USOO694891 OB2

(12) United States Patent (10) Patent No.: US 6,948,910 B2

PolacSek (45) Date of Patent: Sep. 27, 2005

(54) SPIRAL-BASED AXIAL FLOW DEVICES William C. Elmore, Mark A. Heald- “Physics of Waves” (C)
1969 PP 5–35, 203–205, 234-235, ISBN-0486 64926–1,
(76) Inventor: Ronald R. Polacsek, 73373 Joshua Dover Publ., Canada.
Tree St., Palm Desert, CA (US) 92260 A.A. Andronov, AA. Viti, “Theory of Oscillators.” (C) 1966,
(*) Notice: Subject to any disclaimer, the term of this pp. 56–58, 199-200, ISBDN-0486-65508–3, Dover Pub
patent is extended or adjusted under 35 lishing, Canada.
U.S.C. 154(b) by 375 days. Erik Anderson et al., Journal of Experimental Biology, “The
Boundary Layer of Swimming Fish' pp 81-102 (C) Dec. 5,
(21) Appl. No.: 10/194,386 2000, (C) The Company of Biologists, Great Britain.
(22) Filed: Jul. 12, 2002 Stephen Strogatz, “Nonlinear Dynamics and Chaos” (C) 1994
pp. 262-279, ISBDN 0-7382-0453–6 (C) Perseus Books,
(65) Prior Publication Data USA.
US 2004/0009063 A1 Jan. 15, 2004
(Continued)
(51) Int. Cl. ................................................ B64C 11/18
(52) U.S. Cl. ........................................ 416/1; 416/227 R Primary Examiner Edward K. Look
(58) Field of Search ................................. 416/1, 227 R, Assistant Examiner Richard Edgar
416/227A, 223 R, 223 A
(57) ABSTRACT
(56) References Cited
Axial flow devices using rigid spiral band profiled blade
U.S. PATENT DOCUMENTS catenaries attached variably along and around an axially
547,210 A 10/1895 Haussmann
elongated profiled hub, of axially oriented profile Section
1864,848 A 6/1932 Munk ..................... 416/132 R Sequences 75 mapped relative to truncated cones-of
1868,113 A 7/1932 Ljungstrom generation. Upon rotation and lubricity-masked progression
2,552,651 A 5/1951 Skold through axial planes-of-shear, this time-domain Sequence
3,504,990 A 4/1970 Sugden travels in 2-dimensional axial-datum-plane-relative path
3,514,215 A * 5/1970 Williams ................ 416/200 R excursions and ejects frictional adhesions via anguillar
4,445,817 A 5/1984 Wethern reverse Vortex Street thrust due to an after-body accelerating
4,610,601 A 9/1986 Gerfast wave shape-Sequence 48. This guides bound Vortex pres
4,813,633 A * 3/1989 Werle et al. ................ 244/130 Sures at linear path-velocity Substantially parallel to the
4,830,315 A * 5/1989 Presz et al. ................. 244/200 collective plane-of-Shear, conferring higher differential pres
4,830,574 A 5/1989 Wainauski Sures through path-vector-addition, improved force-vector
5,075,964. A 12/1991 Galliet
5,890,875 A 4/1999 Silvano orientation, extended laminar flows, lower form drag and tip
5,961,289 A 10/1999 Lohmann Vorticity. As a wind turbine, path-vectors are added to
2003/001265.6 A1 1/2003 Cho et al. ................... 416/235 inflow, ducting an increased mass flow inward for increased
2004/OO67138 A1 4/2004 Yoshida .................. 416/223 R power extraction per diameter. As a propeller, path-vector
OTHER PUBLICATIONS
Subtraction guides the wave front flight-path-transverse,
allowing higher flight Velocities and improving thrust-per
Harry F. Olsen-“Music, Physics and Engineering” pp torque through enhanced force vectors and mass flow rates.
208-215 (C) 1967, Book No 486-21769-8, Dover Publish
ing, Canada. 7 Claims, 17 Drawing Sheets

axial plane movement

 US 6,948,910 B2
Page 2

OTHER PUBLICATIONS C. A. Marchaj, “Aero-Hydrodynamics of Sailing”, (C) 1979

L. Prandtl, O.G. Tietjens, “ Applied Hydro-and Aerome pp. 131-140, 205–214,253–254.291, 353–381 ISBDN
chanics'C) 1934 pp 166-167, 190-191, 200-209, 300-308, 0-87742-993–6, Intnt Marine Publ., USA.
ISBDN 486-60375-X (C) 1957, Dover Books, USA. Uriel Frisch, “Turbulence” (C) 1995, pp. 242, 21–26,
H.H. Hurt Jr., “Aerodynamics for Naval Aviators” (C) US 103-106, 184-188, ISBDN 0-521-45103–5 (C) 1995 Cam
Navy 1960 pp 67, 64, 57, 53,48, 19/46,227:232,205 Navair
00–80T-80 (C) Office & Chief of Naval Operation. bridge Press, USA.
Kalus Hinecke,"Jet Engines” (C) 1997, pp 34–48 ISBDN Georgi Tolstov, “Fourier Series” (C) 1962, pp 1–39, 80-91,
0-7603–0459–9 C) Airlife Publishing, Great Britain.
Hunter Rouse “Elementary Mechanics of Fluids” (C) 1946 pp ISBDN 0-486-63317-9 C) 1962 Dover Press, USA.
170–171, 254-255, 288-294 ISBDN 0-486-63699-2 (C)
Dover Books, (C) 1978, USA. * cited by examiner
U.S. Patent Sep. 27, 2005 Sheet 1 of 17 US 6,948,910 B2

downwash with tip vortex ... ... N- tip vortex - 15

- BOUND VORTEX WAVELENGTH --
Prior Art

tip vortex loss

U.S. Patent Sep. 27, 2005 Sheet 2 of 17 US 6,948,910 B2

No. ôl
pº
??.No.@"º"

>S-]O\/NTIA
U.S. Patent Sep. 27, 2005 Sheet 3 of 17 US 6,948,910 B2

7Cs)

t
Ss of Revolution
SSC)

logarithmic spiral

Citi 2 is has
equal amplitude expansion Curves
U.S. Patent Sep. 27, 2005 Sheet 4 of 17 US 6,948,910 B2

A r of diffusion

38
U.S. Patent Sep. 27, 2005 Sheet 5 of 17 US 6,948,910 B2

FIG 7a axial retrogression 54

angular velocity

wave path progression

-storia
original element

S.
U.S. Patent Sep. 27, 2005 Sheet 6 of 17 US 6,948,910 B2

Karman Vortex Street 1. e

S sC) Y n S-
g \ ,
56
<2.
59 N9) 9) |
60
U.S. Patent Sep. 27, 2005 Sheet 7 of 17 US 6,948,910 B2

2.
7. (7
lea
U.S. Patent Sep. 27, 2005 Sheet 8 of 17 US 6,948,910 B2

65 4N Q
(2)W.6 (N)
U.S. Patent Sep. 27, 2005 Sheet 9 of 17 US 6,948,910 B2
U.S. Patent Sep. 27, 2005 Sheet 10 of 17 US 6,948,910 B2

FIG12
determine feedback
parameters from dissipation
kog decrement
deterine wake rotatioin
determine effective plane
Meta-Element actuation

choose operating
foil parameters
from known foi

Initialize System
of oscillation
establ. design Meta-Element
determine phase state Major cycle & Minor cle
inflow dependencies W2Logarithmic
friction decrement
Starting reversal SS
feedback parameter Translate sequences into
design new foil series Helical coordinates
Equation of motion
for each phase state Fourier orbit integral calulate dynamic forces
from phase plane spiral correct for surface tilt
determine pressure 8 local sweep angles
distributions calculate downwash -
force coefficients Superimpose on phase
wake inflow vectors

determine wake rotation

determine actuator plane

O adjust actuation plane

design stability parameters
U.S. Patent Sep. 27, 2005 Sheet 11 Of 17 US 6,948,910 B2

later divergence potential E

s 61 low pessure
----rrel-re-rel- - N -- NS
vortex shee of discontrality

FG13b
propeller force decomposition conventional turtline forces

90
\- ---,
-
J.--
prior art re. tangential velocity

N Meta Element Conventional Turbine

N Spiral axial advance downwind force downwind force
Stream Tube velocity vector addition Meta Element torque for equal downwind force
U.S. Patent Sep. 27, 2005 Sheet 12 0f 17 US 6,948,910 B2

