Abstract

In this article, we study the characteristics of steady autorotation of a tethered autogyro. The phenomenon of autorotation refers to the natural spinning of a rotor in a wind field. We explore the viability of tethered autogyros as unmanned aerial vehicles (UAVs) for long-duration and energy efficient hovering applications, such as in monitoring or surveillance. The tether provides mooring and can be used to power the rotor and to transmit wind power to the ground when suitable. This is a novel application of autorotation. It requires a generalized formulation and modeling of autorotation, beyond what is reported in the literature. We adopt a model-based approach where the blade element momentum (BEM) method and catenary mechanics are used to model the aerodynamics and the tether, respectively. The resulting model is highly nonlinear and numerical methods are proposed to solve for the equilibria. The model is validated against existing simulation and experimental results in the literature. It is extended to incorporate new features that are pertinent to our application, such as low rotor speeds, regenerative torque for power generation, combining catenary mechanics with aerodynamics, and varying atmospheric conditions with altitude. We characterize the autorotational equilibria over a range of operating conditions involving multiple independent variables. The analysis reveals an optimal operating range of the tip speed ratio of the autogyro under equilibrium. It also indicates the possibility of power generation in large autogyros stationed at high altitudes.

References

1.
Fletcher
,
C. A. J.
, and
Roberts
,
B. W.
,
1979
, “
Electricity Generation From Jet Stream Winds
,”
J. Energy
,
3
(
4
), pp.
241
249
.
2.
Durre
,
I.
,
Vose
,
R. S.
, and
Wuertz
,
D. B.
,
2006
, “
Overview of the Integrated Global Radiosonde Archive
,”
J. Clim.
,
19
(
1
), pp.
53
68
.
3.
Roberts
,
B. W.
,
Shepard
,
D. H.
,
Caldeira
,
K.
,
Cannon
,
M. E.
,
Eccles
,
D. G.
,
Grenier
,
A. J.
, and
Freidin
,
J. F.
,
2007
, “
Harnessing High-Altitude Wind Power
,”
IEEE Trans. Energy Convers.
,
22
(
1
), pp.
136
144
.
4.
Archer
,
C. L.
, and
Caldeira
,
K.
,
2009
, “
Global Assessment of High-Altitude Wind Power
,”
Energies
,
2
(
2
), pp.
307
319
.
5.
Elliott
,
D.
,
Schwartz
,
M.
,
Haymes
,
S.
,
Heimiller
,
D.
,
Scott
,
G.
,
Brower
,
M.
,
Hale
,
E.
, and
Phelps
,
B.
,
2011
, “
New Wind Energy Resource Potential Estimates for the United States
,”
National Renewable Energy Laboratory
, NREL Report No. PR-5500-50439.
6.
Biscomb
,
L. I.
,
1981
, “
Multiple wind Turbine Tethered Airfoil Wind Energy Conversion System
,” U.S. Patent No. 4,285,481.
7.
Biscomb
,
L. I.
,
1982
, “
Tethered Airfoil Wind Energy Conversion System
,” U.S. Patent No. 4,309,006.
8.
Pugh
,
P. F.
,
1984
, “
Wind Generator Kite System
,” U.S. Patent No. 4,486,669.
9.
Ockels
,
W.
,
2001
, “
Laddermill, a Novel Concept to Exploit the Energy in the Airspace
,”
Aircraft Des.
,
4
(
2–3
), pp.
81
97
.
10.
Houska
,
B.
, and
Diehl
,
M.
,
2006
, “
Optimal Control of Towing Kites
,”
IEEE Conference on Decision and Control
,
San Diego, CA
,
Dec. 13–15
.
11.
Canale
,
M.
,
Fagiano
,
L.
,
Ippolito
,
M.
, and
Milanese
,
M.
,
2006
, “
Control of Tethered Airfoils for a New Class of Wind Energy Generator
,”
IEEE Conference on Decision and Control
,
San Diego, CA
,
Dec. 13–15
.
