AN ANALYSIS OF THE MADARAS ROTOR POWER PLANT- AN ALTERNATE METHOD FOR EXTRACTING LARGE AMOUNTS OF POWER FROM THE WIND '
Volunie 1. Executive Summary
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DSE-2554-78/2(V01.1) Distribution Category UC-60
AN ANALYSIS OF THE MADARAS 'ROTOR POWER PLANT ---- AN ALTERNATE METHOD
FOR EXTRACTING LARGE AMOUNTS OF POWER FROM THE WIND
VOLUME 1 EXECUTIVE SUMMARY
Dale H. Whitford John E. Minardi Blaine S. West Robert J. Dominic
UNIVERSITY OF DAYTON RESEARCH INSTITUTE 300 College Park Avenue
Dayton, Ohio 45469
June 1978 ~
DISCLAIMER -
PREPARED FOR - - -- - .- - - . -.
THE UNITED STATES ENERGY RESEARCH AVD DEVELOPMENT
ADMINISTRATION DIVISION OF SOLAR ENERGY FEDERAL WIND ENERGY PROGRAM
ERDA CONTRACT NO. E(49-18)-2554
T H I S PAGE
WAS INTENTIONALLY
L E F T BLANK
PROJECT SUMMARY
The purpose of the program was to analyze and up-date the
design of the Madaras Rotor Power Plant concept that had been
developed in the 1930's to determine the technical and economic
feasibility of this system to be competitive with conventional
horizontal axis wind turbines. The Madaras concept uses rotating
cylinders, vertically mounted on flat cars, to react with the wind
like a sail and propel an endless train of connected cars around
a closed track at constant speed. Electricity is generated by
alternators on each car that are geared to the wheels. Electrical
power is transmitted from each car to the power house by a trolley
system.
A four-task program consisting of a series of wind tunnel
tests, an electro-mechanical analysis, a performance analysis,
and a cost analysis was conducted. Wind tunnel tests were conducted
to validate rotating cylinder data in the literature and to obtain
non-existing data that relates aerodynamic performance to rotating
cylinder (rotor) geometry. Supporting studies included structural
design, mechanical component design, and an electrical system
design to provide a realistic set of inputs to a performance trade
study which provided the basis for selecting a single rotor con-
figuration and set of operating conditions which were considered
to represent a good, but not necessarily an optimum design.
Studies to determine the minimum spacing between cars governed
by inter-rotor aerodynamic interference also were conducted.
Drawings and specifications of the system were used to
estimate costs, and parametric cost/performance computer runs were
made to correlate plant cost, annual output, and energy cost as
a function of plant size parameters. These cost studies
incorporated appropriate learning curves to account for reduction
in cost resulting from improved production techniques and increased
productivity.
iii
Primary results of this study are:
Madaras plants having circular track plan-forms probably
will not be economically attractive, but those having racetrack
plan-forms appear to be of interest.
o Madaras racetrack plants appear to be competitive with
a farm of MOD-1 horizontal axis machines of equal total power
generation capability (to within the overall accuracy of estimation
for both schemes) in cost per unit rated power and cost per unit
of energy delivered. Cost comparisons were based upon estimates
made in this study and estimates made by 13ightower1 and General
J3lectric2 for the MOD-1 machine. A substantial economic benefit
favoring the Madaras scheme does not appear, although this possibility
may exist (under more "optimal" designs determined through more
detailed analysis).
Madaras racetrack plants having rated capacities as high
as 228 MW and annual energy outputs of 975 x lo6 kW-hr/year were
studied, and analyses indicated that even larger, more efficient
plants could be developed. Thus, Madaras plants can produce energy
in the quantities of interest to the electric utility industry.
Madaras plants are more complex, have higher electrical
and mechanical losses, and hence will require higher operation
and maintenance costs than horizontal axis machines. Further, a
racetrack plant configuration for Madaras plants limits them to
regions having generally unidirectional winds (including reciprocal
directions) in which large expanses of relatively flat land are
available. (However, similarly-sized HA-WTG plants require twice
the land area as Madaras plants.)
At this stage of the investigation, it is not possible to
state conclusively whether or not the Madaras system will significantly
out-perform a similarly-sized horizontal axis wind turbine system.
The Madaras system seems to outperform horizontal axis systems in
the areas of structural durability, economy of scale, amount and
efficiency in use of land, and possibly energy cost. Therefore,
in view of this potential, it appears that an in-depth optimal
design study of the system is warranted.
1. BACKGROUND
TABLE OF CONTENTS
SECTION
2. WIND TUNNEL TESTS
3. ELECTROMECHANICAL DESIGN
3.1 Structural, Mechanical, Site Design
3.2 Electrical Design
4. PERFORMANCE ANALYSIS
5. COST/PERFORMANCE ANALYSIS
6. CONCLUSIONS
PAGE
LIST OF ILLUSTRATIONS
FIGURE PAGE
Madaras Rotor Power Plant.
Internal Support Tower for Madaras Rotor.
Madaras Rotor Tested in 1933 at Burlington, 2 New Jersey.
Comparison of Lift-Drag Polars of a Rotating Cylinder and an Airfoil.
Sidc View, 152 mm Cylinder in Tunnel with Lower 7 Streamlined Fairing.
Front View, 152 mm Cylinder in Tunnel with Lower ' 7 Streamlined airing and Mirror Strut.
152 mm Diameter Cylinder and Car Ready for Simulated 8 Boundary Test, e/d = 3 End Plates, AR = 6.
Freestream CL and CD versus U/V, AR of 3 and 6, 10 and e/d Ratios of 1.25, 2, and 3, and d = 152 mm.
Power Required to Rotate Cylinder for Various End 11 Cap Diameter Ratios and Two Aspect Ratios, and d = 152 I I U U .
CL, CD, Power versus U/V for Boundary Layer Tests 12 fur e/d Ratios of 1.25 and 2; one End Cap on Top or Two End Caps; AR = 3 and 6.
Typical Design Loads for 8.0 m/s (18 mph) Mean Design 13 Wind Speed; Track Speed = 8.9 m/s.
Revised Rnt.nr Car Cnnfi g11raf.i on. 1 5
Rotor Car End Truck Aaacrnbly, 16
Plant Layout. 19
Optimum Motor Size and Maximum Power Output versus 21 Track Diameter, 13.4 m/s (30 mph) Wind Speed.
Electrical Schematic of Circuitry on Each Rotor Car. 23
Net Power Output for One Rotor, Spin Motor Power, and 26 Motor rpm versus Rotor Position on Track as Affected by Use of Viscous Braking, Regenerative Braking, and a Three-Step Transmission to Vary the Spin schedule.
LIST OF ILLUSTRATIONS (Concluded)
FIGURE PAGE
18 Net Power Output from one Rotor v.ersus A , as a 27 Function of Wind Speed. Performance. is Presented for Both a 1370 m (4500 ft) Diameter Circular. .Track and .a Racetrack having 1370 m (4500ft) ~iameter Ends and 488@ M (16,000 ft) Straight Sections.
. . .
19 Mutual ~nterference Loss Factor versus. wind speed 29 for Various Numbers of Rotors on a 1524-m ~iameter Track. Constant Rotor Speed and Track Speed of 186 rpm and 13.4 m/s, Respectively.
20 Modified Design Wind Duration Curve to Represent 30 Wind Conditions at a Rotor Mid-Height. o f 2 5 m (82 ft) Above Mean Terrain Level.
21 Power Duration Curves for the Two Plants Shown in 30 Figure 6.14 Based on the V = 9.6 m/s Design Wind Duration Curve at 25-m Height (Figure 6.13).
22 Unit Plant Cost versus Rated Power for Racetrack 32 Configuration as a Function of Inter-Rotor Spacing, Length of Straight Section of Track, and Number of Rotors. DOE Design Wind Duration Curve: V = 8.1 m/s @ 9 m.
2 3 Energy Cost versus Rated Power for Racetrack 32 Configuration as a Function of Inter-Rotor Spacing, Length of Straight Section of Track, and Number of Rotors. DOE Design Wind Duration Curve: V = 8.1 m/s @ 9 m.
LIST OF TABLES
1 Wind Tunnel Test Conditions
2 Effect of and Cost, Learning Curves, and Mean Wind Speed (V) on Plant and Energy Cost
3 Overall Comparison of Several Madaras and HA-WTG Plants at Two Wind Regions
PAGE
6
FOREWORD
This final report describes the study conducted by the
University of Dayton Research Institute on Contract E(49-181-2554,
sponsored by the Wind Systems Branch, Division of Solar Energy,
United States Energy Research and Development Administration
(now the Department of Energy). The program was later transferred
to the Solar Energy Research Institute. Project monitors on the
program were Dr. Robert Thresher for ERDA and Dr. Irwin E. Vas for
SERI . The study was under direction of Mr. Dale H. Whitford,
who, with Dr. John E. Minardi, conducted the preliminary per-
formance analyses, planned the wind tunnel tests, and analyzed
the wind tunnel test data. Mr. Levere F. Starner and
Mr. Blaine S. West were responsible for the structural analysis
study, axid P4r. Robert J. Dominic conducted the electrical analysis.