axial plane movement

^v
U.S. Patent Sep. 27, 2005 Sheet 13 Of 17 US 6,948,910 B2

VS
U.S. Patent Sep. 27, 2005 Sheet 14 Of 17 US 6,948,910 B2
U.S. Patent Sep. 27, 2005 Sheet 15 0f 17 US 6,948,910 B2
U.S. Patent Sep. 27, 2005 Sheet 16 0f 17 US 6,948,910 B2
U.S. Patent Sep. 27, 2005 Sheet 17 Of 17 US 6,948,910 B2
 US 6,948,910 B2
1 2
SPIRAL-BASED AXAL FLOW DEVICES shaped along their length in order to compensate for these
differences in velocity and resultant vector 10 of the oncom
ing flow.
BACKGROUND The top illustration of FIG. 2 demonstrates that since the
1. Field of Invention
resulting fluid force on the blade at a given location is
approximately perpendicular to the direction of incoming
This invention relates to the field of acceleration or flow, this twisting results in physical forces whose directions
deceleration of fluids using rotation of impulsive or propul vary in their usefulneSS in providing the intended axial
Sive means to impart or extract kinetic energy. It also relates change of momentum of this fluid.
to the Study of animal modes of locomotion using oscillation As shown in the middle of FIG. 3, since in addition to
of, or wavelike deformation of propulsive Surfaces. It thus orientation, the force on any blade Section varies as the
has application to prior art in the field of propellers, impel Square of the local Velocity as well, most purely axial thrust
lers and turbines using annular, Spiral or ring type impulsive of fluid in the Swept disc occurs in a relatively Small annulus
elements. Of particular interest is the following prior art of close to the blade tips 12 where fluid dynamicS recognizes
Sugden, U.S. Pat. No. 3,504,990; Haussmann, U.S. Pat. No. 15
unavoidable flows that result in loss of thrust and formation
547,210, axially elongated helical propulsive and Sustaining of tip vortices 14 that due to their high transverse velocities,
devices as in Butow, U.S. Pat. No. 1,015,540; Clark, U.S. continuously dissipate kinetic energy and physically drag
Pat. No. 3,221,702 discloses means of generating thrust along Vortex Structures.
through wave-like deformations of a vehicle body; As shown in the lower illustration of FIG. 2, since drag
Ljungstrom, U.S. Pat. No. 1,868,113 describing blade ele due to-and induced by-lift in any tipped foil results in an
ments deployed along a curve that is Substantially a cen increase of fluid acceleration-called induced downwash
trifugal catenary. 15-inboard of the tip to offset the pressure lost to vortex
It additionally relates to the mathematical Study of time formation at the tip, the disadvantageous helix angles 16 of
based harmonic oscillating Systems, as well as to the related FIG.3 on the left of the inboard portion of the propeller disc
mathematical Study of waveforms as in the analysis of 25 Spills Significant energy by twisting the slipstream 18 out of
electronic Signals, as well as certain aspects of the wave desired axial alignment resulting in root Vortex losses. This
equation as it relates amplitude, frequency and length of loSS is much beyond that of the drag caused by purely
waveforms to energy content in the physics of wave SyS frictional entrainment of rotation.
tems. Also of particular interest is the classic Scientific AS Seen in FIG. 13a, another consequence of the
literature relating to energy dissipation in oscillating Sys described tip vortex low-pressure wake Structures that
tems: “Theory of Oscillators'-Dover Press- by A. A. develop after passage of the foil is the lateral divergence of
Andronov, “Music, Physics and Engineering-Dover Press flow potential between the upper and lower trailing edge,
by Harry F. Olsen, “Fourier Series”-Dover Press-by causing flows to deviate toward the lines of very low
Georgi Tolstov. equipotential preSSure of the developing tip VorteX behind
Additionally, it relates to the work of Several pioneers in 35 the tail. AS particles leave the tail, this divergent potential
the academic Study of computational models of fluid dynam causes the upper and lower particles to approach and
ics of undulatory and flagellar locomotion, a field of Spe embrace in a Suddenly tightening radius of curvature by way
cialization of the study of Biological Fluid Dynamics. The of the conservation of angular momentum. This results in
most prominent of these is Sir James Lighthill. His book powerfully rotating vortices of path-transverse vector form
“Mathematical Biofluiddynamics'-SIAM 1975-examines 40 ing the So-called Vortex sheet of discontinuity, which
Several concepts that have important bearing on the follow attaches itself to the trailing edge via these filaments
ing methods, in particular his study of large amplitude commensurately powerful Suction cups, dragging Some of
flagellar hydrodynamics, as well as carangiform and anguil these Structures-and their fluid mass entrainments-along
for the ride.
liform propulsion. Also in this context, I refer to the work
done by Massachusetts Institute of Technology’s “ROBO 45 In the case of the conventional wind turbine, the highly
TUNA project that documents the considerable energy loaded annulus 12 of FIG. 3 additionally imposes the
Savings possible using mechanical analogs of carangiform characteristic uneven retardation on the flow Streamlines on
locomotion. the right of FIG. 3, causing Significant Swirl and a thicksheet
Finally, it relates to important recent key developments in of discontinuity resulting in the well-documented Spillage of
the Study of periodic energy transport mechanisms. Such as 50 over half the theoretically available linear kinetic energy.
frequency Spectra, Sub millimeter Vortex filament Structures, These vortex flows 14 additionally also have the disad
and eddy mechanics in fluid dynamic turbulence phenom Vantage of causing very high tip region Spanwise flows and
ena: -“Turbulence” by U. Frisch, Cambridge Press-. actual reversals of flow as shown on top of FIG. 9 with
resulting boundary layer turbulence, loSS of lift and low
BACKGROUND 55 preSSures that additionally occasion different design con
Straints in different applications:
2. Description Of Prior Art Ship's propellers-high tip Velocities causing cavitation in
Presently all relatively efficient axial fluid flow devices in the tip area engendering destructive interblade harmonics,
general use are based on the conventional propeller. All Such Vibration, resonance and blade erosion, appendage and hull
devices function by accelerating or decelerating fluid mass 60 CSOCC
using blades mounted upon an axis and Subsequently Airplane propeller-the propeller is primarily Speed limited
rotated. Due to the differences in rotational velocity of blade by the Severe drag rise of the transonic boundary layer
elements at the differing radial locations of Such a blade, Separation shock wave induced by the tip flows exceeding
various locations therefore encounter flow from various the Speed of Sound at even moderate SubSonic Velocities and
directions. 65 occasioning noise and buffet
As is evident in FIG. 1 of prior art, these blades need Helicopter blade-even though the helicopter disc is not
therefore to be continuously twisted as well as variously purely an axial flow device it nevertheless encounterS Simi
 US 6,948,910 B2
3 4
lar constraints: Vortex noise, blade slap due to Vortex buf These methods assess theoretical conditions of Statistical,
feting and harmonic and resonant oscillations due to rapidly time invariant Steady-state lift on rigid foils that move along
changing differential pressures acroSS the disc due to uneven helices in Euclidean Space as shown in FIG. 4a.
preSSure distribution. AS consequence of this, the Vector and time coefficients of
Additional important factors that State added Sources of loSS the Impulse-Momentum Equations of Motion-, which the
of efficiency that affect the conventional propeller are: equation of Blade Element of Lift does not formally treat,
The ineScapable fact that due to Said blade dynamics, the except for an invariant Velocity of inflow-introduce highly
Slipstream contracts Significantly before and after it laves the skewed inflows in the case of rotation.
theoretical disc of actuation-the Froude Disc of Momen
tum Theory 19-of the middle of FIG. 2 that represents the As is depicted in the lower illustration of FIG. 2, bound
plane of rotating blades 20. This is seen as a significant Vortex upwash is a function of time. Its prerequisite-the
inflow at the propeller tip 22, and locally out of alignment acceleration of fluid mass ahead of its path by the Strong
with intended axial acceleration. This has the effect of attractive force of its low-pressure isobars of potential is
diminishing the size of the effective actuator disc and So normal to lines of equipotential pressure as shown in lower
decrements the mass that it can accelerate relative to its left of FIG. 3. Because this force is a vector, rotation, which
theoretical value. 15 can only affect regions of fluid mass over a diffusing Sector,
Also, Since the propeller works by generating differential involving the rate-of-change tangent-Sector of the Swept
preSSures acroSS this disc area, a sharply contracting Slip angle of tangential motion, this helical path must itself also
Stream implies lower pressure differentials 24 acroSS the disc be considered a Source of propeller inefficiency. According
than an actuator disc that had means to benefit from or to Newton's Second law, a given change in momentum due
ameliorate Such contraction. to any given force-vector is a function of the relative
Since-according to Propeller Momentum Theory duration of this force. The described sector of diffusion
efficiency is developed, and measured by the momentum attending rotation must therefore have weak axial Stream
change involving the highest possible fluid mass involving tube-relative influence, compared to the Steady duration of
the Smallest possible Velocity change 26, this unopposed linear axial-plane motion.
contraction-or its expansion in the case of the turbine-, 25 A propeller blade Section low-pressure force field of
must also be considered a Source of inefficiency through the curved path of the lower left of FIG. 3 has not had time to
resulting decremented mass flow rate in the conventional accelerate the actually encountered incoming fluid particles
propeller. as it diffuses the influence of its low pressure isobars to
An important Structural limitation that results from this particles along the diffusion-arc of the changing vector
blade fluid dynamic that detracts from efficiency is the fact tangent of its curved path, to particles outside its path,
that Structurally, a thin, twisted rotating bar of relatively particles that it will not actually encounter. Rotational
flexible material somewhat akin to a single prong long devices that don’t compensate for this curved path must
tuning fork-of low natural frequency-, has low resistance therefore experience a deficit of inflow velocity and weak
to Coriolis forces, disc loading asymmetry, torsional, reso upwash as shown in FIG. 4a and therefore must be assumed
nant and harmonic oscillation and So needs a massive and 35 not to benefit from the early phases of the upwash/
fluid-dynamically inefficient blade root. downwash cycle of what is, in effect, a special wave System
An additional fact is that the requirement of adequate called the bound Vortex. Such devices accordingly must
Starting performance combined with good cruise perfor operate in their own downwash, behind the wave crest.
mance occasions cruise Speed efficiency compromises To crudely illustrate Schematically these implications
caused by the propellerS Stated Severe design constraints. 40 bearing on the relative efficiency of helical verSuS linear
In spite of their shortcomings, propellers enjoy the con motion on the basis of glide angle, Sailplanes with their
siderable advantage of a precise and repeatable method of Slender wings having a nearly horizontal glide angle, even
design that has allowed a long history of incremental the Space Shuttle with its delta planform and high tip losses
improvement and increasingly high precision of at 19 degrees glide angle is more efficient than the Stream
manufacture, in an engineering discipline where minute 45 lined helicopter with a steeper autorotation descent angle
variations of Shape have Surprisingly large effects on per using foils that are even more slender than those of Sail
formance. This method of design represents a continual planes.
refinement of theories that have been in existence for most To sum the described deficiencies of rotation itself, partly
of a century. owing to the continuing inscrutability of the phenomenon of
One of these theories in wide use-the Blade Element 50 turbulence, and partly due to the millennial legacy of rota
Theory-analyzes Velocity vectors and Viscosity coefficients tion itself, is the practice of this art presently not well
of individual blade Sections at Successive blade radii and integrated with the more evolved time-domain practices in
computes the entire propellers parameters by Summing the related fields that Successfully apply the laws of physics of
individual parameters of these elements. waves and oscillating Systems. As a consequence, the just
Instead of using the plane aligned with vectors of pre 55 described inefficiency of helical motion artifacts and tipped
dominant flow, such methods model actual blade flows by blade vortex that limit economic cost-benefit has been
computed changes of momentum along theoretical tangents generally considered unamenable.
to helices inscribed on Surfaces of revolution generated by Due to Sum of these well-documented disadvantages
blade element motion as reference datum. attending rotation, there have been many attempts to intro
Although no rigorous analysis of actual three-dimensional 60 duce devices to the marketplace that deal with one or more
Vortex formation is made, a well documented database of individual symptoms of the described problem syndrome.
empirical values for Secondary flows provide the correc Among these are Strategies to eliminate tip losses through
tional factors that enable today's high correlation of theo blades forming centrifugal catenary half-loops, or to simply
retical and experimental values. convert rotary motion to linear motion through rotor blades
Importantly, these theories work with assumptive linear 65 in the shape of Segments of Spirals, using the property of the
and Statistical parameters of free Stream Velocity without a boundary layer that can obscure the resulting virtual
time-based rate of change reference frame. motion's different flow directions via the many thin lubri
 US 6,948,910 B2
S 6
cating layerS Sliding over each other. This would be analo Constantly changing compound Sweep, and high Span
gous to a rotating Spiral worm gear that can transmit linear wise flow
motion to its conjugate rack, as shown in FIG 8e. Others Constantly changing flow directions not aligned with a
have attempted to prevent Spanwise flows through chord Surface of revolution-the
wise corrugations parallel to flow in an attempt to prevent theoretical plane of analyses
the lateral divergence pre-conditions of Vortex development. Constantly changing boundary layer differential shear
The Subject of this document incorporates Similar Strate with vectors not aligned
gic Synergies among others using tools provided by Several with the primary dynamic flow field,
modern time-domain disciplines. In addition it employs Constantly varying Viscosity coefficients,
direct means to amend the phenomenon of the highly 1O Rapid reversal of motion,
pulsating and directionally disordered reaction mass of the Rapid reversal of wake Vortex spin direction (Karman
wake that all of these devices are Subject to, and that Vortex Street)
according to the equations of motion, must be considered a
measure of lost linear momentum, Rapid alternation of lifting Surface orientation to the flow
To explain these Strategies and their indispensability to field,
these proposed devices, I now provide a brief Overview. 15 Rapid reversal of flow direction
Time-invariant methods of analysis are particularly ill Rapid reversal of bound vortex spin direction
adapted to analyze forces resulting from unusual-namely Rapid reversal of lift circulation co-efficient
linear wave propagation-anguillar propulsive mechanisms, AS this latter parameter is the very basis of the classical
particularly those of nature. Here all Such mechanisms theory of lift, any design that cannot-due to these
involve time-domain oscillations and flexing of propulsive imponderabilities predict inflow vector, cannot determine
elements undergoing variable rates of change. Such rates of this circulation or the force of lift, or drag.
change become evident when Sectioned by reference planes Flow is by its very nature evasive and turbulence cascades
aligned with their primary axis of motion, and normal to down to infinitesimal time Scales. The possible interactions
their transverse undulations as shown in FIG. 4b. This with it-and possible unintended consequences thereof
motion can be analyzed by comparing the time-regressed 25 are infinite. Therefore this massive analytical overload must
body outlines to time-samples of body-relative isocline be simplified by designing a process that is understandable
acceleration and traveling inclined plane maxima as shown to the existing tools of analysis. The main tool, Blade
in FIG. 4c. Such motion promises high efficiencies, as Element Theory, must be given reliable inflow, viscosity and
carangiform SwimmerS have been clocked at Velocities that blade profiles of known parameters. If lift cannot be
theory predicts to be unattainable for them. determined, foil orientation is not precisely possible. With
For lack of comprehensive tools, however, previous out formulated precision of causal relationships, repeatable
attempts to introduce mechanical analogs of such promis effects became difficult to achieve.
ingly efficient motions of nature as propulsive devices to the Since Some of Such devices proposed to benefit from
marketplace have Suffered from inadequate precision of undulations of reaction masses however, they must be
analysis, thus predictable manufacture, and have-So far 35 presumed to experience undulations of time-domain inflow
have been commercial failures. vectors that demonstrate continuous rates of change of
As a three-dimensional Secondary flow with its many kinetic and potential energy. Without a fully rigorous fluid
degrees of freedom is at present treated as heterogeneous dynamic modeling of Such flows-Still out of reach-,
turbulence by accepted practice, translation, sliding, flexing relative motion could not be determined. Such devices
and undulation are also not rigorously modeled to acceptable 40 orientation to flow and thus preSSure gradients could not be
Standards of engineering practice. The economic investment ascertained to satisfy the Blade Element Theory require
necessary to generate Such theoretical models of nature has ments as well as Standards of manufacturing repeatability.
not yet been generally made available. Without time-domain inflow parameters, Such attempts
Thus, any motion that results in undulation as generated were limited to intuitive experimentation on the basis of
by rotation must involve highly complex compound artifacts 45 trial-and-error and as commercial devices could not hope to
involving changing reference frames and boundary layer compete with the considerable empirical theoretical data
interactions that pose Severe analytic difficulties using State base of a highly refined engineering practice benefiting from
of the art design tools. many decades of incremental data refinement.
Historically, there have been Some attempts to introduce And yet, accurate Velocimetry analysis as to the effect of
devices based on the animal model of locomotion to accel 50 time-domain and boundary layer phenomena have been
erate or decelerate fluid in the hope to improve upon the available in the field of Biofluiddynamics and certainly do
propeller. In particular, many of these have attempted to now exist. Recent government sponsored university research
generate relative motions along various versions of the Spiral advances in the field of mathematical biofluiddynamics
of changing radius. The patents of HauSSmann-1895-and using high-speed Video image Digital Particle Laser Doppler
Sugden-1970 in particular showed the structural advan 55 Velocimetry provide a relatively accurate model of the
tages of Spiral foil Segments joined at their tips. boundary layer, mechanics and vector fields of time
Such devices, especially the Sugden device promoting evolving Vortex dispositions of animal undulatory expand
undulating flow, claimed to demonstrate improved effi ing wave locomotion. To make a computational model of
ciencies in comparison to the propeller. Such motion, all that is additionally needed once Viscosity
Such devices in rotation, however, use: 60 and thus shear-drag is determined, is wave mechanics itself
Constantly changing foil profile elements to relate energy content and orbital inflow.
Constantly changing foil geometry like camber, length, Thus experimental computational three-dimensional
thickness, vector-field animations of fish propulsion have been, and are
Continuously varying rate of change of lift coefficient, now widely available.
(angle of attack) 65 If Such insights into the Vector field dispositions and
Continuously shed Vortices attendant to Such change in boundary layer ejection mechanisms enabling aquatic crea
angle of attack tures their extraordinary reductions of form drag and para
 US 6,948,910 B2
7 8
doxical Speed/power relationships could Somehow be prac enabling phenomena. The first is the lubricity of the many
tically applied to the rotational mode of operation, then my layers of fluid that cling to any dynamic shape called
primary avocation, namely that of creating efficient wind boundary layer.
power devices, might benefit from the prospect of recaptur As is shown in FIG. 5b, any embodied fluid dynamic
ing Some of that half-portion of linear momentum that is shape-here a spinning Saucer shaped toy disc that provides
presently made unavailable using conventional means. lift is accompanied by a field of flow streamlines, that
With this prime aim in mind, I determined to examine the delineate local fluid motion. The main features of this vector
axial shear-plane-relative motion of rotors made of wave field are:
cycle profile Sequences arrayed around 3D Spiral Segments, 1. The dynamic flow providing the pressure differentials that
remapped to truncated cones, that act the part of time generate useful forces
domain cams. This is illustrated on the right of FIG. 5c. FIG. 2. The frictional adhesions including standing vortices 30
5b shows the enabling lubricity mechanism conferred by the entrained by this body
boundary layer that allows axially aligned Stream tubes to be 3. The roiling Vortex wake representing the lost frictional
relatively unaffected by tangential vector Shear. energies that represent the cost of Sustaining Such motion.
These path-oriented profile Sequences would Sequentially 15 Surrounding this body is an exceedingly thin membrane
progreSS along a constant angle to this path at constant 31-the boundary layer-. This layer enables a kinetically
Velocity along both dimensions of the axial shear plane by economical passage for that vast majority of much faster
Shearing through all encountered axial planes-and thus any particles of high kinetic energy making up the dynamic
datum reference plane-moving tangential to that plane. flow that is the actual generator of the pressure differentials
They would additionally eject boundary layer accumulations that create useful forces.
by creating high-rate expanding-wave anguillar propulsion This phenomenon is illustrated by the flight of the tossed
through the effect of the rate-of-change Inclined-Ramp and rotating disc whose dynamic flow field is here illus
contour variations that the smoothed after-body profile trated. Even though most of its Surface is moving in direc
Sequences transmitted, as they transited the shear plane. By tions at variance with the path of its flight, the phenomenon
varying the Spiraling rotor blade as a whole by Such 25 of lubricity-masked directional boundary layer vector
parameters as profile length, radius, angular Velocity and Shear nevertheless enables the characteristic dynamic flow
axial and radial advance, it would be possible to achieve field that enables all linear dynamic flight, that results in its
structural load paths embedded within this rotor blade that amazing feats of Stability and length of flight.
came close to the Structurally advantageous centrifugal The Second phenomena that enables this phenomenon for
catenary curve. Thus, the analytical imponderables of undu this toy disc-orany-devices that rotate in order to impart or
lation of inflow and reaction mass, as well as the time extract momentum, is the overwhelming collective
domain effect of unknown profile-section change sequences enmeshed inertia of the continuum of axially aligned mass
of unknown parameter would simply be bypassed, allowing flow that shows quantifiable resistance to being tangentially
a Systematic periodic function based progressive remapping twisted as a result of the rotation. This resistance itself
of a Single published profile, which can, over a single wave 35 enables analysis along reliable helices of relative motion of
