show that for an
increasing power setting up the angle of attack α and the
lift-to-drag ratio L/D increase. A low angle of attack results in a low
lift force and therefore a low force ratio. The maximum of about L/D=5
occurs in the range 5∘<α<10∘ and is only reached for
up=1. For a higher angle of attack the force ratio decreases again
because of the substantially increasing drag force. The measured dependency
follows the same general trend as for conventional aircraft wings and was
already observed by .
Figure shows the temporal evolution of up and L/D
during pumping cycle operation.
Evolution of the lift-to-drag ratio during pumping cycle operation.
During the traction phases with up=1 we observe periodic drops to
force ratios L/D<4. The drops are correlated with the turning maneuvers and
are caused by the steering-induced deformation of the wing and the additional
drag component of the required side force .
To investigate the effect of the steering on the entire data set in
Fig. , we color the measured L/D data by the steering intensity.
Measured lift-to-drag ratio L/D of the kite plotted over the angle of
attack α of the wing and colored by the relative power setting
up, colored by the steering intensity ranging from blue for no
steering up to yellow and red for strong steering actuation during turning
maneuvers. Table filters no. 1 and no. 2 have been applied.
We can recognize that very strong turning maneuvers coincide with a low
tether force and extreme force ratios. During the traction and transition
phases, the lift-to-drag ratio for a specific power setting is significantly
lower when the steering system is active. This has also been shown in
. Next to the described effects of deformation and
steering-induced drag, there is also a feedback loop because an increasing
drag lowers L/D, which in turn increases αt and to a certain
extent also α. The increasing α lowers L/D further.
Comparison with aerodynamic models
and present two different
real-time-capable models for the dynamic simulation of pumping kite power
systems. In both approaches the aerodynamics of the kite are described by
CL(α) and CD(α) correlations that have been derived
from existing measurement data on two-dimensional sail wing sections.
According to the authors, major adjustments were required to fit the
simulated flight behavior of the kite to measured reference trajectories.
Both dynamic models predict the flight path and power production with
reasonable accuracy for a broad range of operational conditions and are thus
suitable for optimization of kite control.
Two different definitions of the angle of attack are used.
measure the angle from the center chord to the relative
flow velocity vector, while measures it from the
orientation of the wing-mounted IMU. Both definitions are difficult to
reproduce experimentally for subsequent measurement campaigns because the
orientation of the center chord is a virtual geometric property and can only
be estimated, while the IMU is mounted on one of the inflatable struts with
Velcro® tape, which introduces a considerable degree of uncertainty,
even when using the same kite.
To compare the two existing sets of aerodynamic correlations with our
measurement data we first need to eliminate the offsets introduced by the
different definitions of α. For this purpose we shift the L/D
correlations of and in the
α range such that the maxima occur at α=7.5∘, which is
where the maximum average L/D of our data set is located. For reference we
note that the maxima of the unshifted correlations occurred at
α=12.5∘ and α=16∘
.
As stated above the lift-to-drag ratio decreases during turning maneuvers
because of the additional drag of the wing tips. This can be clearly
recognized from the data plotted in Fig. , which exhibit
strong variations when flying crosswind maneuvers during the traction phases.
On the other hand, the existing aerodynamic correlations have been derived
for a wing in straight flight, with symmetric steering input.
, for example, has excluded from his analysis data points
that were associated with strong asymmetric steering input. We have applied a
similar filtering procedure to our data. In Fig. we compare
the filtered data with the existing aerodynamic correlations.
Comparison of measured lift-to-drag ratio with existing aerodynamic correlations. Table filters no. 1, no. 2 and no. 3 have been applied.
The correlation of is mainly based on five data sets
acquired with an LEI V2 kite with 25 m2 wing surface area, as shown in
Fig. b, and one data set acquired with a smaller LEI
Hydra V5 kite, as used for the diagram in Fig. . On the other
hand, the correlation of is based on aerodynamic models
for stalled and unstalled airfoils from , with additional
experience-based modifications for achieving a better fit with the
aerodynamics of an LEI tube kite. For system-level modeling,
distinguish between a large (LEI V3) and a small (LEI Hydra V5) kite using
lift-to-drag ratios of 3.6 and 4.0, respectively, during the traction phases
as opposed to 3.5 and 3.1, respectively, during the retraction phases.
