U.S. patent application number 16/708280 was filed with the patent office on 2020-10-22 for rotary airfoil and design method therefor.
The applicant listed for this patent is Joby Aero, Inc.. Invention is credited to Jeremy Bain, JoeBen Bevirt, Gregor Veble Mikic, Alex Stoll.
Application Number | 20200331602 16/708280 |
Document ID | / |
Family ID | 1000004970574 |
Filed Date | 2020-10-22 |
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United States Patent
Application |
20200331602 |
Kind Code |
A1 |
Mikic; Gregor Veble ; et
al. |
October 22, 2020 |
ROTARY AIRFOIL AND DESIGN METHOD THEREFOR
Abstract
The rotary airfoil 100 defines a cross section and a span,
wherein the cross section is a function of the point along the span
(e.g., spanwise point) and defines an upper surface and a lower
surface at each spanwise point. The rotary airfoil 100 also
defines, at a cross section, a lift coefficient (C.sub.L) that is a
function of the angle of attack at which the airfoil is rotated
through the air. The system can optionally include: a rotor hub to
mount the rotary airfoil, a tilt mechanism to pivot the rotary
airfoil between a forward configuration and a hover configuration,
and a pitching mechanism to change the angle of attack of the
rotary airfoil 100.
Inventors: |
Mikic; Gregor Veble; (Santa
Cruz, CA) ; Bevirt; JoeBen; (Santa Cruz, CA) ;
Bain; Jeremy; (Santa Cruz, CA) ; Stoll; Alex;
(Santa Cruz, CA) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
Joby Aero, Inc. |
Santa Cruz |
CA |
US |
|
|
Family ID: |
1000004970574 |
Appl. No.: |
16/708280 |
Filed: |
December 9, 2019 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
62776853 |
Dec 7, 2018 |
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Current U.S.
Class: |
1/1 |
Current CPC
Class: |
B64C 11/18 20130101;
B64C 11/303 20130101; B64C 29/0033 20130101 |
International
Class: |
B64C 29/00 20060101
B64C029/00; B64C 11/06 20060101 B64C011/06; B64C 11/18 20060101
B64C011/18; B64C 11/30 20060101 B64C011/30 |
Claims
1. An airfoil blade, the blade comprising: a first airfoil cross
section, the first airfoil cross section defining: a chord line
defining a chord length L; a leading edge, comprising a leading
edge radius between 0.002 L and 0.05 L; a trailing edge, comprising
a trailing edge thickness between zero and 0.03 L; a maximum
thickness between 0.07 L and 0.2 L and located between 0.2 L and
0.6 L along the chord line; and a maximum camber between zero and
0.2 L and located between 0.2 L and 0.7 L along the chord line.
2. The airfoil blade of claim 1, wherein: the leading edge radius
is approximately 0.006 L; the trailing edge thickness is
approximately 0.005 L; the maximum thickness is approximately 0.12
L at the position of approximately 0.4 L along the chord line; and
the maximum camber is approximately 0.024 L at the position of
approximately 0.44 L along the chord line.
3. The airfoil blade of claim 2, the first airfoil cross section as
described in Table 1.
4. The airfoil blade of claim 1, the first airfoil cross section as
described in Table 2.
5. The airfoil blade of claim 1, wherein the airfoil blade defines
a blade length between 1 m and 4 m.
6. The airfoil blade of claim 5, wherein the blade is tapered along
the blade length.
7. The airfoil blade of claim 1, wherein the airfoil blade defines
a twisting angle along the blade length, the twisting angle between
20 degrees and 50 degrees.
8. The airfoil blade of claim 1, further comprising an anhedral
blade tip.
9. The airfoil blade of claim 1, wherein the chord length L is
between 0.02 m and 1 m.
10. The airfoil bade of claim 1, wherein a rotor comprises the
airfoil blade, wherein the rotor generates less than 80 dBA at a
measurement distance of 100 meters when operating in a Reynold's
number range between 50 k and 1,000 k.
11. A rotor for a tilt-rotor aircraft, the rotor defining a disc
plane, the rotor comprising: a plurality of airfoil blades, each of
the plurality of airfoil blades defines a lift coefficient curve at
a Reynold's number range between 50 k-10,000 k comprising: a first
angle of attack (AoA) range; a second AoA range, wherein a lower
bound of the second AoA range is greater an upper bound of the
first AoA range, the second AoA range spanning a width of greater
than 5 degrees angle of attack; a semi-critical AoA between the
lower bound of the second AoA range and the upper bound of the
first AoA range; and a maximum coefficient of lift (CL) at a
critical AoA greater than an upper bound of the second AoA range;
and a rotor tilt mechanism, the rotor tilt mechanism configured to
transform the rotor between: a forward configuration, wherein each
of the plurality of airfoil blades operates in the first AoA range
and the disc plane is parallel to a pitch-yaw plane of the
tilt-rotor aircraft; and a hover configuration, wherein each of the
plurality airfoil blades operates in the second AoA range and the
disc plane intersects the pitch-yaw plane.
12. The rotor of claim 11, further comprising a blade pitching
mechanism, wherein in the forward configuration the blade pitching
mechanism orients each of the plurality of airfoil blades at a
forward AoA within the first AoA range, wherein in the hover
configuration the blade pitching mechanism orients each of the
plurality of airfoil blades at a hover AoA within the second AoA
range.
13. The rotor of claim 11, wherein each airfoil further comprises a
bump on the upper surface of the airfoil blade, wherein a
separation point of each airfoil is located on a trailing portion
of the respective bump.
14. The rotor of claim 11, wherein the CL versus AoA curve in the
first AoA range defines a first slope (M), wherein the CL versus
AoA curve in the second AoA range defines a second slope, wherein
the second slope is between zero and 0.95M.
15. The rotor of claim 14, wherein an absolute value of a rate of
change of the second slope is less than 0.05M per degree.
16. The rotor of claim 14, wherein the CL versus AoA curve
comprises a third AoA range between the first AoA range and the
second AoA range, wherein the lift coefficient curve defines a
third slope in the third AoA range, wherein the third AoA slope is
less than half the second slope.
17. The rotor of claim 11, wherein the lift coefficient curve
defines a first slope between 0.1 per degree and 0.13 per degree in
the first AoA range, wherein the life coefficient curve defines a
second slope less than 0.1 per degree in the second AoA range.
18. The rotor of claim 11, wherein the hover configuration operates
below 80 dBA measured from 100 meters.
19. The rotor of claim 11, further comprising a hub, each of the
plurality of blades radiating from the hub in the disc plane,
wherein an electric motor is integrated into the hub.
20. The rotor of claim 11, the aircraft comprising a second rotor
adjacent to the rotor, wherein the second rotor is offset from the
disc plane.
Description
CROSS-REFERENCE TO RELATED APPLICATIONS
[0001] This application claims the benefit of U.S. Provisional
Application No. 62/776,853, filed 7 Dec. 2018, which is
incorporated in its entirety by this reference.
[0002] This application is related to U.S. application Ser. No.
16/409,653, filed May 10, 2019, and U.S. application Ser. No.
16/430,163, filed Jun. 3, 2019, each of which is incorporated in
its entirety by this reference.
TECHNICAL FIELD
[0003] This invention relates generally to the aviation field, and
more specifically to a new and useful rotary airfoil and design
method therefor in the aviation field.
BACKGROUND
[0004] Aircraft that are propelled by rotating external surfaces,
such as rotorcraft and propeller-craft, utilize rotating and often
unenclosed blades (e.g., rotary airfoils) to produce thrust.
However, rotating blades are a significant source of acoustic noise
that is undesirable for aircraft use in several contexts, including
urban and suburban environments, in which high noise levels can be
disruptive. Noise-based flightpath restrictions can significantly
reduce the ability to deploy urban and suburban air mobility
systems.
[0005] Thus, there is a need in the aviation field to create a new
and useful rotary airfoil and design method therefor. This
invention provides such a new and useful system and method.
BRIEF DESCRIPTION OF THE FIGURES
[0006] FIG. 1 is a schematic diagram of the rotary airfoil.
[0007] FIG. 2 is a flowchart diagram of the design method for the
rotary airfoil.
[0008] FIG. 3 depicts a schematic diagram of load variation
resulting from variable inflow conditions in relation to the rotary
airfoil.
[0009] FIG. 4 depicts example curves of lift coefficient variation
with angle of attack, and a comparison of an example of the rotary
airfoil with an example conventional airfoil.
[0010] FIG. 5 depicts an example cross section of an embodiment of
the rotary airfoil.
[0011] FIG. 6 depicts an example of simulated boundary layer
formation, and effective airfoil thickening resulting therefrom,
upon the example of the rotary airfoil depicted in FIG. 5 at an
angle of attack equal to zero.
[0012] FIG. 7A depicts a diagram of the boundary layer separation
point on an example embodiment of the rotary airfoil including a
raised feature proximal the leading edge, and on a conventional
airfoil omitting the raised feature, at a first angle of
attack.
[0013] FIG. 7B depicts a diagram of the boundary layer separation
point on an example embodiment of the rotary airfoil including a
raised feature proximal the leading edge, and on a conventional
airfoil omitting the raised feature, at a second angle of attack
greater than the first angle of attack depicted in FIG. 7A.
[0014] FIG. 8 depicts an example curves of lift coefficient
variation with angle of attack, and a comparison of an example of
the rotary airfoil with an example conventional airfoil.
[0015] FIG. 9 depicts an example curves of lift coefficient
variation with angle of attack, and a comparison of an example of
the rotary airfoil with an example conventional airfoil.
[0016] FIG. 10A depicts a perspective view of an example of the
rotary airfoil.
[0017] FIG. 10B depicts a side view of an example of the rotary
airfoil.
[0018] FIG. 10C depicts a top view of an example the rotary
airfoil.
[0019] FIG. 11 depicts an example of an efficiency plot of the
rotary airfoil.
[0020] FIG. 12A depicts an example of a lift coefficient curve of
the rotary airfoil at a nominal Reynold's number of 10.sup.6.
[0021] FIG. 12B depicts an example of a lift coefficient curve of
the rotary airfoil across a range of Reynold's numbers, where the
solid curve corresponds to Reynolds number 10.sup.6, the dotted
curve corresponds to Reynold's number 5.times.10.sup.6, and the
dashed curve corresponds to Reynold's number 2.times.10.sup.6.
