white paper 7-11-15 for pdf cd
TRANSCRIPT
CSP Ganged Heliostat Technologies
Investigations in a Tensile Based Non-imaging System
Abstract:
Background
Concentrating Solar Power (CSP) and specifically Power Tower or Beam Down type systems
achieve high levels of solar concentration and efficiency. Collecting fields comprise a large
fraction of the system installation and maintenance costs. Technological advances promise
economically competitive solar power. Skysun, LLC proposes a ganged heliostat to significantly
reduce these costs.
Method
Typically, a heliostat requires one each of the following: mirror module, support structure,
dual axis drive, post/pedestal and foundation. Each of Skysun, LLC’s heliostats require: mirror
module, reduced support structure and a single axis drive, eliminating the need for a pedestal and
foundation for each heliostat. The ganged heliostat consists of two cables supporting a plurality
of single-axis actuated heliostats. The cables act both as a supporting structure and as a
translator of focusing motions to the many heliostats. The cables terminate to an actuated
rotational member supported by a substantial post. Cable tension may be variable. This
configuration reduces the ratio of posts and foundations to heliostats, and eliminates dual axis
drive actuators, substituting single axis actuators instead. The ganged heliostat may be rotated to
the vertical for ease of robotic cleaning and water reclamation. The ganged heliostat may also be
inverted, with the reflective surface downward, to protect against weather events such as hail.
Finally, the ganged heliostat may be secured to protect against high wind conditions.
The reflective surface, which can be deformed by cable and heliostat orientation, provides an
efficient means to form a large concave collecting surface laying principally in the horizontal.
Reflected incident rays, being non-normal, suffer from astigmatism. Novel deformations of the
reflective surface eliminate astigmatic aberration. A toric - shaped deformation of the reflective
surface reduces the size of a chosen astigmatic focus, yielding higher concentration. Latitudinal
and longitudinal deformations maintain focus upon a fixed receiver. In the ideal, the astigmatic
focus is reduced to a point.
Conclusion
The goal of this paper is to outline the relatively inexpensive methods utilized by Skysun’s
ganged heliostat prototype and how the methodology may be scaled up. Skysun, LLC proposes
a ganged heliostat to significantly reduce collecting field costs to $75/m2 installed.
Key words: solar concentrating CSP Power Tower Beam Down heliostat astigmatism
deformation ganged
Problem
Skysun, LLC approached the problem of reducing collector cost first as an economic
problem. Positing that since the energy input is free, albeit at low density, the collecting field
should be as large and inexpensive as possible, initially without regard to optical aberrations or
focal location. This lack of constraint produced a large tensile - based ganged heliostat. The
design was inexpensive but suffered from astigmatism and a non-fixed focus. Next, we asked,
can the optical aberrations and focal plane location problems be solved, can the structure
survive high winds and if so, can these challenges be solved economically. The short answer is
yes. The heart of Skysun’s intellectual property describes the various methodologies that solve
the challenges cost - effectively.
Figure 1, Non-normal rays produce astigmatic aberrations
Solution
The Skysun, LLC method employs a concave reflective surface oriented in the horizontal
with its normal axis in the vertical. Obliquely incident radiation is reflected astigmatically.
Toroidal warping of the reflective surface collapses the length of the astigmatic line focus -
minimizing astigmatic aberration. Skysun’s work utilizes the tangential focus due to its
proximity to the reflectors implying a shorter tower height for the receiver, but the method
applies to all astigmatic foci.
Figure 2, Prototype ganged heliostat of 24 mirrors driven by 6 actuators, length 10m.
Lorain County Community College campus, Elyria, Ohio 2014 (Orange construction fence
airbrushed out for clarity.)
