U.S. patent application number 14/135128 was filed with the patent office on 2015-11-19 for methods and systems for conserving power during hover flight.
This patent application is currently assigned to Google Inc.. The applicant listed for this patent is Google Inc.. Invention is credited to Erik Christopher Chubb.
Application Number | 20150331420 14/135128 |
Document ID | / |
Family ID | 53403532 |
Filed Date | 2015-11-19 |
United States Patent
Application |
20150331420 |
Kind Code |
A1 |
Chubb; Erik Christopher |
November 19, 2015 |
Methods and Systems for Conserving Power During Hover Flight
Abstract
An example method may include determining a drag force of an
apparent wind on an aircraft that is coupled to a ground station
via a tether. The method also includes determining a trajectory of
the aircraft to a point downwind of the ground station such that
the aircraft travelling the trajectory causes the tether to unfurl
along a catenary path above ground. The method further includes
determining an orientation of the aircraft to travel the trajectory
in the apparent wind so that an actuator of the aircraft is
configured to provide a vertical thrust in a direction
substantially perpendicular to the ground. The method also includes
determining a vertical thrust for the aircraft at the orientation
to travel the trajectory in the apparent wind. The method also
includes providing instructions to cause the actuator of the
aircraft to provide the vertical thrust to move the aircraft along
the trajectory.
Inventors: |
Chubb; Erik Christopher;
(San Francisco, CA) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
Google Inc. |
Mountain View |
CA |
US |
|
|
Assignee: |
Google Inc.
Mountain View
CA
|
Family ID: |
53403532 |
Appl. No.: |
14/135128 |
Filed: |
December 19, 2013 |
Current U.S.
Class: |
701/7 |
Current CPC
Class: |
Y02E 10/723 20130101;
Y02E 10/72 20130101; F03D 13/30 20160501; F05B 2240/921 20130101;
G05D 1/0866 20130101; B64C 39/022 20130101; F03D 7/026
20130101 |
International
Class: |
G05D 1/00 20060101
G05D001/00; G05D 1/04 20060101 G05D001/04; G05D 1/10 20060101
G05D001/10; B64C 39/02 20060101 B64C039/02 |
Claims
1. A method comprising: sensing a speed of an apparent wind on an
aircraft, wherein the aircraft is coupled to a ground station via a
tether; based on the sensed speed of the apparent wind and Iii) a
weight of the tether, determining, by one or more processors, a
trajectory of the aircraft to a point downwind of the ground
station such that the aircraft travelling the trajectory pulls the
tether along a catenary path above ground; based on the trajectory
and a weight of the aircraft, determining a vertical thrust for the
aircraft to travel the trajectory in the apparent wind; and
providing instructions to cause an actuator of the aircraft to
provide the vertical thrust to move the aircraft along the
trajectory.
2. The method of claim 1, further comprising: determining a drag
force of the apparent wind on the aircraft based on a density of
air, a reference area of the aircraft, or the sensed speed of the
apparent wind; and determining the trajectory based on the drag
force.
3. The method of claim 1, further comprising: determining a drag
force of the apparent wind on the aircraft based on a drag
coefficient, wherein the drag coefficient indicates a resistance of
a surface of the aircraft to air moving against the surface; and
determining the trajectory based on the drag force.
4. The method of claim 1, wherein the aircraft travelling the
trajectory comprises a point common to both the tether and the
aircraft travelling the trajectory.
5. The method of claim 1, wherein determining the trajectory of the
aircraft comprises: determining an azimuth angle for the
trajectory; and determining an altitude corresponding to a
horizontal position on the ground along a line defined by the
azimuth angle.
6. The method of claim 1, wherein determining the trajectory of the
aircraft comprises: determining the trajectory such that the
aircraft traveling the trajectory causes a tension of the tether to
have a horizontal component substantially equal to a drag force of
the apparent wind on the aircraft.
7. The method of claim 1, wherein determining the trajectory of the
aircraft comprises: determining the trajectory such that the
aircraft traveling the trajectory causes a tension of the tether to
have a vertical component substantially equal to a weight of the
tether.
8. The method of claim 1, wherein determining the trajectory of the
aircraft comprises: determining the trajectory such that the
aircraft traveling the trajectory causes a first portion of the
tether to occupy a position on the catenary path previously
occupied by a second portion of the tether.
9. The method of claim 1, wherein determining the trajectory of the
aircraft comprises: determining the catenary path based on a length
of the tether and a tension of the tether, wherein the tension of
the tether is about equal to a drag force of the apparent wind on
the aircraft; and determining a parameter of the catenary path so
that: the catenary path includes a point defined by the horizontal
position of the ground station and the altitude of the ground
station, and a minimum altitude of the catenary path occurs within
a range of horizontal position bounded by the horizontal position
of the ground station and the point downwind of the ground
station.
10. The method of claim 9, wherein determining the trajectory of
the aircraft further comprises: determining the parameter of the
catenary path so that the minimum altitude of the catenary path is
about equal to a predetermined altitude.
11. The method of claim 1, wherein determining the trajectory of
the aircraft comprises: determining a horizontal position
corresponding to an endpoint of the trajectory based on a length of
the tether, the weight of the tether, and a drag force of the
apparent wind on the aircraft.
12. The method of claim 1, wherein determining the trajectory of
the aircraft comprises: determining an altitude corresponding to an
endpoint of the trajectory based on a length of the tether, the
weight of the tether, and a drag force of the apparent wind on the
aircraft.
13. The method of claim 1, further comprising: determining an
orientation of the aircraft to travel the trajectory in the
apparent wind so that the actuator of the aircraft is configured to
provide the vertical thrust in a direction substantially
perpendicular to the ground.
14. The method of claim 1, wherein determining the vertical thrust
for the aircraft comprises: determining the vertical thrust based
on a position and a vertical velocity of the aircraft, wherein the
actuator providing the vertical thrust and a drag force of the
apparent wind on the aircraft pushing the aircraft horizontally
cause the aircraft to follow the trajectory.
15. The method of claim 1, wherein the aircraft includes a tail
wing and is engaged in hover flight, and the method further
comprises: receiving data indicating an initial orientation of the
aircraft, and a speed and a direction of the apparent wind;
determining a position of the tail wing relative to the direction
of the apparent wind configured to cause the apparent wind to
produce a rotational force about a pitch axis of the aircraft to
rotate the aircraft from the initial orientation to a hover
orientation; and providing instructions to move the tail wing to
provide the rotational force to rotate the aircraft to the hover
orientation.
16. The method of claim 15, wherein providing instructions to move
the tail wing to provide the rotational force to rotate the
aircraft to the hover orientation comprises: providing the
instructions based on receiving a notification that a speed of the
apparent wind is sufficient to produce the rotational force.
17. A non-transitory computer readable storage memory having stored
therein instructions, that when executed by a computing device that
includes one or more processors, causes the computing device to
perform functions comprising: sensing a speed of an apparent wind
on an aircraft, wherein the aircraft is coupled to a ground station
via a tether; based on (i) the sensed speed of the apparent wind
and (ii) a weight of the tether, determining a trajectory of the
aircraft to a point downwind of the ground station such that the
aircraft travelling the trajectory pulls the tether along a
catenary path above ground; based on the trajectory and a weight of
the aircraft, determining a vertical thrust for the aircraft to
travel the trajectory in the apparent wind; and providing
instructions to cause an actuator of the aircraft to provide the
vertical thrust to move the aircraft along the trajectory.
18. The non-transitory computer readable storage memory of claim
17, wherein the aircraft travelling the trajectory comprises a
point common to both the tether and the aircraft travelling the
trajectory.
19. A computing device comprising: one or more processors; and
memory configured to store instructions, that when executed by the
one or more processors, cause the computing device to perform
functions comprising: sensing a speed of an apparent wind on an
aircraft, wherein the aircraft is coupled to a ground station via a
tether; based on (i) the sensed speed of the apparent wind and (ii)
a weight of the tether, determining a trajectory of the aircraft to
a point downwind of the ground station such that the aircraft
travelling the trajectory pulls the tether along a catenary path
above ground; based on the trajectory and a weight of the aircraft,
determining a vertical thrust for the aircraft to travel the
trajectory in the apparent wind; and providing instructions to
cause an actuator of the aircraft to provide the vertical thrust to
move the aircraft along the trajectory.