cycle, be deemed regressed-and thus in its effect equal FIG. 4a in conventional devices. This fact allows the col
to-to its published coordinates and thus performance lective multiplicity of coaxial planes of motion to be reduced
CUWCS. to a single theoretical Plane-of-Shear through which all
Because this concept Seemed also to contain disquietingly these devices-whether conventional or not-must, by
paradoxical, and even mutually exclusive operating modes, 40 definition, shear through. Therefore:
namely that a rotating device, while imparting angular 1. In order to function as an improvement over propeller
momentum, should at the same time be one that guides and based devices, any Spiraling or catenary-loop Shear
benefits from a bound Vortex wave System moving along device must first be able to specify the amount of shear
Straight lines, I proceeded to the create the bridging plane twist the device is expected to generate, lest
concepts, computer models and finally actual devices to 45 inflow vector becomes indeterminate. For this, conven
convince myself that rotation can indeed, produce linear tional Reynolds number-based practice, using the
bound Vortex pressure wave motion Substantially parallel to three-dimensional Galilean form of the Navier-Stokes
the axial Shear plane, as long as the Velocity vectorS along equations Serves to estimate total shear StreSS influence
this plane are greater than that of the engendering local on this plane, its cost in turning moment work and
tangential Velocity of rotation. 50 resulting tangential motion of the reaction mass. This
I also established to my Satisfaction that-in the case of form of the equation offers implicit compensation for
Such motion and adequately high Reynolds number differences in boundary layer vector that translate these
Simplifying the tangential Shear effect of the multiplicity of to a helically oriented Velocity gradient resulting in a
incoming axial Stream tubes to a single Schematic axial Shear stress coefficient within the boundary layer itself. This
plane provides the bridging concept enabling a good pre 55 is illustrated by the left sequence of FIG. 4d. As the
dictive Blade Element-Theory based correlation with the Navier Stokes equations confine themselves to measure
measured flow of actual devices. Velocity-gradient-based momentum transfer from layer
Accordingly, I will now outline the advantage of these to layer of this thin lubricating envelope, and the final
bridging concepts. Outermost layer must therefore be presumed aligned to
The Proposed Invention as an Advance in the State of the Art 60 the dynamic flow, the cross-section of the illustrated
These devices propose to advance the art of extracting annular wing with its dynamic flow Streamlines would
momentum from-or imparting momentum to-axial flow, show no difference between Static and rotating States
by ordering the directionally chaotic and pulsatile reaction by hypothetical frictionless means-except for the
mass of the wake of current rotational and Spiral-based Shedding intensity of the trailing Vortex System, as
devices using Several Synergistic Strategies, each of which 65 intra-boundary layer particles experience a greater path
are of advantage in analysis of Spiral-based devices operat length, mixing length and momentum loSS. This lost
ing in the time domain. They depend on the two main kinetic energy must be borrowed from mass
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momentum of the energetic outer layers. This borrowed Theory of Operation
extra mass accumulates, now having lost momentum, Although the fluid dynamic lift equation itself contains no
and is episodically ejected at the tail into time-topology time coefficients—except for inflow velocity-, it nevere
Vortex Structures that reflects this longer path length less is historically derived from Newton's time-domain
coefficient. The work of turning has thus been trans equations of motion. This fact has important bearing on the
ferred to the boundary layer in the form of minute implications resulting from the rotation of lift-producing
polarized angular momentum, which is 'spooled in a blade elements.
topological Sense into asymmetric counter-rotations of Accordingly, the proposed devices design methods
a Karman Vortex Street with slowed central flow. Thus, re-import time-domain impulse-momentum considerations
according to classical theory itself, dynamic flow from these original equations, as the after-body of conven
Streamlines lack a direct mechanism to make them Stray tional profiles is presently design-constrained by the need to
out of alignment with the axial plane before the trailing limit adverse preSSure gradients in order to regain free
edge. AS experience with this configuration shows,
however, that the wake does in fact twist in the direc Stream Velocity and So prevent the Spanwise detachment of
tion of rotation, this entrained, now co-rotating Vortex flow.
sheet must be implicated in this twist, namely by the 15 In principle, impulse-momentum-based interventions
Secondary momentum transfer of the Velocity-gradient using path-transverse Inclined-Plane-based, body-relative
based mechanism of this same theory. The vortex sheet traveling waves-as documented to be highly effective in
is deemed attached to the trailing edge and rotated reducing Such adverse pressure gradients in the motions of
along, importing momentum from the energetic inter aquatic creatures-are readily available to re-import energy
face and pulling and twisting this flow-and thus the to this tail region using Inclined Plane Space quadrature
shear plane itself-through the same momentum trans vector-coupling. These are mechanisms that have analogs in
fer. Thus, for any shear-plane-active spiral devices to the motion of worm/linear rack conjugate enmeshment that
offer any advantage at all, they must first address translates rotary to linear motion, where the 'sliding com
shear-plane-distortion by detaching this Vortex Sheet. ponent of motion is largely eliminated by a Suitable lubri
This is the central Strategy of the proposed class of 25 cating agent.
devices. Thus the prime enabling mechanism of the These devices thus benefit from mechanisms implicit in
device is the detachment of this drag entrainment the Equations of Motion's impulse generating rate-of
through shape Sequence anguillar propulsion. change-inclination of Surfaces the tangential motion com
2. Compound and variable planform Sweep of the rotor ponent of which is masked by the path-compensating
blade'-as imposed by the embedded 3D spiral time lubrication-conferring mechanisms of the boundary layer,
cam-imposes well-documented disadvantageous when computed relative to the axial Shear plane.
spanwise flows and high form drag at economically These mechanisms thus, in effect, duplicate the serial
useful lift coefficients that would negate much of the metamorphosis of traveling wave anguillar phased shape
theoretical advantage of the proposed devices, impose change resulting in its well-researched phase-related travel
high rate-of-change variations in circulation and lift 35 ing pressure wave propulsion.
and thus create unacceptable boundary layer turbulence Such Serial transformations of a body classifies any Such
drag as well as a low lift curve slope. AS these phe time-regressed section of this body as a “Soliton Meta
nomena are mainly due to adverse tail Section pressure Element', a term of convenience that derives from the
gradients, I determined to enlist the mechanism of notion that a physical form engaged in a rate-of-change
anguillar propulsion to enforce tail region Small-wave 40 wave-like metamorphosis has an effect beyond its moment
chordwise near-wake and boundary layer acceleration to-moment aspect of physical undulation but is part of a
and expulsion in order to reduce pressure gradients and fluid-wide continuum of Self-stabilizing processes, a Single
enforce axial plane flow alignment. This required time wave meta-phenomenon encompassing a fluid-wide System
domain analysis of animal modes of locomotion that of angular momentum orbital flows.
involve oscillation using analysis of isocline travel of 45 It can be therefore treated as part of a Single dissipative
body wave and Surface inclination. This is performed oscillating System, Slowly decaying on the time axis behind
using a datum plane containing the primary axis of its origin-of-resonance. Accordingly, rough estimates as to
locomotion and transverse flexing vectors. Speed, dissipation and energy budget can be deduced from
3. This Schematic additionally uses energy-content wave the observed, or desired, coefficients of the wave equation.
equation analysis, the phase plane analysis of oscilla 50 Much is not explained by Such a view, but being a concept
tions for dissipation and resistance to flow-rate-of of convenience gives it the considerable advantage of being
change, or “hysteresis, and Strouhal number to deter able to ignore the many factors of mitigation and nuance that
mine phase, frequency, amplitude and isocline rate-of have-according to this view-considerably leSS immediate
change of body Sections engaged in wave-like bearing.
transformations. 55 It merely observes the fact that the eel, for example, is
In these methods, flexing propulsive bodies including fins Seen to proceed at a speed through the water that is related
and wings are frequency-Sampled for rate-of-change differ to the frequency and amplitude terms of a periodic function,
ential motion normal to and along their axis of Symmetry. as well as the expanding amplitude and expanding distances
It is the Synergy of these time-domain Strategies that result between the body-relative traveling curvature-isoclines of
in final device shapes specified by time-domain mathemat 60 its body coils.
ics. These demonstrate a considerable theoretical advance in This concept thus provides a crude Scheme not only for
efficiency. the analysis of fish and bird propulsion, but any other fluid
To Specify this advantage I will now compare theoretical induced oscillation, including Such widely divergent phe
considerations of State-of-the-art and the proposed devices nomena Such as flutter, Vortex induced resonance, or any
functional basis using Schematic and graphical metaphor to 65 other oscillation of natural flows and their effect on physical
illustrate the classical-parameter-relative implications Surfaces. AS shown in FIG. 4c, all Such motion is charac
derived from Blade Element and Momentum Theory. terized by the rhythmic undulations of form-conferring
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envelopes and their wake vector fields moving in time with Plane-Spiral of wave form generation, which are
the undulating envelope shapes that give rise to them. All abstracted from the-usually-parabolic envelope of
display the characteristic progressive phases of a periodic maxima of this expanding wave 28, as shown in FIG.
waveform. 4c.
AS is well documented by Velocimetry analysis, this In this way does wave form analysis, and the physics of
waveform extends well behind the undulating body itself oscillating Systems result in a drag component for the body,
into the characteristic regions of undulating accelerated-or or body element. From this, and the other known parameters
decelerated-central flows bounded by Standing vortices of of Viscosity-Reynolds number-, a coefficient of drag is
alternating polar rotations called Karman Vortex Street. estimated.
As is shown in FIG. 4d, any fluid dynamic object, whether Next, a time averaged full wave cycle regression of the
rigid or flexible, however physically shaped, is deemed fluctuating contours of this dynamic flow field envelope is
enveloped by this time-based periodic fluctuation of derived from Sampling intervals.
dynamic flow. Here the flow has equipped a flagpole with
closely adhering Standing Vortices 27, allowing fast-moving These provides the envelope and mean chord co-ordinates
air particles outside this envelope a kinetically economical of a theoretical rigid foil element with parameters of drag
passage by conserving their momentum through preSSure 15 or thrust-that can be readily inferred and then be used to
recovery, This results in the characteristic teardrop shape calculate the Velocity and pressure gradients prerequisite to
Statistical envelope contours of the time-regressed dynamic the calculation of Viscous and dynamic forces.
flow continuum, containing within its borders these In the case of the desired profile Sequence of the proposed
lubricity-and shape-conferring Secondary flows. Spiraling rotor, this hysteresis-based regression concept
The frequency of flexion of the “tail” of this flow field allows the use of conventional profiles in the public domain,
relates to the resonant frequency and diameter of the flow treating the full cycle of transitory phase transformations as
field (Strouhal number) and fluid system hysteresis, which a Single Statistical profile of fully regressed original
acts as a kind of streamline-inertia, or flow pattern coordinates, allowing the use of published performance
memory of the oscillating System. These interrelationships, curves. A full periodic function cycle phase Sequence is
along with other factorS Such as Viscosity, govern the 25 accordingly treated as a Single virtual foil element, -a
observed Vortex Shedding frequency. Meta-Element-, of linear Velocity and minute thrust, -as
In view of these observations, and without claim of opposed to drag-. This is deemed a flexible physical
Scientific rigor or even denial of the fact that propulsive foils membrane, aligned with axial flow, and gliding along its
or fins-especially for carangiform propulsion-may well Spiral foil-shaped timing-am and resonator phase Sequence,
be more Significant for thrust as this body wave in linear a concept that is shown in FIG. 5c.
propulsion, the Meta-Element concept is based on the fol I will now describe this method of generating the requisite
lowing admittedly arbitrary working hypothesis: shape change using the example of a wind turbine rotor
1. The Meta-Element is defined as the time-average blade element.
Statistical contour of demarcation of the dynamic flow The coordinates of the physical shape of a full rotor
field 27 of FIG. 4d. All frictional secondary flows such 35 blade are progressively developed by a periodic function
as boundary layers—whether turbulent or laminar-or algorithm method that can be illustrated using a graphic
Separation bubbles, or envelope Shaping Standing analog of this transformation proceSS and shown overem
Vortices, are deemed included during a full cycle of phasized for visual clarity on the left of FIG. 5d. Here a
major Strouhal-Karman Vortex period flexion. It retains conventional public-domain profile is split into a profile
data on the Fourier expansion of the periodic waveform 40 nose, which remains unchanged and a profile tail Section,
for the major cycle. It abstracts energy dissipation-or which is transformed into an 8-phase Sequence, using
import-values from the shape of the curve of envelope wavelength, and amplitude logarithmic spirals of generation
maxima 28 of amplitude and wavelength expansion applied to isocline acceleration control points on the median
terms. chord. These can displace the envelope-shaping chord
2. It makes an assumption that if the mean chord of Such 45 normal rays of graphic construction. The ends of these
Meta-Element fluid dynamic body envelopes undergo displaced rays are Subsequently connected by cubic spline
path-transverse flexions of given frequency and wave curves. This phase fragment is then mated to the Archimedes
length expansion parameters that allowS Such bodies Spiral profile nose, which has been plotted relative to the
locomotion-or retromotion-relative to wake vector truncated cone illustrated on the top right of FIG. 5c, to
field dispositions of FIG. 4b of similar contours but 50 result in a 3-D blade, missing its tail sections. This Spiral
different wavelength, then it will be the Phase-Plane nose blade, deemed attached to the Surface of the cone, is
Spiral logarithmic increment-or decrement then rotated by Small increment via this cone, and the
parameters of the path wave compared to the body next-integral multiple-numbered phase fragment is again
wave that give information on the Velocity as well as mated. This is repeated at equal angular increments of
energy expenditure of this relative body motion. This is 55 rotation of the cone until the entire length of the Spiral nose
a concept analogous to propeller Slip and is also section has been filled with a multitude of full-cycle tail
shown on the lower left of FIG. 7d. Section Sequences. These are Subsequently connected tan
3. AS is well documented in above-mentioned Scientific gentially with cubic spline curves, thereby blending their
references, these parameters include, but are not limited transitions. Upon rotation, the resulting Surfaces tangential
to, wavelength, frequency, and amplitude of flexion. 60 motion through the axial plane-of-shear, provide a Smooth
Since the fluid medium provides Viscous damping, the rate-of-change variation of chord-transverse inclination over
phase-plane orbit of generation of nature is generally the rear portion of the profile, as is shown on the bottom
shown-but not limited-to be of a family of logarith right of FIG. 5d., whereas the axial-plane-relative flattening
mic spirals of FIG. 4c for the inertia-bound flexions of Slope of the isocline parabola provide for the desired accel
nature. 65 eration of the body-relative transverse wave.
4. Information about body-relative dispositions of viscous A full Sequence of these phase fragments in its motion
drag is also inferred from the parameters of the Phase through the plane of shear is a Meta-Element as is shown in
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FIG. 5c. In its effect on the axially aligned predominant sums. This is shown in FIG. 6. Each resulting individual
momentum of flow, it can be visualized as an infinitely profile shape helical Section is entirely anomalous, having
flexible, very thin, but nevertheless physical film-being different values of chord length, thickness, camber and
composed of a Slippery membrane of Segregated and Viscous after-body kink depending on its distance from the axis of
material-that closely adheres and animatedly responds like rotation and the interSected after-body phase range. They
a glove to the rate-of-change isoclines of this resonator were all, however, of recognizable fluid dynamic shape.
Sequence in its tangential path through this plane. AS the Moreover, their angle of attack of helical motion was largely
resulting entire 3-D spiral blade is attended by this physical Self-similar and closely within a range of Meta-Element
film, boundary layer turbulence, profile drag, as well as orientation to axial flow. Their Velocities, being the Vector
induced drag is diminished when compared to conventional Sum of local radius rotational Velocity and that of axial flow,
blades by the propulsion mechanism of anguillar locomo were however, Significantly lower at all radial locations
tion. including the Outermost in the case of the wind turbine
The Meta-Element is thus deemed physical in the sense configuration. Based on these facts, I computed a worst-case
that it is made up of many layers of physical Viscous Scenario contribution to—or detraction from-this helical
lubricant matter, reconciling inner tangential to outer axial 15 motion and found a largely non-existent contribution to
flows. It is deemed permeable at the back to allow for the Meta-Element differential pressure and considerable detrac
expulsion of lubricant accumulations. In the manner of a thin tion due to form drag.
rubber glove it responds to the changing angles of inclined AS only a single field of differential pressure can exist
planes that tangentially transition through it, by converting around Single fluid dynamic Surfaces, and the Meta
this rate-of-change to Shear plane-relative profile-transverse Element's Spiral advance vector-Sum-based relative Velocity
impulses in Space quadrature through force decomposition is designed to be greater than that of helical motion, I
as is shown on the lower right of FIG. 5d. concluded-and Subsequently proved to myself-that the
In this Sense, it acts the part of the oil film contact patch modest adversity attending helical motion of anomalous
of the spiral worm gear of FIG. 8e that converts rotary profile changes does not disable the greatly increased dif
motion to the linear motion of its conjugate rack, using the 25 ferential pressures and efficiencies of the Meta Element.
Same tangential-to-axial motion conversion mechanism. To sum the relatively ancillary effect of helical motion on
Since this resulting Meta Element motion thus effectively this spiral based devices:
duplicates the mechanism of anguillar propulsion in Space 1. The physical device actually shears through the axial
quadrature vector conversion, it is attended by the well plane at linear Velocities that greatly dominate helical
documented reverse Karman Vortex Street containing the Velocities. Fluid must part around this axial plane
observed central jet and bounding vortices as illustrated. progression and create the Velocity-appropriate classi
To ascertain whether this phenomenon is in fact 'real cal pattern of dynamic lift, thereby overwhelming
and not Some form of Wishful thinking-, I measured the ancillary helical influence.
wake rotation of my physical fan prototype and found that 2. AS shown in on the lower right of FIG. 6, during a given
wake rotation was less than the commercial fan it replaced. 35 time Slice, all isobars attending helical motion have an
AS the measured wake rotation was very modest, I could attenuated effect directly ahead of motion, thus weak
conclude that lubricity, the axial shear plane, and the Meta ening inflow and upwash via a Sector of diffusion as
Element itself are mutually interdependent, real phenomena. defined by the helix-tangents Swept during that time,
To analyze this configuration in operating mode, condi whereas linear motion isobar influence extends durably
tions of Shear drag are first estimated using published data 40 and with relative concentration, thus providing addi
attending Viscosity and Velocity of flat plate drag. The tional reason for the linear motion dominance of influ
dynamic forces of profile drag attending this published ence over helical motion.
profile are then used to offset the designed Small increment Having now proposed the definition of the physical Meta
of anguillar thrust and the-very-low induced drag esti Element and its interdependent relationship with the axial
mates are added. Finally, the lift equation is used assuming 45 plane of Shear as a rate-of-change quantifiable process, it can
axial-plane-relative Velocity composed of the vector Sum of now export these quantities in a familiar parameter form as
axial and radial spiral motion components. To this is added bridge concept, or plug-in, enabling use of the classical
the vector component of incoming axial flow. This proceSS analytical framework of momentum theory, as well as con
is shown in FIG. 13d, where the resulting vector diagram is ventional pressure/velocity oriented tools Such as those of
compared to a diagram of a conventional turbine. 50 Helicopter Blade Element analysis for additional refinement.
The resulting lift equation-derived differential pressure To demonstrate the theoretical operational advantages of
forces are conventionally attached normal to the variably these Spiral-based devices using the parameters of analysis
inclined spiral-derived profile-Sequence's Surfaces, as is of classical perspectives, I refer to FIG. 13c, which is a
shown in the lower half of FIG. 13d. They are then corrected 2-dimensional representation of the total Streamline flow
for their angle of orientation relative to the axial plane to 55 field attending the Spiral blade as just previously described
determine the resulting turning moments acting upon the and illustrated on the upper left of FIG. 5c. This is shown as
rotor axis of motion. This is also shown on the bottom of being attached on one end to a body of revolution and on the
FIG. 13d. other end to an annular wing, which in turn is mounted upon
Being a device of rotation, however, there is little doubt this body via tensile spokes. Although only a Single blade is
that physical profile Sections must travel in helical paths in 60 visible for the sake of visual clarity, several such blades
order to provide these described-or envisioned-artifacts. should be deemed similarly attached at equal angles to
There cannot, by definition, be two dynamic flows, provide symmetry. A tower-not shown-holds this rotor
namely one attending helical motion and another as the assembly and a tail Vane-again not shown-allows the axis
result of Some Secondary artifact thereof. This presented a of revolution to align itself parallel to flow direction and
great conundrum in my initial investigations of these 65 largely prevent wake twist.
devices. I therefore examined the resulting blade elements Upon rotation, a Single Meta Element-as being com
relative aerodynamic shape, orientation and Velocity vector posed of the slippery, Viscous film with which its axial Shear
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plane counterpart has Surrounded it-moves as shown along approximately twice that of the Sacrifice of the original