In practice, the prototype utilizes a plurality of flat mirrors; however, canted, curved, film
- like, deformable, or membranous reflective surfaces may be employed. A strip of many
mirrors, or reflectors, is supported by two parallel flexible members such as wire rope. The strip
is oriented in the horizontal with the reflective surface up. The surface of the strip forms a
catenoid; a relatively shallow catenoid approximates a spheroid or paraboloid. At one end of the
strip both flexible members terminate to tension actuators. Varying the flexible member’s
tension in unison changes the focal length of the strip, varying the tension asymmetrically warps
the strip imposing a toric surface contour. The reflective strip has its flexible members terminate
at both ends to an actuated plate, which may rotate about a horizontal axis. The actuated plates
may also be displaced vertically. Asymmetrical vertical adjustment of the plates, and therefore
the reflective surface, was used to maintain the collapsed tangential line focus at a fixed receiver
as the radiation source moves diurnally. This configuration requires six actuators per ganged
heliostat regardless of the quantity of individual heliostats. However, as the prototype scale grew
the post and anchoring structure cost rose. Skysun, LLC solved this problem by allowing each
heliostat to have an additional degree of freedom. The need for vertical displacement of the
reflective strip was eliminated with a hybrid design comprising one actuator per reflective panel,
and two actuators per ganged heliostat controlling the rotational motions. Cable tensioning
adjustment was not necessary while utilizing the hybrid design. However, cable tensioning may
be used for improved accuracy. The hybrid design heliostats, implemented in 6 of the 24 facets
of the heliostat gang of the prototype, were non-motorized. Typically, 3 of the 6 were utilized -
one at each end of the reflective strip and one located near the middle of the strip. A manually
adjusted ball/screw mechanism rotates each heliostat about an axis perpendicular to the
supporting cables (from coincident with the cables to approximately 600
inclination).
Table1, LCCC Prototype Characteristics
Figure 3
Prototype in use 6-23-2015, utilizing 3 hybrid - style heliostats (North, South and middle
heliostats), photo taken 6:36 pm (local noon plus 5 hours). Sagitta approx. 0.4 m, Reflective
Skysun’s Prototype LCCC Campus 2014 – 2015
Heliostat aperture, single flat mirror Heliostats per gang Ganged heliostat aperture
0.09m2
24 2.16m2
Accuracy, winds Calm to 15 mph Accuracy, wind gusts ~ 33 mph
4.2 to 9 mrad 37 mrad
Actuators per gang with vertical displacement Actuators per gang: 2 per gang and 1 per heliostat - hybrid style
6 26
Concentration: Gang Aperture/Focal Area x Cos. zenith angle, max achieved 14
Gangs per array( geometry of prototype’s constructed offset – gang to tower) 15 to 30
Focal ratio ganged heliostat astigmatic Focal ratio array
1.12 0.38
Fixed focus maintained, hours post local noon
6.02
strip length approx. 7.7 m, Receiver height 3.75 m to center off grade, Astigmatic focal length:
middle reflector to center of receiver approx. 8.9 m. LCCC Prototype Data Available.
Wind Survivability
Wind induced oscillation is of particular concern with any tensile structure. Skysun,
LLC, through the Adopt a City program, was assisted by NASA Glenn Research Center and
MAGNET to determine the natural frequencies of the prototype. Three triaxial accelerometers
were placed at various locations on the reflective strip. Induced vibration data was collected
with the strip operating at its high and low extremes of tension. The results are favorable for
wind survivability.
Dr. Paul Bartolotta, of NASA Glenn Research Center, explains in the excerpt below:
6) So the bottom line is that wind-induced oscillation is not a problem for the present setup. As you scale up it probably won’t be an issue either since natural frequencies typically will decrease with increased mass and relative stiffness of the structure. However, I would still measure the natural frequencies to assure that your structure follows this trend.
Full summation can be found in Appendix 1.
Dr. Bartolotta did caution that if wind induced oscillation is still a possibility there are vortex
shedding techniques that could be employed to further reduce the destructive oscillations.
NASA GRC has developed a vortex shedding calculator currently being employed in research on
the prototype.