[0022] FIG. 13A depicts an example of a drag coefficient curve of
the rotary airfoil at different angles of attack.
[0023] FIG. 13B depicts an example of a drag coefficient versus
lift coefficient curve of the rotary airfoil.
[0024] FIG. 14 depicts an example of the forward configuration and
the hover configuration of the rotary airfoil.
[0025] FIG. 15A depicts an example of the pitch axis and the roll
axis of the aircraft.
[0026] FIG. 15B depicts an example of the roll axis and the yaw
axis of the aircraft.
[0027] FIG. 16 depicts an example of the blade pitching
mechanism.
[0028] FIG. 17 depicts a diagram of the rotary airfoil cross
section.
[0029] FIG. 18A depicts an example of the tilt mechanism in the
forward configuration.
[0030] FIG. 18B depicts an example of the tilt mechanism
transitioning between the forward and hover configurations.
[0031] FIG. 18C depicts an example of the tilt mechanism in the
hover configuration.
[0032] FIG. 19A depicts a diagrammatic representation of the rotary
airfoil from a top view.
[0033] FIG. 19B depicts a diagrammatic representation of the rotary
airfoil twist angle.
[0034] FIG. 19C depicts a diagrammatic representation of the rotary
airfoil from a top view.
[0035] FIG. 19D depicts a diagrammatic representation of the rotary
airfoil from a side view.
[0036] FIG. 20 is an isometric view of an example of the tilt-rotor
system with a set of the rotary airfoils.
DESCRIPTION OF THE PREFERRED EMBODIMENTS
[0037] The following description of preferred embodiments of the
invention is not intended to limit the invention to these preferred
embodiments, but rather to enable any person skilled in the art to
make and use this invention.
1. Overview
[0038] As shown in FIG. 1, the rotary airfoil 100 defines a cross
section and a span, wherein the cross section is a function of the
point along the span (e.g., spanwise point) and defines an upper
surface and a lower surface at each spanwise point. The rotary
airfoil 100 also defines, at a cross section, a lift coefficient
(C.sub.L) that is a function of the angle of attack 103 (AoA) at
which the airfoil is rotated through the air. However, the rotary
airfoil 100 can additionally or alternatively include or define any
other suitable components or features.
[0039] The system can optionally include: a rotor hub 550 to mount
the rotary airfoil, a tilt mechanism to pivot the rotary airfoil
between a forward configuration and a hover configuration, and a
pitching mechanism to change the angle of attack of the rotary
airfoil 100 (an example is shown in FIG. 20). However, the system
can additionally or alternatively include or define any other
suitable components or features.
[0040] The rotary airfoil 100 functions to generate an aerodynamic
force as it is rotated through a fluid (e.g., air), which can be
used to propel and/or lift a vehicle (e.g., aircraft). The rotary
airfoil 100 can also function to define, at a cross section, a lift
coefficient at each angle of attack within a range of angles of
attack that reduces and/or minimizes loading variations across the
rotor disc of a propeller utilizing two or more rotary airfoils
100. The rotary airfoil 100 can also function to define a cross
section that includes a feature (e.g., a bump) or geometry that
localizes a boundary layer separation point along the chordwise
direction at a range of angles of attack, as shown in the examples
in FIGS. 7A and 7B. However, the rotary airfoil 100 can
additionally or alternatively have any other suitable function.
[0041] As shown in FIG. 2, the design method 200 can include:
parameterizing the airfoil geometry S100, generating an airfoil
shape according to the parameterization S150; determining the
performance parameters of the airfoil shape S200; and optimizing
the parameters of the airfoil geometry to achieve a performance
threshold S300.
[0042] The design method 200 functions to compute an airfoil shape
(e.g., a cross-sectional shape, a shape of the variation of the
cross-section along the span, etc.). The design method 200 can also
function to parameterize the airfoil shape in a specified manner
that enables iterative computational optimization of the airfoil
shape. The design method 200 can also function to enable
computational prediction of airfoil performance (e.g., via
computational fluid dynamics/CFD). However, the design method 200
can additionally or alternatively have any other suitable
function.
[0043] The rotary airfoil 100 is preferably implemented in
conjunction with an aircraft propulsion system (e.g., propeller,
rotor, etc.), which in turn is preferably implemented in
conjunction with an aircraft. In particular, the aircraft is
preferably a rotorcraft, but can additionally or alternatively
include any suitable aircraft. The rotorcraft is preferably a
tiltrotor aircraft with a plurality of aircraft propulsion systems
(e.g., rotor assemblies, rotor systems, etc.), operable between a
forward arrangement 510 and a hover arrangement 520 (as shown in
the example in FIG. 14). However, the rotorcraft can alternatively
be a fixed wing aircraft with one or more rotor assemblies or
propulsion systems, a helicopter with one or more rotor assemblies
(e.g., wherein at least one rotor assembly or aircraft propulsion
system is oriented substantially axially to provide horizontal
thrust), a lighter-than-air aircraft, and/or any other suitable
rotorcraft or vehicle propelled by rotors. The rotorcraft
preferably includes an all-electric powertrain (e.g., battery
powered electric motors) to drive the one or more rotor assemblies,
but can additionally or alternatively include a hybrid powertrain
(e.g., a gas-electric hybrid including an internal-combustion
generator), an internal-combustion powertrain (e.g., including a
gas-turbine engine, a turboprop engine, etc.), and any other
suitable powertrain.
[0044] The tiltrotor aircraft defines various geometrical features.
The tiltrotor aircraft defines principal geometric axes, as shown
in FIGS. 15A-15B, including: a vertical axis (e.g., yaw axis 506),
a longitudinal axis (e.g., a roll axis 502), and a lateral axis
(e.g., a pitch axis 504). The vertical, longitudinal, and lateral
axes can be defined such that they intersect at the center of
gravity (CoG) of the aircraft, and a pure moment about any one of
the aforementioned axes causes the aircraft 100 to rotate about the
vertical, longitudinal, and lateral axes, respectively. However,
the three principal axes can additionally or alternatively be
defined geometrically (e.g., based on lines of symmetry of the
aircraft in one or more dimensions, based on arbitrary lines
through the aircraft, etc.) with or without reference to the CoG.
For example, the axes can intersect at a geometric center of the
aircraft. The propellers of the tiltrotor aircraft each define a
disc area centered at the axis of rotation of the propeller, and
the disc area is contained by an infinite disc plane extending away
from the axis of rotation. In variations of the aircraft, the disc
planes of each of the plurality of rotors can be coextensive with
any suitable subset of the remainder of the plurality of propulsion
assemblies. In a first example, each disc plane can be coextensive
with each other disc plane in the hover configuration of a first
variation. In a second example, each disc plane can be coextensive
with the disc plane of one other propulsion assembly symmetrically
across the longitudinal axis of the aircraft and displaced from
(e.g., offset from) the disc planes of each other propulsion
assembly. However, the disc planes of the plurality of propulsion
assemblies can be otherwise suitably arranged relative to one
another.
[0045] The term "rotor" as utilized herein, in relation to the
control system or otherwise, can refer to a rotor, a propeller,
and/or any other suitable rotary aerodynamic actuator. While a
rotor can refer to a rotary aerodynamic actuator that makes use of
an articulated or semi-rigid hub (e.g., wherein the connection of
the blades to the hub can be articulated, flexible, rigid, and/or
otherwise connected), and a propeller can refer to a rotary
aerodynamic actuator that makes use of a rigid hub (e.g., wherein
the connection of the blades to the hub can be articulated,
flexible, rigid, and/or otherwise connected), no such distinction
is explicit or implied when used herein, and the usage of "rotor"
can refer to either configuration, and any other suitable
configuration of articulated or rigid blades, and/or any other
suitable configuration of blade connections to a central member or
hub. Likewise, the usage of "propeller" can refer to either
configuration, and any other suitable configuration of articulated
or rigid blades, and/or any other suitable configuration of blade
connections to a central member or hub. Accordingly, the tiltrotor
aircraft can be referred to as a tilt-propeller aircraft, a
tilt-prop aircraft, and/or otherwise suitably referred to or
described.
[0046] In a specific example, the rotary airfoil 100 is integrated
into an electric tiltrotor aircraft including a plurality of
tiltable rotor assemblies (e.g., six tiltable rotor assemblies),
wherein each of the tiltable rotor assemblies includes a rotor that
includes a plurality of blades configured according to the blade
design described herein. The electric tiltrotor aircraft can
operate as a fixed wing aircraft, a rotary-wing aircraft, and in
any liminal configuration between a fixed and rotary wing state
(e.g., wherein one or more of the plurality of tiltable rotor
assemblies is oriented in a partially rotated state). The control
system of the electric tiltrotor aircraft in this example can
function to command and control the plurality of tiltable rotor
assemblies within and/or between the fixed wing arrangement and the
rotary-wing arrangement.
[0047] In a specific example, the rotary airfoil 100 can be
integrated into the tilt-rotor aircraft described in U.S.
application Ser. No. 16/409,653, filed May 10, 2019, which is
incorporated in its entirety by this reference.
2. Benefits
[0048] Variations of the technology can afford several benefits
and/or advantages over conventional rotary airfoils and/or design
methods therefor.
[0049] First, the inventors have discovered that conventional
optimization of airfoil shapes to enhance aerodynamic efficiency
can have adverse and counterintuitive effects on the acoustic
performance of the airfoil and/or propellers utilizing a plurality
of rotary airfoils (e.g., propeller blades). This can be caused by
inflow conditions varying across the rotor disc (e.g., as shown in
FIG. 3), which in turn causes each blade to experience different
inflow conditions (e.g., effective angles of attack) and thus
produce different aerodynamic forces; the disc loading is thus
asymmetric/uneven. The magnitude of loading asymmetry/unevenness
can be proportional to the magnitude of undesirable acoustic
output, and more efficient airfoils (e.g., defining a steeper lift
coefficient curve) can exacerbate the loading asymmetry/unevenness
(e.g., as shown in FIG. 4). Thus, variations of the technology can
generate and utilize unconventional, counterintuitive airfoil
shapes that reduce the impact of inflow condition variations across
a rotor disc defined by the rotating propeller, with corresponding
benefits of reducing undesirable acoustic output.