20. The computing device of claim 19, wherein the aircraft
travelling the trajectory comprises a point common to both the
tether and the aircraft travelling the trajectory.
Description
BACKGROUND
[0001] Unless otherwise indicated herein, the materials described
in this section are not prior art to the claims in this application
and are not admitted to be prior art by inclusion in this
section.
[0002] Many techniques and systems exist for controlling a flight
path of an aircraft. Generally, an ability to change a position or
an attitude of the aircraft will depend on the location and
functionality of actuators included as part of the aircraft.
SUMMARY
[0003] In one example, a method is provided that includes
determining a drag force of an apparent wind on an aircraft coupled
to a ground station via a tether. The method also includes, based
on the drag force and a weight of the tether, determining a
trajectory of the aircraft to a point downwind of the ground
station such that the aircraft travelling the trajectory causes the
tether to unfurl along a catenary path above ground. The method
further includes determining an orientation of the aircraft to
travel the trajectory in the apparent wind so that an actuator of
the aircraft is configured to provide a vertical thrust in a
direction substantially perpendicular to the ground. The method
also includes, based on the trajectory and a weight of the
aircraft, determining a vertical thrust for the aircraft at the
orientation to travel the trajectory in the apparent wind. The
method also includes providing instructions to cause the actuator
of the aircraft to provide the vertical thrust to move the aircraft
along the trajectory.
[0004] In another example, a computer readable storage memory
having stored therein instructions, that when executed by a
computing device that includes one or more processors, cause the
computing device to perform functions is provided. The functions
comprise determining a drag force of an apparent wind on an
aircraft coupled to a ground station via a tether. The functions
further comprise, based on the drag force and a weight of the
tether, determining a trajectory of the aircraft to a point
downwind of the ground station such that the aircraft travelling
the trajectory causes the tether to unfurl along a catenary path
above ground. The functions further comprise determining an
orientation of the aircraft to travel the trajectory in the
apparent wind so that an actuator of the aircraft is configured to
provide a vertical thrust in a direction substantially
perpendicular to the ground. The functions further comprise based
on the trajectory and a weight of the aircraft, determining a
vertical thrust for the aircraft at the orientation to travel the
trajectory in the apparent wind. The functions further comprise
providing instructions to cause the actuator of the aircraft to
provide the vertical thrust to move the aircraft along the
trajectory.
[0005] In still another example, a system is provided that
comprises one or more processors and memory configured to store
instructions, that when executed by the one or more processors,
cause the system to perform functions. The functions comprise
determining a drag force of an apparent wind on an aircraft coupled
to a ground station via a tether. The functions further comprise,
based on the drag force and a weight of the tether, determining a
trajectory of the aircraft to a point downwind of the ground
station such that the aircraft travelling the trajectory causes the
tether to unfurl along a catenary path above ground. The functions
further comprise determining an orientation of the aircraft to
travel the trajectory in the apparent wind so that an actuator of
the aircraft is configured to provide a vertical thrust in a
direction substantially perpendicular to the ground. The functions
further comprise, based on the trajectory and a weight of the
aircraft, determining a vertical thrust for the aircraft at the
orientation to travel the trajectory in the apparent wind. The
functions further comprise providing instructions to cause the
actuator of the aircraft to provide the vertical thrust to move the
aircraft along the trajectory.
[0006] In yet another example, a system is provided that includes a
means for determining a drag force of an apparent wind on an
aircraft coupled to a ground station via a tether. The system
further comprises means for, based on the drag force and a weight
of the tether, determining a trajectory of the aircraft to a point
downwind of the ground station such that the aircraft travelling
the trajectory causes the tether to unfurl along a catenary path
above ground. The system further comprises means for determining an
orientation of the aircraft to travel the trajectory in the
apparent wind so that an actuator of the aircraft is configured to
provide a vertical thrust in a direction substantially
perpendicular to the ground. The system further comprises means
for, based on the trajectory and a weight of the aircraft,
determining a vertical thrust for the aircraft at the orientation
to travel the trajectory in the apparent wind. The system further
comprises means for providing instructions to cause the actuator of
the aircraft to provide the vertical thrust to move the aircraft
along the trajectory.
[0007] These as well as other aspects, advantages, and
alternatives, will become apparent to those of ordinary skill in
the art by reading the following detailed description, with
reference where appropriate to the accompanying figures.
BRIEF DESCRIPTION OF THE FIGURES
[0008] FIG. 1 depicts a tethered flight system, according to an
example embodiment.
[0009] FIG. 2 is a simplified block diagram illustrating example
components of the tethered flight system.
[0010] FIG. 3A depicts a downward looking view of an example
tethered flight system.
[0011] FIG. 3B depicts examples of the aircraft engaging in hover
flight at various horizontal positions and altitudes.
[0012] FIG. 4A depicts a first example catenary path and a second
example catenary path.
[0013] FIG. 4B depicts a third example catenary path and a fourth
example catenary path.
[0014] FIG. 5A depicts an example roll axis of an aircraft.
[0015] FIG. 5B depicts an example pitch axis of the aircraft.
[0016] FIG. 5C depicts an example yaw axis of the aircraft.
[0017] FIG. 6A depicts examples of a pitch axis of an aircraft, a
tail wing, and an apparent wind.
[0018] FIG. 6B depicts examples of a pitch axis of an aircraft, a
tail wing, and an apparent wind.
[0019] FIG. 7 is a block diagram of an example method for
determining a trajectory and an orientation of the aircraft that
causes a tether to unfurl along a catenary path above ground.
DETAILED DESCRIPTION
[0020] The following detailed description describes various
features and functions of the disclosed systems and methods with
reference to the accompanying figures. In the figures, similar
symbols identify similar components, unless context dictates
otherwise. The illustrative system and method embodiments described
herein are not meant to be limiting. It may be readily understood
that certain aspects of the disclosed systems and methods can be
arranged and combined in a wide variety of different
configurations, all of which are contemplated herein.
[0021] Within examples, a processor may be configured to determine
a drag force of an apparent wind on an aircraft tethered to a
ground station. The processor may determine the drag force based on
a density of air, a drag coefficient of the aircraft, a reference
area of the aircraft, or a speed of the apparent wind. The drag
coefficient may represent a tendency of the aircraft to resist
movement of air moving over the surface of the aircraft based on
the shape of the aircraft. The reference area of the aircraft may
represent a cross sectional area of the aircraft in a plane
perpendicular to the apparent wind, but may also represent any area
of the aircraft.
[0022] Next, the processor may determine a trajectory of the
aircraft to a point downwind of the ground station such that by
moving along the trajectory, the aircraft pulls the tether along a
catenary path above ground as the tether is unfurled. The processor
may determine the trajectory based on the drag force and a weight
of the tether, such that a tension of the tether is caused by the
drag force of the apparent wind. For example, a decrease in the
weight of the tether or an increase in the drag force may cause the
point downwind of the ground station to be at a lower altitude. By
further example, an increase in the weight of the tether or a
decrease in the drag force may cause the point downwind of the
ground station to be at a higher altitude.
[0023] The processor may also determine an orientation of the
aircraft for the aircraft to travel toward the point downwind of
the ground station. The aircraft may include an actuator and while
the aircraft is in the orientation the actuator may be configured
to provide a vertical thrust in a direction substantially
perpendicular to the ground. The orientation may be referred to as
zero pitch. The aircraft being in the orientation may allow the
actuator to move the aircraft in a substantially vertical
direction, while the drag force from the apparent wind moves the
aircraft in a substantially horizontal direction.
[0024] Based on the trajectory and a weight of the aircraft, the
processor may determine a vertical thrust for the aircraft at the
orientation to travel the trajectory in the apparent wind. The
processor may determine a vertical acceleration to travel the
trajectory, and may determine the vertical thrust based on the
vertical acceleration, the weight of the aircraft, a weight of a
portion of the tether supported by the aircraft, and gravitational
forces acting on the aircraft and the tether. The processor may
further provide instructions to the actuator to provide the
vertical thrust to move the aircraft along the trajectory.