Optical Ray Tracing Software
In discussions with Dr. Griffin, NASA GRC, and he with non-imaging colleagues, it is
believed that no existing ray tracing software is directly applicable to Skysun’s method without
software development. The cost of this development was expected to substantially exceed the
total Phase A grant budget at Skysun’s disposal. It was deemed economically prudent to build
and test a working prototype. Skysun, LLC built 2 prototypes and tested performance over an 18
month period. In addition to being cost effective, the prototype generated performance and
operational data in an exterior environment, helping to prove its viability.
Actuator Accuracy
One goal of testing the optical methodologies was to determine the ability of inexpensive
actuators to deform the reflective strip to the desired toric surface thereby minimizing the size of
the tangential line focus while maintaining the focus over time at a fixed location on a receiver.
The LCCC prototype actuator accuracy was measured as the angular change of reflected rays
between the center of the reflective strip and the focal area location on the receiver. The smallest
angular change was caused by manually energizing, for as short a period of time as possible, any
one of the actuators controlling the reflective strip. The smallest focal area location change was
approximately 1.5”. The distance from center of reflective strip to center of target averaged
355”, yielding a reflective strip control of 0.0042 radians, or 4.2 mrad. Controlling actuators are
“off the shelf” linear actuators; the tension actuator having a 3000 lb thrust rating and the
rotational actuator having a 250 lb thrust rating. The hybrid heliostats were more accurate (1/2”
to 1”location change at receiver), but were manually adjusted. The ganged heliostat focusing
method employed the two rotational actuators, one at each end of reflective strip, and manual
adjustment of the individual heliostat’s rotational orientation. This hybrid method does not
require any change in cable tension or vertical displacement of the reflective strip substantially
reducing cost.
Accuracy During Windy Conditions
The DOE's SunShot goal is for heliostats to be operational up to 35 mph wind speed.
The 4.2 mrad level of accuracy generally held true for wind speeds (5 to 10 mph) decreasing to
approximately 9 mrad at 15 mph. Testing at the prototype was performed with wind gusts 30 +
mph (33 mph gust recorded at nearby Lorain/Elyria airport, on 4-5-15 approximately 1:33 pm,
no anemometer was employed at site), and video of change in the focal area size was obtained.
Best focus (smallest focal area) prior to gust was 14” x 14” increasing to 26” x 21” at maximum
of gust. Focal area typically stayed focused on target within an area of approximately 2' x 2'
centered on the receiver, where individual heliostat size was 1’ x 1’. Focal area increased in size
primarily in the vertical, predominantly due to reflective strip undulation. Increase in the focal
area vertical dimension was 12” (7” in the horizontal), decreasing accuracy to approximately
37mrad in the vertical (22 mrad horizontally), during the maximum wind gust. No vortex
shedding, or movement limiting hardware were employed. Actual performance may be
somewhat better than measured due to inaccurate focal area measurement. This was caused by
receiver movement in the wind. The receiver was swaying +/-12” in longitude and latitude
during wind gusts and receiver face deviated approximately +/- 15 degrees. Focal area was
measured from video without attempting to correct for receiver movement. A rigid receiver
should allow more accurate measurement of wind induced focal degradation.
Scalability Cost Study 10.1 MWE Prototype (17% efficiency)
Utilizing Rough Terrain
A cost study of a multiple - ganged heliostat collecting field was performed by Skysun team
members. Design is based on the LCCC prototype acting as a scale model, and is depicted in
Figure 4 below. Possible sites were chosen to be near 350
N. Latitude. This is not a limiting
factor, but was used to determine and minimize heliostat shadowing. The method is most cost
efficient utilizing relatively steep grades in excess of 20%. Such terrain accommodates cable sag
with diminished infrastructure (reduced supporting post mass). Soil was assumed to be gneiss or
similar. Numerous high insolation sites with suitable terrain exist throughout the southwestern
United States.