[0050] Second, variations of the technology can provide efficient
forward flight and reduce the acoustic profile of the rotary
airfoil in hover for VTOL applications. In such variations, the
rotary airfoil operates in different regimes of the lift
coefficient curve in the hover and forward flight modes. In such
variants, the rotary airfoil can be configured to operate within an
acoustic range in the hover mode with a minimum dB level of: less
than 30, 40, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110,
or any other suitable dB level; and a maximum dB level of 40, 45,
50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120,
more than 120, or any other suitable dB level. In such variants,
the rotary airfoil (and/or rotor or aircraft including the airfoil)
can be configured to operate within an appropriate acoustic range
in the forward mode with a minimum dB level of: less than 30, 40,
50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, or any other
suitable dB level; and a maximum dB level of 40, 45, 50, 55, 60,
65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, more than 120,
ranges therebetween, and/or any other suitable dB level. The
acoustic range can similarly be determined by transforming this
acoustic range into an EPNL scale (EPNdB), A-weighted (dBA),
C-weighted (dBC), Z-weighted, CNEL, NDL, SEL, SENEL, Leq, Lmax,
and/or other expression of noise level, measured at a distance of 0
m, 10 m, 25 m, 50 m, 100 m, 150 m, 200 m, 300 m, 500 m, 1000 m,
and/or any other appropriate proximity; alternatively, the numbers
discussed above for the acoustic range can be applied to the
aforementioned noise level expressions.
[0051] Conventionally, aircraft operation in hover mode presents
larger inflow variations due to ground effects ("dirty air") which
correspond to an increase in the noise profile due to loading
asymmetry/unevenness. Because hover modes may be used near
human-populated regions where it is most critical to reduce the
noise profile to meet regulatory requirements and improve user
experience, the acoustic profile conferred by variants of this
design can be particularly desirable for hover mode operation in
human- or civilian-facing applications. In such variations, the
rotary airfoil incurs an efficiency penalty (e.g., .about.3%) in
order to improve the acoustic performance during hover (e.g.,
during operation in the hover angle of attack range), where the
lift coefficient curve has a shallower slope than the lift
coefficient curve in the forward angle of attack range. This can
result in minimizing the loading asymmetry/unevenness resulting
from inflow variation, at the cost of increased drag. This effect
can have compounding positive effects when combined with
conventional means of improving the acoustic performance of a
rotary airfoil, such as: tapering the blade along the length,
twisting the blade to change the pitch angle along the length,
angling the blade tip (e.g., anhedral angle, dihedral angle),
optimizing the airfoil cross section for different Reynold's number
ranges on different portions of the blade (e.g., lower Re on inner
portion and higher Re on outer portion), and/or other conventional
approaches to rotor to noise reduction. However, in such variations
the rotary airfoil does not incur a significant efficiency penalty
in forward flight--which represents a majority of aircraft
operation. By operating in a forward angle of attack range during
forward flight, high propulsive efficiency can minimize the cost of
fuel and/or electricity supplied to the aircraft, minimize the
number of refueling/recharging stops, reduce vehicle weight of
energy storage systems, and/or improve the aircraft range. An
example efficiency curve 300 for a rotary airfoil is shown in FIG.
11.
[0052] Third, variations of the technology define an airfoil
geometry where the point of flow separation does not shift as a
function of angle of attack (e.g., in the hover range), or shifts
less than a predetermined distance (e.g., less than 10%, 5%, 3%,
etc, of the chord line) across all operational angle of attack
ranges. This can reduce the drag influence of flow separation,
allowing the aerodynamic stall and/or max lift condition 210 of the
airfoil to occur at higher angles of attack (e.g., greater than 5
deg after semi-critical angle of attack) and resulting in gentle
stall behavior 202 as shown in the example in FIG. 8.
[0053] Fourth, variations of the technology minimize vibrations of
the rotor blade to improve the acoustic performance of the blade
with varying inflow conditions. Varying inflow can result from:
ambient weather factors such as wind, pressure, ground effects, and
other ambient influences; other rotors of the aircraft which can be
located in any plane, which can be: coplanar with the disc plane,
parallel to the disc plane, intersecting the disc plane, orthogonal
to the disc plane, and/or in any orientation relative to the disc
plane; and other sources of variable inflow. In such variations,
the blade profile offers improved vibration characteristics,
improved load distribution, and increasing rigidity in bending and
torsion as a result of: tapering the blade along the length (as
shown in the examples in FIGS. 10A-C), twisting the blade to change
the pitch angle along the length, angling the blade tip (e.g.,
anhedral angle, dihedral angle), optimizing the airfoil cross
section for different Reynold's number ranges on different portions
of the blade (e.g., lower Re on inner portion and higher Re on
outer portion), and/or other conventional approaches to rotor to
noise reduction.
[0054] Fifth, variations of the technology can provide airfoils
that define a small pitching moment. In such variations, the torque
required to maintain a specified blade pitch within a range of
variable blade pitches is reduced versus an airfoil that defines a
larger pitching moment. Thus, variable-pitch propeller systems can
be implemented, using such variations of the technology, with
smaller and/or lower-torque variable-pitch actuators, and thus at
reduced cost and weight.
[0055] Sixth, variations of the technology can provide airfoils
that define smoothly varying and gentle stall behavior (e.g., a
shallow roll-off of lift coefficient with angle of attack above the
stall angle, as shown in FIG. 4). For example, the airfoils can
include a raised feature 125 (e.g., a bump) along the upper surface
(e.g., forward of the chordwise midpoint, aft of the chordwise
midpoint, etc.), followed by a downward taper, that localizes the
boundary layer separation point proximal the raised feature as
angle of attack is increased beyond the stall angle. However,
variations of the technology can otherwise suitably provide
smoothly- and slowly-varying post-stall decrease in lift
coefficient.
[0056] However, variations of the technology can additionally or
alternatively provide any other suitable benefits and/or
advantages.
3. System
[0057] As shown in FIG. 1, the rotary airfoil 100 defines a cross
section and a span, wherein the cross section 110 is a function of
the point along the span (e.g., spanwise point) and defines an
upper surface 120 and a lower surface 130 at each spanwise point.
The rotary airfoil 100 also defines, at a cross section, a lift
coefficient (C.sub.L) that is a function of the angle of attack at
which the airfoil is rotated through the air. However, the rotary
airfoil 100 can additionally or alternatively include or define any
other suitable components or features.
[0058] The rotary airfoil 100 functions to generate an aerodynamic
force as it is rotated through a fluid (e.g., air), which can be
used to propel a vehicle (e.g., aircraft). The rotary airfoil can
define a single airfoil cross sectional profile or multiple cross
sectional profiles.
[0059] The rotary airfoil is preferably used in a propulsion
system, wherein the propulsion system can include: a set of rotary
airfoils, a rotor hub that mounts the set of rotary airfoils (e.g.,
3, 4, 5, 6, or any other suitable number of rotary airfoils), a
tilt mechanism that pivots the set of rotary airfoils between a
forward configuration and a hover configuration, and a pitching
mechanism 530 that changes the pitch angle 535 (and thereby the
angle of attack) of the rotary airfoil 100 (e.g., as shown in the
example in FIG. 16). However, the propulsion system can
additionally or alternatively include or define any other suitable
components or features. The propulsion system can be that disclosed
in U.S. application Ser. No. 16/430,163, incorporated herein in its
entirety by this reference, or be any other suitable propulsion
system.
[0060] The propulsion system is preferably used in an aircraft,
such as a tilt-rotor aircraft, but can additionally or
alternatively be used in any other suitable manner. In variants,
the aircraft can include multiple propulsion systems (e.g., 4, 6,
8, 10, etc.) distributed about the aircraft body (e.g., evenly
distributed about an aircraft center of gravity, unevenly
distributed, etc.) or a single propulsion system. When the aircraft
includes multiple propulsion systems, the disc plane defined by
each propulsion system can be aligned or offset from one or more of
the other propulsion systems on the same aircraft. The aircraft can
be: manually controlled, automatically controlled, selectively
automatically controlled, or otherwise controlled. The aircraft can
be that disclosed in U.S. application Ser. No. 16/409,653,
incorporated herein in its entirety by this reference, but can be
any other suitable aircraft.
[0061] The cross section of the rotary airfoil 100 preferably
defines a leading edge 150, a trailing edge 160, and a chord line
170 extending between the leading edge and trailing edge as shown
in FIG. 17. The chord line preferably defines a chord length 171
(L), which can be used as a reference dimension for the airfoil
cross section. The chord length L can be: <1 cm, 1 cm, 2 cm, 3
cm, 4 cm, 5 cm, 7 cm, 10 cm, 15 cm, 20 cm, 25 cm, 30 cm, 35 cm, 50
cm, <1 cm, 0.02 m-1 m, 1-5 cm, 5-10 cm, 10-15 cm, 15-25 cm,
25-50 cm, >50 cm, and/or any other appropriate length. The
rotary airfoil can define a single chord length or multiple chord
lengths along the span of the rotary airfoil. The leading edge is
preferably arcuate, but can have any appropriate geometry. The
leading edge radius 155 can be a specific dimension, specific
dimension relative to the chord length, or variable relative to the
chord length along the span of the rotary airfoil. The leading edge
can define a leading edge radius, which can be defined relative to
the chord length or otherwise dimensioned (e.g., metric units). The
leading edge radius can be: 0.01 L, 0.02 L, 03 L, 0.05 L, 0.07 L,
0.1 L, 0.15 L 0.2 L, <0.01 L, 0.01-0.03, 0.03-0.05, 0.01-0.05 L,
0.05-0.07 L, 0.07-0.10 L, 0.05-0.10 L, 0.1-0.2 L, >0.2 L, and/or
any appropriate radius. The trailing edge can be arcuate,
sharp/pointed, and/or straight cut. In a first variant, trailing
edge is arcuate and defines a trailing edge radius. The trailing
edge radius can be a specific dimension, specific dimension
relative to the chord length, or variable relative to the chord
length along the span of the rotary airfoil. The trailing edge
radius can be defined relative to the chord length or otherwise
dimensioned (e.g., metric units). The trailing edge radius can be:
0, 0.001 L, 0.002 L, 003 L, 0.005 L, 0.007 L, 0.01 L, 0.015 L 0.02
L, 0.03 L, 0.05 L, 0.07 L 0.1 L, <0.005 L, 0.005-0.01 L,
0.01-0.03 L, 0.03-0.05 L, 0.01-0.05 L, 0.05-0.1 L, >0.1 L,
and/or any appropriate radius. In a second variant, the trailing
edge defines a trailing edge thickness. In a first example of the
second variant, the trailing edge thickness can be two times the
trailing edge radius. In a second example of the second variant,
the trailing edge is straight cut (or approximately straight cut).