[0025] Referring now to the figures, FIG. 1 depicts a tethered
flight system 100, according to an example embodiment. The tethered
flight system 100 may include a ground station 110, a tether 120,
and an aircraft 130. As shown in FIG. 1, the aircraft 130 may be
connected to the tether 120, and the tether 120 may be connected to
the ground station 110. The tether 120 may be attached to the
ground station 110 at one location on the ground station 110, and
attached to the aircraft 130 at two locations on the aircraft 130.
However, in other examples, the tether 120 may be attached at
multiple locations to any part of the ground station 110 or the
aircraft 130.
[0026] The ground station 110 may be used to hold or support the
aircraft 130 until the aircraft 130 is in a flight mode. The ground
station 110 may also be configured to reposition the aircraft 130
such that deploying the aircraft 130 is possible. Further, the
ground station 110 may be further configured to receive the
aircraft 130 during a landing. The ground station 110 may be formed
of any material that can suitably keep the aircraft 130 attached or
anchored to the ground while in hover flight, forward flight, or
crosswind flight.
[0027] In addition, the ground station 110 may include one or more
components (not shown), such as a winch, that may vary a length of
the tether 120. For example, when the aircraft 130 is deployed, the
one or more components may be configured to pay out or reel out the
tether 120. In some implementations, the one or more components may
be configured to pay out or reel out the tether 120 to a
predetermined length. As examples, the predetermined length could
be equal to or less than a maximum length of the tether 120.
Further, when the aircraft 130 lands on the ground station 110, the
one or more components may be configured to reel in the tether
120.
[0028] The tether 120 may transmit electrical energy generated by
the aircraft 130 to the ground station 110. In addition, the tether
120 may transmit electricity to the aircraft 130 to power the
aircraft 130 for takeoff, landing, hover flight, or forward flight.
The tether 120 may be constructed in any form and using any
material which allows for the transmission, delivery, or harnessing
of electrical energy generated by the aircraft 130 or transmission
of electricity to the aircraft 130. The tether 120 may also be
configured to withstand one or more forces of the aircraft 130 when
the aircraft 130 is in a flight mode. For example, the tether 120
may include a core configured to withstand one or more forces of
the aircraft 130 when the aircraft 130 is in hover flight, forward
flight, or crosswind flight. The core may be constructed of high
strength fibers. In some examples, the tether 120 may have a fixed
length or a variable length.
[0029] The aircraft 130 may include various types of devices, such
as a kite, a helicopter, a wing, or an airplane, among other
possibilities. The aircraft 130 may be formed of solid structures
of metal, plastic, polymers, or any material which allows for a
high thrust-to-weight ratio and generation of electrical energy
which may be used in utility applications. Additionally, the
materials may allow for a lightning hardened, redundant or fault
tolerant design which may be capable of handling large or sudden
shifts in wind speed and wind direction. Other materials may be
possible as well.
[0030] As shown in FIG. 1, the aircraft 130 may include a main wing
131, a front section 132, actuator connectors 133A-B, actuators
134A-D, a tail boom 135, a tail wing 136, and a vertical stabilizer
137. Any of these components may be shaped in any form which allows
for the use of lift to resist gravity or move the aircraft 130
forward.
[0031] The main wing 131 may provide a primary lift for the
aircraft 130 during forward flight, wherein the aircraft 130 may
move through air in a direction substantially parallel to a
direction of thrust provided by the actuators 134A-D so that the
main wing 131 provides a lift force substantially perpendicular to
a ground. The main wing 131 may be one or more rigid or flexible
airfoils, and may include various control surfaces or actuators,
such as winglets, flaps, rudders, elevators, etc. The control
surfaces may be used to steer or stabilize the aircraft 130 or
reduce drag on the aircraft 130 during hover flight, forward
flight, or crosswind flight. The main wing 131 may be any suitable
material for the aircraft 130 to engage in hover flight, forward
flight, or crosswind flight. For example, the main wing 131 may
include carbon fiber or e-glass. Moreover, the main wing 131 may
have a variety dimensions. For example, the main wing 131 may have
one or more dimensions that correspond with a conventional wind
turbine blade. The front section 132 may include one or more
components, such as a nose, to reduce drag on the aircraft 130
during flight.
[0032] The actuator connectors 133A-B may connect the actuators
134A-D to the main wing 131. In some examples, the actuator
connectors 133A-B may take the form of or be similar in form to one
or more pylons. In the example depicted in FIG. 1, the actuator
connectors 133A-B are arranged such that the actuators 134A and
134B are located on opposite sides of the main wing 131 and
actuators 134C and 134D are also located on opposite sides of the
main wing 131. The actuator 134C may also be located on an end of
the main wing 131 opposite of the actuator 134A, and the actuator
134D may be located on an end of main wing 131 opposite of the
actuator 134B.
[0033] In a power generating mode, the actuators 134A-D may be
configured to drive one or more generators for the purpose of
generating electrical energy. As shown in FIG. 1, the actuators
134A-D may each include one or more blades. The actuator blades may
rotate via interactions with the wind and could be used to drive
the one or more generators. In addition, the actuators 134A-D may
also be configured to provide a thrust to the aircraft 130 during
flight. As shown in FIG. 1, the actuators 134A-D may function as
one or more propulsion units, such as a propeller. Although the
actuators 134A-D are depicted as four actuators in FIG. 1, in other
examples the aircraft 130 may include any number of actuators.
[0034] In a forward flight mode, the actuators 134A-D may be
configured to generate a forward thrust substantially parallel to
the tail boom 135. Based on the position of the actuators 134A-D
relative to the main wing 131 depicted in FIG. 1, the actuators may
be configured to provide a maximum forward thrust for the aircraft
130 when all of the actuators 134A-D are operating at full power.
The actuators 134A-D may provide equal or about equal amounts of
forward thrusts when the actuators 134A-D are operating at full
power, and a net rotational force applied to the aircraft by the
actuators 134A-D may be zero.
[0035] The tail boom 135 may connect the main wing 131 to the tail
wing 136 and the vertical stabilizer 137. The tail boom 135 may
have a variety of dimensions. Moreover, in some implementations,
the tail boom 135 could take the form of a body or fuselage of the
aircraft 130. In such implementations, the tail boom 135 may carry
a payload.
[0036] The tail wing 136 or the vertical stabilizer 137 may be used
to steer or stabilize the aircraft 130 or reduce drag on the
aircraft 130 during hover flight, forward flight, or crosswind
flight. For example, the tail wing 136 or the vertical stabilizer
137 may be used to maintain a pitch or a yaw attitude of the
aircraft 130 during hover flight, forward flight, or crosswind
flight. In FIG. 1, the vertical stabilizer 137 is attached to the
tail boom 135, and the tail wing 136 is located on top of the
vertical stabilizer 137. The tail wing 136 may have a variety of
dimensions.
[0037] While the aircraft 130 has been described above, it should
be understood that the methods and systems described herein could
involve any aircraft that is connected to a tether, such as the
tether 120.
[0038] FIG. 2 is a simplified block diagram illustrating example
components of the tethered flight system 200. The tethered flight
system 200 may include the ground station 210, the tether 220, and
the aircraft 230. As shown in FIG. 2, the ground station 210 may
include one or more processors 212, data storage 214, program
instructions 216, and a communication system 218. A processor 212
may be a general-purpose processor or a special purpose processor
(e.g., digital signal processors, application specific integrated
circuits, etc.). The one or more processors 212 may be configured
to execute computer-readable program instructions 216 that are
stored in data storage 214 and are executable to provide at least
part of the functionality described herein.
[0039] The data storage 214 may include or take the form of one or
more computer-readable storage media that may be read or accessed
by at least one processor 212. The one or more computer-readable
storage media can include volatile or non-volatile storage
components, such as optical, magnetic, organic or other memory or
disc storage, which may be integrated in whole or in part with at
least one of the one or more processors 212. In some embodiments,
the data storage 214 may be implemented using a single physical
device (e.g., one optical, magnetic, organic or other memory or
disc storage unit), while in other embodiments, the data storage
214 can be implemented using two or more physical devices.
[0040] As noted, the data storage 214 may include computer-readable
program instructions 216 and perhaps additional data, such as
diagnostic data of the ground station 210. As such, the data
storage 214 may include program instructions to perform or
facilitate some or all of the functionality described herein.