a path that is defined by the radial and axial coordinates of inner stream tube, as estimated by the relative contribution
its rotor blade's truncated cone-coordinate remapped of low-pressure versus high preSSure to the total differential
coaxial Archimedes Spiral-of-generation. This path orienta forces attending the generation of all lift.
tion is shown underneath the conic spiral of FIG. 5c. As all These two flows are thus Seen to be mirror images of one
other co-axial planes and their Meta Elements are Simulta another as Seen in the lower diagrams of the diagram of
neously generating the Same orientation, Velocity and thus variations of pressure and Velocity attending each. They are
dynamic flow patterns, these multiplicities can therefore me thus deemed Synergetic and mutually geometrically
modeled as forces attending a single axial datum plane. enmeshed.
The vector Sums of this motion and axial Streamline The Actuator Disc is a legacy concept predating modern
components, as well as the force resultant of this motion are boundary layer theory as well as predating Duct Theory of
plotted to provide a dear Visual metaphor on the lower left Computational Fluid Dynamics. Stretching it into an
of FIG. 13d. This resultant is then decomposed into com Actuator Cone via the rule-based transformations of
ponents of turning moment versus downwind force. These topology, which recognizes these Surfaces to be in an
values are then compared with known operating parameters 15 important Sense identical when plotted with a stretched time
attending conventional turbines in the same drawing. These axis, is mathematically defensible and provides considerable
are seen to generate comparatively large downwind forces. theoretical advantage:
It is seen on the lower right that when compared on the basis 1. For a given extraction-or exchange-of momentum,
of equal amounts of downwind force-called thrust in wind it spreads the deflective impulse of extraction-instead
turbine practice-this vector decomposition shows that the of over the volume of a blade-wide thin disc-to the
Meta Element device, using very conservative values of much greater Volume of mass flow exterior to, as well
Spiral axial advance, generates Several times the turning as within this duct of conic shape itself. It also does this
force per aggregate of downwind force. Over a much longer time, as fluid particles need more
AS Some of these large conventional turbines must be time to croSS this extractive mechanism as compared to
designed to be able to Sustain loads approaching a hundred 25 the time needed to cross the thin Actuator Disc. Thus
tons, these vector decompositions make clear that they mass-flow-Specific impulse, deformation shear and
extract a relatively Small amount of energy at the expense of downwind force per given values of power extraction
relatively great amounts of mass flow linear momentum that are much lower.
they make unavailable to themselves and to downwind 2. In the case of wind turbines, the analytical convention
turbines. of the Actuator Disc concept itself has imposed a
This in turn illustrates the phenomenon of the upwind and Strategy of erecting a massive barrier to flow, which can
downwind expansion of the theoretical stream tube 90 of left be up to twice the equivalent swept area of a flat plate.
FIG. 13b predicted by Momentum Theory, which limits the This imposes many tons of blade root and tower base
amount of energy capture of this Stream tube to the well forces requiring expensive means to assure rigidity,
known “Betz Limit” of approximately 59 percent of the 35 resulting in devices whose aspect is industrially Stark
theoretically available power attending the mass flow rate and obtrusive, provoking proven public resistance to
available in this “tube, a limit that has in fact never thus far these harsh intrusions upon cherished pristine and
been exceeded by any conventional device. pastoral landscape. The Actuator Cone based devices
To illustrate the Momentum Theory implications upon on the other hand, have a very low tower load and So
these proposed devices, I now refer to FIG. 13c, which has 40 could slowly Sway upon slender towers, Steered by
re-oriented the Froude or Rankine Actuator Disc 20 of FIG. their tail vanes. Here they would no longer be limited
2-which reflects the plane of orientation of the Swept disc to decelerating a Single Stream tube, but rather an
of rotating sails or blades in a usage of convention dating incoming elliptically expanding funnel of arc of
back for Several thousand years-into an Actuator Cone of oscillation, involving even greater mass flow and
modern duct configuration reflecting the actual Swept Sur 45 thereby extract more energy. The period of this Sway
face of orientation of the moving spiral blades on the left could be coordinated in a networked Synergy in the case
of FIG 5c. of a wind farm to allow greater total energy for turbines
AS-for purposes of pressure-Velocity-relation based operating downwind. Importantly, this quaint motion,
analysis-the original Froude Actuator Disc is deemed Semi reminiscent of trees, along with the inherent Sculptural
permeable and composed of an infinity of rotating blades, So 50 qualities and Visual continuity of Spiral motion might
too is this Actuator Cone of FIG. 13c deemed open a the well disarm Some aspects of public objection.
front and composed of a Semi-permeable conic membrane To Summarize, as Blade Element vector analysis shows,
exactly as in the Actuator Disc-that extracts a given the proposed duct/spiral-based device extracts Several times
quantity of momentum in exchange for a given amount of the turning force for a given amount of downwind force as
impulse of turning force. AS is Seen, its orientation allows a 55 compared to he conventional wind turbine. AS the rough
Simple flow-net analysis of flows that reflects its property as calculations using the parameters of Momentum Theory and
a duct of fluid continuum, allowing upstream and down Duct Theory Show, the impulse of power extraction through
Stream control Volume adjustment and energy conservation. deflection is transferred to an interlocked Stream tube System
The resulting low-pressure isobar orientation just outside that involve up to three times the mass flows rates consid
of the contracting Semi-permeable Surfaces of the Actuator 60 ered by the Actuator Disc.
Cone-as per Bernoulli-Theorem-based derivation AS power eXtraction is a relation of impulse to
causes the original Stream tube core to be enveloped by an momentum, these devices spread this impulse to greater
additional outside Stream tube mantle, which is decelerated mass flow rates and do it without the unintended conse
by the shallow angle of deflection into this low-pressure quence of converting linear momentum into the chaotic
region. 65 angular momentum of turbulence of FIG. 3.
This decelerating Stream tube mantle's Sacrifice to total Thus, it has become evident to myself and will also
upstream and downstream momentum loSS must therefore be become apparent for anyone who has access to the tools of
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lift analysis and the flow net, that the Betz Limit-as being 54 of FIG. 7a as well as their relative advantages
an artifact of the legacy orientation of the Actuator Disc and depending upon application-in the ability to tailor force
affecting a stream tube of Disc diameter-is not directly vector alignments that minimize/maximize torque or maxi
applicable to this duct-based device, which should exceed mize useful forces. Since these forces attach normal to Spiral
this limit. Surfaces, final vector decomposition must be corrected for
AS will be shown Subsequently, in its function as a device the average spiral angle of inclination of these Surfaces.
of propulsion, the Meta Element device will demonstrate When compared to the conventional propeller vectors in
increased thrust-per-torque and through the ability to tailor FIG. 1, it is seen that these devices generate more thrust
resultant forces, will allow operation at flight Velocities per-torque by being able to direct greater amounts of final
previously unattainable by the convential propeller by forces in the desired al direction and by apportioning thrust
Simple reorientation of the Actuator Disc into an Actuator loading 78 more evenly acroSS its Swept cones of actuation
as is shown in FIG. 11.
Cone using truncated cones and spiral parameters. 1. A full 360-degree cycle thus constitutes a full cycle
This has now concluded the exposition of the theory of Meta element
operation affecting the entire family of these proposed 2. An integral harmonic Subcomponent of this wave
devices common theoretical operating principles. What 15
within the frequency range of natural eddy formation
follows is a more detailed perspective on the theoretical known to fluid dynamicists as Strouhal number is
operational aspects of Specific applications. To teat these Superimposed in the form of a harmonic Sub cycle
with full justice, Some of the same ground must be restated, Sequence 48 generated by using a parabolic envelope of
in order that the ambiguities due to the lack of extensive maxima 50 for the harmonic component transpositions
mathematical format be eliminated as much as possible. of increasing amplitude, re-mapping the aft portion of
Since the Meta-Element in motion on both dimensions of the mean camber line.
the totality of axial planes is an expression of a time Series Finally the vector-shear based momentum transfer of the
waveform with its harmonics that in its operating cycle boundary layer is computed using flat plate equivalents, or
encloses a volume 94 as shown in FIG. 13c, it opens the from the equations of Navier-Stokes.
possibility of using the normally unavailable out-of-phase 25 The effect of this momentum transfer on the deformation
potential kinetic energy of periodic harmonic oscillation of of the Meta-Element shear plane is finally steered by
this resonantly coupled Volume of fluid mass. Stabilizing it through the variation of the major out-of-plane
This is accomplished by correctly phasing impulse trains force modifierS Such as Sweep and Surface pressure gradient
from the Meta-Element cascade of Successive passage to in an iterative recursion.
benefit from the momentum of phase shifted fluid elastic To explain Schematically the advantages conferred by the
rebound 59 exactly as it occurs in nature, as is shown in FIG. ability to detach the Meta-Element orbital flow field pressure
8e. wave from the underlying physical surface, I refer to prior
FIG. 7d further illustrates tis concept. An incrementally art as show in FIG. 8.
consecutive Meta-Element phase fragment Series on the Here a conventional wind turbine flow field-redrawn
right is designed to follow the contour of a periodic wave. 35 from the contours of an actual photograph of the wind tunnel
The operating angle at which the Meta-Element meets Streamlines as delineated by Smoke trails-is compared with
oncoming flow is thus a function of compound waveform, the flaw field of the Meta-Element based axial plane spiral
path wavelength 44, intercepting the Shorter incidence based System of OScillation.
wavelength 46. The conventional air turbine generates power by creating
AS it is a well-documented prime prerequisite for the 40 a well documented highly turbulent, noisy field of
efficient development of high forces that this angle be kept enmeshed, interlocking masses of turbulent air that counter
a constant as possible throughout the operating range, these rotate 64 in a Self-reinforcing System that persists far down
proposed devices make use of a periodic function for a Stream.
cosine wave that includes an infinity of odd numbered The impulse of blade passage upon the inertially inter
harmonics. AS was shown previously, this slope can also be 45 locked incoming axial Stream tube of initially exclusive
generated by path resultants 45 of a Spiral of Archimedes, axial momentum that generates this phenomenon thus cre
when remapped to truncated conoids-of-revolution. ates an intermittent angular momentum reaction that is
This motion generates constant operating angles of related in magnitude to these sharp impulses 58 of episodic
inflow, except at the Short reversal Sequence, where the angular acceleration of Single direction.
Meta-Element changes tack, i.e. reverses its orientation to 50 The blades of this turbine encounter air that is therefore
the inflow and generates a Vortex of reversal. already in the process of accommodating itself to this
The passage of the resulting blade in forward motion can rotation in a phenomenon well known to designers of Such
be visualized in its effect on the axial plane of Stationary devices as blade cascade interference. This effect manifests
fluid. Here, as is shown in FIG. 7a, any single waveform itself in reduced inflow vectors 56. This concept is meta
concavity/convexity forming the resulting time axis topo 55 phorically similar to the idea of birds of passage flying in the
logical helix worm rotating forward at axial velocity will Sinking air of their preceding leader, rather than laterally
Stay Stationary relative to particles on this plane, while the displaced, in their classic V formation.
topological worm as a whole moves forward. Another metaphor would be idea of letting the angular
The back-to-back truncated cones, with their spirals-of kinetic energy imparted to a rotating toy disc on a String-a
generation, are deemed rotationally enmeshed with this 60 “YOYO-in the form of angular momentum, to go to
single worm concavity as is shown in FIG.7b. Progressive waste, rather than use it to cause the disc to climb back up
rotation of these conic spirals generates a Stationary conoid the String.
convexity relative to this stationary plane. Progressive pro By contrast, the wind turbine designed according to
file phase elements are plotted as phase angle harmonic Meta-Element time Series polarized Oscillation creates the
integral multiples of the fundamental angular Velocity of 65 classic low-turbulence reverse Karman Vortex Street, the
these cones-of-generation's Surface. This sequence is illus Source of the documented unequaled efficiency of creatures
trated as axial progression 52 of FIG. 7c and retrogression of nature.
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It accomplishes this by varying the interplay of the major with fluid mass momentum as Sharing contours with a
parameters of influence that determine Meta-Element wave dynamic flow that has the character of a non-linear
period, harmonic overtone, shape, orientation and thrust as damped preSSure wave System that can be expressed as a
well as the boundary layer influences that determine Meta Fourier Series periodic function. This periodic function
Element orientation. Finally, it largely neutralizes tangential includes those harmonic Subcomponents that produce the
components of force by using a variety of means to prevent characteristic resonant Vortex Shedding at the tail. This
flow excursion from purely axial motion. entrains periodic vertical flexion of the vector field that
The effect of these axial plane Velocity and acceleration cycles faster than hysteresis based System frequency
vectors then attach to the inclined Surfaces in the form of response. It Views the phase plane Spiral curves of this
dynamic differential pressure patterns that create tangential oscillation as an information Source for values of body
relative Viscous friction.
forces by acting at right angles to the inclination of these 2. All fluid dynamic bodies are therefore deemed an integral
Surfaces. part of a phase locked oscillating System involving fluid
Additionally, in this way, does the potential energy con masses exhibiting the fluid dynamic equivalents of
tained in the moment of momentum of the oscillating fluid resistance, capacitance and inductance. Since the particles
reaction mass become available to the phase-shifted cascade 15
of Such masses move in elliptical or circular orbits, Such
of Successive rotor passage. oscillations interchange angular momentum with Such
The benefits of Such a scheme is manifold: bodies, and thus have mechanisms to conserve this angu
1. Fluid reaction masses arrayed in the highly patterned, lar momentum. But as is shown in FIG. 13a, since any
coherent and low turbulence Karman wave-vortex rigid object-especially a rigid tail-cannot accommo
pattern-as shown in the upper portion of FIG. 8e-are date itself to the high frequency wave potentials of the
documented to rapidly widen and attenuate, thus involv Small waveleSS harmonic component Sub orbits, it devel
ing a higher reaction mass with a lower mass Specific ops an interfering phase lag with the prime wave
impulse, unlike the propellers high Specific impulse's component, causing these disordered high frequency
counter rotating turbulent wake which forms a Self insu energies to precipitate into rapidly pulsing vertical
lating System that continually dissipates kinetic energy 25 moments 61 at the tail. This results in the formation of a
and persists in time. Surface of discontinuity that acts as a barrier to the phase
2. A highly patterned System of bi-directional time-Series path continuity of particle orbits. Significant high fre
oscillations can be exploded by the Meta-Element-free quency components of angular momentum of the bound
to move in both dimensions of the axial plane by choosing Vortex are discharged into this roiling Surface of
the timing of Succeeding passages to occur out-of-phase discontinuity, creating a highly concentrated area of dis
59 as in FIG. 8e-, thus recapturing some of the kinetic Sipation through Small Scale turbulent intermixing. This
energy potential of the oscillating inflowing fluid mass phenomenon distorts the waveform, and degrades
and also conserving more kinetic energy of the air tube as oscillation-rebound-based mechanisms of energy conser
Vation through phased elastic energy recovery.
a whole. A similar effect is used in nature by all migrating 3. As is shown in FIG. 13a, the conventional propeller is
birds as well as schooling fish that benefit from reaction 35 additionally burdened by a Secondary consequence
preSSure waves created by their neighbors, as this is a attending this Surface of discontinuity, as the divergent
form of free energy. The effect of this for the Meta flows 61 of the upper and lower surfaces fail to rejoin at
Element turbine is a Significant increase in torque per fluid the trailing edge and So develop distortions of the Surface
momentum loSS through beneficially shifted force vectors of discontinuity that terminate in medium Scale Vortices
60. This is schematically shown in the relatively attenu 40 containing high levels of lost energy in the form of
ated wave/vortex System downstream. moment of momentum.
3. Unlike a propeller, which imparts Sharp, episodic, and The wake of fishes is known to contain much smaller
Staccato impulses 58 on that axially arrayed limited mass amounts of Vorticity and turbulence, allowing them their
of fluid confined to the immediate vicinity of its operating observed unequalled efficiencies. Thus, Strategies here out
disc of actuation, the Meta Element, in its oscillating 45 lined include Soliton Meta-Element tail flexion to re-export
motions Simultaneously and Synergistically interacts with lost capacitive energies to the flow, restoring the coherence
a much greater fluid reaction mass that has been Set in of the oscillating System through feedback of lost short
polarized resonant oscillation in all axial planes of the wavelength harmonics.
azimuth. Thus the Meta-Element device spreads its Meta-Element hypothesis thus sees the induced wake
impulse bad to a much greater mass flow resulting in a 50 losses of the rigid tail conventional propeller as being the
Smooth, non-pulsing Surge 53 analogous to a spiral gear result of an unintended conversion of Significant energies of
rack conjugation, when compared to the Spur tooth pull impulse to disorderly angular moment of momentum.
sations of Single tooth engagement. This, in turn allows the coherent wave attending lift to
4. Finally, a turbine employing a Soliton wave engendering become disordered and So to discharge Some of its moment
Meta-Element progressing axially forward 59-against 55 of momentum into a cascade of chaotic flows of decreasing
the ambient fluid Stream-will generate Significant Scale. This cascade ends in generating useleSS heat and
increases in differential pressure intensities resulting from Sound. In doing So, it also provides a ready escape for the
this vector addition as this wave front virtual velocity waste of meaningful amounts of kinetic energy that might
will be significantly higher than ambient Stream Veloci otherwise remain available.
ties. The resulting higher pressures act on intermediating 60 It is the primary goal of these methods to interrupt this
spiral Surfaces and the resulting beneficially shifted force Specific causal chain.
VectorS 60 provide greatly expanded torque per given These Strategies, however, use the momentum transfer of
fluid momentum loSS, permitting highly unusual values of fluid shear props of the lubricating boundary layer as the
torque per unit of downwind as well as blade drag. principal enabling mechanism.
To Summarize Meta Element time considerations: 65 This layer's behavior in flows containing shear-in-vector
1. Meta-Element hypothesis conceives of all bodies and turbulence is unfortunately not presently fully modeled
whether rigid or not-that are interchanging impulses by the Scientific community.
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Thus, the possibility existed that these Strategies, however reversal 55 that is generated is of much smaller intensity,
promising, might well lack insight on Some unexpected as the phase shifted Successive passages attenuates it
detrimental interactions, and thus unintended consequences. Without Significant tip vortex formation, leSS induced
For this reason I set out to build Such a device. I first downwash wake rotation 64 together with improved ele
generated the unusual coordinates of a propeller device by ment orientation 60 combine to Significantly reduce wake
computer program. Because of paucity of means I confined corkScrew, pulsation and noise.
the design to purely radial motion. This design also did not Summary of this Compound Motion:
include the harmonic spiral Sub Oscillation, or axial motion. The thin lubricating sheath of the boundary layer com
However, this prototype construction of an electrical fan bined with the inertia of coherently oscillating flow
using a propulsive element made by these methods showed memory of hysteresis Substantially prevents the rotational
good correlation with the predictions of this model and motion of the catenary half loop embodying the Spiral cam
provided Significantly greater airflow, thrust, flow and Sequence of resonators from Substantially deflecting the
dynamic flow.
coherence, leSS near and far wake turbulence as well as Therefore the Meta-Element presents the inertially domi
Significantly leSS noise than the commercial fan blade it nating preponderance of local plane axially aligned
replaced. Precise measurements of electrical consumption, 15
fluid, -itself resistant to immediate angular deflection reac
Velocity and near and far wake area Show significantly tion by reason of its overwhelming inertia-, with the
greater mass airflow per torque with a blade not incorpo Sustained presence-in-time of a moving wave of rarefaction,
rating above mentioned boundary layer Scavenging features. accompanied by one of compaction, moving along both
Compared to other axial flow devices, propellers use dimensions of the axial plane of motion as shown in FIG.8.
relatively large and thus efficient impulses on large mass To accommodate their passage, axial Stream tubes have no
flows of fluid. other choice but to divide around this phenomenon in the
The proposed innovation extends this idea even further. It classical pattern of high and low Velocity flows that generate
also operates on large masses of fluid. But it operates the differential pressures of lift.
completely unlike a heavily tip-loaded blade, which inter Since a local Soliton bound-Vortex wave propagating on
mittently imparts Sharp energetic pulses of varying radial 25 the axial plane experiences the transition of Successive
intensity to local axial fluid Stream tubes and then leaves the resonators' Sliding through its plane as a local moving shape
locality entirely for the rotational part cycle until its return. in the process of shape transformation, this virtual shape
This phenomenon imparts the characteristic clapping animated by the transiting wave-resonator-train thus cannot
noise, pressure pulsations, and Vortex formation with leave its orbitally and inertially coupled axial plane fluid
counter rotating inner core, induced drag and sharp Velocity Stratum.
variations, flow reversals and pressure peaks of the wake. Thus, the temporarily contained differential preSSures
Thus, the stream tubes proceeding parallel to any given generated by the high and low velocity stream division
axial plane in the proposed invention constantly remain have no opportunity to discharge. This is much unlike the
within the influence of the transiting phase Sequence of the case of the propeller where the containing Surfaces—i.e. the
Soliton Meta-Element as it travels at constant Speed and 35 open propeller blade tip-Suddenly leaves the locality