The trailing edge thickness can be a specific dimension, specific
dimension relative to the chord length, or variable relative to the
chord length along the span of the rotary airfoil. The trailing
edge thickness can be defined relative to the chord length or
otherwise dimensioned (e.g., metric units). The trailing edge
thickness can be: 0, 0.001 L, 0.002 L, 003 L, 0.005 L, 0.007 L,
0.01 L, 0.015 L 0.02 L, 0.03 L, 0.05 L, 0.07 L 0.1 L, <0.005 L,
0.005-0.01 L, 0.01-0.03 L, 0.03-0.05 L, 0.01-0.05 L, 0.05-0.1 L,
>0.1 L, and/or any appropriate thickness.
[0062] The cross section of the rotary airfoil defines a thickness
between an upper surface and a lower surface. In a first variant,
the upper and lower surfaces are above and below the chord line,
respectively, as shown in FIGS. 1 and 5. In a second variant, the
upper surface and the lower surface both lie above the chord line.
In a third variant, the upper surface lies above the chord line and
a portion of the lower surface (proximate the trailing edge) lies
above the chord line. The upper and lower surfaces can be
asymmetric (e.g., defining a rotary airfoil that is asymmetric
about the chord line), but can alternatively be symmetric (e.g.,
defining a symmetric airfoil). The cross section can vary in any
suitable manner along the span of the rotary airfoil. For example,
the cross section can twist along the span while maintaining the
same scaled shape (e.g., wherein the ratio between the thickness at
each chordwise section and the chord line remains static as the
chord line changes length along the span, wherein the camber line
maintains the same shape along the span as the length of the camber
line changes, etc.) such that the angle of attack of each point
along the span differs. In another example, the cross-sectional
shape can vary along the span (e.g., wherein the upper surface
defines a more pronounced raised feature at a first portion of the
span, and the raised feature is less pronounced in a second portion
of the span). However, the cross section can define any other
suitable spanwise variation (including, for example, no
variation).
[0063] The upper surface functions to manipulate the flow field of
the inflowing air 101 such that the average velocity of the flow
field is higher than that of the flow field proximal the lower
surface and the average static pressure is lower. The lower surface
(e.g., the pressure surface) functions to manipulate the flow field
of the inflowing air such that the average velocity of the flow
field is lower than that of the flow field proximal the upper
surface, and the average static pressure is higher (e.g., in the
hover configuration).
[0064] The rotary airfoil can have any appropriate thickness. The
thickness for a cross section of the rotary airfoil is defined as
the distance between the upper and lower surfaces at a chordwise
location. The rotary airfoil can have any appropriate maximum
thickness. The maximum thickness of the rotary airfoil can be a
specific dimension, specific dimension relative to the chord
length, or variable relative to the chord length along the span of
the rotary airfoil. The maximum thickness 175 can be defined
relative to the chord length or otherwise dimensioned (e.g., metric
units). The maximum thickness can be: 0.050 L, 0.075 L, 0.100 L,
0.110 L, 0.115 L, 0.120 L, 0.125 L, 0.130 L, 0.135 L, 0.140 L,
0.150 L, 0.200 L, 0.25 L, <0.075 L, 0.05-0.10 L, 0.100-0.150 L,
0.120-0.130 L, 0.05-0.25 L, >0.25 L, and/or any appropriate
thickness. The maximum thickness can occur at any appropriate
chordwise location 176. Preferably, the maximum thickness can occur
at a chordwise location of: 0.20 L, 0.25 L, 0.30 L, 0.33 L, 0.35 L,
0.36 L, 0.363 L, 0.365 L, 0.37 L, 0.40 L, 0.45 L, 0.50 L, 0.55 L,
0.60 L, <0.20 L, 0.20-0.30 L, 0.30-0.40 L, 0.35-0.38 L,
0.40-0.50 L, 0.50-0.60 L, >0.50 L and/or any appropriate
chordwise location.
[0065] The airfoil thickness preferably defines a camber line 172
extending between the leading edge and the trailing edge. The
camber line preferably lies above the chord line, but can have any
appropriate geometry. The camber line can define any appropriate
maximum camber. The maximum camber 173 of the rotary airfoil can be
a specific dimension, specific dimension relative to the chord
length, or variable relative to the chord length along the span of
the rotary airfoil. The maximum camber can be defined relative to
the chord length or otherwise dimensioned (e.g., metric units). The
maximum camber can be: 0.01 L, 0.02 L, 03 L, 0.05 L, 0.07 L, 0.10
L, 0.15 L 0.20 L, <0.01 L, 0.01-0.03, 0.03-0.05, 0.01-0.05 L,
0.05-0.07 L, 0.07-0.10 L, 0.05-0.10 L, 0.10-0.20 L, >0.20 L,
and/or any appropriate camber. The maximum camber can occur at any
appropriate chordwise location 174. Preferably, the maximum camber
occurs between the leading edge and the chordwise location of
maximum thickness, but can alternately happen between the trailing
edge and the chordwise location of maximum thickness, at the same
chordwise location as the maximum thickness, or at any appropriate
chordwise location. The maximum camber can occur at a chordwise
location of: 0.20 L, 0.25 L, 0.26 L, 0.27 L, 0.28 L, 0.29 L, 0.30
L, 0.31 L, 0.32 L, 0.33 L, 0.34 L, 0.35 L, 0.36 L, 0.363 L, 0.365
L, 0.37 L, 0.40 L, 0.45 L, 0.50 L, <0.20 L, 0.20-0.30 L,
0.30-0.40 L, 0.35-0.38 L, 0.40-0.50 L, >0.50 L and/or any
appropriate chordwise location. The camber line can define any
appropriate leading edge camber angle 156. The leading edge camber
angle of a cross section of the rotary airfoil can be a specific
dimension or variable along the span of the rotary airfoil. The
leading edge camber angle can be: <1 deg, 0 deg, 1 deg, 2 deg, 3
deg, 4 deg, 5 deg, 7 deg, 10 deg, 12 deg, 15 deg, 17 deg, 20 deg,
30 deg, 45 deg, >45 deg, 1-5 deg, 5-10 deg, 10-15 deg, 15-20
deg, 20-30 deg, 30-45 deg, and/or any appropriate angle. The camber
line can define any appropriate trailing edge camber angle. The
leading trailing edge camber angle of a cross section of the rotary
airfoil can be a specific dimension or variable along the span of
the rotary airfoil. The trailing edge camber angle can be: <1
deg, 0 deg, 1 deg, 2 deg, 3 deg, 4 deg, 5 deg, 7 deg, 10 deg, 12
deg, 15 deg, 17 deg, 20 deg, 30 deg, 45 deg, >45 deg, 1-5 deg,
5-10 deg, 10-15 deg, 15-20 deg, 20-30 deg, 30-45 deg, and/or any
appropriate angle.
[0066] The thickness of the airfoil can be measured perpendicular
to the camber line ("American convention) and/or measured
perpendicular to the chord line ("British convention").
[0067] The airfoil thickness can define any appropriate upper
camber 178 relative to the upper surface of the airfoil and the
chord line. The maximum upper camber preferably occurs between the
trailing edge and the chordwise location of maximum camber, but can
alternately occur between the leading edge and the chordwise
location of maximum camber, at the same chordwise location as the
maximum camber, or at any appropriate chordwise location.
[0068] The airfoil thickness can define any appropriate lower
camber 179 relative to the lower surface of the airfoil and the
chord line. Preferably, the maximum lower camber occurs between the
leading edge and the chordwise location of maximum upper camber,
but can alternately occur between the trailing edge and the
chordwise location of maximum upper camber, at the same chordwise
location as the maximum upper camber, or at any appropriate
chordwise location.
[0069] The airfoil thickness can define a semi-critical separation
point 140, which functions to create a stagnating zone in the flow
atop the airfoil, which thickens the boundary layer and pushes the
effective trailing edge upwards away from the upper surface of the
airfoil (e.g., as shown in FIG. 6). The thickening of the boundary
layer 204 and upward displacement of the effective trailing edge
can function to reduce the lift coefficient at a given angle of
attack (e.g., flattens the C.sub.L(.alpha.) curve). The
semi-critical separation point can also function to localize the
boundary layer separation point along the upper surface with
increasing angle of attack (e.g., as shown in FIGS. 7A-7B), instead
of allowing the separation point to move upstream as the angle of
attack is increased, leading to "gentle" stalling behavior (e.g.,
wherein the lift coefficient rolls off slowly with increasing angle
of attack past the stall point, as shown by example in FIG. 4). The
semi-critical separation point is can be located at a chordwise
point 177 of: 0.05 L, 0.10 L, 0.15 L, 0.20 L, 0.25 L, 0.30 L, 0.35
L, 0.40 L, 0.45 L, 0.50 L, 0.55 L, 0.60 L, 0.65 L, 0.70 L, 0.75 L,
0.80 L, 0.85 L, 0.90 L, 0.95 L, <0.25 L, 0.25-0.50 L, 0.50-0.75
L, >0.75 L, 0.20-0.80 L, and/or in any other suitable location
along the upper surface.
[0070] The semi-critical separation point can be defined for a
range of attack angles and/or range of Reynold's numbers as shown
in the examples in FIGS. 12A-B. The Reynold's number can be: 10 k,
30 k, 50 k, 100 k, 200 k, 300 k, 400 k, 600 k, 800 k, 1000 k, 1500
k, 2000 k, 3000 k, 5000 k, 10000 k, <50 k, 50 k-100 k, 50 k-1000
k, 50 k-10000 k, 100 k-300 k, 300 k-1000 k, 1000 k-10,000 k,
>1000 k, >10M, and/or any other appropriate Reynold's number
range. The semi-critical attack angles can be: 0 deg, 1 deg, 2 deg,
3 deg, 4 deg, 5 deg, 5.5 deg, 6 deg, 6.5 deg, 7 deg, 8 deg, 9 deg,
10 deg, 11 deg, 12 deg, 13 deg, 14 deg, 15 deg, >15 deg, <0
deg, 5-10 deg, 6-8 deg, 8-10 deg, 1-6 deg, 10-15 deg, and/or any
other appropriate angle.