12.
Lansdorp
,
B.
, and
Williams
,
P.
,
2006
, “
The Laddermill – Innovative Wind Energy From High Altitudes in Holland and Australia
,”
Windpower 2006
,
Adelaide, Australia
,
Jan. 1
.
13.
Das
,
T.
,
Mukherjee
,
R.
,
Sridhar
,
R.
, and
Hellum
,
A.
,
2011
, “
Two Dimensional Modeling and Simulation of a Tethered Airfoil System for Harnessing Wind Energy
,”
Proceedings of the ASME Dynamic Systems and Control Conference
,
Arlington, VA
,
Jan. 1
.
14.
Fechner
,
U.
,
van der Vlugt
,
R.
,
Schreuder
,
E.
, and
Schmehl
,
R.
,
2015
, “
Dynamic Model of a Pumping Kite Power System
,”
Renew. Energy
,
83
(
C
), pp.
705
716
.
15.
Riegler
,
G.
,
Riedler
,
W.
, and
Horvath
,
E.
,
1983
, “
Transformation of Wind Energy by a High-Altitude Power Plant
,”
J. Energy
,
7
(
1
), pp.
92
94
.
16.
Riegler
,
G.
, and
Riedler
,
W.
,
1984
, “
Tethered Wind Systems for the Generation of Electricity
,”
J. Solar Energy Eng.
,
106
(
2
), pp.
177
181
.
17.
Vermillion
,
C.
,
Glass
,
B.
, and
Rein
,
A.
,
2013
, “Lighter-Than-Air Wind Energy Systems,”
Airborne Wind Energy
,
U.
Ahrens
,
M.
Diehl
,
and R.
Schmehl
, eds.,
Springer
,
Berlin/Heidelberg
, pp.
501
514
.
18.
Das
,
T.
,
Mukherjee
,
R.
, and
Cameron
,
J.
,
2003
, “
Optimal Trajectory Planning for Hot-Air Balloons in Linear Wind Fields
,”
AIAA J. Guid. Control Dyn.
,
26
(
3
), pp.
416
424
.
19.
Charnov
,
B. H.
,
2003
,
From Autogiro to Gyroplane: The Amazing Survival of an Aviation Technology
,
Praeger Publishers
,
Westport, CT
.
20.
Leishman
,
J. G.
,
2004
, “
Development of the Autogiro: A Technical Perspective
,”
J. Aircraft
,
41
(
4
), pp.
765
781
.
21.
Glauert
,
H.
,
1926
, “
A General Theory of the Autogyro
,” Presented by the Director of Scientific Research Air Ministry, Reports and Memoranda No. 1111 (Ae. 285).
22.
Gessow
,
A.
, and
Myers
,
G. C.
, Jr.
1952
,
Aerodynamics of the Helicopter
,
Macmillan Company
,
New York
.
23.
Lock
,
C. N. H.
,
1927
, “
Further Development of Autogyro Theory—Part I
,” National Advisory Committee for Aeronautics, Reports and Memoranda No. 1127 (Ae. 299).
24.
Lock
,
C. N. H.
,
1927
, “
Further Development of Autogyro Theory—Part II: A General Treatment of the Flapping Motion
,” National Advisory Committee for Aeronautics, Reports and Memoranda No. 1127 (Ae. 299).
25.
Wheatley
,
J. B.
,
1934
, “
An Aerodynamic Analysis of the Autogiro Rotor With a Comparison Between Calculated and Experimental Results
,” National Advisory Committee for Aeronautics, Report No. 487.
26.
Gessow
,
A.
, and
Crim
,
A. D.
,
1952
, “
An Extension of Lifting Rotor Theory to Cover Operations at Large Angles of Attack and High Inflow Conditions
,” National Advisory Committee for Aeronautics, Technical Note No. 2665.
27.
Cuerva
,
A.
,
Sanz-Andres
,
A.