constant angle of attack. All other axial planes Simulta entirely.
neously experience the Meta-Element in different Synergis Here they can implode into a high Velocity tip vortex,
tic phases. precisely at the location where the Sudden, explosive appear
In all Such planes, they experience neither the entire ance of the highly loaded propeller tip is followed by its
absence of the Meta-Element from their locality of influence 40 equally Sudden, implosive local disappearance.
at any moment, or Significant pulsation nor therefore inter AS there is no open tip, there are no preconditions for
mittence of impulse, thus generating leSS noise and com preSSure-induced, wasteful, implosive and noisy Vortex
pensatory Vortex flows. flows.
All other coaxial Strata are Simultaneously experiencing The third source of improvement over the conventional
the Meta-Element in complementary phases traveling at the 45 propeller based device deals with the phenomenon of the
Same Speed and angle of attack. boundary layer itself.
Therefore, all fluid stream tubes in the whole of the In any foil generating lit, the dynamic flow Surrenders
annulus swept by the half loop embodying the Meta Some of its kinetic energy to envelop what it SeeS as an
Element experience an analogous constant non-pulsating obstacle to its Smoothly energy-conserving flow with an
and relatively evenly distributed Surge 53 of FIG. 8e. 50 appropriate lubricating envelope.
The previously described deficiencies of propeller devices The fluid particles that make up this envelope are few at
are addressed by the following Schematic of Strategy: the nose of the foil and slide over each other in Smooth
1-Using an absolutely even distribution of pressure field lamina 41 generating low drag as shown in FIG. 10.
propagation Velocity of the Meta-Element caused by its So on however, depending on prevailing
Archimedes Spiral Cam-induced radial and axial 55 Viscosity, -through the mechanism of frictional
excursions-not in the rotational but the axial plane-. A entrainment-these intermix and accumulate to a thick
high and even Velocity acroSS the axial plane predicts envelope of Violently turbulent particles 21 that are continu
even and correctly aligned pressure loading acroSS most ously losing momentum to heat and creating large Scrubbing
of the annulus, thus minimizing croSS flows. Additionally, drag coefficients. The boundary layer export to dynamic
a significantly greater portion of torque is converted to 60 flow of frictional drag is thus cumulative and therefore
thrust through the improved resultant vectors in the axial exponentially concentrated toward the tail.
direction. At Some point of their passage particles lose enough
2-Eliminating blade tips. As is shown in FIG. 8, a given momentum to lose their resistance to random motion, espe
local companion Soliton pressure field constantly follows cially in conditions of low viscosity. Here they start to
the reversing spiraling Mete-Element back and forth; it 65 oscillate and impinge on Strata of different energy levels and
lacks the opportunity to discharge potential energy into even reverse their motion, pooling in a time-based tidal
conventional tip vortex formation. The Starting Vortex of accumulation toward the trailing edge.
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This phenomenon increases drag through the mechanism action with axial plane orbits 51-is known to present
of violent vortex-based intermixing of layers of different opportunities of operating with drag coefficients that can be
levels of retardation causing high Velocity Scrubbing of the a fraction of those lifting foils operating with mostly turbu
Surface and thus high frictional drag. lent boundary layers.
In conditions of high lift, or high Mach number and thus Additionally, it has been proven that any Such boundary
adverse pressure gradients, boundary layer material accu layer ejection-using any available method-allows the
mulates on the back of the Suction side of the foil and generation of unusually high lift coefficients before flow
eventually flows backward, forming pockets of accumula separation. Well-documented experiments with a belt 65 as
tion. shown in FIG. 10 moving in the direction of flow, allowed
This ultimately causes the dynamic flow to detach from angles of attack approaching 90 degrees before Stall.
the Surface, resulting in premature loSS of lift, high drag and Removing such boundary layer material by Suction 52 has
premature Stall. been proven to achieve Similar-though less dramatic
Even using moderate operating lift coefficients, the wake effects.
of a conventional propeller contains a wide band-Vortex In these here-proposed devices, Such boundary layer
sheer-of this slowed material roiling with Spiraling eddies 15 effect is implemented by Superimposing an integral har
which ultimately rolls up into large diameter tip vortices monic waveform with an exponentially expanding envelope
causing the well documented losses due to induced drag. limiting amplitude and wavelength on the tail Section of the
The accumulation of boundary layer material can thus be Meta-Element. The resulting harmonic wave motion con
appreciated as among the main constraining parameter of tains Specifically tailored energies to overcome expected
design of all lifting devices. Without consideration of the Viscous losses.
boundary layer, the practice of fluid dynamics would not be
possible. This envelope is constructed as S-led by the differential
Thus the very conceptual foundation of the proposed equation governing the term of Viscous dissipation phase
invention's designed mode of operation is the attempt to plane logarithmic spiral. This waveform of exponential
influence the development and relive extent of this layer. maxima envelope 66 progressively affects only the aft
These concepts analyze the relative retardation of this slow 25 envelope median of the Meta-Element as shown in a visually
moving layer as a tidal flow, as being time based and exaggerated Schematic in FIG. 10. The actual affected area
cumulative. is generally limited to the aft half chord of the tail section
itself.
As shown in FIG. 13c, the proposed invention uses this The resulting hysteresis parameter Oscillation harmonic
property of the relatively slow accumulation of Such mate Subcomponent results in a traveling ripple 86 of FIG. 11
rial to advantage by presenting the pervasive low pressure
field existing ahead of and all acroSS the entry to its Swept along the tail of the virtual element 82 at exponentially
annulus area with the rapidly shifting sides-and isobars increasing Velocity and amplitude.
of the propulsive element going through its spiral reversals. This wave thus acts in the manner of a peristaltic pump by
Rapidly shifting isobars predict less tidal cumulative flow of creating a traveling pressure pulse referenced to relative
boundary material, as it is Sustained pressure differentials 35 Meta-Element chord percentage at a Speed referenced to
over time that is the prime causal factor of Such accumula local dynamic Stream Velocities that forcibly conveys
tions. slowed boundary material back toward the rapidly flexing
The underlying physical Surfaces sliding through a given tail of the Meta-Element.
axial plane of the Virtual element do in fact entrain additional This latter action widely distributes this slowed material
boundary layer particles and thus generate additional vis 40 to regions of the free Stream that have the energy potential
cous drag, but these experience neither Steady nor uniformly to readily reaccelerate it. This effectively thins the wake
adverse preSSure gradients, as they constantly encounter through four mechanisms:
rapidly changing pressure gradients. This encourages larger 1-These traveling corrugations of the Meta-element tail
regions of laminar flow, which is known to exhibit much Section reconcile the boundary layer Velocity differen
lower drag than turbulent flow and can thus more than 45 tials shown in FIG.13a involving the upper and lower
compensate for the effects of this additional shear Velocity. rejoining Streams through their equal Velocity pressure
As is shown on the right of FIG. 7d the traveling wave Wave propagation
Sequence of Spiral corrugations 48 on the after body of the 2- The hysteresis based high frequency of vertical flex
physical profiles, -the Meta-Element phase fragments ion which attenuates natural periodic eddy formation
additionally impart a wave train of transverse flexion of the 50 at Strouhal Number frequency-by preempting its
Virtual element tail Section. motive cause, being the progressive accumulation and
They employ that requisite Fourier harmonic hysteresis periodic Shedding of Slowed boundary layer material
based wave frequency and amplitude and expanding wave 3-The geometrically extended trailing edge with its
length that can Scavenge Such boundary layer accumulation Vertical component of hysteresis-referenced motion
through means of the resulting rapidly traveling pressure 55 and physical orientation-benefits thrust vectorially
wave packets. from the unequal lateral components of the flows above
They additionally use the geometric distributing action of and below the trailing edge and
the high frequency transverse flexion of the tail tip. This 4-The extra physical trailing edge length resulting from
deforms the sheet of discontinuity of FIG.13a into corru the Spiraling wave train terminating in trailing edge
gations that help to prevent slowed boundary layer Segre 60 diagonal corrugations enables greater momentum
gation by physically distributing it to larger regions of transfer due to a physically wider admixture of the
dynamic flow. upper and lower flows-as mediated by the longer
Absent a steady unfavorable pressure gradient, the con interface of these rejoining flows of differing lateral and
ditions for tidal boundary layer accumulations are also axial velocities above and below the camber neutral
relatively absent Hence, more lift for leSS Viscous drag. 65 axis.
AS becomes evident from FIG. 10, any such boundary This has the effect of a momentum transfer based Sub
layer control-here enabled through the novel sliding inter Stantial interlocking, enmeshing and reconciling of these
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two flows of inequality of axial and lateral momentum by ents into the pressure recovery section of the virtual foil by
minimizing and physically disrupting the insulating and means other than the conventional variation of preSSure
Separating barrier sheet of discarded highly turbulent gradient, namely by the export of precise quanta of energy
lubrication-the vortex sheet-of FIG. 13a that normally into the boundary layer by the exponentially expanding
bars this re-enmeshment. traveling wave 66 of FIG. 11.
This action substantially reduces this thin sheet of wake Thus, until now, Velocity profiles due to after-body shape
discontinuity made of shed Viscous boundary layer material camber variation and their resulting pressure gradients were
that normally Separates laterally and axially divergent upper the Sole means of accommodating primarily boundary layer
and lower flows. mediated phenomena.
If these rejoining flows have leSS divergence of axial and These boundary layer Scavenging methods here detailed
lateral momentum, Such Smaller residual differences will now offer an additional technique to the designer of these
cause Significantly less local axially oriented Vortex devel devices resulting in new families of Meta-Element foil
opment and its associated turbulence and drag. Sections characterized by thinner and shorter laminar flow
Since this is a phenomenon well documented in the wake foils, shorter recovery Sections, with optimized resulting
of fish, Such Strategies may well also benefit these proposed 15 force vectors resulting in leSS drag.
devices in an analogous fashion. Benefit of Solution to Slip Stream Contraction Disadvan
A further Significant benefit is the restoration of the energy tage.
conserving mechanism of wave oscillation, which depends Another element of advantage of the proposed invention
on the phase completion of integral particle orbits 72 as has to do with the phenomenon of the contraction-or
shown in FIG. 11 that make up its motion. Since all expansion in the case of the turbine-of the Slipstream 22 as
harmonic wave components of wavelengths shorter than the shown in FIG. 2 that is a source of efficiency losses in the
length of the Meta-Element will be prevented from com conventional propeller-based devices.
pleting their natural orbits as a consequence of physical This contraction occasions another loSS deemed uname
passage, only Such proposed Meta-Element harmonic flex nable through built-in operating properties of the propeller,
ion can reconstitute these missing harmonic components. 25 and yet is partially remedied and So is made to aid efficiency
Such a Scheme prevents the precipitation of this disturbance in the proposed invention through the following additional
of passage into the documented disordered flows of chaotic mechanism of benefit, entirely unanticipated by conven
moment of momentum attendant to rigid tail passage. tional practice:
AS this Vortex formation caused by vector divergence of As shown in FIG. 8, the Meta-Element benefits from a
rejoining flows is also known to be implicated in tip Vortex momentary angular orientation 59 to this inflow, due to the
formation, this method of boundary layer control theoreti physical orientation of rotor surfaces. This benefits the
cally affects every term of drag and loss of lift known to the transitioning Meta-Element significantly through the favor
art of fluid mechanics. ably shifted vectors of the contracting inflow providing it
Such purposive procedural intervention-no matter what with vectors that the propeller discards. The benefit is three
its ultimate degree of effectiveneSS-agrees well with aca 35 fold:
demic theory that promises-and has experimentally 1- The increment of force resulting from the forward axial
proven-unusually large benefits from any method of vector component 60
removing boundary layer accumulations. 2-The lessened contraction of the actuator annulus
The employment of the momentum transfer of the sliding resulting from rotor peripheral Surface orientation oppos
resonant element train for these novel pressure wave arti 40 ing Such contraction-predicts an increment of efficiency
facts could not, however, be contemplated by an academic through increased mass flow as well as increased periph
model using rate-of-change invariant rigid foil theory. eral differential preSSures acroSS the annulus allowing a
Prior art inventions that did not decompose axial and higher ratio of torque to drag.
transverse Velocity changes resulting from oscillation 3-The purposeful containment of differential pressures at
dynamics into phase plane parameters of wave frequency, 45 the periphery of the rotor by design ameliorates the chief
propagation gradient, amplitude and envelope analysis, con cause of excessive induced downwash and thus high
taining rate-of-change vectors, could not promulgate Such levels of induced wake rotation 64 of the conventional
procedural design elements, nor State their degree of propeller. Additionally, Since the Small reversal tip Vortex
expected benefit. 45 rotates in Space quadrature, it does not reinforce the
A shear-stressed, thin boundary layer is additionally leSS 50 comparatively small Meta-Element wake rotation 62,
liable to early transition into turbulent flow states as its field which thus can rapidly attenuate. Thus, the Meta-Element
of opportunity-large pools of accumulated boundary layer wake contains leSS wasted energy in the form of useleSS
material with low inertia-is Smaller. rotation of reaction masses.
Importantly, operations under conditions of high lift can Benefits through axial retrogression: cavitation and tran
be expected to improve dramatically if the boundary layer is 55 Sonic flight-:
given less opportunity to Stop, reverse, and accumulate-a A further novel element of advantage has to do with the
primary cause for breakdown of the dynamic flow and ability to so vary fore and aft deployment of the hub
Subsequent catastrophic Stall or transonic buffet. Higher attachment of arched spiral segments 33 of FIG. 5c that the
maximum coefficients of lift thus become theoretically fea virtual foil of the Meta-Element of FIG. 7c is given an axial
sible. 60 progression 52 or regression-FIG. 7d component 54 to its
These procedurally derived shape variations have thus motion.
proven to be of benefit in responding to losses caused by In the case of a propulsion device, use of an axial
phenomena previously thought unamenable in man made retrogression component significantly improves resultant
devices. force alignment with the axis of thrust beyond even its
A significant element of advance promised by the design 65 existing advantage, resulting in greater thrust for torque.
procedures of the proposed invention has to do with the If the pressure wave propagation can be Successfully
ability of these methods to expressly design preSSure gradi disengaged from the resonant element train by careful
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adjustment of the parameters that cause proper Meta flow retarding pressure distribution, as well as its greater
Element axial plane radial orientation and thrust, the highly than flat plate form drag co-efficient, must expand to
Swept helical element tip Sequence will experience apparent accommodate its Severe loSS of Velocity when it crosses the
inflow neutrality and can thus travel at velocities that would actuator disc plane.
otherwise cause the onset of compressibility phenomena. This causes the effective tube diameter to decrease from
As shown on the lower middle in FIG. 10, the compress its theoretical size identity with the rotor disc so that only a
ibility shockwave 57 phenomena are a function of lift certain portion of the theoretical kinetic energy is actually
coefficient, as the lower Surface in the transonic regime available at the disc of actuation.
remains relatively unaffected. This phenomenon, described by the noted German aero
This circumstance allows significantly higher operating dynamicist Betz in the early part of twenty century, has been
Velocities, as the helically oriented physical elements can be a major factor in the so-called “Betz Limit”, a theoretical
designed to experience flow neutrality in this region ceiling on turbine performance of a given diameter that has
particularly, deriving thrust from relatively energetic tail yet to be exceeded.
Sequence harmonic motion involving the relatively AS becomes evident in by visual comparison in FIG. 13c,
compressibility-immune aft foil Section. 15 here exaggerated for clarity, the Meta-Element turbine, as
AS forward axial Velocity components can Substantially compared to the conventional turbine-Viewed simply as an
diminish, or even actually Vanish for the propagating pres obstacle to ambient flow-presents a much more fluid
sure wave, the hysteresis artifact of the Meta-Element can dynamically favorable pressure distribution and aerody
operate in a purposely designed virtual Velocity regime, namic shape to the approaching air that combine to favor
where the wave-front experiences only the much lower inflow funneling 37 and allows greater mass air flow for a
radial velocities. Here the actual fluid relative velocity given amount of flow retarding force coefficient.
through the modification of the local pressure wave virtual This combination of features is designed to exceed Such
Velocity. Flight into Velocity regimes previously closed to Stated previous performance limits.
the propeller thus become theoretically possible. Additionally, Since this proposed turbine constrains radial
In the case of a turbine, use of an advancing Meta 25 expansion of the approaching flow by means of Such Inflow
Element wave-front axial component results in Significant Funneling, it stabilizes any directional wind instabilities
improvements of power extracted from a given Velocity of Such as yaw-though its negative pressure feedback
flow through the resulting Substantial augmentation of mechanisms, which act in the manner of an aerodynamic
resultant vectors forward shift as shown in FIG. 13c, duct.
allowing higher torque components for a given retardation Such yaw correction ability is of considerable benefit,
of flow. This predicts greater percentages of kinetic energy Since the conventional propeller-based turbine is known to
extraction from a given mass flow, using inner rotor counter severely lag in yaw-response that is known to impose severe
rotation or a tail Vane Stator-to offset air Steam listing performance and Stability penalties.
momentS. The last advantage of the proposed invention has to do
This velocity and vector augmentation additionally favors 35 with its shape.
power extraction from low wind Speeds, as the Meta As shown in FIG. 9, an enclosed, highly triangulated rotor
Element apparent inflow velocity is greatly increased shape with its mutually Supportive A-frame arches close to
through the vector addition of spiral axial advance accom centrifugal catenary curvature offers a natural rigidity, com
panying the Meta-Element AS previously outlined, the air paratively high natural frequency and intrinsic resistance to
mass interacting with the turbine will experience signifi 40 dynamic, harmonic and Coriolis forces.
cantly leSS momentum loSS per increment of torque than the It does not need a massive blade root, as it experiences
comparable conventional turbine through the beneficial redi primarily tension throughout its operating envelope. It
rection of force resultants So made possible. encounters little bending, torsion or blade tip interference
Benefits Through Actuator Volume Mass Flow Increase: phenomena.
Any conventional turbine's performance as a device that 45 Thus, its design has less need to compromise with Struc
collects torque in exchange for Some of the momentum of a tural consideration and can thus be much lighter, thinner and
theoretical column of air of rotor diameter extending ahead more fluid dynamically efficient throughout its length.
of it is calculated with a variant of “Momentum Theory”. AS a water propeller, this design offers built in resistance
This theory Substitutes a mathematical abstraction called to foreign object fouling and cavitation without the need to
“actuator disc' for the propeller's plane of rotation in order 50 Sacrifice any efficiency to do So, unlike the conventional
to circumvent the theoretical difficulties inherent in analyZ weed-less propeller.
ing the extremely complicated interdependence of flows Due to its non-injurious shape, it can be used in certain
acroSS this interface. applications previously closed to open tip propellers.
This theory’s well proven expression for efficiency uses Additionally, its novel layered manufacturing methods
the geometric Size of this actuator disc area together with 55 114 as shown in FIG. 23 allow minute air entrainment to
mass Velocity change in an equation that can be Summarized further reduce friction and Susceptibility to cavitation.
as follows: AS it generates very little blade impulse phenomena and
“The device using the greatest possible actuator disc area So is relatively immune to interblade interference, it can be
to effect the Smallest possible mass momentum change has located closer to hull or appendage, permitting increased
the greatest efficiency'. 60 diameter and thus even additional efficiency as replacement
From this point of view the Meta-Element turbine with its rotor in existing applications.
greatly increased actuator disc virtual array 92 of FIG. 13c Benefits of Unprecedented Scalability and Economic Cost
enclosed in a volume 94 of fluid that counteracts its radial benefit:
expansion, and thus predicts much higher efficiency from the AS the wind turbine rotor Segments of Substantially cen
terms of this equation. 65 trifugal catenary shape display high natural frequency and
Additionally, as illustrated in FIG. 13b, the column of air rigidity, they offer high resistance to Strong or variable wind,
approaching the conventional propeller disc with its highly and tower turbulence. As Such 'TENSEGRITY Structures
 US 6,948,910 B2
29 30
are Subject primarily to tensile forces, they can be Scaled to Summation of My Solutions to Present Wind-generation
unprecedented physical size-and therefore economic Problems:
viability To Summarize the tangible and intangible benefits of the
Benefits of Public Acceptability: proposed turbine:
The Meta-Element turbine generates a low, Steady, non If the world-wide stated public policy goal of wide-scale
Staccato noise footprint Due to its unprecedented lift over adoption of environmentally beneficial, cost competitive
drag ratio, it operates economically in lower as well as energy production methods could be viewed as achievable
higher wind Speeds than conventional turbines. Unlike a not only as the result of the development of economically
conventional wind turbine, which can generate tens of tons Successful devices offering relative cost-basis benefit, but
upon its blade roots and massive tower, it generates rela also by offering Such Strategies that Successfully address
tively Small amounts of downwind force, allowing it to Store those intangible considerations affecting public acceptance
the energy of gusts in the deflection and energy Storage of a and embrace, then these proposals will be seen to certainly