[0071] The semi-critical separation point can be defined by one or
more separation features arranged along one or more chordwise or
spanwise points along the airfoil. The separation feature can
define the semi-critical separation point before, on, or after the
separation feature. Examples of separation features that can be
used include: a sphere segment, catenoid, conoid, lune, wedge,
cone, teardrop, and/or separation features with any other suitable
geometry.
[0072] In a first variant, as shown in FIG. 5, the upper surface of
the airfoil cross section preferably defines a separation feature
followed (in the chordwise direction) by a downward taper, which
defines the semi-critical separation point. In a specific example,
the cross section defines a bump and subsequent taper having a
shape substantially as shown in FIG. 5. In alternative examples,
the separation can have any other suitable shape (e.g.,
scale-invariant dimensions, non-dimensional shape, etc.), such as a
groove, channel, change in surface roughness, and/or different
feature.
[0073] In some variations, the lower surface of the airfoil can
define a bump substantially as described above in relation to the
upper surface. The bump can be identically shaped and positioned in
relation to the bump on the upper surface of the cross section but
can alternatively be asymmetrically shaped and/or positioned in
relation to the bump on the upper surface (e.g., a more or less
pronounced bump, positioned further towards or away from the
leading edge than the upper bump, etc.). In further alternatives,
the bump can be omitted from the upper surface and included solely
on the lower surface.
[0074] In a second variant, the semi-critical separation point is
related to the specific geometry of the cross section, such as: a
change in curvature of the upper camber, a change in curvature of
the lower camber, a change in curvature of the camber, local
maximum in the camber, local maximum in the upper camber, and/or
local maximum in the lower camber.
[0075] In a first example, the airfoil cross section is defined by
Table 1. In a second example, the airfoil cross section is defined
by Table 2. However, the airfoil cross sections can be otherwise
defined.
TABLE-US-00001 TABLE 1 Chordwise Thickness Chordwise Thickness
Chordwise Thickness Chordwise Thickness position position position
position position position position position (x/L) (t/L) (x/L)
(t/L) (x/L) (t/L) (x/L) (t/L) 1 0 0.1557 0.0644 0.0952 -0.0302
0.8747 -0.0008 0.9686 0.003 0.1393 0.0619 0.109 -0.0317 0.9059
0.001 0.9372 0.0064 0.1237 0.0594 0.1237 -0.0331 0.9372 0.0019
0.9059 0.0107 0.109 0.057 0.1393 -0.0344 0.9686 0.0017 0.8747
0.0159 0.0952 0.0546 0.1557 -0.0355 1 0 0.8436 0.0222 0.0822 0.0521
0.1729 -0.0365 0.8126 0.0291 0.0702 0.0495 0.191 -0.0374 0.7819
0.0363 0.0591 0.0468 0.2098 -0.0381 0.7513 0.0434 0.0489 0.0439
0.2295 -0.0387 0.721 0.0501 0.0397 0.0406 0.2499 -0.0392 0.691
0.0561 0.0314 0.037 0.271 -0.0396 0.6613 0.0616 0.0241 0.0329
0.2929 -0.0398 0.6319 0.0663 0.0177 0.0283 0.3155 -0.0398 0.6029
0.0705 0.0123 0.0233 0.3387 -0.0397 0.5742 0.0742 0.0079 0.0182
0.3626 -0.0394 0.546 0.0773 0.0044 0.0133 0.3871 -0.039 0.5182 0.08
0.002 0.0086 0.4122 -0.0383 0.491 0.0822 0.0005 0.004 0.4379
-0.0375 0.4642 0.0839 0 0 0.4642 -0.0364 0.4379 0.0852 0.0005
-0.0029 0.491 -0.0351 0.4122 0.0859 0.002 -0.0053 0.5182 -0.0336
0.3871 0.086 0.0044 -0.0075 0.546 -0.0319 0.3626 0.0857 0.0079
-0.0097 0.5742 -0.0299 0.3387 0.0848 0.0123 -0.0121 0.6029 -0.0277
0.3155 0.0835 0.0177 -0.0144 0.6319 -0.0252 0.2929 0.0817 0.0241
-0.0167 0.6613 -0.0224 0.271 0.0797 0.0314 -0.0189 0.691 -0.0194
0.2499 0.0774 0.0397 -0.021 0.721 -0.0162 0.2295 0.0749 0.0489
-0.0231 0.7513 -0.0129 0.2098 0.0723 0.0591 -0.025 0.7819 -0.0095
0.191 0.0697 0.0702 -0.0269 0.8126 -0.0063 0.1729 0.067 0.0822
-0.0286 0.8436 -0.0033
TABLE-US-00002 TABLE 2 Chordwise Thickness Chordwise Thickness
Chordwise Thickness Chordwise Thickness position position position
position position position position position (x/L) (t/L) (x/L)
(t/L) (x/L) (t/L) (x/L) (t/L) 1 0 0.1557 0.069 0.0952 -0.0278
0.8747 0.0031 0.9686 0.0029 0.1393 0.0661 0.109 -0.029 0.9059
0.0031 0.9372 0.0063 0.1237 0.0632 0.1237 -0.03 0.9372 0.0026
0.9059 0.0105 0.109 0.0602 0.1393 -0.0308 0.9686 0.0016 0.8747
0.0155 0.0952 0.0571 0.1557 -0.0315 1 0 0.8436 0.0214 0.0822 0.0539
0.1729 -0.032 0.8126 0.0278 0.0702 0.0507 0.191 -0.0323 0.7819
0.0345 0.0591 0.0472 0.2098 -0.0324 0.7513 0.041 0.0489 0.0436
0.2295 -0.0324 0.721 0.0471 0.0397 0.0398 0.2499 -0.0321 0.691
0.0528 0.0314 0.0356 0.271 -0.0317 0.6613 0.0579 0.0241 0.0312
0.2929 -0.0311 0.6319 0.0626 0.0177 0.0264 0.3155 -0.0303 0.6029
0.0667 0.0123 0.0214 0.3387 -0.0293 0.5742 0.0705 0.0079 0.0165
0.3626 -0.0281 0.546 0.074 0.0044 0.012 0.3871 -0.0268 0.5182
0.0771 0.002 0.0077 0.4122 -0.0253 0.491 0.0799 0.0005 0.0034
0.4379 -0.0237 0.4642 0.0823 0 0 0.4642 -0.022 0.4379 0.0842 0.0005
-0.0023 0.491 -0.0201 0.4122 0.0857 0.002 -0.0044 0.5182 -0.0182
0.3871 0.0867 0.0044 -0.0065 0.546 -0.0161 0.3626 0.0871 0.0079
-0.0088 0.5742 -0.014 0.3387 0.087 0.0123 -0.0111 0.6029 -0.0119
0.3155 0.0864 0.0177 -0.0134 0.6319 -0.0097 0.2929 0.0853 0.0241
-0.0156 0.6613 -0.0075 0.271 0.0838 0.0314 -0.0177 0.691 -0.0053
0.2499 0.0819 0.0397 -0.0197 0.721 -0.0032 0.2295 0.0797 0.0489
-0.0216 0.7513 -0.0013 0.2098 0.0772 0.0591 -0.0234 0.7819 0.0004
0.191 0.0746 0.0702 -0.025 0.8126 0.0017 0.1729 0.0719 0.0822
-0.0265 0.8436 0.0027
[0076] In a first variation of the first example, the airfoil cross
section is defined by a set of at least 5 points selected from
Table 1. In a second variation of the first example, the airfoil
cross section is defined by a set of at least 10 points selected
from Table 1. In a third variation of the first example, the
airfoil cross section is defined by every point in Table 1. In a
fourth variation of the first example, each point is within a
margin of the value in Table 1, where the margin can be:
<0.0001, 0.0001, 0.0005, 0.001, 0.005, 0.01, and/or any
appropriate margin. The margin can be the same or different for the
chordwise position (x/L) and the thickness position (t/L).
[0077] In a first variation of the second example, the airfoil
cross section is defined by a set of at least 5 points selected
from Table 2. In a second variation of the second example, the
airfoil cross section is defined by a set of at least 10 points
selected from Table 2. In a third variation of the second example,
the airfoil cross section is defined by every point in Table 2. In
a fourth variation of the second example, each point is within a
margin of the value in Table 2, where the margin can be:
<0.0001, 0.0001, 0.0005, 0.001, 0.005, 0.01, and/or any
appropriate margin. The margin can be the same or different for the
chordwise position (x/L) and the thickness position (t/L).
[0078] In a third example, the rotary airfoil can define a first
airfoil cross section defined by Table 1 and a second airfoil cross
section defined by Table 2. The first and second airfoil cross
sections can be associated with different spanwise portions of the
airfoil, and/or combined with any other suitable cross sections.
Between the first and second cross sections, the airfoil blade can
include any suitable blending, interpolation, and/or other
smoothing.
[0079] The rotary airfoil can define a span of any appropriate
length (e.g., blade length). The span can be sized relative to a
cross sectional chord length, independent of the chord length,
and/or any appropriate length. The span can be: 5 L, 10 L, 15 L, 20
L, 25 L, 50 L, <5 L, 5-25 L, 25-50 L, >50 L, <5 cm, 5 cm,
10 cm, 25 cm, 30 cm, 35 cm, 40 cm, 45 cm, 50 cm, 60 cm, 70 cm, 80
cm, 90 cm, 1 m, 1.25 m, 1.5 m, 1.75 m, 2.5 m, 5 m, 10 m, 15 m, 20
m, 5-25 cm, 25-50 cm, 50-100 cm, 0.1 m-15 m, 1-2 m, 1-4 m, 5-10 m,
10-20 m, >20 m, and/or any other suitable length.
[0080] The rotary airfoil can define any appropriate pitch angle.