The authors wish to express their appreciation for the
excellent contribution to this program made by the personnel
of the Gas Dynamics Laboratory, Aerospace Engineering Department,
University of Michigan. Overall guidance, assistance in develop-
ing the test plan, development of the method for generating the
simulated atmospheric boundary layer, and coordinating all
aspects of the University of Michigan effort was provided by
Professor William W. Willmarth. Test supervision and scheduling
of support for the tests was provided by Mr. David R. Glass.
Mr. Daniel 0. Scharf was responsible for directing tests and
processing the data, and Mr. Charles Hogan, Mr. Leo Griffin, and
Mr. Cletus, Iott were responsible for instrumentation, model
installation, and o p e r a t i o n of. the w i n d tunnel.
We also want to acknowledge other major contributions:
the vortex anlaysis study conducted by Professor Harold Larsen
of the Air Force Institute of Technology; the detailed structural
and mechanical design layout done by Mr. Francis Shannon of
Maier and Associates; the econom.ic analysis conducted by
Mr. John L. McClellan; and the aerodynamic consultation provided
by Dr. Frank L. Wattendorf.
We are especially appreciative of the support of the
Detroit Edison Company and the assistance given by Mr. Walker L.
Cisler, former Chairman of the Board of that Company; the consul-
tation provided by Mr. Russell F. Hardy, former Chief Engineer
of the Madaras Rotor Power Project; and the helpful comments and
critique of this work given by Dr. E.E. Lapin of the Aerospace
Corporation.
EXECUTIVE SUMMARY
BACKGROUND
Analytical studies, wind tunnel experiments, and full-
scale aerodynamic tests of the wind-powered, Madaras Rotor Power
Plant were conducted in the 1929 to 1934 time period. This
system invented by Julius D. Madaras consisted of 27.4-m high by
6.8-m diameter cylinders which were vertically mounted on flat
cars and rotated by electric motors to convert wind energy to
Magnus-effect forces. The forces propelled an endless train of
18 cars around a 457-m diameter, closed track (Figure 1).
Figure 1. Madaras Rator Power Plant.
Alternators geared to the car axles were calculated to produce
up to 18 NW of electric power at a 8 . 9 m/s track /speed in a 13.4
m/e wind, Twiae during eaah orbit of a rotor car around the track (at points i 90° from the wind), each spinning rotor
in turn must be de-spun to a stop, and then spun-up in the opposite direction. This cycle is necessary in order to assure
that the propulsive farce changes direction so that all rotors are eropelling the train in the same angular direction.
Force measurements obtained from a full-size rotating cylinder
mounted on a stationary platform (Figures 2 and 3) proved that
the concept was technically feasible, but the project was
discontinued prior to pilot plant demonstration because of the
Depression. The reason for using a rotating cylinder instead of
an airfoil to propel the train is that a rotating cylinder
generates a lift force about ten times larger than that of an
airfoil (Figure 4 shows lift-coefficient, CL, versus drag
coefficient C,.
Figure 2 . Ineermf Sapport Figure 3. Marlaras Rotor T m x fnx mdaras Tested in 1933 Rotor. at Burlington,
New Jersey.
A unique Leature ol: this p w y r a m was that it was
sponsored and monitored by a consortium of seven electric
utility companies, with the Director of Research of the Detroit
Edison Company serving as project monitor.
The University of Dayton Research Institute has conducted
studies of the Madaras system to verify the initial computations
made by Madaras and his co-workers. These studies have included
a thorough review of the literature of the Madaras program
(contained in a set of 14 unpublished technical reports obtained
from Detroit Edison) as well as discussions with two key men who
had worked with the original
CYLINDER
/ TYPICAL LOW SPEED AIRFOIL
I I I 0 2 4 6 8
Madaras project. One of
these men is Mr. Russell F.
Hardy who was the Chief Engineer
of the Madaras Rotor Power
Corporation, and the other is
Mr. Walker Cisler, who
recently retired from the
position of Chairman of the
Board of the Detroit Edison
Company. Our studies also
have included a review of all
wind tunnel tests on rotating
cylinders conducted since the
mid 19201s, performance
simulation studies, and Figure 4. Comparison of Lift-
Drag Polars of a economic analysis.
Rotating Cylinder and an Airfoil. Cost estimates in 1934
done by an outside consulting
engineering firm indicated that 18,000 kW plants would cost
$38.50/kW and the cost of power at the busbar would vary from
1.23 to 2.30 mills/kWh, depending upon annual wind conditions.
Thus, both the capital cost and the cost of electric power at
the busbar of Madaras plants were predicted to be only one-third
that of steam power plants in 19 34.
The primary objective of this program is to demonstrate
the degree in which Madaras power plants having capacities in the
10 MW to 200 MW range are competitive with horizontal axis wind
turbines,
The research into the Madaras system conducted by
the University of Dayton Research Institute (UDRI) prior to
this program lead to several unanswered questions concerning
the system. These questions were:
a What is the fewest numberofrotors required to extract the maximum amount of power per unit land area from the wind?
What aerodynamic performance can be expected from full-sized cylinders operating in the lower levels of the atomspheric boundary layers in terms of the various geometric and operational design ~ 7 a ~ i i I h l t ? ~ w h i c h r 7 f f w A t - l p ~ r f n r m a n c l ~ ?
r WhaL d ~ e LIle desiyu ~t=qui~e~ike~~Ls Tor sLxucLura1, electrical and mechanical subsystems; and what performance af a Madaras system can be expected when modern, commercially-available electrical and mechanical components are used?
What is the capital cost and the cost of electric power generated by modernized Madaras plants of different sizes in various climatic areas of the United States?
Design criteria selected for this system are based on
those used for the General ~lectric study of large horizontal
axis wind machines to tadlitate dire~t oomparison of results.
The primary ground rules far this study were:
e This was a conceptual design trade study of the basis rirystem proposed by Madaras. Only off-the- shelf hardware and available technology were to be used. Thus a system design optimizatian analysis was heynnd the scnpe nf the prrrgram.
Design wind conditions included:
a Wind d u ~ n t . i o n curves having 8.1 m/s mean w i nrl speed at 9 m height above ground.
Structure must withstand winds of 53.6 m/s with the rotor train standing still on the track.
Structure must be able to operate in wind gusts to 26.8 m/s while operating at the rated wind speed of 13.4 m/s.
Design life of 30 years for rotating parts and SO years for static parts.
System must withstand hail up to 2.5 cm diameter, operate in a temperature range of -51°C to +4g°C, and operate in snow, rain, lightning, icins, salt vapor, and windblown sand and dust.
2. WIND TUNNEL TESTS
Wind tunnel tests were conducted in the University of
Michigan's 2.1 m x 1.5 m (7 ft x 5 ft) subsonic wind tunnel to:
Validate existing wind tunnel data on rotating cylinders.
Develop aerodynamic characteristics of rotating cylinders with end plates as a function of cylinder and end plate geometry.
a Obtain data on power required to rotate the cylinder.
0 Evaluate rotating cylinder performance in an atmospheric boundary layer.
In all tests, flow conditions were designed to represent
adequately those of a full-sized Madaras rotor.
Both 50 mm diameter and 152 mm diameter wind tunnel test models were tested, with the smaller model being used primarily
to develop background, isolate problem areas, and to obtain
design information for the larger cylinder. All cylinders were
equipped with internally-housed motors capable of rotating
the cylinder at speeds from 0 to 20,000 rpm. High speeds are
required on models as small as these to obtain proper surface
speed to wind speed ratios (U/V) and to provide sufficiently
accurate resolution of loads on the wind tunnel 6-component
balance system, (The full-sized cylinder will be designed to
rotate at speeds of about 186 rpm.)
Over 200 test runs were conducted in the overall test
series. A summary of the test conditions is presented in Table 1.
A unique aspect of the test series was the series of
tests conducted in a simulated atmospheric boundary layer, For
these tests, a boundary layer similar to that of wind blowing
over grassy plains was simulated by wooden quarter-round strips
TABLE 1
, . WIND TUNNEL TEST CONDITIONS
. . . . . . . . . . . . . . . . . . . . . . . . .
placed traverse to the wind flow along the floor of the tunnel.
These strips which were placed at 0.3 m intervals from the
entrance to the 6.1-m-long test section up to the model, simulated
the boundary layer profile quite well across the width of the
tunnel.