[0041] In a further respect, the ground station 210 may include the
communication system 218. The communications system 218 may include
one or more wireless interfaces or one or more wireline interfaces,
which allow the ground station 210 to communicate via one or more
networks. Such wireless interfaces may provide for communication
under one or more wireless communication protocols, such as
Bluetooth, WiFi (e.g., an IEEE 802.11 protocol), Long-Term
Evolution (LTE), WiMAX (e.g., an IEEE 802.16 standard), a
radio-frequency ID (RFID) protocol, near-field communication (NFC),
or other wireless communication protocols. Such wireline interfaces
may include an Ethernet interface, a Universal Serial Bus (USB)
interface, or a similar interface to communicate via a wire, a
twisted pair of wires, a coaxial cable, an optical link, a
fiber-optic link, or other physical connection to a wireline
network. The ground station 210 may communicate with the aircraft
230, other ground stations, or other entities (e.g., a command
center) via the communication system 218.
[0042] In an example embodiment, the ground station 210 may include
communication systems 218 that allows for both short-range
communication and long-range communication. For example, the ground
station 210 may be configured for short-range communications using
Bluetooth and for long-range communications under a CDMA protocol.
In such an embodiment, the ground station 210 may be configured to
function as a "hot spot", or as a gateway or proxy between a remote
support device (e.g., the tether 220, the aircraft 230, and other
ground stations) and one or more data networks, such as a cellular
network or the Internet. Configured as such, the ground station 210
may facilitate data communications that the remote support device
would otherwise be unable to perform by itself.
[0043] For example, the ground station 210 may provide a WiFi
connection to the remote device, and serve as a proxy or gateway to
a cellular service provider's data network, which the ground
station 210 might connect to under an LTE or a 3G protocol, for
instance. The ground station 210 could also serve as a proxy or
gateway to other ground stations or a command station, which the
remote device might not be able to otherwise access.
[0044] Moreover, as shown in FIG. 2, the tether 220 may include
transmission components 222 and a communication link 224. The
transmission components 222 may be configured to transmit
electrical energy from the aircraft 230 to the ground station 210
or transmit electrical energy from the ground station 210 to the
aircraft 230. The transmission components 222 may take various
different forms in different embodiments. For example, the
transmission components 222 may include one or more conductors that
are configured to transmit electricity. And in at least one such
example, the one or more conductors may include aluminum or any
other material which allows for the conduction of electric current.
Moreover, in some implementations, the transmission components 222
may surround a core of the tether 220 (not shown).
[0045] The ground station 210 could communicate with the aircraft
230 via the communication link 224. The communication link 224 may
be bidirectional and may include one or more wired or wireless
interfaces. Also, there could be one or more routers, switches, or
other devices or networks making up at least a part of the
communication link 224.
[0046] Further, as shown in FIG. 2, the aircraft 230 may include
one or more sensors 232, a power system 234, power
generation/conversion components 236, a communication system 238,
one or more processors 242, data storage 244, program instructions
246, and a control system 248.
[0047] The sensors 232 could include various different sensors in
different embodiments. For example, the sensors 232 may include a
global positioning system (GPS) receiver. The GPS receiver may be
configured to provide data that is typical of GPS systems (which
may be referred to as a global navigation satellite system (GNNS)),
such as the GPS coordinates of the aircraft 230. Such GPS data may
be utilized by the tethered flight system 200 to provide various
functions described herein.
[0048] As another example, the sensors 232 may include one or more
wind sensors, such as one or more pitot tubes. The one or more wind
sensors may be configured to detect apparent or relative wind. Such
wind data may be utilized by the tethered flight system 200 to
provide various functions described herein.
[0049] Still as another example, the sensors 232 may include an
inertial measurement unit (IMU). The IMU may include both an
accelerometer and a gyroscope, which may be used together to
determine the orientation or attitude of the aircraft 230. In
particular, the accelerometer can measure the orientation of the
aircraft 230 with respect to earth, while the gyroscope measures
the rate of rotation around an axis, such as a centerline of the
aircraft 230. IMUs are commercially available in low-cost,
low-power packages. For instance, the IMU may take the form of or
include a miniaturized MicroElectroMechanical System (MEMS) or a
NanoElectroMechanical System (NEMS). Other types of IMUs may also
be utilized. The IMU may include other sensors, in addition to
accelerometers and gyroscopes, which may help to better determine
position. Two examples of such sensors are magnetometers and
pressure sensors. Other examples are also possible.
[0050] While an accelerometer and gyroscope may be effective at
determining the orientation of the aircraft 230, errors in
measurement may compound over time. However, an example aircraft
230 may be able mitigate or reduce such errors by using a
magnetometer to measure direction. One example of a magnetometer is
a low-power, digital 3-axis magnetometer, which may be used to
realize an orientation independent electronic compass for accurate
heading information. However, other types of magnetometers may be
utilized as well.
[0051] The aircraft 230 may also include a pressure sensor or
barometer, which can be used to determine the altitude of the
aircraft 230. Alternatively, other sensors, such as sonic
altimeters or radar altimeters, can be used to provide an
indication of altitude, which may help to improve the accuracy of
or prevent drift of the IMU. The aircraft 230 may include a
thermometer or another sensor that senses air temperature as
well.
[0052] As noted, the aircraft 230 may include the power system 234.
The power system 234 could take various different forms in
different embodiments. For example, the power system 234 may
include one or more batteries that provide power to the aircraft
230. In some implementations, the one or more batteries may be
rechargeable and each battery may be recharged via a wired
connection between the battery and a power supply or via a wireless
charging system, such as an inductive charging system that applies
an external time-varying magnetic field to an internal battery or a
charging system that uses energy collected from one or more solar
panels.
[0053] As another example, the power system 234 may include one or
more motors or engines for providing power to the aircraft 230. In
one embodiment, the power system 234 may provide power to the
actuators 134A-D of the aircraft 130, as shown and described in
FIG. 1. In some implementations, the one or more motors or engines
may be powered by a fuel, such as a hydrocarbon-based fuel. In such
implementations, the fuel could be stored on the aircraft 230 and
delivered to the one or more motors or engines via one or more
fluid conduits, such as piping. In some implementations, the power
system 234 may be implemented in whole or in part on the ground
station 210.
[0054] As noted, the aircraft 230 may include the power
generation/conversion components 236. The power
generation/conversion components 236 could take various different
forms in different embodiments. For example, the power
generation/conversion components 236 may include one or more
generators, such as high-speed, direct-drive generators. The one or
more generators may be driven by one or more rotors or actuators,
such as the actuators 134A-D as shown and described in FIG. 1.
[0055] Moreover, the aircraft 230 may include a communication
system 238. The communication system 238 may take the form of or be
similar in form to the communication system 218 of the ground
station 210. The aircraft 230 may communicate with the ground
station 210, other aircrafts, or other entities (e.g., a command
center) via the communication system 238.
[0056] In some implementations, the aircraft 230 may be configured
to function as a "hot spot" or as a gateway or proxy between a
remote support device (e.g., the ground station 210, the tether
220, other aircrafts) and one or more data networks, such as
cellular network or the Internet. Configured as such, the aircraft
230 may facilitate data communications that the remote support
device would otherwise be unable to perform by itself.
[0057] For example, the aircraft 230 may provide a WiFi connection
to the remote device, and serve as a proxy or gateway to a cellular
service provider's data network, which the aircraft 230 might
connect to under an LTE or a 3G protocol, for instance. The
aircraft 230 could also serve as a proxy or gateway to other
aircrafts or a command station, which the remote device might not
be able to otherwise access.
[0058] As noted, the aircraft 230 may include the one or more
processors 242, the program instructions 244, and the data storage
246. The one or more processors 242 can be configured to execute
computer-readable program instructions 246 that are stored in the
data storage 244 and are executable to provide at least part of the
functionality described herein. The one or more processors 242 may
take the form of or be similar in form to the one or more
processors 212, the data storage 244 may take the form of or be
similar in form to the data storage 214, and the program
instructions 246 may take the form of or be similar in form to the
program instructions 216.