The pitch angle can be static or variable. The pitch angle can be
defined as the angle of the chord line with respect to the rotor
disc plane at any appropriate spanwise position on the blade. In a
specific example, the pitch angle is defined relative to a spanwise
position of 75% the length (radially outward). The pitch angle of
the rotary airfoil can be: <-15 deg, -10 deg, -5 deg, -5 deg, -4
deg, -3 deg, -2 deg, -1 deg, 0 deg, 1 deg, 2 deg, 3 deg, 4 deg, 5
deg, 7 deg, 10 deg, 12 deg, 15 deg, 17 deg, 20 deg, 21 deg, 22 deg,
25 deg, 30 deg, 35 deg, 45 deg, 60 deg, 90 deg, 1-5 deg, 5-10 deg,
10-15 deg, 15-20 deg, 20-25 deg, 25-30 deg, 30-35 deg, 35-45 deg,
>45 deg, and/or any appropriate pitch angle. In a first variant,
the pitch angle is variable via the pitching mechanism. In a second
variant, the effective angle of attack is controlled by motor RPM,
with different speeds corresponding to different effective pitch
angles.
[0081] The rotary airfoil can define a twist angle along the span.
The twist angle can be a change in the angle of the chord line
(e.g., relative to blade geometry, relative to the rotor disc
plane, etc.) across a spanwise segment of the rotary airfoil (e.g.,
across the full length of the airfoil) and/or otherwise defined.
The (absolute value of) twist angle can be 0 deg, 1 deg, 2 deg, 3
deg, 4 deg, 5 deg, 7 deg, 10 deg, 12 deg, 15 deg, 17 deg, 20 deg,
25 deg, 30 deg, 35 deg, 40 deg, 45 deg, 50 deg, 10-60 deg, 20-50
deg, 1-5 deg, 5-10 deg, 10-15 deg, 15-20 deg, 20-25 deg, 25-30 deg,
30-35 deg, 25-35 deg, 35-40 deg, 40-50 deg, >50 deg, and/or any
appropriate twist angle.
[0082] The rotary airfoil can define any appropriate spanwise
geometry. Preferably, the upper surface of the rotary airfoil is
generally in a vesica piscis geometry, but can additionally or
alternately be tapered toward the tip, have constant cross
sectional area, have variable cross sectional area, and/or have any
other appropriate geometry. The taper angle can be the same or
different on the leading edge, the trailing edge of the airfoil, on
an inner portion of the rotary airfoil, and/or at the tip. In an
example in FIG. 19C, angles 193, 194, 195, and 196 can be the same
or different. These angles can be any appropriate angle. 193 and
195 can be: <-10 deg, -10 deg, -5 deg, -4 deg, -3 deg, -2 deg,
-1 deg, 0 deg, 1 deg, 2 deg, 3 deg, 4 deg, 5 deg, 7 deg, 10 deg, 12
deg, 15 deg, 17 deg, 20 deg, 30 deg, 45 deg, 1-5 deg, 5-10 deg,
10-15 deg, 15-20 deg, 30-30 deg, 30-45 deg, >20 deg, and/or any
appropriate angle. 194 and 196 can be 0 deg, 1 deg, 2 deg, 3 deg, 4
deg, 5 deg, 7 deg, 10 deg, 12 deg, 15 deg, 17 deg, 20 deg, 30 deg,
45 deg, 60 deg, 90 deg, 1-5 deg, 5-10 deg, 10-15 deg, 15-20 deg,
30-30 deg, 30-45 deg, 45-60 deg, 60-90 deg, >20 deg, and/or any
appropriate angle.
[0083] The tip of the rotary airfoil can have any appropriate
geometry. The tip can be flat, rounded, or pointed, and can be a
point, edge, face, and/or other appropriate geometry. The rotary
airfoil can have any appropriate tip angle 198, as shown in FIG.
19D. The blade tip can be anhedral, dihedral, un-angled, and/or at
any suitable angle. The tip angle can be: 0 deg, 1 deg, 2 deg, 3
deg, 4 deg, 5 deg, 7 deg, 10 deg, 12 deg, 15 deg, 17 deg, 20 deg,
25 deg, 30 deg, 37 deg, 45 deg, 52 deg, 60 deg, 1-5 deg, 5-10 deg,
10-15 deg, 15-20 deg, 30-30 deg, 30-45 deg, >60 deg, and/or any
appropriate angle.
[0084] The rotary airfoil can have any appropriate twist angle 192,
as shown in FIG. 19A and FIG. 19B. The twist angle preferably
changes the effective angle of attack along the span 191 of the
rotary airfoil. The blade twist angle is preferably defined between
the innermost and outer (tip) cross sections, but can be defined
between any two cross sections, a section of the blade, and/or at
any suitable angle. The twist angle can be: 0 deg, 1 deg, 2 deg, 3
deg, 4 deg, 5 deg, 7 deg, 10 deg, 12 deg, 15 deg, 17 deg, 20 deg,
25 deg, 30 deg, 35 deg, 40 deg, 45 deg, 1-5 deg, 5-10 deg, 10-15
deg, 15-20 deg, 20-25 deg, 25-30 deg, 30-35 deg, 25-35 deg, 35-40
deg, >40 deg, and/or any appropriate twist angle.
[0085] The rotary airfoil can have any appropriate rotary airfoil
mounting angle 197, as shown in FIG. 19D. Preferably, angle 197 is
0 deg, but can be positive or negative. The rotary airfoil mounting
angle can be: -10 deg, -5 deg, -4 deg, -3 deg, -2 deg, -1 deg, 0
deg, 1 deg, 2 deg, 3 deg, 4 deg, 5 deg, 7 deg, 10 deg, 12 deg, 15
deg, 17 deg, 20 deg, <0 deg, 1-5 deg, 5-10 deg, 10-20 deg,
>20 deg.
[0086] The rotary airfoil can be constructed with any appropriate
materials using any appropriate manufacturing technique. The rotary
airfoil can be composite (e.g., carbon fiber, fiberglass, etc.),
metal, metal alloy, plastic, and/or a combination thereof (e.g.,
internal support members of different material/manufacture), but
can additionally or alternately include any appropriate materials.
The rotary airfoil can be solid, hollow (with a single or multiple
cavities), and/or otherwise constructed. The rotary airfoil can
have any appropriate mass. The rotary airfoil can be: <1 kg, 1-3
kg, 3-5 kg, 5-10 kg, 10-50 kg, 50-100 kg, 100-250 kg, >250 kg
and/or any other appropriate mass.
[0087] The rotor hub rotatably mounts rotary airfoil blade(s). The
rotor hub can mount any suitable number of rotary airfoil blades.
There are preferably 5 rotary airfoil blades, but there can be 2,
3, 4, 6, >6 blades, and/or any appropriate number of blades. The
blades can have any appropriate relative relationship about the
axis of rotation. In a first variant, the blades are symmetrically
mounted. In a second variant, the blades are mounted in the
arrangement described in U.S. application Ser. No. 16/430,163,
filed Jun. 3, 2019, which is incorporated in its entirety by this
reference. The rotary airfoil blades are preferably radially
mounted about the axis of rotation via mechanical bonding,
fasteners, and/or other mounting technique. The rotary blades can
be directly and/or indirectly mounted. The rotary airfoil blades
can be partially and/or fully supported by the blade pitching
mechanism and/or other component. The rotary airfoil blades can be
integrated into the rotor hub (e.g., one component), separate from
the rotor hub, and/or otherwise configured. In a first example,
there is a separate power source connected to the rotor hub, such
as an engine, rotor of a motor, or other power source. In a second
example, the hub is integrated into the stator of an electric
motor.
[0088] The optional pitching mechanism can change the angle of
attack of one or more rotary airfoil blades on the rotor. There can
be a single pitching mechanism or multiple pitching mechanisms
(e.g., one per rotor, multiple per rotor, one per blade, etc.). The
pitching mechanism can actuate blades independently or actuate
multiple simultaneously. The pitching mechanism can be integrated
into the rotor hub, connected/mounted to the rotor hub, and/or
separate from the rotor hub. Preferably, the pitching mechanism can
be electromechanically actuated, but can additionally or
alternately be hydraulic, pneumatic, and/or ground adjustable (by a
human operator or other input). The pitching mechanism can be
variable between a finite or infinite number of positions. The
pitching mechanism can be: a controllable-pitch propeller (CPP), a
swashplate, a ground adjustable rotor, and/or other pitching
mechanism.
[0089] The optional tilt mechanism 540 functions to transition the
orientation of each rotor between the hover configuration and the
forward configuration as shown in the example in FIG. 18A-C. The
tilt mechanism can also function to restrict the possible motion of
the rotor disc 104 such that radial projection of the propeller
disc toward the airframe 110 (e.g., the disc plane) in the hover
and forward configurations does not intersect any portion the
aircraft wherein a pilot is located. In the configuration wherein
the disc plane is forward of the pilot region in the forward
configuration, the disc plane preferably does not intersect the
pilot region at each point during transition between the hover and
forward configurations, inclusive of the endpoints (e.g., the hover
configuration and forward configuration). Transitioning the
orientation can include: pitching the propeller disc about an axis
parallel to the pitch axis of the aircraft; translating a portion
of the rotor assembly (e.g., relative to the attachment point on
the aircraft); rotating the rotor disc about an axis parallel to
the yaw axis of the aircraft; and any other suitable translation or
rotation and/or combination of the aforementioned transition
modalities.
[0090] The tilt mechanism associated with each rotor preferably
adjusts each rotor between the hover configuration and the forward
configuration (e.g., in conjunction with transition of the aircraft
100 between the hover mode and the forward mode); however, in
additional or alternative variations, adjustment can be performed
by a single tilt mechanism associated with all propellers (e.g., a
tilting wing rigidly fixed to each rotor mounting point), by a
number of tilt mechanisms different from the number of propellers
of the plurality of propellers (e.g., wherein a set of six
propellers are subdivided into pairs, and each pair is transitioned
by a single tilt mechanism between the hover and forward
configurations), and/or otherwise suitably performed. In a first
variation, the aircraft 100 includes six propellers and six tilt
mechanisms, wherein one tilt mechanism of the six tilt mechanisms
is associated with one rotor of the six rotors (e.g., the rotors
and tilt mechanisms have a one-to-one correspondence). In another
variation, two or more rotors of the plurality of rotors are
coupled to a single tilt mechanism such that actuation of the
single tilt mechanism transitions the two or more rotors between
the hover and forward configuration (e.g., wherein two or more
rotors are rigidly coupled to a wing, and the tilt mechanism
rotates the wing about the pitch axis to operate the aircraft
between the hover configuration and the forward configuration).