Test Variables Cylinder Diameter
Aspect Ratio (AR)
End Plate Diameter to Cylinder Diameter Ratio (e/d)
Free-Stream Reynolds Number Range
Cylinder Surface Speed to Wind Speed Ratio (U/V)
NutkIter of End P l a L e s
Type Flow Free Stream Atmospheric Boundary Layer
Cylinder sn Model Car
Cylinder and Car on Embankment
Typical photographa of tho 152 mm test mudel during the
free stream tests are shown inFfgures5 and 6, and a typical
boundary layer test model is shown in Figure 7.
It can be seen that the free stream tests were conducted
with either a bottom fairing or both a bottom and top fairing.
Actually, the bottom fairing was used to isolate the model support
sting (which was mounted to the balance system ) from the air
flow. The top fairing was merely a mirror-imaqe strut that was not
fastened to the model, but which cleared the top of the model by
about 0.8 mm. By comparing data obtained with the single
and double fairings, the effect of the fairing on the aerodynamic
coefficients was ascertained, and then the data were corrected
accordingly. No correction of this sort was required for the
boundary layer tests.
+ Test Combinations
50 nim 4
1, 2, 3
4 2 x 10 to 7.4 x 104
0 - 6
1, 2
x x
x
---. 152 mm 3,4,5,6 1.25,2,3
7 lo4 to 3 x lo5
0 - 6
1, 2
x x
x
x
Figure 5. Side View, 152 mm Cylinder in Tunnel With Lower Streamlined Fairing.
Figure 6. Front View, 152 mm Cylinder in Tunnel With Lower Streamlined Fairing Only and Mirror Strut.
' I X - - , , -,,,;. ,;'g ;=La,#-s, - -
Figure 7. 152 rim Diameter Cylinder and Car Ready for Simulated Boundary Layer Test, e/d = 3 End Plates, AR = 6.
Typical free stream test results for the shortest aspect
ratio (AR = 3) and longest (AR = 6) cylinder for all of the
three end plate sizes (e/d ratio) are presented in Figure 8.
Here, the lift and drag coefficients are plotted as a function
of U/V, the surface speed of the rotor divided by the wind speed.
This parameter is analogous to the angle of attack of an airfoil.
Results conformed with our expectations, and curve shapes and
magnitudes correlated well with previously-published data for
comparable geometries. Primary observations of importance are:
o Cb increasesdramatically with increased end plate slze, especially between e/d = 1.25 and e/d = 2.
e For large values of AR, the benefit of increasing e/d beyond 2 is questionable. Thus, it appeared that an optimum design point may occur near e/d = 2.
a Up until stall occurs, end plate size increases tend to decrease drag coefficient. This is a result of reduced induced drag resulting from an apparent increase in aspect ratio caused by the end plate.
The power required to rotate the cylinder is presented
in Figure 9. Two observations are of particular importance:
a There is a significant increase in power absorbed by the rotor for e/d > 2.
e There is little difference in power absorbed as a f~nction of AR.
Thus, by combining the observations from Figures 8 and 9,
it appeared that a good design would be achieved for a rotor
having AR = 6 and e/d = 2. This combination would provide high
lift, low drag, and reasonable power levels for spinning the rotor.
We also concluded ,that aspect ratios greater than 6 might be
even more attractive; however, since wind tunnel size prevented testing a larger cylinder, data f0.r larger aspect ratios would have
to be obtained by extrapolation and use of the conventional
induced drag equation which is a function of cL2 and AR.
Although not presented in the interest of brevity,
measurements of lift moment and drag moment also were obtained
u/v U / V
F i g u r e 8. F r e e s t r e a m CL and CD v e r s u s U/V, AR of 3 and 6 , and e /d R a t i o s of 1 .25 , 2 , and 3 , .:nd d = 152 mm.
u / v 6 ' 20bo ' 4600 ' 6600 ' 8 0 ' 6 ~ 0 0
RPM
Figure 9 . Power Required t o Rota te Cyl inder f o r Var ious End Cap Diameter Ra t io s and Two Aspect R a t i o s , and d = 152 mrn.
f o r use i n computing t h e c e n t r o i d p o s i t i o n of t h e s e f o r c e s a s
a func t ion of U/V. These measurements w e r e o f p a r t i c u l a r i n t e r e s t
when we conducted t h e boundary l a y e r t e s t s e r i e s , because t h e
primary reason f o r t h i s t e s t series was t o o b t a i n aerodynamic
d a t a f o r u se a s an independent check o f o u r model f o r p r e d i c t i n g
t h e combined e f f e c t o f t h e two a i r l o a d d i s t r i b u t i o n s t h a t are
imposed on t h e r o t o r : (1) t h e uniform a i r load v e r s u s r o t o r
h e i g h t caused by motion a long t h e t r a c k ; and ( 2 ) t h e nonuniform
atmospher ic boundary f low d i s t r i b u t i o n w i t h h e i g h t caused by t h e
wind. The combination of t h e s e two f lows t o o b t a i n t h e r e s u l t a n t
v e l o c i t y y i e l d s a h e l i c a l load d i s t r i b u t i o n w i t h h e i g h t .
S ince t h i s combination of a i r f lows cannot be ob ta ined i n a
wind tunne l it was necessary t o develop an empi r i ca l model based
on o u r t e s t s .
Typica l boundary l a y e r d a t a a r e p re sen ted i n F igure 10 .
A s w i th t h e f r e e s t r e a m r e s u l t s , t h e d a t a t r e n d s and accuracy
a r e s a t i s f a c t o r y , and t h e d a t a v e r i f i e d w e l l o u r p r e d i c t e d c e n t r o i d
p o s i t i o n s by ou r model.
12 1 A R = 6 e/'d - 2
10; I END CAP -- ' ,-r--- 2END CAPS - - - - -
8
- -
4
2 . I 0 - /
P
0 . 0 I 2 3 4 5
F i g u r e 10. C L r C D ~ Power v e r s u s U/V f o r Boundary Layer T e s t s f o r e / d R a t i o s o f 1 . 2 5 and 2 ; one End Cap on Top o r Two End Caps; AR = 3 and 6 .
Most of . the obse rva t ions from t h e boundary l a y e r d a t a
were s i m i l a r t o t h o s e f o r t h e f r e e s t ream d a t a . I n a d d i t i o n ,
it was concluded t h a t t h e u se of t o p and bottom end p l a t e s
( i n s t e a d o f one a s Madaras, planned) would be b e n e f i c i a l t o
performance.
3 . ELECTROMECHANICAL DESIGN
Design l o a d s on t h e r o t o r , r o t o r s u p p o r t , tower c a r ,
and t r a c k were developed from i n p u t t i n g t h e des ign c r i t e r i a i n t o
ou r Madaras performance s imu la t ion program, which p r e d i c t s t h e
f o r c e s on t h e v a r i o u s components a s a f u n c t i o n o f angu la r p o s i t i o n
on t h e t r a c k . Typica l aerodynamic loads normal and t a n g e n t i a l
t o t h e t r a c k f o r an o p e r a t i o n a l w i n d c o n d i t i o n a r e shown f o r
one-half of t h e o r b i t i n F igure 11. The loads . f o r t h e o t h e r o r b i t
h a l f a r e t h e same. . .
+ - DEG . .
Figurc 11. Typicz l D e a i ~ n Loads for 8 . 0 m/s ( 1 8 mpl!) Mean Design Wind Speed; Track Speed = 8 . 9 m / s .
Results of the load analysis for the three wind con-
ditions (i.e., operational, operational + gust, and static operations at hurricane conditions indicated that the operational
gust load was the most severe. Other load conditions analyzed
were :
Aerodynamic loading on the end cap.
~cceleration loads caused by:
a Rotor travel around the curved track. 8 Centrifugal body force caused by rotor rotation
at 186 rpm. i Arlyular accele~atiuri duririy rotor spin-up frun~
0 to 186 rpm.
a Snow and icc loadc~~
Wheel and lateral restraint loads (idler wheels bearing on the side of the track were used to react lateral loads instead of a flanged wheel.
e Car weight.
e Cyclic fatigue loading.
3.1 Structural, Mechanical, Site Design
The rotor car design concept which evolved from
our studies is depicted in FiGure 12. A summary of the overall
design follows:
e Dimensions
AR = 8 e/d = 2 Cylinder length = 38.1 m (125 ft) Cylinder diameter = 4.9 m (16 ft) End cap diameter = 9.8 m (32 ft) Track gauge = 11.0 m (36 ft) Car length = 19.2 m (63 ft) Car height = 3.8 m (12.5 ft) Car width = 17.4 m (57 ft) Gross car weight = 328,000 Kg (723,000 lb)
e Structural Configuration and Materials
R0to.r :. Semimonicoque, longer on trusses, circumferential truss stiffeners, and circumferent.ially corrugated s k i n . A l l 2024-~4 Alclad aluminum alloy.