Slender fiberglass tower. AS Such motion, as well as that of offer improved tangible cost benefit of unprecedented
degree.
the restful non-flickering, curved shapes, faintly whimsical They additionally offer unprecedented Solutions to docu
motion of its spiral rotor is reminiscent of the motion of 15 mented esthetic objection, which affect public readineSS to
trees, So that one of the public-wide objections to conven embrace change itself.
tional turbines Stark aspect of industrial Sharp angularity They do this by offer a pleasing novel iconography of
and their overpowering obtrusion upon cherished landscapes moving organic forms, curves and spirals that has the
may well be moderated. esthetic appeal, and Soothing physiological impact of col
Especially in its application in wind farms, it makes orful kites dancing in the wind. They offer a Visual experi
possible extremely cost efficient, Small footprint installa ence that leads the eye along a predictable linear recurrence,
tions of architectural and Sculptural qualities that provide the non-flickering Smooth trajectory, in an unbroken, non
esthetic value of an organic, natural form of low Sound, low Staccato visual continuum. Documented visual mechanisms
footprint, and pleasingly restful motion. Therefore it prom Such as the persistence of vision can encompass Such motion
ises a likelier degree of public tolerance-the documented as a Single unified totality.
key to the wide adoption of wind power itself. 25 AS Such it will tend to be inherently non-injurious to
These benefits thus offer unprecedented, and in the light wildlife, as well as unlikely to provoke the built-in invol
of present and prior art-high cost benefit ratioS. untary human physiological responses to the Stroboscopic
Structural Advantages: visual flickering of massive conventional turbine blades
Conventional turbine blades have very low natural that whistle the approach of a blade moving at guillotine-like
frequencies, as they are made of Very slender, elongated, Velocities.
thin, unsupported Strips of thus necessarily flexible blades. If Such qualities then help to confer to these proposed
These are intrinsically less resistant to torsion, experience wind turbines Such unquestioned notorious benefit and lack
high bending moments, and thus incur high levels of alter of controversy as do—for instance-large trees, or equally
nating stresses, resonant oscillations, flutter and fatigue. large physical objects of art, or public monuments of
Due to their length to mass ratio, large wind turbine blades architecture, then these devices, together with their tangible
are thus akin to a very long-and very expensive-resonant 35
and economic benefits might offer a Solution to a presently
Single prong tuning forks with intrinsically high root loads, evidenced intractable public resistance that has-So far
Susceptibility to inertial Self-coupling and tower resonant prevented wide adoption of an eminently practical form of
coupling instabilities and So present formidable engineering energy that is insensitive to Supply constraints and price
challenges. They have very low angular Velocity and So need fluctuation.
expensive gear trains with their own elastic modulus and 40 To Summarize Schematically the Foregoing Background
Sensitivity to inertial shock and resonance. Exposition:
They thus need equally expensive measures to If turbines and propellers of present technology and
compensate-Such as upwind operation, employment of proposed prior art are considered to be offering methods
expensive exotic structural materials and methods of based on Strategies and procedures of generating thrust-or
manufacture, complicated pitch changing mechanisms or 45 torque-, these conventional methods offer procedures that
teetering arrangements and massive blade roots with their passively tolerate:
weight and losses of efficiency. Noise
Additionally, such wind turbines are notoriously difficult A Severely fluctuating and wasteful pressure field propa
to control in regard to output regulation or resistance to high gation Velocity,
or variable winds and must simply be shut down at relatively 50 Resulting in wasteful force orientation and
moderate wind Speeds, just when wind energy is most High torque for low thrust in propellerS-or high drag for
available. Their whistling noise, Visual flickering, lack of low torque in turbines
esthetics, lack of wide public acceptance-and marginal High boundary layer entrainment,
economic basis—has prevented their wide-scale adoption in Wasteful, turbulent vortex sheet of discontinuity,
areas of less than high average wind Velocity and low 55
Strong, turbulent tip vortex,
population density. Actuator disc contraction, -or expansion in turbines
Thus they are located away from population centers and Limited lift coefficient,
are limited to the few high wind locations that have Early transonic compressibility drag,
adequately low property value or population density.
They therefore impose the additional expense of long 60 Induced wake rotation,
distance electrical distribution on their economic cost basis. High levels of lost energy deposited as turbulence and
Due to these factors-using the aforementioned relatively noise.
wasteful and expensive Strategies-has a free natural High Cost of manufacture
resource of almost unlimited potential for the production of Low esthetic value
low cost energy that does not generate greenhouse gasses, So 65 Low public acceptance and tolerance
far produced only marginal and limited benefit to Society at In contrast these novel concepts offer a methodical pro
large. cedure of using hysteresis and vector-Shear to create axial
 US 6,948,910 B2
31 32
plane-polarized bound Vortex orbital flows through Succes unable to economically generate power for the overwhelm
Sive embodiment Sequences of resonator Sequences to ing majority of the population living on the landmass that
Create: experiences wind resources that are Class 3 or less.
Procedurally induced pressure field propagation direction What is therefore needed, is a class of devices that work
and Velocity and low noise to concentrate and focus mass flow rates by Strategies that
And procedurally induced boundary layer Scavenging have analogs in optical concentrators, using the Bernoulli
equations of duct design to create focused acceleration
Objects and Advantages through gradual Venturi control volume constriction of mass
The entire surface of the earth is bathed with Solar energy flow rates. Such ducts are the mirror image of efficient
that averages approximately one half kilowatt for every profiles of aerodynamic bodies of revolution, which act to
Square meter of Surface during daylight. If this figure is conserve Stream tube mass flow rate through cogent varia
tion of after-body pressure gradient.
extrapolated to the Square mile, it is Seen that the electro Embodying Such mechanisms of concentration, the pro
magnetic energy equivalence of over a million horsepower posed devices generate low downwind force for a given
per Square mile is unevenly heating our ground, water and amount of power extraction. They create a modern energy
atmosphere and causing fluids to continually power our 15
conservative permeable duct as defined by the conic Surface
weather streams of diffuse fluid motion at all times. This swept by its highly efficient, slender blades. As these are
represents an amount of theoretically available power that attached at both ends and thus lack an open tip, they have no
dwarfs our total human energy consumption by an almost ready means of generating a strong conventional tip vortex.
inconceivable factor. This resulting converging duct is essentially a funnel; it
Most of this flow kinetic energy however, whether in enlists the intrinsic tendency of fluid Stream tubes to cir
rivers, tidal flows, waves or wind itself, resides in diffuse cumvent regions of higher pressure by taking advantage of
flows of less than 5 meters per Second; flows that present this evasion's beneficial Suction force vectors as it crosses
Strategies and devices are not able to economically access. the duct walls and that thereby creates enhanced upwash and
Any Society that can Somehow find ways to tap this vast reduced downwash.
25
potential energy would enjoy an equally vast economic In this way, previously unavailable resources could
benefit through the drastic reduction of what is in effect an become available. Therefore it is my prime object to provide
onerous energy tax-impound burdening its entire economic for devices of rotation the very qualities that allow high
base. LeSS economic burden would mean deceased depen performance Sailplanes their high values of lift to drag.
dence on Supply reliability, collective competitive cost However, as all devices that rotate blades impose the
advantage and thus would also provide the private Sector previously described inefficiencies precisely because of the
competitive impetus for wide Scale adoption. It would described upwash deficit caused by this rotation, helicity
additionally provide pathways of reducing international ten itself must therefore be transformed to the linearity of
Sions caused by competition for increasingly Strained relative motion that is the prerequisite to the fully developed
resources. It would engage private economic incentive to 35
upwash attending efficient, fully developed bound Vortex
achieve universally Stated public policy goals of reduced circulation. Also, tail-Section Vorticity and Spanwise flow
production of carbon dioxide, that have not thus far been must be minimized through Meta-Element thrust. Unless
achievable neither by edict nor international agreement. this is done, the convergent duct funnel Surface would
These proposed devices have the provision of Such advan become a barrier of discontinuity of helicoidal vortex sheet
tage as their prime object. 40 turbulence like that attending the conventional turbine and
The key to economically tap the vast power inherent in therefore unable to function -or be analyzed-as a Ber
low velocity diffuse flows is to enable the same kind of noulli Equation device.
efficiencies that allowed Burt Rutan's VOYAGER aircraft to To Summarize the advantages that these devices offer in
fly around the world without refueling. Such efficiencies are their application of extracting power from fluid Stream, they
primarily achieved by limiting the intensity of the horse 45
C
shoe Vortex System attending the System of differential Devices of collection rather than diffusion, concentrating
preSSures that is the very enabling mechanism of all fluid the upstream continuum of very large mass flows into
dynamic lift. To the extent that these energy-robbing Vortex Small regions of differential pressure waves using the
flows can be minimized, devices of relatively low drag and wave System energy conserving mechanism of linear
high lift will result. 50 propagation to achieve vastly enhanced power extrac
Our present wind turbines and propellers are devices that tion that Spreads the deflection impulse and its resulting
generate very high drag for a given amount of beneficial momentum change to three times the mass flow enter
force. Rather than being high lift-to-drag devices, they ing its Swept diameter compared to the mass flow of
generate high drag-to-lift. Sailplanes generate over 40 times conventional practice. Previous limits to power extrac
the values of lift over drag, whereas in conventional wind 55 tion from a stream tube of less than Swept disc
turbines this ratio is reversed when downwind force is diameter, including the Betz Limit, no longer apply to
accounted for. Such a duct.
Conventional turbines function by diffusing flows rather Devices of TENSEGRITY in that most of their members
than focusing their energies, rather like a prism that diffuses act in tension and thus can provide unprecedented
light rays as opposed to a parabolic mirror or magnifying 60 Structural integrity per-Scale as well as unprecedented
glass that concentrates them into an area of focus. Large economies of greatly reduced Structure-cost basis
wind turbines generate many tons of downwind force in Devices of Sculptural aspect, quiet and restful motion and
eXchange for comparatively Small amounts of beneficial thus well Suited as esthetic as well as economic assets
torque. They erect a barrier of discontinuity to what is for public and private Spaces.
essentially a fluid-wide energy continuum, thereby creating 65 Devices of unprecedented cost benefit
massive flow evasions, mass-flow Spillage through It is my further object to make available for use in all axial
divergence, circumvention and its turbulence. They are thus flow devices the advantages possessed by all Spiral-motion
 US 6,948,910 B2
33 34
gear conjugation mechanisms that is conferred to them by FIG. 7a shows Meta-Element axial retrogression
their innate ability to translate rotary to linear motion. AS the FIG. 7b shows construction of cones-of-generation from
bound Vortex that is the enabling mechanism for the gen wave-function-generated helical body-of-revolution
eration of all fluid dynamic forces is in effect a System of FIG. 7c shows Meta-Element axial progression
waves of rarefaction and compression, and waves-unless
guided in cavities-have energy conservation mechanisms FIG. 7d shows Meta Element construction along trun
cated cone coordinates
that allow them full conservation of angular momentum only
when they travel at constant Velocity and direction, these FIG. 8 shows Meta-Element dynamics compared to prior
proposed devices have as their all-encompassing object to art Schematics
empower rotating devices with the energy conservative FIG. 9 shows Meta-Element sequence construction sche
efficiencies of high lift to drag linear bound vortex wave matics
front propagation. FIG. 10 shows boundary layer dynamics and harmonic
These advantages will be seen to provide unprecedented sub cycle flexion
duct-design-based propulsive efficiencies in the area of FIG. 11 shows Meta-Element dynamics compared to prior
high-Speed flight, enabling higher than turbo-prop economy 15
art
at turbo-fan velocity with lower noise.
Finally, as the most important of the described inefficien FIG. 12 shows Meta-Element schematic design flow chart
cies and high noise attending propeller-based devices can be FIG. 13a shows fixed geometry dynamics of prior art
ascribed to bound Vortex pressures implosively escaping FIG. 13b shows Meta-Element turbine dynamics and
into the wasteful tip vortex and its associated Surface of actuator Volume
discontinuity helicoidal Vortex sheet, these devices have as FIG. 13c shows Meta-Element turbine duct actuator vol
their object to provide unprecedented efficiency by Simply UC
tying the bound VorteX extremities together into a Vortex FIG. 13d shows Meta-Element/conventional turbine vec
ring. AS Spiral blades catenaries with their ends attached to tor comparison
walls, they can be modeled as an annular wing attended by 25
FIG. 14 shows Meta-Element water propellers
a traveling vortex ring. A TENSEGRITY annular wing of
bound Vortex ring, as a Soliton of Conservation of Angular FIG. 15 shows Meta-Element fixed wind turbine
Momentum, provides the theoretically lowest induced drag FIG. 16 shows Meta-Element rotating element wind tur
and thus ultimate values of lift-to-drag as well as the highest bine
possible structural integrity per increment of mass. FIG. 17 shows Meta-Element oscillating element wind
If it can be Stated that the generation of lift forces requires turbine
first the acceleration and then the deflection of mass flow, FIG. 18 shows Meta-Element hydraulic turbine river
then vertical lift will be provided most efficiently by the System application
device that generates more lift per increment of induced drag
to achieve deflection of higher mass flow through Smaller 35 FIG. 19 shows Meta-Element hydraulic turbine seashore
impulse spread over a longer duration. Thus the ultimate System application
logical extrapolation of the lift equation itself dictates an FIG. 20 shows Meta-Element turbine and propeller lay
annular wing that provides horizontal propulsion as well as ered Structures
Vertical lift, making possible the great advantage of efficient LIST OF REFERENCE NUMERALS
vertical takeoff combined with efficient high-speed flight. 40
Readers will find further advantages and objects of the 10 velocity and vector
invention from a consideration of the ensuing detailed 12-pressure distribution
description of the actual key mechanisms for assuring the 14 tip vortices
intended plane of actuation, thus the steering of the Meta 15 induced downwash
Element, and the detailed description and accompanying 45 16 helix angles
drawings of proposed methods, processes and devices. 18 slipstreams
19 Froude Disc
DESCRIPTION OF DRAWING FIGURES 20 disc of actuation
FIG. 1 shows propeller beta angles and tip loSS drag 21 turbulent boundary layer
vector of prior art 50 22 propeller inflow contraction
FIG. 2 ShowS propeller inflow contraction, and upwash 24 pressure differentials acroSS disc
time dependency of prior art 26 Velocity change
27 secondary flows
FIG. 3 shows propeller force field diffusion of prior art 28 parabolic envelope of maxima
FIG. 4a Shows upwash deficit of prior art 55 30 standing vortices
FIG. 4b shows Meta Element application to prior art 31-boundary layer
FIG. 4c shows Meta Element wave dynamics 32 helical resonators
FIG. 4d shows Shear plane/boundary layer interrelation 33-spiral cam
FIG. 5b shows Meta-Element vector-shear of boundary
34-hysteresis cycle footprint
layer 60 35-resonator fragment
36 helical physical elements
FIG. 5c shows Meta-Element dynamics and Archimedes 37 inflow funneling
Spiral nose on conoid Surface 38 physical element Sequence
FIG. 5d shows Meta-Element phase construction and 39 plane of rotation
isocline dynamics 65 40 lead element
FIG. 6 shows Meta-Element vs. helical element isobar 41-laminar-boundary layer
Sector of diffusion 42-reference datum location
 US 6,948,910 B2
35 36
43 Meta-Element stream tubes 2. Axial slipstream oriented boundary-lubricity-artifact
44-path wavelength virtual profile sections 78 aligned with the indefinably, but
45 Reversal or starting vortex Slowly twisting Slipstream reacting to frictional and dynamic
46-incidence wavelength tangential forces.
48 harmonic Sub cycle Sequence It thus becomes the task of analysis to determine the relative
49 tail Section spiral corrugation predominance and effect of Such relative motions, and their
50 parabolic envelope of amplitude maxima fluid particle-relative motion artifacts. AS only the precise
51 phase plane Spiral determination of inflow vectors can ascertain whether the
52 boundary layer removal by Suction device functions as an helical Archimedes Screw or as a
53 spiral worm gear wave device relying on sliding interaction with the
54 axial retrogression Slipstream, -or as a hybrid combination thereof , the
55 starting or reversal vortex effect of the device on the angular rotation and Velocities of
56 inflow vector force diagram the Slipstream must be determined to at least Statistical levels
57 compressibility shockwave of accuracy.
58 impulse intensity 15 Unlike the propeller, where Such motion is constant, in
59 phased energy recovery coordinate frames that are artificially fixed, the wave-based
60 inflow vector shift device presents relatively much greater difficulties of analy
61 surface of discontinuity sis of flows that by their very nature vary in three dimen
62 Meta-Element wake rotation Sional Velocity and direction.
64 conventional wake rotation As all wave-based devices moving in fluid should-by
65 moving belt boundary layer control definition-ideally cause axial accelerations as a response to
66 exponential envelope of maxima their rotation, this analysis must therefore include the effect
70 sine wave particle orbits of blade profile wave-path motion on particle orbits affecting
72-cosine wave with odd numbered harmonics series inflow vectors.
74 prior art shape Sequences 25 Generally, Such wave motion may be two dimensional and
75 helically oriented physical sections very slow-as in the meandering of rivers or long wave
76 fluid inflow vector gradients oscillations of Ships, or very rapid, and three-dimensional
78 axial slipstream oriented sections as in the resonant motions of hummingbird wings or insect
79 phase lag flight-where Systems of wave trains create highly ordered
80 out-of-plane viscous forces energies and particle motions that can be modeled using the
81 Sweepback angle differential equations of wave mechanics.
82 resonance cycle pressure gradient wave In the case of rotating wave-generating devices, these
83 major cycle phase lock pulse must generate Such undulation of their reaction mass by
84 plane of actuation progressively varying their blade profile shapes along an
85 out-of-plane dynamic forces 35 undulating wave path that they progreSS along, in order to
86 traveling hysteresis-term pressure wave induce intended undulating accelerations. The difficulty of
87 forward motion component of axial progression analysis of this wave path is thus the imprecision implicit in
88 conventional disc of actuation the indefinable twisting of the multitude of axial shear.
89 axis of harmonic component flexion Unlike the propeller, which creates motion along helices
90 actuator disc 40 of a Supposed Euclidean cylindrical coordinate System, a
92 Meta-Element actuator volume annuli wave device must-by definition-create motion along
94 Meta-Element Solid of actuation these shear planes whose canonical coordinates are a func
96 counter rotating tip generators tion of three dimensional particle-Velocity inflows, and thus
98 leading edge cuff Subject to periodic-function-related coordinate translations.
99 counter rotating body of revolution 45 As shown in the prior art of the top left of FIG. 11, blade
100 air pump profile Sequences 74 following Such a designed wave
101 lateral force aerodynamic servo path, -here a simple Sine wave-generating low and high
102 feathering axis servo motor frequency potential and kinetic energies acting with precise
103 tuned mass balance regularity only on the time Series phase plane-tough not
104 mixing foil cascade 50 necessarily in Cartesian Space-, interact with these ener
105 Meta-Element hydraulic turbine gies in a phase related interchange between potential and
106 vented plenum kinetic momentum to create bound Vortex local particle
108 bi-directional exit orbits 70. As seen, these reverse polarity every 180 degrees
110 variable pitch feathering axis mechanism of this motion along with the reversal of the orientation of
111 rotatable variable pitch spinner disc 55 the profile.
112 axially oriented stators If Such motion's impulse-momentum interchanges occur
114 layer construction in the proper phase relationships, Such Systems propagating
115 air entrainment passage in fluid become coherent reverse-Karman-Vortex Systems,
SOLITON META-ELEMENT DETAILED where the Square law of frictional dissipation causes gradual
DESCRIPTION
60 decay of Oscillation amplitudes Some interval after passage
of the blade.
To illustrate the detailed analysis of out-of-effective-shear AS all rotational devices creating lift must function by
plane forces for any wave-based device, I now refer to the creating and benefiting from bound Vortex orbital motion,
bottom of FIG. 11. All such devices create useful forces by. the problem of analysis becomes Similar to the process of
1. Helically oriented profile sections 75 aligned with 65 phased meshing contact of conjugate gears whose paths of
known angular and posited, estimated axial Velocities, Slid rolling contact is specified by phase related equations of
ing through the axial Shear plane, creating motion.
 US 6,948,910 B2
37 38
Thus it is the combined frequency spectrum of orbit of the Higher values of turbulence drag and wake pulsation must
great mass of particles affected by these time dependant occur as a consequence. This process then entrains further
energies that affect the actual fluid inflow 76 of wave-based Self-reinforcing feedback cycles of drag-based phase lag and
devices. Different periodic waves thus present different additional helical Section load.
inflow distributions. AS the effort to produce the database of operating
These waveforms may be simple as in a pure Sine wave, co-efficients of efficient families of foil sections can involve
or contain the high frequencies of the harmonic spectrum of man-months of effort by highly skilled engineers, it can be
complex waveforms 72 here a saw tooth cosine harmonic appreciated that the modeling parameters of a single Such
expansion compound wave. Section-operating in Statistically indefinable flows
AS the computation of the expected efficacy of any fluid cannot be easily or economically determined.
dynamic device has to start with the determination of the AS Such a device needs a great multitude of Such Sections
fluid inflow paths in order to properly align its working for its continuum of motion, its fluid interactions can be seen
“blade” profile sections with the effective plane of to be exceedingly difficult to model using the limited con
actuation-this ideally being the axial plane in the case of ventional tools of fluid dynamics. Thus, any advantage for
wave based devices-it must therefore take into account 15 Such a device over the propeller is difficult to State to
these time-based flows, as well as the time invariant rigorous Standard, as the feedback-based development cycle