[0059] Moreover, as noted, the aircraft 230 may include the control
system 248. In some implementations, the control system 248 may be
configured to perform one or more functions described herein. The
control system 248 may be implemented with mechanical systems or
with hardware, firmware, or software. As one example, the control
system 248 may take the form of program instructions stored on a
non-transitory computer readable medium and a processor that
executes the instructions. The control system 248 may be
implemented in whole or in part on the aircraft 230 or at least one
entity remotely located from the aircraft 230, such as the ground
station 210. Generally, the manner in which the control system 248
is implemented may vary, depending upon the particular
embodiment.
[0060] FIG. 3A depicts a downward looking view of an example
tethered flight system 300 which may include a ground station 310,
a tether 320, and an aircraft 330. Also depicted in FIG. 3A are an
azimuth angle 340 and an apparent wind 350. As shown in FIG. 3A,
the ground station 310 may be coupled to the tether 320 at a first
end of the tether 320 while the tether 320 may be coupled to the
aircraft 330 at a second end of the tether 320. The aircraft 330
may be configured to freely fly in an azimuthal direction about the
ground station 310. A position of the aircraft 330 may be
characterized in part by the azimuth angle 340 between a reference
angle and the azimuthal position of the aircraft 330. The ground
station 310 may be rotated so as to deploy the aircraft 330 in a
direction parallel to the apparent wind 350.
[0061] FIG. 3B depicts examples of the aircraft 330 engaging in
hover flight at various horizontal positions and altitudes. The
aircraft 330 may be tethered to the ground station 310 via the
tether 320. FIG. 3B also depicts the apparent wind 350, a ground
360, a horizontal distance 370, and an altitude 380 of the
aircraft.
[0062] Hover flight may be characterized by the aircraft 330
travelling at an attitude such that a primary force resisting a
force of gravity on the aircraft 330 is provided by the thrust of
the actuators of the aircraft 330. The aircraft 330 may be deployed
in a direction parallel to the apparent wind 350. In such a
configuration, the actuators may be oriented to provide thrust in a
direction substantially perpendicular to the ground 360 and the
main wing may be oriented so that the main wing is not configured
to apply a lift force to the aircraft 330 in a direction
perpendicular to the ground 360. During hover flight, lift
generating surfaces of the main wing, the tail wing, and the
horizontal stabilizer may not be effective in generating lift as
the lift generating surfaces may either be oriented to face
substantially parallel to a direction of travel of the aircraft
330, or may not be impacted with a sufficient apparent wind 350 to
generate a lift force. In hover flight, forces causing the aircraft
330 to move along a flight path may include forces provided by the
actuators and the apparent wind 350.
[0063] Hover flight may begin with deploying the aircraft 330 from
the ground station 310 in a hover-flight orientation. The ground
station 310 may be rotated so as to deploy the aircraft 330 in an
azimuthal direction parallel with the apparent wind 350. Deploying
the aircraft 330 in the direction of the apparent wind 350 may
enable the aircraft 330 to travel the horizontal distance 370 from
the ground station 310 while the actuators of aircraft 330 are
thrusting in a substantially vertical direction. The tether 320 may
be paid out or reeled out as the aircraft 330 achieves increasing
horizontal distance 370 from the ground station 310. Hover flight
may include the aircraft 330 ascending, descending, or hovering
over the ground 360 at an altitude 380 above the ground 360.
[0064] FIG. 4A depicts a first example catenary path 402 and a
second example catenary path 404. A cable, chain, tether or similar
object may hang along a catenary path when the object is supported
at a first end and second end, but otherwise allowed to freely hang
and react to gravitational forces.
[0065] Within examples, a catenary path of the tether can be
equivalent (or about equal) to the trajectory of the aircraft if a
common point of the tether and the aircraft, i.e. a point where the
tether connects to the aircraft, is defined to travel both the
trajectory of the aircraft and the catenary path of the tether. To
calculate the catenary path of the tether, the processor may
determine the drag force (F) on the aircraft due to an apparent
wind using an equation [1]:
F = .rho. 2 C d Av 2 [ 1 ] ##EQU00001##
The determination may first include determining or receiving
parameters of the equation [1] such as a density of air surrounding
the aircraft (.rho.), a drag coefficient of the aircraft (C.sub.d),
a reference area of the aircraft (A), and a speed of the apparent
wind impacting the aircraft (v). The drag coefficient may be
dependent on a number of variables, such as a shape of the aircraft
and the speed of the apparent wind. The reference area of the
aircraft may be a cross-sectional area of the aircraft in a plane
perpendicular to a direction of the apparent wind. However, the
reference area may be any area of the aircraft. The drag force on
the aircraft may be proportional to the density of air, the drag
coefficient, the reference area, and a square of the speed of the
apparent wind, as depicted in the equation [1]. Data representing
the parameters may be received by the processor from sensors of the
aircraft or ground station, or may be stored in memory. For
example, the processor may determine the density of air based on
receiving data representing an air temperature and pressure, may
receive data representing the speed of the apparent wind, but may
retrieve data representing the drag coefficient and the reference
area from memory. Once the drag force is determined, the drag force
may be used as a parameter of an equation [2]:
h = T 0 .mu. [ cosh ( .mu. x T 0 ) - 1 ] [ 2 ] ##EQU00002##
[0066] The equation [2] may define a relationship between an
altitude of the tether (h), the horizontal position of the tether
(x), a tension of the tether (T.sub.0) at a lowest point of the
catenary path, and a length and a weight of the tether (or a weight
per length of the tether (.mu.)). (T.sub.0 may also represent a
horizontal component of the tension at any point on the tether.) A
"cos h" function may be a hyperbolic cosine function, which may be
equivalently expressed as exponential functions as in an equation
[3]:
h = T 0 .mu. ( ( ( .mu. x T 0 ) + - ( .mu. x T 0 ) ) 2 ) - 1 [ 3 ]
##EQU00003##
The equation [3] may define a relationship between an altitude of
the tether (h), the horizontal position of the tether (x), a
tension of the tether (T.sub.0), and a length and a weight of the
tether (or a weight per length of the tether (.mu.)).
[0067] The drag force (F) calculated using the equation [1] may be
equated with the tension of the tether (T.sub.0) in the equation
[2] (or equation [3]). By equating the tension of the tether with
the drag force, the equation [2] may represent a scenario in which
any tension of the tether is due to the drag force on the aircraft
and the weight of the tether. In the example, an actuator of the
aircraft may be positioned to provide a thrust in a direction
substantially perpendicular to the ground. By providing thrust in a
substantially vertical direction, the actuator may save power for
vertical propulsion that may otherwise be used to produce an
additional tension on the tether. For x>0, the equation [2]
generally defines a path of the tether in which the altitude (h) of
the tether increases as the horizontal position (x) of the tether
increases. A rate of increase of the altitude with respect to the
horizontal position may increase as the horizontal position
increases. It should be noted that a path of the tether will have a
finite length limited by the length of the tether, whereas the
equation [2] and the equation [3] define an altitude for all
positive and negative values of horizontal position.
[0068] The relationship between the altitude and the horizontal
position of the tether may also be expressed using the equation
[3]. A constant ".epsilon." may represent Euler's number or a base
of a natural logarithm (approximately 2.71828). The equation [3]
may represent a function relating the horizontal position of the
tether and the altitude of the tether that is equivalent to the
function represented by the equation [2]. Other equations or
functions that define the relationship between the horizontal
position of the tether and the altitude of the tether equivalent to
the equation [2] and the equation [3] may exist.
[0069] The first example catenary path 402 and the second example
catenary path 404 may be catenary paths representing relationships
between a horizontal position of the tether and an altitude of the
tether. The first example catenary path 402 and the second example
catenary path 404 may be determined based on varying parameters of
the equation [1] and the equation [2] (or the equation [3]). The
horizontal position of the tether may be represented on an x-axis
and the altitude of the tether may be represented on an h-axis. The
first example catenary path 402 or the second example catenary path
404 may be calculated by using the equation [1] to calculate a drag
force of the aircraft due to an apparent wind. Next, the equation
[2] or the equation [3] may be used to calculate the first example
catenary path 402 or the second example catenary path 404 by using
the drag force determined with the equation [1].