Overall, we find a reasonable agreement between our measured data and
existing aerodynamic characterization attempts. The correlations of
and slightly overestimate the
lift-to-drag ratio, with force ratios L/D>4 even for angles
α>15∘. This is consistent with the common assumption of a high
angle of attack during the traction phase . Our measurements, however,
show that the angle of attack is lower and generally does not
exceed α=15∘. The lift-to-drag data proposed by
for traction and retraction phases correspond very well
with the average lift-to-drag ratios measured in these phases. The depowered
kite (up<0.5) and the powered kite (up=1) show different
trends. The data plotted in Fig. indicate that the
lift-to-drag ratio of the depowered wing depends mainly on the power setting
up, while the effect of the angle of attack is only minor. In
contrast to this, the force ratio of the powered kite depends mainly on the
angle of attack with L/D decreasing for increasing α.
With Eq. () we have formally separated three
fundamental contributions to the angle of attack α of the wing. While
the tether angle of attack αt and the line angle λ0
represent the contributions due to flight motion and pitching of the entire
kite with respect to the tether, the depower angle αd, which is
linked to the relative power setting up by Eqs. () and (), also causes a complex deformation of the
bridled membrane
wing (see Sect. ). The spanwise twisting and
bending has a strong secondary effect on the aerodynamics of the wing, and
accounting only for the dependency on α leads to considerable
uncertainty in the measured aerodynamic characteristics. This effect is one
of the contributing factors to the broad spreading of the data in
Fig. . For this reason, we recommend keeping the relative
power setting as a separate influencing parameter, next to the angle of
attack, to improve the aerodynamic characterization of a pumping cycle AWES
over the whole flight envelope. In fact, the transition from a powered to
depowered state of the wing should be regarded as a sequence of different
wings.
Lift coefficient
The tests considered in this study are based on a constant force control
strategy for the traction phases, with a set value Ft,o=3.25 kN.
Whenever the actual tether force Ft drops below this value, the
ground station reduces the reeling speed vt; when the force exceeds
this value, it increases the reeling speed. This control strategy ensures
that the aerodynamic loading of the system is limited despite operating in a
fluctuating and varying wind environment.
In Fig. we plot the measured lift coefficient CL of
the kite as a function of the relative flow velocity va, colored by
the heading.
Measured lift coefficient CL of the kite as a function of
the relative flow velocity va and colored by the heading. The heading range
from down to up covers both heading angle ranges 180∘>ψ>0∘ and 180∘<ψ<360∘ equally (see Fig. ).
The diagram only includes data from the traction phases and when Ft>3 kN. Flight situations that do not meet this condition are, for example, the
transitions to and from the retraction phase or sharp turning maneuvers.
Because of Eq. () and the constant force control the data
points are correlated by
CLva2=const.
Figure clearly shows how the flight motion of the kite
adjusts continuously to the force balance that varies along the crosswind
maneuvers to maintain the commanded tether force Ft,o. As a result of
gravity, the kite flies faster, with lower α and CL on
trajectory segments with a downwards component, while it flies slower with
higher α and CL on segments with an upwards component. Because
of the constant force control, the relative flow velocity va exhibits
an inversely proportional behavior to the angle of attack α and the
lift coefficient CL. The inversely proportional correlation of
α and va can also be recognized in Fig. .
Van der Vlugt et al. (2019, Sect. 2.4) show that the angle of attack of a massless kite
with a constant power setting does not vary along its flight path through a
constant uniform wind field. The described effect of gravity and the natural
wind environment induce a variation in the angle of attack, although the
power setting is kept constant at up=1 when flying crosswind
maneuvers. Because of the constant power setting, the wing does not deform
and the variations in CL and L/D can be attributed solely to
changes in the angle of attack.
Figure shows the measured lift coefficient CL as a
function of the angle of attack, colored by the heading of the kite.
Measured lift coefficient CL of the kite as a function of the angle of attack, α, colored by the heading.
To better differentiate the effect of the heading, we subdivide the range
from pointing downwards to pointing upwards into 10 classes. The heading
classes are equidistant in cosψ, i.e., Δcosψ=0.2, as
indicated by the circular legend in Fig. . Per class we
compute the average data point and display this as a symbol according to the
color legend.
The dark blue data point with the lowest angle of attack thus represents the
average of all measured flight conditions with a heading that is most closely
aligned with the gravity vector.
Despite the filtering, Figs. and still show
a considerable dispersion of the measured data. The various
idealizations required to model the flexible membrane kite system and the
assumption of quasi-steady flight with negligible inertial effects contribute
to that as does the fact that the evaluated pumping cycles differed in
flight path, wind conditions and many other parameters. Yet, we can recognize
two clear trends in the averaged data:
the lift coefficient increases with the angle of attack, and
the angle of attack and lift coefficient are higher when flying upwards.
The first trend reflects the common aerodynamic characteristics of a wing, while the second trend is
caused by the constant force control strategy and was already observed by .