Cap: Semimonicoque, radial trusses at 45' increments, stressed skin. All 2024-T4 Alclad aluminum alloy.
~ i ~ u r e 12. Revised Rotor Car Configuration.
Support Tower: Monocoque c y l i n d e r on t o p of t r u n c a t e d cone, s k i n t h i c k n e s s v a r i a b l e from 9 .5 mm t o 12.7 mm, a l l o f ASTM A-242 co r ros ion - r e s i s t a n t steel.
e Rotor C a r : Semimonocoque, frame o f b u i l t - u p l o n g i t u d i n a l and l a t e r a l box beams 0.9 m t o 1 .22 m deep, p i p e s k i r t s u p p o r t , r e c t a n g u l a r t u b e i n t e r - c o s t a l ~ , and 3 mm-thick s t r e s s e d s k i n . S t r u c t u r a l s t e e l frame w i t h ASTM A-242 c o r r o s i o n - r e s i s t a n t s teel s k i n . F loo r s t e e l - r e i n f o r c e d c o n c r e t e f o r b a l l a s t and environ- mental p r o t e c t i o n for e l e c t r i c a l cql..?l,pment. .
e Suspension system:
Four, two-wheel t r u c k s , one a t each curlier uE .Llie car. Wh@cls a r e 1 . 2 m d iameter w i t h a 2.79 mrn t r e a d , fo rged AISC 1045 s t e e l hardened t o dep th of 25 mm. ~ a c h t r u c k i s coupled through a speed i n c r e a s e r to a 250 kW, 4160 V induc- t i o n g e n e r a t o r . Thus, 1 0 0 0 kW of gener- a t i n g c a p a c i t y i s provided f o r each r o t o r c a r . See F igu re 1 3 .
- I ~ " " . . w ~ o .
i.I.rrrS ' -.-
- - . . - . . . . . . #O':?l-- .- .- . . .
vat- ii P-.OW. .s .~.~. . .H;?&,J
[;z-L..< PO" .2,.,,j SIOIQ, 1 0 1 I 1 " i .
Figure 13. Rotor Car End Truck Asseinbly.
The primary c o n s i d e r a t i o n given t o m a t e r i a l s f o r t h e
r o t o r was reduced weight and reduced s t r e s s e s caused by h igh body
s t r e s s e s r e s u l t i n g from th.e h igh c e n t r i f u g a l f o r c e s r e s u l t i n g from
r o t a t i o n a t 186 rpm. Alclad aluminum a l l o y provided t h e b e s t des ign
from t h e s t r e s s and c o r r o s i o n r e s i s t a n c e s t a n d p o i n t s .
Weight was n o t a problem f o r t h e car and t h e r o t o r
suppor t tower, s o s t e e l was used. Corrosion r e s i s t a n t s teel
was used on a l l weather s u r f a c e s . '
The d e s i g n c o n d i t i o n governing o v e r a l l c a r weight
was complete ly unexpected: t h e weight of 328,000 Kg (723,000 l b )
was r e q u i r e d t o p rov ide a s u f f i c i e n t l y l a r g e wheel normal f o r c e
and hence f r i c t i o n a l f o r c e t o d r i v e t h e 250 kW g e n e r a t o r w i thou t
s l i p p i n g .
Another c o n s i d e r a t i o n i n t h e s t r u c t u r a l d e s i g n was
t o d i v i d e t h e r o t o r and c a r s t r u c t u r e i n t o modules and segments
s o t h a t f a c t o r y p r e f a b r i c a t e d u n i t s could be mass-produced and
d e l i v e r e d t o t h e s i t e f o r f i n a l assembly. For example, t h e rotor c y l i n d e r and cap would be f a b r i c a t e d i n e i g h t 45' segments
( r e l a t i v e t o t h e c i r c u l a r c r o s s - s e c t i o n ) i n l e n g t h s t h a t cou ld be
shipped by t r u c k o r r a i lway c a r .
Major mechanical components i n a d d i t i o n t o t h e
suspens ion system sh.own i n F igu re 1 3 i n c l u d e t h e r o t a r s p i n
system gea r ing , d r i v e sh .a f t , d r i v e g e a r s , and t h e r o t o r b e a r i n g s ,
shown i n F igu re 12. Of p a r t i c u l a r i n t e r e s t are t h e upper and lower
r o t o r suppor t b e a r i n g s , which are ve ry l a r g e . The upper b e a r i n g
s u p p o r t s t h e e n t i r e r o t o r weight and s u p p o r t s t h e r e l a t i v e l y
smal l amount o f r a d i a l load p r e s e n t a t t h i s l o c a t i o n , whereas
t h e lower b e a r i n g r e a c t s on ly r a d i a l l o a d s . ~ e a r i n g s s i z e s a r e :
o Upper bea r ing : 256 m (8.39 f t ) OD by 2 . O 1 m (6.60 f t ) I D , r o l l e r bea r ing .
Lower bea r ing : 3.39 m (11.11 f t ) OD by 3.21 m (10.55 f t ) , I D , c y l i n d r i c a l r o l l e r b e a r i n g .
A l l b e a r i n g l o a d s w i l l be t r a n s m i t t e d t o t h e tower, and thence
t o t h e r o t o r c a r .
Power transfer from the rotor car will be accomplished
by a three-slipper, spring-loaded trolley arm attached to the car.
Power will be collected by an overhead, triple-tracked, rigid
trolley rail on the inside of the track. The trolley will be
supported by commercial light posts spaced about 12.2 m apart.
The rotor cars will be coupled together in an endless.
train by two wire ropes (70 mm diameter) attached to the main frame
structure mid-point of the front and rear of each car. The point
of attachment will be 3-m above the track-sufficient to allow
.for the catenary deflection between cars.
Dynamic balancing of the rotor in the field after
assembly was proven to be simple and effective in 1930: the
rotor was rotated by its motor, and lead weights were fastened
to structural members along the length of the rotor until smooth
operation was observed on vibration measuring instrumentation.
Similar methods would be used for balancing the rotors described
herein.
A typizal site layout, road bed, and rail configuration
is shown in Figure 14. A racetrack configuration is envisioned;
however, actual track length and diameter will be larger than that
shown in Figure 14. The site included:
Cross-section service road around the outside of the track.
A spur track leading to an assembly-maintenance, and a control building.
e Drains,utilities, roadbed, and track.
e Trolleys, power distribution, and telemetered control system.
a Two viaducts under the track to faciliate access to the "in-field" portion of the track in order that the land can be used foq agriculture.
The roadbed will consist of two parallel independent
tracks. Each track will be built as follows:
An excavated, welleompacted soil base.
e A 1.6-m high ballast foundation of crushed coarse and fine aggregate.
i..
e A 36-cm-thick by 2.4-m-wide pavement o f s t e e l r e i n f o r c e d c o n c r e t e .
o A f l a t r a i l made of 51-cm wide by 10-cm t h i c k s t e e l b o l t e d t o t h e c o n c r e t e pavement every 1.2-m of t r a c k l e n g t h .
3 . 2 E l e c t r i c a l Desiqn
The e l e c t r i c a l d e s i g n cons idered f o u r components.
a Rotor Spin System Cont ro l and Ins t rumen ta t ion
e Genera tor System System
e E l e c t r i c a l I n t e r f a c e System
The r o t o r s p i n system s e l e c t e d c o n s i s t s of a 4 5 0
kW, 500 v o l t dc motor on each c a r w i t h a s i l i c o n - c o n t r o l l e d -
r e c t i f i e r d c motor c o n t r o l system. Dynamic b rak ing o f t h e r o t o r
can b e e i t h e r by r e g e n e r a t i v e b r a k i n g o r by a l lowing v i scous
d r a g t o d e c e l e r a t e t h e r o t o r . D i r e c t i o n r e v e r s a l w i l l be achieved
by r e v e r s i n g p o l a r i t y of power l e a d s t o t h e a rmature , and speed
c o n t r o l w i l l b e achieved by ba l anc ing t h e i n p u t power l e v e l t o
t h e a rma tu re a g a i h s t t h e demand of t h e c o n t r o l f u n c t i o n s i g n a l .
A motor v o l t a g e , c u r r e n t power, o r speed p r o f i l e t i m e h i s t o r y
can b e used a s a motor c o n t r o l f u n c t i o n , o r an e x t e r n a l s i g n a l
from t h e c e n t r a l computer can be used f o r c o n t r o l . This concept
w a s s e l e c t e d o v e r o t h e r methods because of t h e need f o r con-
t i n u a i l y v a r i a b l e speed c o n t r o l a s a f u n c t i o n of wind speed and
r o t o r p o s i t i o n on t h e t r a c k ; and t h e need f o r r o t o r s p i n d i r e c t i o n
r e v e r s a l twice each o r b i t of t h e t r a c k .