[0070] As depicted in FIG. 4A, the first example catenary path 402
and the second example catenary path 404 may have an altitude of
zero (h=0) at a horizontal position defined as x=0. A designation
of an origin for a two-dimensional space defined by horizontal
position and altitude may be arbitrary. For example, x=0 may
represent a horizontal position of the ground station, or x=0 may
represent a horizontal position at which a minimum altitude of the
first example catenary path 402 or the second example catenary path
404 occurs. If x=0 represents the horizontal position of the ground
station and h=0 represents an altitude at which the tether couples
to the ground station, the first example catenary path 402 and the
second example catenary path 404 may both represent tether paths in
which a minimum tether altitude occurs at the ground station
(x=h=0). By further example, a maximum tether altitude for the
first example catenary path 402 and the second example catenary
path 404 may occur at an end of the tether coupled to the
aircraft.
[0071] At least one parameter of the equation [2] (or the equation
[3]) used to determine the first example catenary path 402 may
differ from a parameter of the equation [2] (or the equation [3])
used to determine the second example catenary path 404. For
example, the tension of the tether (T.sub.0) represented by the
first example catenary path 402 may be less than the tension of the
tether (T.sub.0) represented by the second example catenary path
404, while the weight per length of the tether (.mu.) represented
by the first example catenary path 402 and the second example
catenary path 404 may be equal. A difference in tether tension
represented by the first example catenary path 402 and the second
example catenary path 404 may be caused by a difference in the
density of air (.rho.), the drag coefficient (C.sub.d), the
reference area (A), or the speed of the apparent wind (v), as
depicted in the equation [1]. Alternatively, the tension of the
tether (T.sub.0) represented by the first example catenary path 402
may be equal to the tension of the tether (T.sub.0) represented by
the second example catenary path 404, while the weight per length
of the tether (.mu.) represented by the first example catenary path
402 may be greater than the weight per length of the tether (.mu.)
represented by the second example catenary path 404. By further
example, a quantity (T.sub.0/.mu.) corresponding to the second
example catenary path 404 may be twice that of a quantity
(T.sub.0/.mu.) corresponding to the first example catenary path
402. The variation in (T.sub.0/.mu.) for the first example catenary
path 402 and the second example catenary path 404 may be based on
varying weights per length of tethers (.mu.), or based on a
difference in tether tensions T.sub.0, which may be caused by
differing drag forces (F).
[0072] An equation [4] may resemble equation [2], but may further
include an h-axis parameter (a) and an x-axis parameter (b):
h = T 0 .mu. [ cosh ( .mu. ( x - b ) T 0 ) - ( 1 - a .mu. T 0 ) ] [
4 ] ##EQU00004##
The h-axis parameter (a) may be determined so that a minimum
altitude of a catenary path may occur at a specific altitude above
(or below) a point defined as h=0. For example, if a=5, then a
minimum tether altitude of a catenary path defined by the equation
[4] may occur at h=5. By further example, if b=7, then a minimum
tether altitude of a catenary path defined by the equation [4] may
occur at x=7. An equation [5] may also include an h-axis parameter
(a) and an x-axis parameter (b) that affect a catenary path
similarly to the h-axis parameter (a) and the x-axis parameter (b)
of the equation [4]:
h = T 0 .mu. ( ( ( .mu. ( x - b ) T 0 ) + - ( .mu. ( x - b ) T 0 )
) 2 ) - ( 1 - a .mu. T 0 ) [ 5 ] ##EQU00005##
[0073] FIG. 4B depicts a third example catenary path 406, and a
fourth example catenary path 408. The third example catenary path
406 may be defined by the equation [4] with an h-axis parameter (a)
of a.sub.1 and an x-axis parameter (b) of b.sub.1. As depicted in
FIG. 4B, the third example catenary path 406 may be defined by
substituting (b.sub.1) for (b) and (a.sub.1) for (a) in the
equation [4], resulting in
h = T 0 .mu. [ cosh ( .mu. T 0 ( x - b 1 ) ) - ( 1 - a 1 .mu. T 0 )
] [ 6 ] ##EQU00006##
which may define an altitude of h=a.sub.1 at a horizontal position
x=b.sub.1. A point (h=a.sub.1, x=b.sub.1) on the third example
catenary path 406 may correspond to a minimum tether altitude for
the third example catenary path 406. In this case, h=0 may
represent the ground and h(x=0) may represent an altitude at which
the tether couples to the ground station which, based on the
equation [6], may be
h ( x = 0 ) = T 0 .mu. [ cosh ( .mu. T 0 ( - b 1 ) ) - ( 1 - a 1
.mu. T 0 ) ] . [ 7 ] ##EQU00007##
[0074] As depicted in FIG. 4B, the fourth example catenary path 408
may have an altitude of h=a.sub.2 at a horizontal position
x=b.sub.2, which may be a minimum tether altitude for the fourth
example catenary path 408. The fourth example catenary path 408 may
be defined by the equation [4] and an h-axis parameter (a) of
(a.sub.2) and an x-axis parameter (b) of (b.sub.2). In this case
h=0 may represent the ground and h(x=0) may represent an altitude
at which the tether couples to the ground station which, based on
the equation [4], may be
h ( x = 0 ) = T 0 .mu. [ cosh ( .mu. T 0 ( - b 2 ) ) - ( 1 - a 2
.mu. T 0 ) ] [ 8 ] ##EQU00008##
[0075] The third example catenary path 406 and the fourth example
catenary path 408 may be portions of a same curve translated to
accommodate differing definitions of the origin of the
two-dimensional space of altitude and horizontal position. That is,
the third example catenary path 406 and the fourth example catenary
path 408 may be defined by an equal tension of the tether (T.sub.0)
and weight per length of the tether (.mu.), but differ only in the
h-axis parameters and x-axis parameters that define the third
catenary path 406 and the fourth example catenary path 408.
[0076] The catenary paths illustrated in FIG. 4 are examples only,
and the catenary paths may vary based on varying parameters of
Equations [1]-[8].
[0077] Causing the aircraft to travel a catenary trajectory may
allow the actuator of the aircraft to provide thrust in a
substantially vertical direction, allowing the drag force of the
apparent wind to provide a force to move the aircraft in a
horizontal direction. To maintain a hover orientation in which the
actuator is configured to provide a substantially vertical thrust,
a control surface of the aircraft may be used to adjust an
orientation of the aircraft to the hover orientation, allowing the
actuator to expend energy to produce a substantially vertical
thrust.
[0078] FIG. 5A depicts an example roll axis 502 of an aircraft 530.
In one embodiment, the aircraft 530 may include actuators
positioned to apply a torque thrust to the aircraft 530 about the
roll axis 502 of the aircraft 530, causing the aircraft 530 to
rotate about the roll axis 502. To land and couple the aircraft 530
onto the ground station it may be useful for the aircraft 530 to
assume a particular roll angle with respect to a reference roll
angle. During forward flight, roll adjustments of aircraft 530 may
be made by changing a position of flaps on the main wing of the
aircraft 530. It should be noted that the definition of the roll
axis 502 is arbitrary and the roll axis 502 may constitute a
different axis in another embodiment.
[0079] FIG. 5B depicts an example pitch axis 504 of the aircraft
530. The aircraft 530 may include actuators 534A-D positioned to
apply a torque thrust about the pitch axis 504 of the aircraft 530.
To pitch the aircraft 530 in a negative direction, the actuators
534A and 534C may provide thrust while the actuators 534B and 534D
are idle. Alternatively, the aircraft 530 may be pitched in a
positive direction by causing the actuators 534B and 534D to
provide thrust and causing the actuators 534A and 534C to be idle.
Using the actuators 534A-D to provide pitch control for the
aircraft 530 may be useful during hover flight, during which the
tail wing of the aircraft 530 may not be configured to provide a
torque about the pitch axis 504 of the aircraft 530. It should be
noted that definitions of positive and negative pitch and the pitch
axis 504 are arbitrary and not meant to be limiting. The pitch axis
504 may constitute a different axis in another embodiment.
[0080] FIG. 5C depicts an example yaw axis 506 of the aircraft 530.
The aircraft 530 may include the actuators 534A-D positioned to
apply a torque thrust about the yaw axis 506 of the aircraft 530.