The average lift coefficient plotted in Fig. exhibits a steep
slope for lower angles of attack.
At α=9∘ we measure an average value CL=0.7, while at
α=12.5∘ this value has risen to CL=1.0, which is close
to the ideal case of a two-dimensional lifting surface. For wings with a low
aspect ratio, such as the considered soft kite, we generally expect a more
gentle slope of the lift coefficient. The increasing camber and flattening of
the wing for higher angles of attack are two mechanisms that can contribute
to this steep slope (see Sect. and
Fig. ). Since we use a constant reference wing surface area in
Eq. () these mechanisms increase the lift coefficient.
Because the power setting of the kite is kept constant during the traction
phase we cannot actively control the angle of attack of the wing. Instead,
the angle results from the quasi-steady force equilibrium of the kite and is
thus affected by the varying gravitational force contribution and the wind
environment. Our analysis shows that for operation with constant force
control the heading of the kite has the strongest influence on the angle of
attack during crosswind maneuvers. When the kite is flying upwards, drag and
gravitational force point in similar directions, while for downwards
flight, both forces point in opposite directions. This causes the differences
in relative flow velocity in Fig. and in angle of attack in
Fig. .
Conclusions
In this study we present a method to determine the lift-to-drag ratio and
lift coefficient of a soft kite during flight operation by in situ
measurement of the relative flow. Tailored towards a kite system with
a suspended control unit, the flow sensor is installed in the power lines and
independently measures the magnitude of the relative flow velocity, the
sideslip angle and an orthogonal inflow angle from which the angle of attack
of the wing is derived. The effect of gravity on the individual kite
components is taken into account in processing the data as is the
aerodynamic drag of the kite control unit and measurement setup. Further included
are a smoothing procedure to remove the effect of low-frequency
oscillations induced by the ground station and filtering procedures to
remove the effects of too-low tether tension and high steering intensity.
We distinguish three fundamental contributions to the angle of attack of the
wing: the tether angle of attack αt, which is related to the
flight motion of the kite, the line angle λ0, which characterizes
the pitch of the entire kite relative to the tether, and the depower angle
αd, which characterizes the pitch of the wing relative to the
kite due to depower actuation. While λ0 is influenced by the
interaction of the tether force and the gravitational and aerodynamic forces
acting on the individual kite components, αd is inversely
related to the relative power setting up and correlated with a
spanwise twisting and bending of the bridled membrane wing.
The measurements show that the lift-to-drag ratio of the kite increases with
the relative power setting. For straight flight the maximum ratio is reached
at an angle of attack of 8∘ and a moderate lift coefficient.
Steering maneuvers reduce the lift-to-drag ratio. For the investigated data
set the variation of the angle of attack during the traction phases is
limited to about 8∘. Because of the constant force control operation
of the ground station, the angle of attack is inversely related to the
relative flow velocity. During the traction phase, the angle of attack and
the lift coefficient are both increased, yet strongly influenced by the
effect of gravity, which varies with the heading of the kite. When flying
upwards, the flight speed of the kite decreases and the angle of attack
increases to compensate for the effect of gravity; when flying downwards, the
speed increases and the angle decreases.
We find that the aerodynamic characteristics of the bridled membrane wing depend
not only on the angle of attack, as is common for rigid wings, but also
on the level of aerodynamic loading. For the investigated C-shaped wing, we
observe, for example, that increasing the loading causes the wing to flatten,
which enlarges the projected area and amplifies the effective aerodynamic
force. Because the loading is actively controlled by the relative power
setting, we can use this parameter to correlate the effect of the loading on
the aerodynamic characteristics. How exactly the power setting affects the
wing shape depends strongly on the layout of the bridle line system.
Our measurements show that accounting only for the dependency on the angle of
attack variation, as is commonly done, leads to considerable uncertainty in
the aerodynamic characteristics.
We expect that using the relative power setting as a secondary influencing
parameter will improve the aerodynamic characterization of a pumping cycle
AWES over the whole flight envelope.
Using a Kalman filter, as shown by , could help to
increase the accuracy of the measured data and the actual state of the system
by including knowledge about system behavior and the data from other onboard
sensors, such as the inertial measurement unit. Another possible improvement
of the analysis would be to retrofit the power and steering lines with force
sensors to assess the aerodynamic load distribution on the wing.
The effect of the kite control unit is considerable as it contributes about
40 % of the total kite mass and 10 % of the drag. Because of the suspension
in the steering lines it can exhibit unpredictable movements, particularly
during turns and when the tether force is low during the retraction phase. This
adds uncertainty to the calculated orientation of the kite. Moving the
control unit towards the bridle point and connecting it to power and steering
lines could potentially avoid this problem.