[0091] In variations, the tilt mechanism can displace the entirety
of an electric motor and the rotor away from the airframe (e.g.,
wing, pylon, etc.), relative to the remainder of the propulsion
assembly 120. Displacement is preferably performed by a tilt
mechanism including a linkage (e.g., as shown in FIGS. 18A-C); in
such variations, the tilt mechanism of at least one rotor includes
a linkage that displaces the electric motor and rotor parallel to
the roll axis in the hover configuration (e.g., forward or rearward
from the wing or pylon).
[0092] In additional or alternative variations, the tilt mechanism
can rotate the rotor itself to transition between the forward and
hover configurations. In an example of the aircraft in such a
variation, the tilt mechanism of a left outboard rotor assembly,
the right outboard rotor assembly, the left rear rotor assembly,
and the right rear rotor assembly each include a pivot that rotates
each propulsion assembly between the forward configuration and the
hover configuration.
[0093] In a specific example, the tilt mechanism is the tilt
mechanism described in U.S. application Ser. No. 16/409,653, filed
May 10, 2019, which is incorporated in its entirety by this
reference. However, any other suitable tilt mechanism can be
used.
[0094] However, the aircraft can additionally or alternatively
include any suitable number of rotors associated with any suitable
number of tilt mechanisms in any suitable manner.
[0095] The lift coefficient for a cross section of the rotary
airfoil non-dimensionally defines the lift (e.g., perpendicular
force) performance of the rotary airfoil, at a range of angles of
attack (e.g., the lift coefficient is defined as C.sub.L(.alpha.)),
in relation to the fluid density of the surrounding fluid (e.g.,
air), the fluid velocity, and a reference area (e.g., a surface
area of the airfoil, a cross sectional area of the airfoil, the
square of a salient length scale such as a chord length or span
length, etc.). In variations, C.sub.L(.alpha.) is preferably
shallow (e.g., has a minimal slope) within a desired angular range
of operation (e.g., 8.degree..ltoreq..alpha..ltoreq.10.degree.)
such that any variation in effective angle of attack due to inflow
variation results in a minimal variation in lift force generated by
the airfoil (e.g., as shown in FIG. 4). In an example, the rotary
airfoil defines a lift coefficient that is approximately constant
with angle of attack (e.g., has a slope of approximately zero)
within a desired range of angles of attack (e.g., angular range of
operation). However, the lift coefficient can have any other
suitable slope at any desired ranges of angles of attack (e.g., the
lift coefficient can define any other suitable shape).
[0096] The shallow slope of the lift coefficient in the desired
angular region of the lift coefficient curve 201 can function to
provide a psychoacoustic benefit during operation of a propeller
utilizing two or more of the rotary airfoils defined by such a lift
coefficient curve. For example, a shallow slope can attenuate
higher harmonics of the acoustic output of such a propeller
operated with its blades at an effective angle of attack within the
desired range, which can provide a psychoacoustic advantage (e.g.,
without reducing the overall acoustic power output) and/or reduce
the overall acoustic power output in potential exchange for a
reduction in aerodynamic efficiency (e.g., which may result in a
steeper variation of lift coefficient with increasing angle of
attack). The acoustic benefit can be more pronounced at higher
frequencies (where the output is also more psychoacoustically
sensitive).
[0097] The variation of lift coefficient with angle of attack of
the rotary airfoil also preferably exhibits shallow roll-off after
the stall point in comparison with a different airfoil shape, as
shown by example in FIG. 4. This can function to prevent large load
discrepancies between blades from developing when all or part of
one or more blades is in a localized stall condition. This can also
function to prevent rapid loss of propulsive power (or lift force)
when all or part of one or more rotary airfoils is in a localized
stall condition.
[0098] The lift coefficient curve preferably defines a max CL point
210 (corresponding to maximum lift) at a critical angle of attack
245. Below the critical angle of attack, the lift coefficient curve
preferably defines a semi-critical angle of attack, corresponding
to the onset of flow separation at the semi-critical flow
separation point 220 on the upper surface of the airfoil.
[0099] The lift coefficient curve can define one or more slopes.
Slopes for the coefficient of lift curve can be determined as: the
derivative of the coefficient of lift curve at a particular angle
of attack (e.g., of a function approximating the curve), by the
slope formula (change in lift coefficient over change in angle of
attack), or otherwise calculated. The slope formula can be applied
over any appropriate step size. The step can be for the angle of
attack: a single degree change in angle of attack, a range across
the angle of attack (e.g., first angle of attack range, second
angle of attack range), a fraction of a range across the angle of
attack (e.g., 1/4 of the second angle of attack range), a fixed
step size in the lift coefficient (e.g., for a 0.1 change in the
lift coefficient), and/or otherwise calculated. The slope of the
lift coefficient can further define a rate of change of the slope,
using the same, similar, or different technique as the slope
calculation. The rate of change of the slope of the lift
coefficient curve can be determined as the second derivative,
across part of a region as a change between two steps of the slope
curve (which can be overlapping or non-overlapping), across an
entire region of the lift coefficient curve, or otherwise
calculated. The rate of change of the slope of the lift coefficient
curve can be determined as a statistical deviation from a line or
curve, evaluating the curvature of the lift coefficient curve
(minimum curvature, maximum curvature, and/or average curvature),
and/or otherwise determined.
[0100] Below the semi-critical angle of attack, the airfoil
operates in a first angle of attack range 250 (e.g., forward
range). The lift coefficient curve defines a linear (or
near-linear) regime within first angle of attack range,
corresponding to attached flow over the upper surface of the
airfoil. The first angle of attack range has sufficient width such
that variable inflow over the rotor disc area does not result in
significant pressure drag or inefficiencies (as shown in the
examples in FIGS. 13A-B). The first angle of attack range can have
a width of: <1 deg, 1 deg, 2 deg, 3 deg, 4 deg, 5 deg, 7 deg, 10
deg, 1-4 deg, 4-6 deg, 6-10 deg, >10 deg, and/or any other
appropriate width. The first angle of attack range can have a lift
coefficient curve slope 255 of: <0.100 deg.sup.-1, 0.100
deg.sup.-1, 0.105 deg.sup.-1, 0.110 deg.sup.-1, 0.115 deg.sup.-1,
0.120 deg.sup.-1, 0.125 deg.sup.-1, 0.130 deg.sup.-1, 0.135
deg.sup.-1, 0.140 deg.sup.-1, >0.140 deg.sup.-1, 0.100-0.110
deg.sup.-1, 0.110-0.120 deg.sup.-1, 0.115-0.125 deg.sup.-1,
0.120-0.130 deg.sup.-1, 0.110-0.130 deg.sup.-1, >0.130
deg.sup.-1, and/or any other appropriate slope. Preferably, the
lift coefficient curve is approximately linear across the first
angle of attack range, but can additionally or alternately be
concave up (increasing rate of change of the slope), concave down
(negative rate of change of the slope), and/or have any appropriate
characteristics. The first angle of attack range can be defined by
a minimum angle of attack and maximum angle of attack. The minimum
angle of attack for the first angle of attack range can be: -10
deg, -7 deg, -5 deg, -3 deg, -1 deg, 0 deg, 1 deg, 2 deg, 3 deg, 4
deg, 5 deg, 6 deg, 7 deg, 8 deg, 9 deg, 10 deg, <1 deg, <0
deg, and/or any other appropriate minimum angle of attack. The
maximum angle of attack for the first angle of attack range can be:
1 deg, 2 deg, 3 deg, 4 deg, 5 deg, 6 deg, 7 deg, 8 deg, 9 deg, 10
deg, 11 deg, 12 deg, 13 deg, 15 deg, and/or any other appropriate
maximum angle of attack.
[0101] Above the semi-critical angle of attack and below the
critical angle of attack, the airfoil operates in a second angle of
attack range 260 (e.g., hover range). The second angle of attack
range preferably has a shallower slope of the lift coefficient
curve than the first angle of attack range, and corresponds to
separated flow over the upper surface of the airfoil between the
semi-critical separation point and the trailing edge, but can
alternatively have a steeper or the same slope as the first angle
of attack range. The second angle of attack range can have a
smaller, larger, or the same width as the first angle of attack
range. The second angle of attack range is preferably separate and
distinct from the first angle of attack range, but can additionally
or alternatively overlap with the first angle of attack range. The
second angle of attack range can abut (e.g., be adjacent to) the
first angle of attack range, or be separated by a third angle of
attack range. However, the second angle of attack range can be
otherwise related to the first angle of attack range.
[0102] The second angle of attack range can have any appropriate
characteristics on the lift coefficient curve. Preferably, the
second AoA range is sufficiently wide such that inflow variations
still have effective angles of attack which fall in this regime.