To yaw the aircraft 530 in a negative direction, the actuators 534C
and 534D may provide thrust while the actuators 534A and 534B are
idle. Alternatively, the aircraft 530 may be yawed in a positive
direction by causing the actuators 534A and 534B to provide thrust
and causing the actuators 534C and 534D to be idle. Using the
actuators 534A-D to provide yaw control may be useful during hover
flight during which the vertical stabilizer of the aircraft 530 may
not be configured to provide a torque about the yaw axis 506 of the
aircraft 530. It should be noted that definitions of positive and
negative yaw and the yaw axis 506 are arbitrary and not meant to be
limiting. The yaw axis 506 may constitute a different axis in
another embodiment.
[0081] FIG. 6A depicts examples of a pitch axis 602 of an aircraft
630, a tail wing 636, and an apparent wind 650. At times, it may be
useful to change a pitch angle of the aircraft 630. To change the
pitch angle of the aircraft 630 and conserve power otherwise
consumed by an actuator of the aircraft 630, the tail wing 636 may
be configured to orient a surface of the tail wing 636 to face the
apparent wind 650 so that the apparent wind 650 applies a drag
force to the tail wing 636. The drag force may result in a torque
moment that causes the aircraft 630 to rotate with respect to the
pitch axis 602 in a direction indicated in FIG. 6A.
[0082] FIG. 6B depicts examples of a pitch axis 602 of an aircraft
630, a tail wing 636, and an apparent wind 650. At times, it may be
useful to change a pitch angle of the aircraft 630. To change the
pitch angle of the aircraft 630 and conserve power otherwise
consumed by an actuator of the aircraft 630, the tail wing 636 may
be configured to orient a surface of the tail wing 636 to face
substantially perpendicular to the apparent wind 650 so that the
apparent wind 650 applies a lift force 652 to the tail wing 636.
The lift force 652 may result in a torque moment that causes the
aircraft 630 to rotate with respect to the pitch axis 602 in a
direction indicated in FIG. 6B.
[0083] FIG. 7 is a block diagram of an example method 700 for
determining a trajectory and an orientation of the aircraft that
causes a tether to unfurl along a catenary path above ground, in
accordance with at least some embodiments described herein. Method
700 shown in FIG. 7 presents an embodiment of a method that, for
example, could be used with a computing device. Functions of the
method 700 may be fully performed by a processor of a computing
device, by a computing device, or may be distributed across
multiple processors or multiple computing devices and/or a server.
In some examples, the computing device may receive information from
sensors of the computing device, or where the computing device is a
server the information can be received from another device that
collects the information.
[0084] Method 700 may include one or more operations, functions, or
actions as illustrated by one or more blocks of 702-710. Although
the blocks are illustrated in a sequential order, these blocks may
in some instances be performed in parallel, and/or in a different
order than those described herein. Also, the various blocks may be
combined into fewer blocks, divided into additional blocks, and/or
removed based on the desired implementation.
[0085] In addition, for the method 700 and other processes and
methods disclosed herein, the flowchart shows functionality and
operation of one possible implementation of present embodiments. In
this regard, each block may represent a module, a segment, or a
portion of program code, which includes one or more instructions
executable by a processor for implementing specific logical
functions or steps in the process. The program code may be stored
on any type of computer readable medium, for example, such as a
storage device including a disk or hard drive. The computer
readable medium may include a non-transitory computer readable
medium, for example, such as computer-readable media that stores
data for short periods of time like register memory, processor
cache, and Random Access Memory (RAM). The computer readable medium
may also include non-transitory media, such as secondary or
persistent long term storage, like read only memory (ROM), optical
or magnetic disks, or compact-disc read only memory (CD-ROM), for
example. The computer readable media may also be any other volatile
or non-volatile storage systems. The computer readable medium may
be considered a computer readable storage medium, a tangible
storage device, or other article of manufacture, for example.
[0086] In addition, for the method 700 and other processes and
methods disclosed herein, each block in FIG. 7 may represent
circuitry that is wired to perform the specific logical functions
in the process.
[0087] At block 702, the method 700 includes determining a drag
force of an apparent wind on an aircraft coupled to a ground
station via a tether. A processor may determine the drag force
using a drag force equation, such as equation [1]. More
specifically, the processor may calculate the drag force based on a
proportionality between the drag force and a density of air,
between the drag force and a reference area of the aircraft,
between the drag force and a drag coefficient, or between the drag
force and a square of the speed of the apparent wind. The drag
coefficient may indicate a resistance of the aircraft to air moving
against a surface of the aircraft and may be dependent on a shape
of the aircraft or the speed of the apparent wind.
[0088] At block 704, the method 700 includes, based on the drag
force and a weight of the tether, determining a trajectory of the
aircraft to a point downwind of the ground station such that the
aircraft travelling the trajectory causes the tether to unfurl
along a catenary path above ground. The catenary path may represent
a shape of the tether caused by gravity acting on the tether while
the tether is supported at a first end by the ground station and
supported at a second end by the aircraft. The processor may
determine the trajectory by determining an azimuth angle for the
trajectory that is parallel to a direction of the apparent wind.
The processor may further determine a series of altitudes that
correspond to a series of horizontal positions of the tether along
the azimuth angle.
[0089] The processor may determine the trajectory based on the drag
force equation and a catenary equation, such as equations [1]-[8]
such that the aircraft travelling the trajectory in the apparent
wind causes a tension of the tether to have a horizontal component
substantially equal to the drag force of the apparent wind. In this
way, the trajectory may be optimized so that the tether is
maintained above a minimum altitude, the apparent wind pushes the
aircraft in a horizontal direction, and the actuator of the
aircraft provides a vertical thrust substantially perpendicular to
the ground. The trajectory determined by the processor may also
cause a tension of the tether to have a vertical component equal to
a weight of a portion of the tether. That is, the aircraft
travelling the trajectory may restrain the tether from touching the
ground or from dropping below a certain altitude, but may not
require thrust to be provided by an actuator to place additional
tension on the tether.
[0090] The aircraft travelling the trajectory may also cause a
first portion of the tether to occupy a position on the catenary
path previously occupied by a second portion of the tether. As the
aircraft travels the trajectory and increases a distance of the
aircraft from the ground station, the tether may be reeled out by
the ground station to accommodate the increased distance of the
aircraft from the ground station. An overall shape of the tether
suspended by the ground station and the aircraft may remain
unchanged as the tether is reeled out, except that an additional
section of the catenary path adjacent to the aircraft may be added
to a previous path of the tether. In this way, once a position on
the catenary path has been occupied by a portion of the tether, the
position may continue to be occupied by other portions of the
tether as the tether is reeled out.
[0091] The method 700 may also include the processor receiving data
representing a horizontal position of the ground station, an
altitude of the ground station, and a length of the tether. The
processor may then determine the catenary path based on the length
of the tether and a tension of the tether so that the aircraft
travelling the catenary path causes a tension of the tether to be
about equal to the drag force of the apparent wind on the aircraft.
The tension may occur at the minimum altitude of the catenary path.
By minimizing the tension of the tether caused by the actuator of
the aircraft, an energy dissipated by the actuator may be
minimized. The processor may then determine parameters of the
catenary path that cause the catenary path to include a point
defined by the horizontal position of the ground station and the
altitude of the ground station. The processor may also determine
the parameters so that a minimum altitude of the catenary path
occurs within a range of horizontal position bounded by the
horizontal position of the ground station and the point downwind of
the ground station. The processor may receive data representing a
minimum tether altitude and determine the parameters so that a
minimum altitude of the catenary path is about equal to the minimum
tether altitude.
[0092] The catenary path may be determined by the processor based
on the equation [4] (or equation [5]). (T.sub.0) may represent a
tension of the tether at a lowest point of the catenary path, or a
horizontal component of the tension at any point on the tether. To
reduce the energy consumed by the actuator, the tension T.sub.0 may
be about equal to the drag force of the apparent wind defined by
the equation [1]. (.rho.) may represent a density of air, (C.sub.d)
may represent the drag coefficient of the aircraft, (A) may
represent the reference area of the aircraft, and (v) may represent
the speed of the apparent wind. In the catenary equation, (.mu.)
may represent the weight per length of the tether, (a) may
represent a vertical adjustment parameter, (b) may represent a
horizontal adjustment parameter, (h) may represent altitude, and
(x) may represent horizontal position.