One of t h e major r e s u l t s o f t h e s p i n motor s tudy
was t h e d i scove ry t h a t t h e r e w e r e t h r e e sou rces of s p i n motor
l o s s e s , t h a t t h e s e l o s s e s were h i g h l y s i g n i f i c a n t , and t h a t
Madaras cons idered o n l y one o f t h e s e l o s s mechanisms. These
loss sources are:
Power r e q u i r e d t o overcome t h e v i scous f r i c t i o n of t h e r o t o r caused by sp inn ing ( t h e on ly one cons idered by Madaras) . Power r e q u i r e d t o overcome r o t o r i n e r t i a whi le a c c e l e r a t i n g th.e r o t o r from 0 t o 186 rpm, and t h e l o s s i n power d u r i n g r o t o r d e c e l e r a t i o n (Madaras assumed complete recovery o f t h e i n e r t i a l energy of t h e sp inn ing r o t o r by r e g e n e r a t i v e b r a k i n g ) .
a Power l o s t i n h-eat ing motor windings d u r i n g t h e low speed, acce l e ra t i ' on s t a g e d u r i n g which t i m e t h e inotor i s o p e r a t i n g a t very low e f f i c i e n c y ( i - e . , from 0 t o 45 pe rcen t e f f i c i e n c y a s t h e motor speed i n c r e a s e s s lowly from 0 t o 70 p e r c e n t of no-load s p e e d ) .
Of t h e s e t h r e e mechanisms, t h e l a t t e r i s by f a r
t h e most severe : on ly 4 4 pe rcen t of t h e power i n p u t t o t h e
motor i s d e l i v e r e d t o t h e s h a f t du r ing each s t a r t - u p c y c l e .
Of cou r se , l o s s e s dec rease t o o n l y about 10 p e r c e n t when t h e r o t o r
reaches f u l l speed.
Madaras a l s o e r r e d when he assumed f u l l c a p t u r e
of t h e sp inn ing r o t o r s i n e r t i a l energy by r e g e n e r a t i v e b rak ing .
However, even du r ing b rak ing , v i s cous f r i c t i o n abso rbs c o n s i d e r a b l e
amounts of power be fo re it i s a v a i l a b l e f o r r e g e n e r a t i v e b rak ing ,
and then t h e "motor-turned-generator" h e a t i n g l o s s e s ( l i k e t h e
t h i r d type of motor h e a t i n g l o s s above) absorb s o much power,
t h a t t h e r e i s on ly about 3 p e r c e n t
of t h e power o r i g i n a l l y i n p u t t o L ~ ~ I = 11OFT133.5rnl
ocyl . 18 F T I S . S ~ ) t h e s p i n motor can be recovered 1 4 0 0 ~ \ Wm,. 45,592 186 RPM SLUG-FT2 (6305m-~q-5edI
V, = 3 0 MPl4(13.4m/~l dur ing r e g e n e r a t i v e b rak ing . Thus, 1200 I ROTOR w e e l e c t e d t o u s e n a t u r a l v i s cous
1~~~ f o r c e s t o de-spin t h e r o t o r i n o r d e r
t o save w e a r on t h e s p i n motor and
t o red.uce t h e c o s t of power t r a n s f e r
equipment. -<-.,....,:-
The s e l e c t i o n o f t h e 450 MAXIMUM NET POWER OUTPUT 7 kW s i z e f o r t h e s p i n motor was
O-/ governed by a t r a d e s tudy u t i l i z i n g
- t / o u r Madaras p l a n t performance
1 (6: 0) (12 20) (1830) (2440) -400
0 2000 4 0 0 0 6000 8000 s imu la t ion s tudy , The r e s u l t s of
TRACK DIAMETER - FEET im) t h i s s tudy a r e shown i n F igu re 15.
From t h i s s t u d y , w e dec ided t h a t a
F igure 15. Optimum Motor good des ign p o i n t occur red a t a 450
Size and Maximum kW motor s i z e and a 1 3 7 2 m (4500 f t ) Power Output ve r sus Track t r a c k d i ame te r . This curve i s f o r a Diameter, 13.4 c i r c u l a r t r a c k ; however, a s w i l l m / s (30 mph) Wind Speed.
be described later, a racetrack pattern improves performance
considerably over that in Figure 15.
The generator selected for the Madaras system
was sized for 1 MW rated output from each rotor car at a rated
wind speed of 13.4m/s.~ three-phase, 60 Hz alternating current
induction generator was considered to be the best for a Madaras
plant. Although a synchronous generator is more efficient, the
problems of aligning and maintaining precisely in phase all
generators on all rotor cars in a plant seemed to overweigh the
added efficiency one would gain from a synchronous generator.
Since it is planned to use four 250 kW generators on each rotor
car (because of wheel drive torque limitations mentioned in the structural section) the alignment problem is more severe. Then,
because of possible variations in car speed caused by stretching
and contracting of the interconnecting cables as well as possible
wheel slippage, additional circulating current power losses
could be realized.
It is believed that the efficiency of the
induction generator would be in the 80 percent to 85 percent range, with a leading power factor of from 0.8 to 0.9. This
power factor would be corrected by a synchronous reactor s y s t e m
at the control building distribution station.
A schematic diagram of the complete electrical
system on each rotor car is presented in Figure 16.
The control system will include the following
component-s :
A minicomputer-based primary controller in the control h01.1 ae,
A microcomputer-based controller on each car.
A two-way radio telemetry system to link all the car units to the primary controller.
A wind sensor network dispersed around the track and hard wired underground to the primary controller.
e Monitoring instruments and control actuator circuits on each car and on system network components.
Main & Branch Breakers, Circui ts, etc, 120 Vac, 10 - 10 each - 20 Amp Ci rcu i ts
l i g h t i n g Transformer & Breaker 24001120 Vac 20 KVA, 10
Telemetry Antenna 4 each l nduct ion Gen. 4160V, 30 , 250 KVA
4160V, 30 , 40 Amp
4160V, 30 , 40 Amp
J160V, 30 , 150 Amp
4160V, 30 , 75 Amp
4160V, 30 , 75 Amp
41601500V, 30 WYI
Ground Brushes To Tracks Tracks Must Be Grounded ~ o ' p o w e r System Grid Ground
F i g u r e 1 6 . E l e c t r i c a l S c h e m a t i c of C i r c u i t r y on E a c h Rotor C a r .
An o p e r a t o r s s t a t i o n i n t h e c o n t r o l house c o n s i s t i n g of mon i to r ing in s t rumen t s and manual ove r - r ides of t h e pr imary c o n t r o l l e r .
S tandard equipment would be used f o r t h e s e i t ems ,
s o f u r t h e r d e s c r i p t i o n i s n o t war ran ted i n t h e summary. Power
p l a n t c o n t r o l would be au tomat ic ; however, CRT, pane l d i s p l a y s ,
and h a r d copy r e a d o u t s would be a v a i l a b l e f o r moni tor ing and
manual c o n t r o l modes a l s o would be provided.
System network e lements r e q u i r e d t o i n t e r f a c e
w i t h t h e v a r i o u s e l e c t r i c a l subsystems i n c l u d e :
8 Car t r o l l e y and f e e d e r bus (4160V, 3 phase, 500 ampere c a p a c i t y ) .
D i s t r i b u t i o n c i r c u i t t o t h e t r o l l e y f e e d e r bus (power p ick-of f from t h e t r o l l e y every three-and- one-half r o t o r c a r spac ings t o l i m i t t r o l l e y amperage t o 500 amperes) .
e Synchronous r e a c t o r s f o r power f a c t o r c o r r e c t i o n .
a U t i l i t y f e e d e r c i r c u i t s .
a S u b s t a t i o n .
The system network components would be 4160V,
60 Hz , 3 phase equipment. The s u b s t a t i o n would i n c l u d e t r a n s -
fo rmers t o i n t e r f a c e t h e system w i t h t h e commercial power g r i d
as w e l l a s t h o s e t o produce 480 V, 3 phase a r ~ d 120 V 1 phase
power f o r u t i l i t y c i r c u i t s used f o r l i g h t i n g and p l a n t equipment.
The subsystem would be l o c a t e d a d j a c e n t t o t h e
c o n t r o l house t o s i m p l i f y and s h o r t e n a l l f e e d e r c i r c u i t s .
4 . PERFORMANCE ANALYSIS
The o b j e c t i v e s of t h i s s tudy were: (1) t o conduct a des ign
t r a d e s t u d y of t h e v a r i o u s p l a n t o p e r a t i o n a l parameters ; ( 2 )
t o de te rmine t h e e f f e c t o f mutual i n t e r f e r e n c e between r o t o r s
on power p l a n t o u t p u t a s a f u n c t i o n of i n t e r r o t o r spac ing ; and
(-3) t o de te rmine t h e n e t power o u t p u t i n t h e form of power
d u r a t i o n cu rves c o r r e c t e d f o r mutual i n t e r f e r e n c e e f f e c t s .