,
Mesegeur
,
J.
, and
Espino
,
J. L.
,
2006
, “
An Engineering Modification of the Blade Element Momentum Equation for Vertical Descent: An Autorotation Case Study
,”
J. Am. Helicopter Soc.
,
51
(
4
), pp.
349
354
.
28.
Wheatley
,
J. B.
,
1937
, “
An Analytical and Experimental Study of the Effect of Periodic Blade Twist on the Thrust, Torque, and Flapping Motion of an Autogiro Rotor
,” National Advisory Committee for Aeronautics, Technical Note No. 591.
29.
Houston
,
S. S.
,
2002
, “
Analysis of Rotorcraft Flight Dynamics in Autorotation
,”
J. Guid. Control Dyn.
,
25
(
1
), pp.
33
39
.
30.
Thomson
,
D.
, and
Houston
,
S.
,
2008
, “
Advances in the Understanding of Autogyro Flight Dynamics
,” Ser. AHS Annual Forum, AHS, Montreal, Canada.
31.
Wheatley
,
J. B.
,
1933
, “
Wing Pressure Distribution and Rotor-Blade Motion of an Autogiro as Determined in Flight
,” National Advisory Committee for Aeronautics, Technical Note No. 475.
32.
Floros
,
M.
, and
Johnson
,
W.
,
2007
, “
Stability and Control Analysis of the Slowed-Rotor Compound Configuration
,”
J. Am. Helicopter Soc.
,
52
(
3
), pp.
239
253
.
33.
Floros
,
M.
, and
Johnson
,
W.
,
2009
, “
Performance Analysis of the Slowed-Rotor Compound Helicopter Configuration
,”
J. Am. Helicopter Soc.
,
54
(
2
), p.
22002
.
34.
Rezgui
,
D.
,
Lowenberg
,
M.
, and
Bunnies
,
P.
,
2008
, “
A Combined Numerical/Experimental Continuation Approach Applied to Nonlinear Rotor Dynamics
,” Progress in Industrial Mathematics at ECMI, vol. 15.
35.
Rezgui
,
D.
and
Lowenberg
,
M.
,
2015
, “
On the Nonlinear Dynamics of a Rotor in Autorotation: A Combined Experimental and Numerical Approach
,”
Philos. Trans. R. Soc. A
,
373
(
2051
), p.
23
.
36.
Mackertich
,
S.
, and
Das
,
T.
,
2016
, “
A Quantitative Energy and Systems Analysis Framework for Airborne Wind Energy Conversion Using Autorotation
,”
American Control Conference
,
Boston, MA
,
July 6–8
, IEEE, pp.
4996
5001
.
37.
Rimkus
,
S.
,
Das
,
T.
, and
Mukherjee
,
R.
,
2013
, “
Stability Analysis of a Tether-Airfoil System
,”
American Control Conference
,
Washington, DC
,
June 17–19
.
38.
Salih
,
B.
,
2014
, “
An Introductory Study of the Dynamics of Autorotation for Wind Energy Harvesting
,” Master’s Thesis,
University of Central Florida
,
Orlando, FL
.
39.
Mackertich
,
S.
,
2016
Dynamic Modeling of Autorotation for Simultaneous Lift and Wind Energy Extraction
,” Master’s Thesis,
University of Central Florida
,
Orlando, FL
.
40.
Beer
,
F. P.
,
Johnston
,
E. R.
,
Eisenberg
,
E. R.
, and
Mazurek
,
D.
,
2007
,
Vector Mechanics for Engineers: Statics
, 8th ed.,
McGraw-Hill
,
New York
.
42.
Archer
,
C. L.
,
2013
, “An Introduction to Meteorology for Airborne Wind Energy,”
Airborne Wind Energy
,
U.
Ahrens
,
M.
Diehl
, and
R.
Schmehl
, eds.,
Springer
,
Berlin/Heidelberg
, pp.
81
94
.
You do not currently have access to this content.