[0093] For example, the horizontal position of the ground station
and the altitude of the ground station may be x=0 and h=5,
respectively. For purposes of illustration, a quantity
(T.sub.0/.mu.) may be equal to 1. In this case, the catenary
equation may take a simplified form, h=cos h(x-b)-(1-a). The
processor may then determine the parameters (a) and (b) such that
the altitude of the tether at a horizontal position represented by
x=0 is h=5. The processor may first determine (a) such that a
minimum altitude of the catenary path corresponds to the minimum
tether altitude. For example, to yield a catenary path in which the
minimum altitude of the path is h=1, the processor may determine
(a) to be equal to 1, based on a minimum value of cos h(x-b) being
equal to 1. The catenary equation may then be expressed as h=cos
h(x-b). Next, the processor may determine (b) such that an altitude
of the catenary path at x=0 is h=5, by solving an equation 5=cos
h(0-b). There may exist two such values of (b) that solve the
equation, b.apprxeq.2.29243 and b.apprxeq.-2.29243. The processor
may determine that determining (b) to be equal to 2.29243 will
cause the minimum altitude of the catenary path to occur at a
position between the ground station and the point downwind of the
ground station (i.e. the minimum altitude may occur on a positive-x
side of the x-axis). In this example, (b) may be determined to be
2.29243 by the processor. By further example, referring to FIG. 4,
the third example catenary path 406 may depict a catenary path
corresponding to parameters b=1 and a=2, while the fourth example
catenary path 408 may depict a catenary path corresponding to
parameters b=3 and a=4. (Note that in this example, the x-axis and
the h-axis may not share a common scale.) Accordingly, the altitude
of the third example catenary path 406 at x=0 may be
h.apprxeq.2.543 and the altitude of the fourth example catenary
path 408 at x=0 may be h.apprxeq.13.068.
[0094] The processor may also determine a horizontal position and
an altitude corresponding to an endpoint of the trajectory based on
the length of the tether, the weight of the tether, and the drag
force. Once the catenary path is determined, an arc length (s) of
the catenary path from a horizontal position x.sub.1 to a
horizontal position x.sub.2 can be determined using an equation
[9]:
S = .intg. x 1 x 2 1 + ( h x ) 2 x [ 9 ] ##EQU00009##
where (h) is the altitude of the catenary path defined by the
equation [4]. If a total length of the tether is known, (s) in the
equation [9] can be set equal to the total tether length, and a
horizontal distance between the ground station at x.sub.1 and the
point downwind of the ground station at x.sub.2 can be determined.
For purposes of illustration, the ground station may have a
horizontal position x=0=x.sub.1, the tether may have a length of 50
and (a) may equal 2 and (b) may equal 1, yielding equation
[10]:
h(x)=cos h(x-1)-(1-2) [10]
In this case, the endpoint of the trajectory would be determined
using an equation
50=.intg..sub.0.sup.x.sup.2 {square root over (1+sin
h.sup.2(x-1))}dx [11]
[0095] A solution to the equation [11] may be
x.sub.2.apprxeq.5.582. An altitude (h) of the endpoint of the
catenary path may be determined by the processor using the equation
[4] and the horizontal position of the endpoint. In the case of
x.sub.2=5.582, h may be approximately 49.86.
[0096] At block 706, the method 700 includes determining an
orientation of the aircraft to travel the trajectory in the
apparent wind so that an actuator of the aircraft is configured to
provide a vertical thrust in a direction substantially
perpendicular to the ground. The processor may first receive data
representing a direction in which the actuator is configured to
provide thrust relative to an axis of the aircraft. Next, the
processor may determine an angle of rotation of the aircraft
relative to the axis of the aircraft such that at the angle of
rotation, the actuator is configured to provide the vertical thrust
in a direction substantially perpendicular to the ground. In other
words, the processor may determine an orientation of the aircraft
based on a relative orientation of the actuator with respect to the
aircraft, such that the actuator is configured to provide a
substantially downward thrust perpendicular to the ground. Limiting
the thrust of the actuator to be in the vertical direction may
allow the aircraft to rely on the force of the apparent wind to
travel in the horizontal direction.
[0097] At block 708, the method 700 includes determining a vertical
thrust for the aircraft at the orientation to travel the trajectory
in the apparent wind based on the trajectory and a weight of the
aircraft. The processor may also receive data representing a
weight, a position, and a vertical velocity of the aircraft, and a
weight of a portion of the tether supported by the aircraft. With
the data, the processor may determine a gravitational force acting
on the aircraft based on the weight of the aircraft and the weight
of the portion of the tether supported by the aircraft. The
processor may determine the weight of the portion of the tether
supported by the aircraft based on a weight per length of the
tether and a length of the portion of the tether. The processor may
next determine a vertical acceleration of the aircraft based on the
position and the vertical velocity of the aircraft, wherein the
aircraft achieving the vertical acceleration and the drag force
pushing the aircraft horizontally cause the aircraft to follow the
trajectory. Finally, the processor may determine the vertical
thrust based on a force to counteract the downward force and
achieve the vertical acceleration.
[0098] At block 710, the method 700 includes providing instructions
to cause the actuator of the aircraft to provide the vertical
thrust to move the aircraft along the trajectory. The processor may
provide the instructions to the actuator or a control system of the
aircraft that controls the actuator.
[0099] The processor may further receive data indicating an initial
orientation of the aircraft, and a speed and a direction of the
apparent wind. The processor may use the data to determine a
position of the tail wing relative to the direction of the apparent
wind configured to cause the apparent wind to produce a rotational
force about a pitch axis of the aircraft. The rotational force may
be configured to rotate the aircraft from the initial orientation
to a hover orientation. As shown and described in FIGS. 6A and 6B,
the tail wing 636 of the aircraft may be configured to provide
pitch control while the aircraft is in a hover orientation. The
tail wing 636 may provide pitch control in a first direction by
orienting the tail wing so that the apparent wind produces a drag
force against the tail wing. The drag force may create a pitch
moment in a first direction about the pitch axis of the aircraft,
as shown in FIG. 6A. The tail wing may provide pitch control in a
second direction by orienting the tail wing so that the apparent
wind produces a lift force against the tail wing. The lift force
may create a pitch moment in a second direction about the pitch
axis of the aircraft, as shown in FIG. 6B. Lastly, the processor
may provide instructions to the control system of the aircraft (or
the ground station) to move the tail wing to provide the rotational
force to rotate the aircraft to the hover orientation.
[0100] The tail wing may be configured to produce the lift force
based on the apparent wind achieving a threshold speed, such as 15
meters per second. The processor may provide the instructions to
move the tail wing to provide the rotational force based on
receiving a notification from a sensor of the aircraft that the
speed of the apparent wind is greater than or equal to the
threshold speed. Unless the apparent wind has a speed greater than
the threshold speed, the tail wing may not be configured to provide
a lift force configured for pitch control of the aircraft while the
aircraft is in the hover orientation. Deploying the aircraft along
the catenary path and using the tail wing for pitch control may
increase a margin between a nominal actuator output and a maximum
actuator output, thereby increasing an ability of the aircraft to
respond to disturbances (e.g. wind gusts) that cause deviations
from the catenary path or a particular attitude of the
aircraft.
[0101] It should be understood that arrangements described herein
are for purposes of example only. As such, those skilled in the art
will appreciate that other arrangements and other elements (e.g.
machines, interfaces, functions, orders, and groupings of
functions, etc.) can be used instead, and some elements may be
omitted altogether according to the desired results. Further, many
of the elements that are described are functional entities that may
be implemented as discrete or distributed components or in
conjunction with other components, in any suitable combination and
location, or other structural elements described as independent
structures may be combined.
[0102] While various aspects and embodiments have been disclosed
herein, other aspects and embodiments will be apparent to those
skilled in the art. The various aspects and embodiments disclosed
herein are for purposes of illustration and are not intended to be
limiting, with the true scope being indicated by the following
claims, along with the full scope of equivalents to which such
claims are entitled. It is also to be understood that the
terminology used herein is for the purpose of describing particular
embodiments only, and is not intended to be limiting.
* * * * *