Archimedes Screw co-ordinate flows that the helically for such a device is effectively closed.
aligned Sections 75 experience Simultaneously. Despite their Stated inefficiencies, propeller based devices
These well-documented facts give an idea of the com have evolved to relative Sophistication by offering predict
plexities of analysis facing the wave-based device's basic able motion relative to predictable cylindrical coordinates
mechanism of operation, which can be Summarized as the using predictable profile Sections. Their commercial Success
difficulties of determining: is due to a simple model based on a simple motion involving
1. Inflow vector stability heavily researched profiles, which allows increasingly
2. Plane of Shear tangential momentum transfer due to evolved iteration based on feedback, in a field of endeavor
rotation 25 where the complications of possible interactions very
3. Phase lag stability factor quickly lead to inscrutability.
AS these devices must all function by creating quantifiable Due to the foregoing reasons, and despite their promise,
and Stable States via Stable planes of interaction with time wave devices of prior art Suffer from an intrinsic lack of
based energies propagating linearly, the momentum import predictability due to the mutual interactions of an excess of
upon this plane resulting from the physical Surface's sliding degrees of from of analysis.
Shear force and preSSure distribution must be ascertainable, To overcome these difficulties, Meta-Element hypothesis
lest this orientation become unstable and the resulting tan contains:
gential excursions of the plane of Shear 84 cause linear wave Means of radical Simplification of coordinate relative
propagation to weaken or become disordered. motion
To show this graphically, the greatly abridged Sequence of 35
Means of enlisting the vast performance database com
fluid dynamic profile shapes 74 making up the infinite Series piled for public domain profile Sections
of continuous variation of profile Sections of Such undulat Analytical methods to determine the influence of wave
ing devices of prior art that uses variations of a simple Sine system orbital flows on the known hydrodynamic influ
wave path in order to achieve its goal of reaction mass ences affecting Slipstream rotation.
undulation, any-even Small-excursions of the 40
These latter hydrodynamic influences include:
multiple -non-parallel-planes of actuation, the axial
Shear planes, immediately causes a wave interaction with a 1. Viscous entrainment of the boundary layer exporting
physical blade element section 74 that is finitely out-of momentum to the dynamic flow 80 at the tail.
phase, a Section of a contour that is not optimized for the 2. Tailoring of the tangential dynamic forces resulting
actually prevailing inflow vectors, and fluid angular 45 from pressure gradients including the effect of Sweep
momentS. 81 dynamic force resultants 85
Computational Fluid Dynamics has no tools to ascertain 3. Tail-Section traveling pressure gradients 86 affecting
these vectors this time. Therefore these shapes must be tangential flows
designed for motion along posited Cartesian co-ordinates AS the interaction of these influences is mutual and
paths in time invariant Space, rather than the time-attentive 50 complex it becomes desirable to Simplify the degrees of
orbital flows of the -unfortunately unascertainable-actual freedom to cull these possible interactions.
local wave particle motion. Therefore all interactions can be AS both Viscous drag and lift coefficients at defined States
seen to exhibit the overwhelming likelihood of developing of Viscosity are available as performance curves in condi
Significant phase lag 79 causing turbulence and its shear tions of steady-state flow for published foil section
plane deformation in the direction of rotation. AS different 55 coordinates, it becomes necessary to design wave paths of
profile shapes create different shear-plane deformations, motion of Substantial linearity that in turn generate linear
indeterminate Shear planes cannot be unified to a single inflows in order to be able to employ foil profile-sections of
reliable plane of Shear, making precise analysis on the basis known parameter. This results in the ability to Specify
of relative motion very difficult. precise shapes relative to a precise frame of reference using
If such individually deformed planes of shear 84 move 60 mathematic algorithms and enabling feedback-based evolu
unpredictably along with Such undefined Sum of drag-caused tion.
total twist of the Slipstream-as it accordingly must-, the To ensure Synchrony of the wave path mediated processes
effective wavelength of particle orbits must also change occurring in these different frames of reference, the Soliton
indeterminately, and the efficient mechanism of linear wave Meta-Element method uses Several Strategies:
propagation must become disabled. 65 1. To clock the energy conserving mechanism of a
This imposes indeterminably higher dynamic loads on the time-referenced System of oscillation, it creates a pro
helical sections 75, cess cycle-the Soliton Meta-Element-to induce
 US 6,948,910 B2
39 40
wave phase lock through forced System feedback by by these procedures to be negative, i.e. that thus pro
means of major path cycle 83 and minor profile-relate vides minute thrust.
cycle forced resonance pulse 82 attentive to hysteresis 2-AS it is not limited by inertia, its motions are not limited
parameters of the oscillating fluid continuum. to those waveforms generating Simple Harmonic Motion
2. To ensure Significant linearity of flow and of “circula but uses compound periodic forms containing high fre
tion orbit momentum, it chooses a major-cycle wave quency harmonics.
form 72 that provides substantially linear conversion of 3-As it is defined by the boundary sheath that partitions
dynamic flow from its process of shape change, it can be
the combined angular velocities of this waveforms made to parallel any path definable by a periodic function,
Fourier harmonicS expansion to result in linear inflow change shape, disappear as well as reappear to this flow,
velocities 76 through the means of the combined orbital as well as coalesce into another Meta-Element.
motion of a large number of Fourier Spectrum harmonic The Meta-Element thus is seen to form a link between the
wave components. time-series phenomena and the Blade Element tools of fluid
3. It imports the well researched mean chords and enve dynamics, whose methods operate with Euclidean Solids.
lopes of foils of known parameter and disposes them The methodology encompassing these parameters of
15
relative to these now known particle paths, using con influence is depicted in the flowchart of FIG. 12.
ventional Blade Element theory. WATER PROPELLER-DETAILED
4. To ensure the stability of the effective shear plane, it DESCRIPTION
uses a calculus of variation of known parameters as Based on the foregoing methods and Strategies implied by
affect out-of-plane flows, as well as precise Meta the Meta-Element interaction with the axial shear plane, I
Element tail preSSure gradient reductions 86 through a now detail the design process resulting in the manufacture of
hysteresis parameter based tail isocline acceleration a water propeller.
favoring Substantial low drag flow. Having chosen a waveform that assures Substantially
This latter traveling isocline-based Meta-Element tail linear inflow paths, the design of the proposed water pro
flexion, as previously described in FIG. 5c is a key device pulsion device follows a Sequence of Steps to arrive at a
useful for moderating a heretofor-inflexible parameter dic
25 design conforming to the desired specification.
tating the limits of pressure gradient to a foil recovery Such conventional locations might include but not be
Section shape. limited to-the following:
Diameter
By using a period of flexion within the hysteresis inertia Angular Velocity
memory response time of System of oscillation, the dynamic Advance Ratio/Pitch
effect of all transverse motion vectors of symmetry 66 Area
cancel, and only a phase-lagged traveling pressure wave 86 Meta-Element Axial Retrogression
is discernible to time-based flow. This systematic time series Desired Profile
shape change allows for hysteresis-based regression of Boundary Layer Interactions
phased shape change back to the published profile 35 Hub Geometry
co-ordinates with their known values. Torque
This traveling pressure wave acts to Scavenge accumula Slip ratio
tions of boundary layer material and ensures the precondi Anticipated dynamic forces
tion of greater extents of laminar flow. The waveform and actuation plane stability factors of
To mediate this process, the Meta-Element implements 40 FIG. 12 are determined. When these are ascertained, the
these functions by two physical devices that-upon multi-loop iterative design recursion FIG. 12 begins with
rotation-work together to share this division of labor. these Steps:
1. A spiral cam in the form of a profile leading edge that 1. Based on the desired diameter, area and hub diameter and
ensures faithful phased meshing with phased orbital length, the anticipated dynamic forces, the radial limits of
flows as modified by fluid acceleration gradients, that 45 the annulus of rotation, as well as Meta-Element retro
also createS precise profile envelope contours and gression are determined to result in a Archimedes Spiral/
that-importantly-enSures major cycle phase lock Screw 2-dimensional wave form.
through a highly localized and forcibly clocked phase 2. Based on the annulus and torque/Slip ratio the number of
reversal pulse. lobes are ascertained
2. Resonant element phased cycle Sequences affixed to 50 3. Based on this, the Meta-Element foil selection as to chord
this cam that restores the higher harmonic wave fre length and foil shape is made and the representation of
quencies damped out by its own passage, by reconsti this foil as well as its mean chord is Stored as a collection
tuting them via resonant entrainment as well as by of data points.
phase locking and rejoining these harmonic high fre 4. The waveform is now represented as a time domain
quency energies to the basic wave cycle. This resonant 55 equation or a collection of data points. The incidence and
entrainment also has the assignment to provide Small path wave differential angles are now calculated.
Scale impulse oscillating System feedback to offset the 5. Based on anticipated System dissipation, the logarithmic
frictional dissipative constant as deduced from the increment of the transverse harmonic motion parabolic
phase plane logarithmic decrement of wave amplitude envelope of tail flexion amplitude maxima is chosen.
attending known Viscous dissipation. Additionally, by 60 6. Based on anticipated local flow velocities on the foil
providing pressure gradient tailoring through traveling Suction and preSSure Side the wavelength gradient of the
wave tail flexion 82, low friction and steady shear plane traveling spiral tail corrugation-or differential corruga
predictabilities are maintained. tions is chosen to effect boundary layer transport.
To summarize the concept of the Meta-Element: Detailed Graphical Functional Analog of Coordinate
1-It is the statistical dynamic flow contours delineated by 65 Transformation Algorithm
the physical boundary layer, it contains parameters of 1.To construct the Meta-Element cycle Sequence, the chosen
waveform, as well as a coefficient of drag that is designed profile Section is first remapped as a mean chord with
 US 6,948,910 B2
41 42
chord-normal rays to locate the envelope coordinates for 7. This database is now duplicated in the desired angular
Subsequent shape change. This is shown on lower left of increment to result in the desired number of lobes.
FIG. 5d under the title of “wave length expansion”. Next 8. Total force integrations can now be made, ascertaining lift
the harmonic wavelength increment is represented as by transferring Meta-Element dynamic forces to the tan
expanding control points along the aft chord, here desig gent of inclination of local Surfaces. Wake rotation and
nated as points "a'-h' as envelope ray origins. These are effective actuating plane is similarly determined and
derived from the plotted parabolic curve that is defined by varied by Sweep and tail flexion in an iterative recursion.
points “a'-h'. Next the harmonic amplitude increment is 9. When the above calculus of variation is complete, the
represented as rays, here designated as rays "1-8” under completed data points are Suitably Smoothed by interpo
the title of “amplitude expansion curves”. Next, these are 1O lation via the use of a cubic spline or other means. They
arrayed in regular angular increments to form the ampli are then provided a Suitable hub attachment and Subse
tude expansion logarithmic Spiral. AS is shown in phase 1, quently machined by CNC mill.
the logarithmic spiral center is aligned with the mean 10. If their is no axial retrogression, all data points parallel
to the rotational plane can be separated out in the Specified
chord and all mean chord control points along with their increments to conform to the desired material thickness to
envelope rays, are displaced chord-normal by the chord 15
be used in later laser cut layers of the blade. This involves
normal relative location of their points-of-correspondence the additional Step of connecting the inner and outer
on the logarithmic spiral. Now their envelopes are recon envelope data points by means of a cubic spline curve-or
Stituted by the use of cubic Spline curves of interpolation. other means-as well as mapping the Separate keyed hub
Next, the Spiral is turned by the chosen equal increment layer with its connecting Support spokes to the inner nodal
and the described process is repeated, until all 2 PI radian points of each propulsive element layer.
phases of the Meta-Element cycle is complete. The fore 11. In case of axial variance this former method is varied to
going process description of necessity is Schematical and result in a 3-dimension Section plane Substantially parallel
devoid of Some mathematical detail due to the needs of and normal to the leading edge that is used to Section the
the presentation format. Many algorithmic variations of database into convenient layers that can contain Structural
this Scheme are possible. In particular, the shape varia 25 recesses contributing to Strength per weight as shown in
tions controlled by the process can be applied to envelope FIG. 20, or act as an air plenum for later introduction of
contours collectively, as well as to the individual sides of laser-cut Surface orifices enabling friction reducing
the profile tail section allowing differentially tailored minute air entrainment 115.
accelerations on the Suction and preSSure Side. 12. This is repeated for all layerS until the complete propul
. The Cartesian coordinate plane is transformed to the Sive element data points including hub and Support Struc
ture exists as a data base.
cylindrical coordinates of conoid(s) of revolution with 13. Low volume manufacture of this device could consist of
sides defined by the described more cycle equiangular CNC controlled laser cutting of all keyed layers, then
saw tooth cosine periodic function of full Fourier har Sliding them onto their keyed hub, mounting them in a
monics. This is shown on the bottom of FIG. 7d with gantry, brazing them together in a foundry and finally
coordinates of co-latitude and azimuth-relative longitude. 35 powder coating the results with an abrasion resistive, low
. The mapping of the foil mean chord nose Section is friction coating that eliminates all Surface irregularities.
asSociated with the inboard phase angle of conoid-relative Given the flexibility of design using these methods,
longitude and latitude coordinates. The first Meta Element innumerable variations as to number of lobes, reversal
phase fragment data points are associated with this nose variations and axial retrogression become possible. An
Section parallel to its plane of longitude and at chosen 40 example of such a propeller is shown in FIG. 14. The
fixed orientation as is shown. Now the process is repeated after-body corrugations-embodying the Meta-Element har
for the nose Section, which is aligned with the next monic Sub cycle-have been greatly exaggerated to provide
incremental plane of longitude and next incremental line graphical clarity.
of latitude and the Sequential numbered tail Section FIG. 14a shows a propeller displaying exponential axial
Sequence of integral multiple phase angle relative to the 45 retrogression on the shear plane with the Meta-Element
change of conoid angle of longitude. This is repeated as proceeding along a path in a single direction.
shown in Such a way that the mean-chord-normal rays of FIG. 14b shows a propeller displaying linear axial regres
nose Section coordinate points always stay equidistant and Sion with the Meta-Element changing ends at the radial
equiangular to the tangents of the Sides of the conoids limits and reversing orientation, as well as its direction of
even during the reversal Sequence, one phase of which is 50 motion.
shown at the top of the image of back-to-back conoids. This additionally improves the propeller's resistance to
This is continued until the entire axial plane path as shown foreign object fouling and also makes its shape leSS injuri
at the top of FIG. 7a-7c under the title “axial progression” OUIS.
and “axial retrogression' is complete as a three dimen WIND TURBINE DETAILED DESCRIPTION
Sional dataset. 55
. With mean chord data points established, the envelope The proposed wind turbines are devices of high lift to drag
contour is collectively or individually recreated by the and low downwind force, and as such relatively free of the
polar ray distances and tangents associated with the economic imperatives that presently dictate size and design
corresponding local chord data point, using cubic spline configuration of conventional turbines. They thus offer
CUWCS. 60 unusual design flexibilities, allowing them to address Some
. This is repeated for every desired phase angle increment of the aesthetic considerations that presently prevent public
with the exception of the Starting and reversal Vortex acceptance in other than rural Settings. The main objection
Sequence, which are created by a process of phased to conventional turbines in urban Settings is the Overpow
interpolations between the phase States to be connected. ering bulk of the installation required to Sustain the high
. The total area of helical elements is analyzed for Viscosity 65 loads of anticipated wind extremes.
and incremental drag and this integrated value is used for If, in order to generate an economically meaningful
System dissipative constant. quantity of power, rotor Size and tower dimensions can be
 US 6,948,910 B2
43 44
kept to dimensions that could unobtrusively blend in with Speeds. AS these broad inner blades are lightly loaded,
Scenic character and architectural elements, applications and do not need to transmit torque, they can be made
previously dosed to wind power would become possible, as of inexpensive nested tubular materials, rigid sheet
these are presently constrained by Zoning permit leading edge cuff 98, tensioned trailing edge Strip, and
The Second most important consideration affecting wide fabric envelope. These slow-turning blades can Simply
Scale urban adoption is the noise and the Visual impact of the be Scaled to length in order to achieve constant power
Stroboscopic flickering of the Spinning blades. All of the output from any reasonable wind resource and as is
versions of the proposed turbines have no gearbox and shown on the accompanying graph in FIG. 16a,
open-tipped blade and are therefore unusually quiet. They designed to develop full output at low wind Speed. AS
present visually unified Slow and inherently non-flickering wind increases, these inner blades progressively
Spiral motion. Additionally, using slender fiberglass towers, decrease their angle to the wind under electronic con
these devices can Store the energy of gusts in Small Swaying trol. AS the Small actual working rotor blades automati
deflections. Such motion-reminiscent of trees-can more cally decrease their angle of attack in high wind
easily present harmonic Scenic counterpoint and integrate Speed-as is shown in the vector decompositions of
with dusters of herbage and no longer dominate by over 15 FIG. 13c-they have no need to cease operation in high
whelming contrast or dashingly obtrude upon the Scenic wind. Along with these blades, inner hoop-outer hoop
quality of landscape, or its pastoral character. 99 counter-rotating working elements of FIG. 16b
Public aversion to Stark, massive and industrial monu actually make a Small contribution-due to their
described duct-based forward force vector
mentality upon treasured and unique landscape character is efficiency-to the tangential force necessary for this
universal and thus a likely motive behind negative Zoning motion. Optionally, rather than driving a generator,
board rulings. If this is So, Scales that do not overwhelm these devices intrinsic high angular vet and high
landscape Scenic elements, forms that are rounded, and output makes possible the economic benefit, weight
motions that are perceived as sinuous and slow, cultural advantage and fail-safe operational Simplicity of driv
evocations that are playful, quaint or intriguing do not 25 ing light Scroll, centrifugal or Roots compressors fed
present the harsh cuts of massive angularity that presents by Stagnation preSSures or air pumps 100 that preSSur
Such inharmonious juxtaposition with the curvilinear forms ize the tower as a storage plenum, and thus provide an
and Sinuous motions of nature.
inexpensive energy-leveling and energy-storage
Given these devices relative freedom from purely eco mechanism. On a cost-benefit basis, this Scheme may
nomic imperatives, the vast talent pool of landscape outweigh the moderate loSS of nominal efficiency that
architects, urban planners and Visual artists-well practiced accrues to air compression VS. direct electrical genera
in overcoming objection by providing communities with tion and thus also allows a conveniently sited, acces
aesthetic asset-, can be enlisted to address these hostilities, Sible generator interface at ground level, especially
and thus wind farms proposing these devices will likely Suited to variable conditions of wind. AS output power
experience less resistance. 35 of any turbine varies as the third power of the apparent
These wind turbines allow many design variations that wind Speed, the Meta-Element computer Simulation of
take advantage of the device's high output to downwind tip elements of moderate 8' radius, using inexpensive
force and Structural qualities giving great resistance to 40' blades, predicts unprecedented cost benefit, com
Coriolis and other destabilizing forces: pared to any other method of power generation, let
1. As shown in FIG. 15, turbines of unprecedented scale 40 alone by conventional wind turbine. Such a turbine has
may be built of modular components loaded mostly in the advantage of low initial cost, low maintenance,
tension, using very light and efficient Meta-Element infinite adjustability via electronically controlled servo
catenary half loops fixed upon aerodynamically envel loops, unprecedented cost-benefit in Very low wind
oped rings of tubing tensioned by cable stayS. Such a Speeds and no need to curtail operation in high wind, as
device, being relatively insensitive to gusting as well as 45 the turbine is progressively Sowed via a simple blade
tolerant of very high wind Speeds, directionally feathering servo loop 102.
unstable inflow as well as tower shadow is a self 3. The variant device shown on the left of FIG. 17 uses the
aligning device. Not shown is the aerodynamic fabric Same slow rotation of wide-chord high-Solidity of many
hub that forms its inner hub Surface as described in blades, which allows operation in deeper waters than is
FIG. 5c. It has a greatly expanded operating envelope, 50 presently economically feasible, out of Sight from the
making Sites of lower wind Speed economically mainland. This device would mount on an empty and
feasible, whereas its spiral motion and low noise foot ballasted wave-piercing Steel or fiberglass tube, con
print make it leSS objectionable for location in Sites of Structed ashore and towed to the Site and moored by use
higher population density. Not shown for Visual clarity, of inexpensive fiberglass cable/cement block catena
is the possible fabric aerodynamic hub enclosure of 55 ries. Due to the aforementioned Self-reefing qualities,
FIG. 5c and possible aerodynamic anti-twist tail-vanes. very low downwind force-and therefore acceptable
2. FIG. 16 shows a turbine deploying the actual power heeling moment-and unprecedented Size would
generating Meta-Element turbines 96 at the tip of many enable massive economic benefit in its ability to gen
aerodynamic high-Solidity multiple blades that rotate erate onboard hydrogen at vast Scale. The production of
slowly and have the Sole purpose of generating the 60 hydrogen is presently as expensive as it is energy
tangential Velocity that concentrates and thus funnels intensive. Physical law stipulates that it takes more
the momentum of the diverging much larger inner energy to convert Seawater to hydrogen than is con