Objectives of the major investigations in the design
trade study were to select for final cost analysis:
a Most efficient rotor geometry and size
a Spin motor size and track diameter (already described in Figure 15).
a Track speed and rotor rpm.
a Spin motor schedule.
These results then were merged to define the plant con-
figuration and operating conditions that appeared most attractive
from a performance standpoint and in view of certain cost and
efficiency consideration;.
Our Madaras plant performance simulation program was used
for this study. This program has provisions for inputting all data,
geometrical and operational parameters, and all losses developed
in the earlier studies, and simulates plant performance for any
set of these conditions for any wind speed. Output in the terms
of power output/rotor for a circular track of diameter D, and for
a racetrack having straight section S of any length required.
As a result of these studies, the following plant con-
figurations and operational conditions were selected for the
cost analysis.
e Rotor Geometry
a A R = 8 8 end plate diameter = 9.8 m a e/d = 2 (.32 ft) .a height = 38 m two end plates 2
(125 E t ) r, a ~ e a - 18G m2 (2000 ft ) a diameter = 4.9 m ,
(16 ft)
Spin Motor Schedule (see Figure 17 for 1/2 of cycle)
8 filaximum angular acceleration at 450 kW to ,186 rpm a Constant 186 rpm until track position of 245O a Viscous drag braking to stop 8 Reverse rotation direction and repeat cycle
9 Track Speed
a Circular Track = 8.9 m/s (20 mph) a Race Track = 13.4 m/s (30 .mph)
1.6- V,,, = I3Am/s AR = 8 Vt = 55.9 m/s e/d = 2 I ROTOR DIAMETER = 4.9m
n = 186 RPM TRACK DIAMETER = 1372 m
INSTANEOUS POWER GENERATED
INITIAI. CYCl F: WITH RFGFNFRATIVF RRBKING ; 3 A f l kW a ------ LYLLt W l l H t l t S l VlSLUUS HHAKINt i : 4 S b kW
-******** EFFECT OF USING 3 -STEP TRANSMISSION AND IMPROVED VISCOUS BRAKING : 505 kW
- 0 . 8 - I I I I I I I I I I
90 100 120 140 160 180 2 0 0 2 2 0 2 4 0 2 6 0 2 7 0 ROTOR POSITION ON TRACK - 8 DEGREES
F i g u r e 17. Net Power Output f o r One Rotor , Spin Motor Power, and Motor rpm v e r s u s Rotor P o s i t i o n on Track a s Affected by u s e o f Viscous Braking, Regenerat ive Braking, and a Three-Step Transmisskon t o Vary t h e Spin Schedule.
C i r c u l a r Track = 1372 m ( 4 5 0 0 f t ) a Racetrack - 1 3 7 2 m r n i i d . i amc te r w i t h 3050 rn (10,000
f t ) t o 19,210 m (63,000 f t )
Wind Speeds
13.4 m / s (30 mph) max 3.0 m/s ( 1 0 mph) min
A p l o t showing t y p i c a l performance o f a c i r c u l a r and a
r a c e t r a c k p l a n t i s p r e s e n t e d i n F igu re 18. I t i s i n t e r e s t i n g t o
n o t e t h a t t h e l o c i o f optimum performance o f t h e r a c e t r a c k and
c i r c u l a r p l a n t s occur a t a l l wind speeds a t t r a c k speeds of 13.4
m / s and 11.2 m / s , r e s p e c t i v e l y . (The parameter X r e p r e s e n t s t h e
t r a c k speed (VL) t o windspeed (VW) r a t i o . ) A lower t h a n optimum
t r a c k speed f o r t h e c i r c u l a r p l a n t s was s e l e c t e d t o improve annual
energy y i e l d by r educ ing i n t e r - r o t o r , mutual i n t e r f e r e n c e , l o s s e s .
The d a t a i n F igure 17 do n o t i n c l u d e t h e r e d u c t i o n i n performance
caused by m u l t i p l e r o t o r mutual i n t e r f e r e n c e .
F igu re 1 8 . N e t Power Output from one Rotor v e r s u s X a s a Funct ion of Wind Speed. Performance is Presen ted f o r Both a 1370 m (4500 ft) Diameter C i r c u l a r Track and a Racetrack having 1370 m (4500 f t ) Diameter Ends and 4880 m (16,000 f t ) S t r a i g h t S e c t i o n s .
The mutual i n t e r f e r e n c e s tudy , conducted by P r o f e s s o r
H.C. Larsen o f t h e A i r Force I n s t i t u t e o f Technology, made u s e
o f t h e v o r t e x a n a l y s i s which he developed f o r ana lyz ing t h e
G i romi l l , now under development by t h e McDonnell A i r c r a f t Company. 1
S i n c e t h e G i romi l l and t h e Madaras system a r e e s s e n t i a l l y com-
p a r a b l e i n concep t , and s i n c e t h e a n a l y s i s has been v a l i d a t e d by
wind t u n n e l s t u d i e s , t h e method was cons idered a p p r o p r i a t e f o r
t h e Madaras r o t o r mutual i n t e r f e r e n c e s tudy .
P r o f e s s o r L a r s e n ' s a n a l y s i s e s s e n t i a l l y de te rmines t h e
e f f e c t o f a l l v o r t i c e s shed from each r o t o r i n t h e p l a n t on
t h e v o r t i c e s sh.ed by a l l o t h e r r o t o r s i n a power p l a n t , and then
d e t e r m i n e s t h e e f f e c t o f t h i s v o r t e x f i e l d on t h e wind v e l o c i t y
v e c t o r a t a l l p o i n t s around t h e t r a c k o r b i t . The n e t e f f e c t i s
t h a t t h e v o r t e x f i e l d causes changes i n t h e wind v e l o c i t y v e c t o r
which reduces t h e magnitude o f t h e r o t o r ' s p ropu l s ive f o r c e al.ong
t h e t r a c k . A s r o t o r spac ing d e c r e a s e s , mutual i n t e r f e r e n c e l o s s e s
i r i c r ea se u n t i l a p o i n t i s reached where it is counte r -produc t ive
t o add m o r e r o t o r s
The e f f e c t o f i n t e r f e r e n c e i s i n t e n s i f i e d a s
t h e number of r o t o r s , N i n c r e a s e s and wind speed dec reases . The
wind speed a t which a cu rve ends r e p r e s e n t s t h e c u t - i n wind speed.
Beyond t h a t p o i n t , o u t p u t power i s undef ined. The d a t a from
F i g u r e 19 were used i n con junc t ion wi th d a t a from F i g u r e 1 8
t o deve lop t h e n e t o u t p u t from a t o t a l Madaras p l a n t t a k i n g i n t o
accoun t a l l e lec t romechanica l , aerodynamic, and mutual i n t e r f e r e n c e
l o s s e s .
The l a s t a s p e c t of t h i s s tudy was t o develop power
d u r a t i o n cu rves f o r va r ious - s i zed Madaras p l a n t s . These power
d u r a t i o n cu rves w e r e o b t a i n e d from t h e s t a n d a r d wind d u r a t i o n
c u r v e hav ing a mean wind speed of 8 . 1 m / s a t a h e i g h t o f 9
m e t e r s i n accordance w i t h ou r des ign s p e c i f i c a t i o n s . This curve
was up ra t ed t o a h e i g h t of 2 5 m ( t h e c e n t e r h e i g h t of t h e Madaras
r o t o r ) by t h e u s u a l 0.167 power law. An a d d i t i o n a l wind d u r a t i o n
c u r v e f o r Medicine Bow, ~ y o m i n g , a l s o was used t o p rov ide a
means f o r comparing Madaras p l a n t performance w i t h t h a t of a
l a r g e array of MOD-1 wind t u r b i n e g e n e r a t o r s a t Medicine Bow.
These wind d u r a t i o n cu rves and t h e r e s u l t i n g power d u r a t i o n
c u r v e s from two Madaras p l a n t s i s p re sen ted i n F igu res 2 0 and 2 1 ,
r e s p e c t i v e l y .
Figure 19 . Mutual In te r fe rence Loss Factor versus Wind Speed f o r Various Numbers of Rotors on a 1524-m Diameter Track, Constant Rotor Speed and Track Speed of 186 rpm and 1 3 . 4 m / s , Respectively.
CUMMULATIVE HOURS 2 GIVEN WIND SPEED OCCURS
F i g u r e 2 0 . Modified Design Wind Durat ion Curve t o Represent Wind Condi t ions a t a Rotor Mid-Height o f 25 m ( 8 2 f t ) Above Mean T e r r a i n Level.