Since the slope of this curve is shallower, the acoustic impact of
resulting from these inflow variations is reduced. The second angle
of attack range can have a width of: <1 deg, 1 deg, 2 deg, 3
deg, 4 deg, 5 deg, 7 deg, 10 deg, 1-4 deg, 4-6 deg, 6-10 deg,
>10 deg, and/or any other appropriate width. The second angle of
attack range can have a lift coefficient curve slope 265 defined
relative to a slope of the lift coefficient curve over the first
angle of attack range (m.sub.1) or defined independently of
m.sub.1. The second angle of attack can have a slope of: 0.99
m.sub.1, 0.99 m.sub.1, 0.98 m.sub.1, 0.95 m.sub.1, 0.90 m.sub.1,
0.85 m.sub.1, 0.80 m.sub.1, 0.75 m.sub.1, 0.50 m.sub.1, 0.25
m.sub.1, 0.15 m.sub.1, 0.10 m.sub.1, 0.95 m.sub.1-0.99 m.sub.1,
0.90 m.sub.1-0.99 m.sub.1, 0.80 m.sub.1-0.99 m.sub.1, 0.80
m.sub.1-0.90 m.sub.1, 0.50 m.sub.1-0.99 m.sub.1, 25 m.sub.1-0.99
m.sub.1, 0.25 m.sub.1-0.75 m.sub.1, 0.25 m.sub.1-0.50 m.sub.1, 0.10
m.sub.1-0.90 m.sub.1, >0 deg.sup.-, 0.020 deg.sup.-, 0.040
deg.sup.-, 0.060 deg.sup.-, 0.080 deg.sup.-, 0.100 deg.sup.-1,
0.120 deg.sup.-1, 0.130 deg.sup.-1, 0.100-0.110 deg.sup.-1,
0.110-0.120 deg.sup.-1, 0.120-0.130 deg.sup.-1, 0.110-0.130
deg.sup.-1, >0.130 deg.sup.-1, and/or any other appropriate
slope. Preferably, the lift coefficient curve is approximately
linear across the second angle of attack range (as shown in the
example in FIG. 9), but can additionally or alternately be concave
up (increasing rate of change of the slope), concave down (negative
rate of change of the slope), and/or have any appropriate
characteristics. The rate of change of the slope of the lift
coefficient curve for the second angle of attack range can be <0
deg.sup.-1 and: >-0.0001 deg.sup.-2, >-0.0003 deg.sup.-2,
>-0.0005 deg.sup.-2, >-0.0007 deg.sup.-2, >-0.001
deg.sup.-2, >-0.0015 deg.sup.-2, >-0.002 deg.sup.-2,
>-0.003 deg.sup.-2, >-0.004 deg.sup.-2, >-0.005
deg.sup.-2, >-0.007 deg.sup.-2, >-0.01 deg.sup.-2, and/or any
appropriate rate of change of the lift coefficient curve.
[0103] Between the first angle of attack range and the second angle
of attack range, there can be a third angle of attack range (e.g.,
flow transition region), which contains the semi-critical angle of
attack. Preferably, the third angle of attack range corresponds to
a sharp increase in the drag coefficient versus lift coefficient
curve 410 (example shown in FIG. 13B), but can correspond to any
appropriate shape of the drag coefficient versus lift coefficient
curve. The third angle of attack range can have any appropriate
width, the width can be: <1 deg, 0.5 deg, 1 deg, 1.5 deg, 2 deg,
2.5 deg, 3 deg, 1-3 deg, >3 deg, and/or any other appropriate
width. The third angle of attack range can have any appropriate
lift coefficient curve slope. The slope can be positive and/or
negative across this region, and can be defined relative to a slope
of the lift coefficient curve over the first angle of attack range
(where M=m.sub.1), defined relative to a slope of the lift
coefficient curve over the second angle of attack range (where
M=m.sub.2), and/or defined independently of m.sub.1 and/or m.sub.2;
it can have be: M, 0.95M, 0.9M, 0.7M, 0.5M, 0.3M, 0.2M, 0.1M,
0.05M, 0, -0.05M, -0.1M, -0.3M, -0.5M, -0.7M, -0.9M, -M, between
-0.5M and 0.5M, between 0 and 0.5M, between 0 and 0.9M, 0
deg.sup.-1, 0.020 deg.sup.-1, 0.040 deg.sup.-1, 0.060 deg.sup.-1,
0.080 deg.sup.-1, 0.100 deg.sup.-1, >0.100 deg.sup.-1, 0-0.100
deg.sup.-1, <0 deg.sup.-1, and/or any other appropriate slope.
Preferably, the lift coefficient curve is approximately linear
across the third angle of attack range, but can additionally or
alternately be concave up (increasing rate of change of the slope),
concave down (negative rate of change of the slope), have an
inflection point in the lift coefficient curve, and/or have any
appropriate characteristics. The rate of change of the slope of the
lift coefficient curve for the third angle of attack range can be
any appropriate value.
[0104] In a first example the airfoil blade comprises a first
airfoil cross section, the first airfoil cross section defining: a
chord line defining a chord length L; a leading edge, comprising a
leading edge radius between 0.002 L and 0.05 L; a trailing edge,
comprising a trailing edge thickness between zero and 0.03 L; a
maximum thickness between 0.07 L and 0.2 L and located between 0.2
L and 0.6 L along the chord line; and a maximum camber between 0
and 0.2 L and located between 0.2 L and 0.7 L along the chord
line.
[0105] In a specific variant of the first example, the leading edge
radius is approximately 0.006 L; the trailing edge thickness is
approximately 0.005 L; the maximum thickness is approximately 0.12
L at the position of approximately 0.4 L along the chord line; and
the maximum camber is approximately 0.024 L at the position of
approximately 0.44 L along the chord line.
[0106] The airfoil cross section can further define a drag
coefficient vs AoA curve 400, an example of which is shown in FIG.
13A.
[0107] However, the system can include any other additional
components.
4. Method
[0108] As shown in FIG. 2, the design method 200 can include:
parameterizing the airfoil geometry and generating an airfoil shape
based on the parameterization S100; determining the performance
parameters of the airfoil shape S200; and optimizing the parameters
of the airfoil geometry to achieve a performance threshold
S300.
[0109] Block S100 includes parameterizing the airfoil geometry and
generating an airfoil shape based on the parameterization. Block
S100 functions to determine numerical parameters that collectively
define a functional description of the shape of the airfoil
geometry (e.g., the shape of the airfoil cross section), and
generating such a shape using the numerical parameters. Block S100
can also function to provide an input to subsequent Blocks of the
method 200 (e.g., Block S200), as a starting condition for an
iterative optimization of the geometry.
[0110] However, in alternative variations, Block S100 can include
otherwise suitably parameterizing the airfoil geometry.
[0111] Block S200 includes determining the performance parameters
of the airfoil shape. Block S200 functions to analyze the
aerodynamic performance of the airfoil shape defined parametrically
(e.g., in accordance with one or more variations of Block S100).
Block S200 can include determining the lift coefficient, drag
coefficient, and/or moment coefficient of the rotary airfoil; Block
S200 can additionally or alternatively include determining any
other suitable performance parameters (e.g., aerodynamic
performance parameters, structural performance parameters, etc.).
The outputs of Block S200 preferably include the performance
parameter values at a range of inflow conditions (e.g., angles of
attack, inflow velocity, fluid densities and temperatures, etc.);
however, Block S200 can additionally or alternatively generate any
other suitable outputs. The ranges for which the values are
determined preferably include the range of inflow conditions
expected for nominal and extreme operation of a propulsion system
implementing the rotary airfoil; however, Block S200 can
additionally or alternatively determine values of performance
parameters across any suitable range of inflow conditions.
[0112] In variations, Block S200 can be performed numerically. For
example, Block S200 can include numerically defining an airfoil
geometry using the parameterization output of Block S100, and
simulating the response of the airfoil geometry to various flow
conditions using a computational fluid dynamics (CFD)
airfoil-analysis program (e.g., Xfoil). In such variations, the
outputs of Block S200 include numerically-derived estimates of the
performance parameters (e.g., lift coefficient, drag coefficient,
etc.).
[0113] In further variations, Block S200 can be performed using
physical models. For example, Block S200 can include manufacturing
a three-dimensional blade embodying the determined airfoil shape,
and testing the three-dimensional blade at a range of inflow
conditions in a physical airfoil assessment facility (e.g., wind
tunnel). In such variations, the outputs of Block S200 include the
directly measured performance parameters. In such variations, the
three-dimensional blade can be manufactured using various
methodologies (e.g., additive manufacturing, 3D printing,
conventional machine tool operations, foam cutting, etc.) out of
any suitable materials (e.g., non-structural materials suitable for
aerodynamic modeling, structural materials, etc.).
[0114] Block S200 can additionally or alternatively be performed
using a combination of numerical analysis and physical modeling.
However, Block S200 can be otherwise suitably performed.
[0115] Block S300 includes optimizing the parameters of the airfoil
geometry to achieve a performance threshold. Block S300 functions
to iterate the airfoil geometry towards achieving the desired
performance parameter values.
[0116] Block S300 can include prescribing a weight function in
terms of the performance parameters, which are in turn related to
the airfoil geometry by way of the analysis thereof to obtain the
performance parameters (e.g., in Block S200). For example, the
weight function can be defined as a function f(C.sub.L). The weight
function can additionally or alternatively be defined to include
the slope of the lift coefficient with angle of attack, or
otherwise suitably defined. However, Block S300 can additionally or
alternatively include defining any other suitable weight
function.
[0117] Block S300 can include minimizing the prescribed weight
function, in order to determine the optimal parameters. Such
minimization preferably includes minimizing an expression of the
form .intg.C.sub.Df(C.sub.L)dC.sub.L. Block S300 can, in
variations, include minimizing an integral of the form
.intg. dC L d .alpha. f ( C L ) dC L , ##EQU00001##
to account for minimizing the slope of the lift coefficient with
angle of attack. However, the weight function can be otherwise
suitably minimized. Minimizing can be performed using any suitable
minimization or optimization algorithm.
[0118] Block S300 can, in variations, include performing iterative
weight function prescription and/or minimization, while varying the
values of the geometric parameters determined as an output of
airfoil parameterization (e.g., Block S100). In such variations,
the airfoil shape parameters can act as the independent variables
of the optimization, and the output variables (e.g., dependent
variables) are the performance parameters.
[0119] Block S300 is preferably performed iteratively until the
output performance parameters converge to values below a
performance threshold. In variations, the performance threshold
includes a slope of the C.sub.L(.alpha.) curve, and in particular
includes the slope of the curve in the operating range of angles of
attack (e.g., between 7 and 11 degrees). In such variations, the
threshold slope can have any suitable value (e.g., a zero slope, a
minimal slope, a slope less than that generated by a flat plate
airfoil, etc.). In additional or alternative variations, the
performance threshold includes a roll-off slope of the
C.sub.L(.alpha.) curve at angles greater than the stall angle.
However, Block S300 can additionally or alternatively include
performing Block S300 over a single iteration and/or without
convergence to less than or equal to a performance threshold
value.
[0120] Although omitted for conciseness, the preferred embodiments
include every combination and permutation of the various system
components, which can be combined in any suitable permutation or
combination and/or omitted in whole or in part from variations of
the preferred embodiments.
[0121] As a person skilled in the art will recognize from the
previous detailed description and from the figures and claims,
modifications and changes can be made to the preferred embodiments
of the invention without departing from the scope of this invention
defined in the following claims.
* * * * *