Stream tube into the operating-disc edge high Speed tip tained in that quantity of produced hydrogen itself. The
region. This results in very high apparent wind Veloci cost-basis is thus mainly determined by the cost of
ties at the actual working area of the turbines and that 65 input power, and makes Sense only if Such input power
therefore enables extremely cost-efficient generation of is inexpensive. AS the automatic process-control tech
power especially in Sites of very low average wind niques for generation of hydrogen by electrolysis has of
 US 6,948,910 B2
45 46
late approached 90 percent efficiency, and the ability to have the potential of Satisfying the present level of the
store it at 5000 PSI is commercially available, the World's electrical power consumption many times over.
expense of long distance electrical transmission would AS the operation of iceboats and land yachtS has shown,
be avoided in favor of regular Supply ship visits to what any device that generates-and benefits from-bound
is essentially an offshore hydrogen factory that collects Vortex pressure waves advancing against prevailing ambient
free power, uses it to convert Seawater to deionized inflow, -depending on its lift to drag ratio-can generate
water through reverse osmosis, converts that in turn to very high differential pressures from the enhanced apparent
hydrogen, preSSurizes it and Stores it in transferable velocities resulting from the vector addition of these relative
preSSure vessels. These would be exchanged by regular
Supply vessel Visits. Most of our landmass is Sur motions. These differential pressures can be many times the
rounded by vast, relatively shallow, windswept preSSures possible from nominal ambient Velocity as mea
expanses of ocean, outside Sea-lanes of navigation, Sured by the Stationary observer, resulting in measured
much of it under lease to energy exploration enter competition iceboat Speeds of over 140 mph, this being
prises. Such leases would become exponentially more many times the prevailing wind Speed.
valuable, if every Square mile of this leased area turned 15
AS the resulting dynamic forces are related to these
out to contain the energy equivalence of a major Velocities exponentially-by the Square of the Velocity-the
discovery of fossil fuel. This would as well be a useful vector addition of Meta-Element relative motion to even
application in Shallow coastal waters and could addi moderate ambient fluid Speeds can be seen to potentially
tionally Serve as a navigational beacon in low visibility generate significantly higher resulting forces.
conditions. The variant devices shown in the middle
and on the right of FIG. 17 achieve this higher apparent As the Meta-Element turbine's detached pressure wave is
expressly designed to advance against prevailing flow, this
Velocity by a meshed countervailing oscillation enabled Same phenomenon is used to advantage to extract energy
by passive tuned Spring mass balance 103, Such motion from the flows of very low velocity prevailing in rivers, tidal
entirely controlled by electronic Servo loop activating flows and Shore-bound incoming ocean gravity wave ellip
either tail Vane or feathering axis Stepper motor control. tical orbital flows.
Such installations would be useful in areas where any 25
level of noise, or blade passage proximity might be Taking advantage of the recent revolutionary advances in
objectionable. The device on the right shows how this Silicon-based power conditioning technologies and
arrangement might be used to evoke cultural themes advanced polymers, the following low maintenance Schemes
that have demonstrated greater public acceptance, Such of ultra-low environmental impact can provide significant
as the traditional Dutch windmill. This mechanism point-of-use electrical power generation capacity and peak
would be implemented using slow Speed counter rota demand leveling through its built-in Storage reservoir
tion against pairs of tuned compression or torsion capacity, particularly in locations where electric power
Springs incorporating Stops that Stores and returns infrastructure is undeveloped.
kinetic energy. The entire motion would be controlled 1. As shown in FIG. 18, a Meta-Element turbine 105 is
by electronic Servo loops. 35 interposed between the flow of an intake close to the
An important additional feature implicit in all of the riverbank that empties into a Stream-wise concrete
foregoing air turbine devices has to do with its purposeful Venturi tube based constriction exit finitely raised into
addressing of certain public objections that may in fact have the high velocity flow of the central channel, which
a basis in physiological Self e involuntary conditioned assists wastewater ejection via beneficial preSSure gra
response. 40 dients. The conduit for this flow is ordinary plastic
Such resistance is generally represented is having purely Sewer pipe. The exit is cast from concrete. Care is taken
esthetic basis, but may also involve a reaction of distrust to to prevent silting by a mixing foil cascade 104 ben
the massive turbine blade, the whistling tip descending at efiting preSSure recovery and means preventing down
Stream Sift accumulation.
Velocities of up to hundreds of miles an hour. Since Such
blades have been actually been thrown several hundred feet, 45 2. FIG. 19 shows a variant of this scheme. A plastic
I believe that our conditioned reflexive response to such conduit Spanning at least 2 wavelengths in order to
devices may well predispose uS to unconscious hostility and minimize lateral displacement wave drag forces and
therefore condition us to limbic-System-bred esthetic dislike, aligned with prevailing wave motion, is moored off
by mechanism of conditioned response. The Meta-Element shore at appropriate depths and provided with many
turbine addresses these latter public resistances through 50 Self aligning Meta-Element turbine devices running in
design features that Substantially eliminate the Sense an anti-fouling protective plastic conduit Venturi
experience of overwhelming Speed, and of perspective shaped duct, powering simple, fail-safe and redundant,
disjointed motion of Separated massive elements. high molecular weight injection molded plastic dis
HYDRAULIC TURBINE SYSTEM-DETAILED
placement pumps rotating around molded spherical
DESCRIPTION
55 bearings that feature one way plastic hinged flapper
valves. In this way, both tidal directions can be used to
As the Meta-Element turbine is a device with the novel pump this flow up to an onshore reservoir made of a
advantage of unprecedented parameters of lift to drag-or banded vertical plastic pipe array of Suitably Sculptural
torque for downstream force for a device of rotation shape that feed the actual Meta-Element turbine shafted
Similar to the kind of efficiency advantage that a high 60 to the electrical generator. Wastewater flow can be
performance Sailplane displayS when compared to glide assisted by a vented plenum 106 and a Venturi based
path angle of the Space shuttle-it is uniquely Suited to bi-directional exit 108 similar to the variant of the
exploit the vast potential kinetic energies of the World's very previous drawing.
low velocity-2 feet per Second or more-natural water To Summarize the Benefits of the Meta-Element Hydraulic
flows. 65 Turbine:
Such energies-if truly exploitable on a Sound economic As a device exhibiting high values of lift-to-drag, and thus
basis and in an operationally simple and robust fashion torque to downs m force, it functions Superbly as a low-head
 US 6,948,910 B2
47 48
hydraulic turbine. This quality additionally allows the Meta and other dynamic forces. In the absence of inner loop
Element turbine to focus and thus funnel the kinetic energy counter rotation, considerations of Stage Sealing will need
of a large Volume into a very Small, and economic operating the addition of compressor case Supported axially oriented
area. This opens the possibility of tapping the inexhaustible Stators 112 in the nesting shape of the half loop compressor
Solar powered flows of the earth's water based weather element of FIG. 20 to prevent tangential flow and reversal in
cycle, at point-of-use, by Small local modular increment, and the tip area. This device's excellent suitability for weight
without resort to expensive and ecologically disruptive Saving layer construction, diffusion bonding, and EDM post
dams. This can bring vast economic benefit particularly to machining facilitates Strength to weight optimization.
areas of low levels of economic development and infrastruc
ture with relatively low levels of investment, incrementally 1O
TURBINE ELEMENT DETAILED
expandable as additional need arises. It can additionally DESCRIPTION
provide the overwhelming majority of populations that
inhabit river basins, or near tidal flows, or Seashores non All design features of the compressor element-except
controversial peak-power energy resources without environ for substitution of Meta-Element Axial Retrogression-are
mental impact and with relatively Small economic expendi incorporated in the construction of the turbine element. Just
ture. 15 as in the air turbine, due to the Substantially greater tangen
As a device of fixed geometry, built-in resistance to tial forces generated by the element orientation due to axial
fouling and of great Simplicity, it is Superbly able to exploit progression, inner loop counter rotation, or a turbine shape
the corrosion, marine bio-adhesion and friction controlling nesting Stator Stage is indispensable.
capacities of certain modern high-density polymers. The major differences are in the use of materials that have
Using Such injection molded plastics in mass production, greater thermal resistance as well as the built-in design of
Such devices-and their Systems-promise to provide a transpiration mass flow through the layered construction of
cost-benefit that greatly exceeds that of even the Meta the turbine element 114, of FIG. 20, which includes a
Element wind turbine.
Additionally, as this estimate of operational cost-benefit is plenum to facilitate the introduction of the cooling film.
based on a very conservative computer model that has been Stage Sealing may be accomplished generally as in the
validated by measurement of a functional prototype, this
25 compressor, or via a single Substantial Spiral, film-cooled tip
Scheme provides a uniquely powerful and unprecedented extension 116-here exaggerated for clarity-riding in a
economic argument for the adoption of methods that by their mating casing depression.
very nature are not only economically but also ecologically This all too brief description is well aware of and makes
highly beneficial, all the while purposely addressing other no Small matter of the many open questions thrown up by
well-known political and cultural antipathies based on this format-constrained attempt to introduce a radically
esthetic obtrusivity and other intangible resistances by Sim novel concept in a field as Sophisticated and technically
ply hiding the devices underwater. mature as the design of the modern gas turbine.
AIR PROPELLER AND FAN-DETAILED These unusual geometries undoubtedly introduce difficult
DESCRIPTION
35
technical challenges especially in regard to low and high
Using the same methods and parameters of design as the preSSure compressor and turbine counter rotation, Stator
aforementioned water propeller, -including Meta-Element arrangement and tip Sealing.
Retrogression-the three-dimensional database of an air The predictions of Substantial efficiency gains by the
propeller is constructed by taking the design constraints of conservative Meta-Element computer model, as well as the
the relative preponderance of centrifugal and other dynamic 40
considerable Structural benefit of the centrifugal catenary
forces into account. Thus the air propeller will incorporate shapes intrinsic relative immunity to the existing major
lobes of close to centrifugal catenary curvature to minimize problem Syndromes of blade fatigue, blade failure and
bending forces. It will additionally incorporate Substantial heat-tolerance Stricture, may be Sufficiently promising,
Meta-Element boundary layer Scavenging corrugations par however, to consider these additional benefits:
ticularly in the outer reversal portions to minimize transonic 45 1. Gains of unusually high efficiency through the opti
buffet In order to minimize mass, profiles become increas mizing of force Vector, Smooth non-pulsating diffusion,
ingly thin in the outboard Sections. Such a propeller may maximizing of inflow vectors using axial progression,
take many forms and may additionally be controllable in allowing widened operating envelopes
pitch. The lower half of FIG. 20 shows a fixed pitch 4-lobe 2. Unusually low levels of noise, and Significant reduction
embodiment of small axial retrogression described in FIG.
7a using lightly loaded helically oriented inner Supporting 50 of Specifically low attenuation noise radiation spectra.
blade-spokes to Support the catenaries of the actual pro AS noise is a significant design constraint on aircraft
pulsive element. operating close to population centers, this itself is a
This arrangement can be varied using a larger hub-Spinner Significant advantage
and 2 lobes with a linear hydraulic variable pitch mechanism 3. Unusual resistance to Stall and Surge due to the novel
110 using blade axis feathering mechanism mounted in 55 feature of boundary layer control
differentially twisting Spinner disc Stages 111 that upon 4. Should existing or modified geometries favor lower
differential twist, coordinated with the feathering axis tor turbine inlet flow velocities, unusually high turbine
Sion mechanism, allow variable rotor orientation for con efficiency gains through Meta-Element axial progres
Stant Speed operation. This method exploits the intrinsic Sion would permit Substantially higher torque per given
torsional flexibility of thin catenaries combined with Superb 60 momentum change.
resistance to thrust-induced bending, flutter and harmonic 5. Higher turbine inlet temperature enabled by the cen
oscillation due to the devices thin, fore-and-aft triangulated trifugal catenary shape providing high resistance to
stance of Substantially centrifugal catenary curve. flutter and resonance, great resistance to bending
COMPRESSOR ELEMENT DETAILED forces, in turn allowing the use of thinner and fluid
DESCRIPTION 65 dynamically more efficient shapes of a lower thermal
AS with the air propeller, a major Strategy of design of the mass that thus is easier to cool through transpiration
compressor element emphasizes resistance to centrifugal flows.
 US 6,948,910 B2
49 SO
CONCLUSIONS, RAMIFICATIONS AND SCOPE d) associating said progressive individual integral coor
OF INVENTION dinate Sets with the front element coordinate Set of Said
Thus the methods of the hysteresis based Meta-Element time spiral band blade such that for every increment of
Series as well as its resulting high lift to drag physical fundamental Subtended angular change of axial azi
devices provide the venue to greatly improved cost-benefit muth of Said front element, the next numbered phase
for all axial flow devices. angle increment-of-generation of each Successive asso
While my above description contains much s these should ciated individual phase angle fragment shall be an
not be construed as limitations on the Scope of the invention, integral multiple of the front element coordinate Set
but rather as an exemplification of Several preferred embodi angular change
ments thereof. Many other variations are possible. 1O e) connecting the envelope construction rays with tangen
For example: tial and axial cubic spline interpolation curves or their
An annular wing that combines the function of thrust and functional equivalents to establish a continuous physi
lift, combining these in turn with the stream tube cal envelope shape
convergence/divergence functions of a duct and contributing f) constructing a plurality of Said blades according to
to, or acting as primary lift provider, by Simple inclination these coordinates and attaching them at various loca
to the axis of fight, of Superior lift to drag ratio, of very light 15
weight through the use of centrifugal catenary Structural tions of a hub and Such fixed Support that allows Said
shapes. blade assembly to rotate
An annular hydrofoil that also functions as a duct and whereby, upon rotation of the resulting continuously shape
combines the function of thrust and lift, of Superior lift to Sequenced bands through the axial Shear plane multiplicity,
drag ratio, of very lightweight through the use of centrifugal the body-relative fluid acceleration caused by the body
catenary Structural elements, and of very high resistance to relative isocline acceleration attending anguillar or carangi
foreign object fouling. form propulsion of aquatic creatures is Substantially dupli
A sail that combines the functions of delivery of torque for cated through the mechanism of Spaced-quadrature vector
propulsion and improved Side force vectors forward incli coupling and as Such, useful for the expulsion of boundary
nation due to its Superior lift to drag ratio, of very light 25 layer accumulations as well as for limiting Spanwise flow,
weight through the use of centrifugal catenary Structural turbulence, and undulation of reaction mass.
shapes, easy variation of output and built-in reef-ability, and 2. A method of boundary layer control as in claim 1 except
to allow the vehicle to progreSS directly into prevailing wind that the compound periodic function progressively remaps
direction. the axial profile Section upper and lower envelope individu
Any other devices that accelerate or decelerate flow can ally using differential Starting helix angles and acceleration
additionally benefit from the ease and low cost of low parabolas to result in a multiplicity of individual incremental
Volume manufacture implicit in the computer aided design phase angle fragments as can define a single periodic
and manufacture of the proposed invention. function cycle and associating Said individual envelope
Accordingly, the Scope of the invention should not be coordinate Sets with the front element coordinate Set of Said
determined by the embodiments illustrated, but by the 35 Spiral band blade Such that for every integral increment of
appended claims and their legal equivalents. angular change of numbered azimuth plane-of-association
What is claimed is: of Said front element, the numbered phase angle increment
1. A method of inclined-plane-based boundary layer trans of-generation of the individual phase angle fragment shall be
port implemented by forming discretely oriented convexities an integral multiple thereof,
and concavities of Such variations of angle to bulk fluid flow 40 whereby, upon rotation of the resulting Spiraling bands,
upon the rear working Surfaces of that class of rotor blades the expulsion of boundary layer accumulations will
that have the shape of rigid continuous profiled spiral or ring result with minimum pulsation, noise and undulation.
bands, implemented by adding progressive phase-angle 3. A method of boundary layer control as in claim 1 except
fragmental increments-of-amplitude to progressive axial that the compound periodic function is a half-rectified
plane-relative profile coordinates as can effect Such Surface 45 Square wave or saw tooth wave function of Such frequency
to-axial plane chord-wise progressive variation of change of as to be inaudible, that progressively remaps the axial profile
inclination as can accelerate fluid, the shape of which is Section upper and lower envelope into convexities only
characterized by two axial-plane-relative isocline parabolas using discrete profile-relative Suction and pressure Side
of fluid acceleration, as well as by a constant Subtended differential Starting helix angles and acceleration parabolas
angle of axial azimuth connecting Successive azimuth 50 whereby upon rotation of the resulting spiraling bands,
increment axial-Section maxima of convexity, Said curves the expulsion of boundary layer accumulations will
and angle that together evidence Such variable convexity and incur minimum expense of manufacture, as well as
together comprising the Steps of: minimum pulsation, noise and undulation.
a) translating the coordinates of a conventional fluid 4. A rotor of manufacture that can beneficially interchange
dynamic profile tail Section envelope chord-wise coor 55 kinetic energy with axial flows, consisting of a plurality of
dinates into logarithmic coordinates defining exponen blades, each of which form continuously profiled, rigid
tial wavelength expansion isocline control points, Spiral or ring bands, the progressive forward-portion axial
b) constructing an amplitude expansion logarithmic spiral Sections of which have fixed chord-axis-wise orientation to
to offset logarithmic decrement Viscous dissipation, the axial Surface inclination of coaxial truncated cones-of
then its corresponding parabolas of amplitude maxima, 60 generation along Said cones progressive increments of axial
then envelope construction means and envelope recon azimuth and co-latitude coordinates, each Said spiral bands
Struction cubic Spline being attached at azimuth variations around and axial loca
c) progressively remapping the individual phase angle tion along an elongated aerodynamic hub of body-of
axial profile Section envelope collectively into a mul revolution that is itself attached to fixed supports which
tiplicity of individual integral multiple incremental 65 enable it to rotate, Said continuously profiled bands com
phase angle fragments as can define a Single periodic bining means to eject boundary layer accumulations through
function cycle tail Section variations of disposition of convexity and con
 US 6,948,910 B2
S1 52
cavity governed by a periodic function, Such variations of or divergence with the function of acceleration or decelera
convexity physically delineated by characteristic fluid-flow tion of axial flow as well as with the function of boundary
relative expanding angles of isocline parabolas and axial layer transport, consisting of a plurality of blades that
plane-relative angles of parabolas of maxima of chord individually form continuously profiled, rigid spiral or ring
normal convexity, as well as by a Subtended coaxial angle of 5 bands, the progressive axial forward Sections of which have
constant azimuth increment defining the disposition of Suc fixed chord-axis-wise orientation to the axial-plane-relative
cessive axial Section maxima of convexity, Surface inclination of coaxial truncated conoids-of
whereby Such rotors can efficiently interchange fluid generation along Said conoids progressive increments of
momentum change with an impulse of tuning force azimuth and axial co-latitude coordinates, Said spiral bands
generated by deflecting mass flows rates with low being attached at azimuth variations around and axial loca
frictional dissipation and limited Spanwise flow. tion along an elongated aerodynamic body of revolution that
5. A rotor of manufacture according to claim 4, wherein is itself attached to fixed Supports which enable it to rotate,
Said spiral band blades are attached at one end to an axial allowing Said rotating blade plurality's outer catenaries to
location along the midsection of Said elongated aerodynamic progressively Sweep out the outlines of a requisite duct
body-of-revolution that is itself attached to fixed supports 15
shape, Said continuously profiled bands combining means to
which enable it to rotate and at the other end at an azimuth
variation of a large-diameter coaxial annular peripheral eject boundary layer accumulations through tail Section
profiled rim-band, itself also endowed with said tail-section variations of convexity and concavity governed by a peri
variable convexity, Said rim being in turn Supported by odic function and Said convexities physically delineated by
tensile spokes upon the nose region of Said rotative aerody characteristic helix-relative expanding isocline parabolas
namic body-of-revolution, and axial-plane-relative parabolas of maxima of chord
whereby Such a rotor will capture the momentum attend normal convexity, as well as by a Subtended axial angle of
ing greater than working diameter mass air flows constant axial azimuth increment connecting Said Successive
quietly, for modest expenditure of material resource. axial Section maxima of convexity,
25
6. A rotor of manufacture according to claim 4 wherein whereby Such a duct can impart measured radial accel
Said spiral band blades tail Section working Surface contains erations or decelerations to converging or diverging
continuously variable corrugations of convexity only, as peripheral flows and can therefore dispense with the
defined by Said collective parabolas of isoclines, resulting in expense and drag of a fixed duct, entrain greater mass
Side-differential isocline parabolas attending the high pres flow rates per diameter of operation by reducing
Sure and low pressure Sides of working Surface tail Section unwanted fluid tube expansion or contraction and thus
and resulting in discrete inclinations of convexity only can function to reduce or increase tip velocity, function
whereby ease of manufacture is added to aforesaid advan to reduce frictional dissipation as well as function to
tage. limit Spanwise flow due to planform variable Sweep.
7. A rotating axial flow duct-rotor of manufacture, com
bining the function of controlling Stream tube convergence k k k k k