PLANT l
PLAN'T l o
HOURS I N ONE YEAR
F i q u r e 21. Power Dura t ion Curves f o r t h e Two P l a n t s Shown i n F igure 6.14 Based on t h e V = 9.6 m / s Design Wind ~ u r a t i o n Curve a t 25-m Height ( F i g u r e 6 . 1 3 ) .
5. COST/PERFORMANCE ANALYSIS
Cost estimates in a modular form suitable for scaling
Madaras plants to a wide range of sizes were developed by a
professional engineering firm which specializes in cost estimating.
In addition, generalized equations describing plant geometry were
developed in terms corresponding to the modular cost variables.
Our analysis indicated that even the most efficient
circular plant was not sufficiently economical for further con- sideration. Even when accounting for the effects of an 85 per-
cent learning curve on the rotor and track, the manufacture of
500 plants comprised of 20 rotors on a 1372-m diameter track
and a 16.5 percent annual cost and a 30 year life; the minimum
installed cost of a 7.85 MW circular plant would be $1539/kW
in a region where mean wind speed is 8.1 m/s at a 9-m height.
For this same plant, the expected energy cost would be 6.2C/kW-hr,
based on annual energy output of 37.76 x lo6 kW-hr, and land
cost of $1500/acre.
On the other hand, large racetrack plants appear to be
quite attractive. Figures 22 and 23 contain parametric plots,
respectively, of cost/kW and cost/kW-hr versus rated power.
These plots indicate the relationship of the following parameters
on cost and'rated power output:
b : inter-rotor spacing in number of rotor diameters, d, where d = 4.9 m (16 ft)
S r length of the straight section of the racetrack
N = number of rotors
These curves do not reflect the effect of learning curves, do
not include land cost, and Figure 23 is based on annual costs
equal to 16.5 percent of total plant cost.
It should be remembered that the racetrack plant is
dependent upon a unidirectional wind (including reciprocal
directions) for proper operation. Such areas as those near 'large
bodies of water or near the Great Plains area, such as Medicine
Bow, Wyoming, would be ideal sites for such a'plant.
RATED POWER - MW
F i g u r e 21. Un i t P l a n t Cost ve r sus Rated Power f o r Racetrack Con- f i g u r a t i o n as a Funt ion o f In te r -Rotor Spacing, Length o f S t r a i g h t Sec t ion o f Track, and Number o f Rotors . DOE Design Wind Dura t ion Curve: V = 8 . 1 m / s @ 9 m.
RATED POWER - MW
Figure 22. Energy Cost ve r sus Rated Power f o r Racetrack Con- f i g u r a t i o n a s a Funct ion of In te r -Rotor Spacing, Length of S t r a i g h t Sec t ion of Track, and Number of Rotors . DOE Design Wind Durat ion Curve: V=8.1 m / s @9m.
32
Table 2 presents cost and performance data for the two
largest Madaras plants studied. Plant numbers indicate size;
i.e., for Plant 49-60, inter-rotor spacing is 49 rotor diameters
(d - 4.9 m), and the length of the straight track section is 60,000 ft (18,300 m). The suffix M - indicates a Medicine Bow, Wyoming, wind duration curve. Sea level air density was used
for Table 2 configurations. TABLE 2
EFFECT OF LAND COST, LEARNING CURVES, AND MEAN WIND SPEED (7) ON ?LAXT AND' EiiERG-Y COST - SEA LEVEL DEiJSITY
---
(1) Does not include land cost
(2) Based on annual cost = 16.5% of plant cost.
The separate and combined effect of learning curves, land
No. Plts. - 1 10 100
1 10 100
1 10 100
1 10 100
Plant No. -
43-60
44-60
49-60M
14-60M
.cost, and mean wknd speed on Madaras plant and energy cost are shown
in Table 2. Costs are in 1978 dollars. These data indicate that
Annual Output
10bkW-hr
931
975
1103
1170
land cost has an insignificant effect on energy cost because plant
*n
Acre
745
7 4 8
74 5
748
No. Rotors
- 170 1700 17000
190 1900 19000
170 1700 17000
190 1900 19000
-- v 9 -m Height
m/s
8.1
8.1
9.7
9.7
cost is high relative to land cost, and also because we elected to
'R
MW
211
228
211
228
purchase only that land required for the track and road, the power
Rotors-85%L.C.; Track 9aL.C.
station, and the area enclosed by a fence line offset 100 ft from
Plant''' Cost
$/kW
722 492 342
681 463 321
722 492 342
681 463 321
all plant tracks and buildings (An in Table 2 ) . The "infikld" area
inside the track would be retained by the owner for agricultural
purposes. Viaducts under the track at each end would provide i
Energy Cost s C/kW-hr (2)
Land Cost $/Acre
0
2.69 1.84 1.28
2.62 1.78 1.24
2.27 1.55 1.08
2.19 1.49 1.03
500
2.70 1.84 1.28
2.63 1.79 1.24
2.28 1.56 1.08
2.19 1.49 1.03
1000
2.71 1.85 1.29
2.64 1.79 1.25
2.28 1.56 1.09
2.20 1.50 1.04
1500
2.72 1.86 1.30
2.64 1.80 1.25
2.29 1.57 1.09
2.20 1.50 1.05
3000
2.73 1.88 1.32
2.66 1.82 1.27
2.31 1.58 1.11
2.22 1.50 1.06
access to the property, and the property would be a large, open,
unbroken expanse that would be attractive for large scale farming
(about 6460 acres for Plant 44-60).
The learning curve effect on energy cost for a given
plant can be seen by comparing one column of figures under a
given land cost or by comparing Plant 49-60 with Plant 44-60. These
data indicate that energy from Madaras plants is sensitive to
learning curves. Madaras plants also are more economical as they
are built larger, as shown drammatically in Figure 22, and to
a much smaller extent on Table 2 (compare Plant 49-60 with
Plant 44-60 energy costs) . Comparisons of the Madaras system with horizontal
axis wind turbine generators (HA-WTG) were made to determine
whether or not Madaras plants showed promise of producing electrical
energy at a lower cost than HA-WTGts ( the basic objective of this
study). Comparisons were made with HA-WTG plants proposed by
Mr. S .J. Hightower2 of the Bureau of Reclamation, Department of
Interior for installation at Medicine Bow, Wyoming. These two
plants consisted of 49 and 98 MOD-1 WTGts, respectively, designed 3
by the General Electric Company . These plants were selected for
the comparison because they utilized large, modern HA-WTG1s, and
because the study included all costs required to connect the
HA-WTG array into a complete plant, just as this Madaras plant
study has done.
Equitable bases for the comparison were developed,
and these bases were coordinated with Hightower. The more important
ground rules for the comparison were:
1978 dollars
5 year construction period
Construction interest at 7%
Plant Life of 30 years
Financing:
Federal Annual Fixed Rate = 8.41% Private Annual Fixed Rate = 15%
a Operation and ~aintenance annual cost 2% of base plant cost
a Land purchased
a Net area (An) in Table 2 for Madaras Plant
a 1500 ft diameter per HA-WTG (specified by Hightower)
a Same learning curve equations and 85% learning curve for WTG and Madaras rotor
Cost elements in the estimate for both plants included
all direct costs for equipment, electrical connection, and land;
management, engineering, and overhead; contingencies; and interest.
The comparison was made for the following two sets of
conditions:
Medicine Bow -air density ratio=0.81 (2131 m elevation)
a Two plant sizes, each type: z 98 MW, 196MW
a Mean Wind speed = 9.7 m/s @ 9-m height
a Federal financing
a Land cost = $200/acre
a Other Site -air density ratio = 1.0 - sea level Same two plant sizes
a Mean wind speed = 8.1 m/s @ 9-m height
a Private financing
Land Cost = $3000/acre
The results of this comparison are shown in Table 3,
which describes the geometry, performance, installed cost, and
annual cost and energy of each plant. Plant ID numbers assist
in the comparison; i.e., Madaras Plant 1 is compared with HA-WTG
Plant la; Plant 2 is compared with HA-WTG Plant 2a, etc. Plant 3
(also 6) was added for completeness since it was the largest
Madaras plant analyzed. The cost results for Plants 3 and 6 in
Table 3 do not agreg with those in Table 2, bccause costs in
Table 2 were altered to conform to the comparison ground rules
upon which the data in Table 3 are based.
TABLE 3
OVERALL COMPARISON O F SEVERAL MADARAS AND HA-WTG PLANTS AT TWO WIND REGIONS
( 1 ) WTG spaced i n t h r e e rows, s t a g g e r e d , e q u i l a t e r a l t r i a n g u l a r a r r a y a t 15 r o t o r d iamete r (d = 6 1 m) ( 2 ) Contingencies i n HA-WTG p l a n t inched i n s i t e and f a c i l i t i e s f i q u r e . ( 3 ) I n c l u d e s al lowance f o r funds used d u r i n g c o n s t r u c t i o n , due t o o u t r i g h t purchase o f I l h d . ( 4 ) The s u f f i x l e t t e r M r e f e r s t o Medicine Bow p l a n t s ; a l l o t h e r s f o r wind d u r a t i o n cu rve V = 8 .1 m/s. ( 5 ) Cont ingenc ies f o r HA-WTG p l a n t s a r e inc luded i n t h e e l e c t r i c a l connect ion c o s t . ( 6 ) Fixed c h a r g e s f o r Medicine Bow p l a n t s based o n F e d e r a l f i n a n c i n g a t f i x e d c h a r g e o f 8.41 p e r c e n t . A l l
o t h e r s , f i x e d c h a r g e = 15 p e r c e n t . ( 7 ) Based on a i r d e n s i t y r a t i o o f 0.81-7000 ft(2134rn) above msl .
Cost estimates of MOC-1 systems, used without modifications, were obtained from ~ i ~ h t o w e r ~ and from General 131ectric3. Both the Madaras estimates and the MOD-1 estimates2t3 were based on engineering studies, not on manuractured hardvrare cost.
The major observations drawn from the data in Table 3
are :
Plant cost is about equal for both systems.
o Annual energy output and hence plant factor is higher for the Madaras plants than for the HA-WTG plants at the 8.1 m/s mean wind speed region. MOD-1 performance data for this other site were obtained from General Electric.1
Madaras plants use considerably less gross land area than HA-WTG units spaced 15 rotor diameters apart (915 m); less net area needs to be purchased for Madaras plants; and the remaining land area in the "infield" of a Madaras plant can be used more efficiently for agriculture or industry than the broken up tracts of land scattered among arrays of HA-WTG plants.
Annual operation and maintenance costs of Madaras plants are greater because of their added complexity.
Energy cost of Madaras plants at Medicine Bow varies from 4 percent to 12 percent higher than that for comparable HA-WTG plants; and at the other site, Madaras plant energy cost is from 13.5 percent to 22.2 percent less than HA-WTG cost.
e Madaras plant energy cost relative to HA-WTG energy cost is unaffected by the magnitude of the annual fixed cost rate, but land affects the relative cost position of HA-WTG plants because HA-WTG plants use considerably more land area than Madaras plants.
6. CONCLUSIONS
This conceptual design study of the Madaras Rotor Power
Plant included an analysis of all major components of the Madaras
system. The study has successfully addressed each of the
unanswered questions outlined in Paragraph 1, and has fulfilled
the basic study objective. It is believed that a reasonably
efficient conceptual design for the Madaras system has been
developed, and that this design fulfills all criteria initially
established.
'~orneich ,T. R. , Proceedings of the Third Biennial Conference and Workshop on Wind Energy conversion Systems, Volume 1, September 19 to 21, 1977, Sponsored by the United States Department of Energy.
The more significant conclusions drawn from this study
are itemized below.
1. Madaras plants having capacities from 7.9 MW to 228
MW with annual energy output varying from 32 x lo6 kW-hr to
1170 x lo6 kW-hr are feasible. No limitations were noted that
would restrict maximum plant capacity to 228 MW. Thus, Madaras
plants are capable of providing plant capacities of interest to
electric utility companies.
2. Madaras plants having circular Lrack coaIiyurdLiur~s
are not economically competitive with HA-WTG plants because of
the large electric losses of the spin motor and the mutual inter-
ference losses which limit the number of rotor cars to about 20
per plant. The minimum track diameter appears to be 1372 m
(4500 ft) , and little improvement in performance is noted as track diameter increased.
3. Losses in a Madaras plant are significantly larger
than those of a HA-WTG plant. The aerodynamic and mechanical
losses are tolerable, but there is need to reduce the electrical
losses significantly. Until electrical and interference losses
are substantially reduced, racetrack plant confiqurations must
be used for Madaras plants.
4. For both circular and racetrack plant configurations,
minimum energy cost is obtained where minimum inter-rotor spacing
is about 44 rotor diameters (d = 4.9 m) and the minimum track
diameter (end diameter of a racetrack) is about 1372 m.
5. The free stream and boundary layer wind tunnel data
obtained during this study are the most complete set of data on
rotating cylinder versus geometry and wind speed profile available
in the literature. Thls set of data can be used directly to predict
full-sized rotating cylinder performance.
6. It is believed that the 125-ft high (38 m) Madaras
rotor offers a. superior structural alternative to 200-ft to 300-ft
(61 m to 91 m) diameter, flexible wind turbine blades when subjected to wind, gust, and tower loads.
7. The potential problem areas and disadvantages of
Madaras plants relative to HA-WTG plants are:
The Madaras system is more complex, has higher losses, and will require higher operation and maintenance costs than a horizontal axis wind turbine system.
The use of a racetrack plant configuration is necessary for optimum Madaras plant performance (at this time). Thus, Madaras plants will be limited to regions having nearly unidirectional winds or to those regions in which off-axis winds have an angular variation of less than f45O and which occur only a small portion of a total year.
8. The advantages of the Madaras plant over a comparably-
sized HA-WTG plant are:
a A rotating cylinder rotor structure is simpler and can be built to have greater structural strength, durability, and reliability as compared to large, flexible rotor blades exposed in a wind and gust environment.
a Madaras plants show higher sensitivity to economy of scale.
o Madaras plants use land more efficiently and use less land than HA-WTG plants.
9. The Madaras Rotor Power Plant concept using a race-
track plant configuration appears at least to be economically
competitive with horizontal axis wind turbine generators, and
more probably the concept shows promise of out-performing
horizontal axis systems from a number of standpoints: structural
durability, economy of scale, energy yield, and efficient use
of land. The results of this study indicate that, although the
Madaras concept does not represent a major breakthrough in wind
energy conversion technology, Madaras racetrack plant energy
cost varied from 12 percent higher to 22 percent lower than the
energy cost of MOD-1 plants. This advantage, although attractive,
is diminished by the Madaras system's limited application arising
from a possible scarcity of large, flat, land areas having
sufficiently unidirectional wind velocities, if further studies
indicate only racetrack plant configurations are feasible.
10. Although more efficient HA-WTG systems (MOD-2)
are being developed, it is believed that more efficient Madaras
systems also can be developed given the opportunity to conduct
the necessary design studies.
11. At this stage of the investigation, it is not
possible to state conclusively whether or not the Madaras system
will significantly out-perform a similarly-sized horizontal
axis wind turbine system. However, the results of the present
study, which are thought to be conservative, are sufficiently
encouraging to warrant further investigation. Areas requiring
further fit.11d y i nnl i.iil,e :
Definition of mutual interference for racetrack plants and for circular track plants havinq track end diameters greater than 8000 ft (2439 m)
Development of optimal spin schedules which include modulating rotor speed at all points along the track such that the propulsive force is optimized at all times
a Further consideration of different types of electrical equipment, transmissions, and braking techniques
Analyses of different end plate designs which promise to reduce viscous friction and inertia loads, and hence reduce spin power, without a prnpnxtionate deereast in aeroilyr.iesn\il: per Lur.~~~irl.ri(:~-!
Reduction of rotor weight and inertia by optimized design and use of new materials and construction techniques that ire cost effective. Included in this analysis should be the consideration of larger rotors, and ti Pam en^. winding . . techniques.
In-depth otudiea of power collection a ~ ~ i l distribution as well as system control
A thorough study of manufacturing technique^ t n dnvel.op the most cost-effective methods for. producing Madaras plants, and the determination of detailed costs of mass-produced units
A I . i . fe cycle cost study to include cystem reliability, as well as maintenance, operation, and depreciation ,:' costs of the system
REFERENCES
Fe.a..s.i.b i.l.i.t: '. 'I.n.v.e.s't:ia:a.t i'o.n. .+he. '~i.~.~.~.i'l.l ' .for 1. B r u l l e , R .V . , 2 - Generat ion o f 'E lec t r ' i c ' Powe'r',' Midte'r"m. Repo'r't,' Ap'r'i'l' No.v'einber 1975, Energy Research and Development Adminis t ra t ion , November 1 n 7 c
2 . Hightower, S t a n l e y J . , "A Proposed Plan f o r I n t e g r a t i o n of Wind Turbine Genera tors w i t h a Hydroe l ec t r i c System," Presen ted a t t h e Annual Meeting of t h e Missour i Basin Systems Group, Sioux F a l l s , S.D., March 9, 1977.
3 . Korneich, T . R . , Proceedings of t h e .Third B ienn ia l Conference and Workshop on Wind Energy Conversion Systems, Volume 1, September.19 t o 21, 1977, Sponsored by t h e United S t a t e s Department of. Energy. Paper by R . J . Barchet of t h e General E l e c t r i c Co., Volume I , page 76.
*U.S. GOVERNMENT PRINTING OFFICE: 1979-640-258-18?i6 41