General Characteristics of the Collecting Field
Table 2 10.1 MWE Prototype Characteristics
The collecting field is an array of 15 parallel rows of reflectors, each row comprising 4
ganged heliostats; each ganged heliostat reflective strip is 200m x 8m, comprising either13 or18
heliostats (depending on shadowing constraints). Heliostats are single-axis actuated mirror
modules of 64m2
aperture each. Each of the mirror modules is actuated by a linear actuator of
approx. 1500Kg thrust. The heliostats are supported by 2 parallel cables ( 31.75mm dia. 6 x 37,
steel), spaced 4.5m apart . The cables terminate at a rotational arm supported by a post. The
rotational arms rotate about a horizontal axle, which is parallel to the supporting cables, and is
located at the top of the posts. Each rotational arm is actuated by a gear - reduced electric motor,
or similar. A total of 5 posts support four ganged heliostats in each row, the inner 3 posts share
support of 4 ganged heliostats. Posts are 4m high. Post construction is steel: plate girder or HSS,
with box plates. Post foundations are approx 2.5m depth. Drilled shaft is approximately 1m dia.
back filled with concrete. Posts located at row ends utilize a cable - stayed ground anchor. See
Figures 4, 5 and 6.
Solar Collector Field Heliostat Total Aperture Reflective Strip Aperture Each
59,520 m2
832 to 1152 m2 (992m2 average) Heliostat Aperture Each 64 m2
Heliostat Description Actuated single axis Number of Heliostats Heliostats per Ganged Heliostat
930 13 to 18
Ganged Heliostat per Array Actuators per Ganged Heliostat Tower Height
60 2 75m
Hybrid Heliostat Field Sketch 10MWE
PlanReflective ganged strips, 15 total, each comprising 4 strip segments, 200 m long each x 8 m wide, cable spread 4.5 m
Post ( black dot ) 75 total
Receiver or target, 75 m height
Outer strips 832 m^2 eachInner strips 1152 m^2 eachArray total reflective Area = 59,520 m^2
232 m
Elevation 800 m
Receiver or target, 75 m height, not to scale
PostsReflective strip segment
Rolling grade of +/- 20% to 35%
Figure 4
Plan Heliostat, Cables, Post and Rotational Arm
Heliostat rotational axis
Post Box Girder/HSSCable Spread 4.5 m
Rotational Plate Axle
Heliostat: 4 sections Each Sub unit: 2 m x 8 m
Heliostat Axle
Rotational Arms
PostReflective strip of heliostats
Wind MitigatingHardware
Sag 20 m, Span/ Sag = 10
Grade 30%Approx.
Elevation, Single Strip
Figure 5
Post Forces and Detail
Shadowing: Outer 2 strips 50% dense = 832 m^2, Inner 2 strips 70% dense = 1152 m^2
Plan STRIP, 4 total
Post, 5 total Ground anchor, 2 totalAll posts experience same tension.Tension is constant in operation.Wind load will vary tension.
Elevation
100 Kips cable and ground anchor – 67 Kips horizontal tension
67 Kips
200 m
Post Box Girder or HSS
Cable – heliostat support
Rotational Arm, HSS
Figure 6
Heliostats
Heliostats are 64 m2 each, comprised of 4 similar sub units, each sub-unit being 2m x 8m of
reflective surface area. Mirror sub unit construction is mirror cell upon open web joist. Two sub
units are joined for the inner half of the heliostat between cables and one sub unit each outside of
cable. All 4 subunits are mounted to an axle located at the heliostat’s neutral axis and
perpendicular to the supporting cables. The axle is supported by 2 bearing surfaces, one on each
cable. An actuator rotates the heliostat about the heliostat’s neutral axis. See Figures 5 and 7.
Heliostat Sub unit DetailArea 16 m^2, 2 m x 8 m, 4 units comprise 1 heliostatWeight 297 Kg, 19 Kg/m^2Cell, frame and joist 105 KgGlass mirrors 160 KgAxle 32 Kg
Mirror facets 1 m x 1 m, or largerDesign typical for glass mirrors, reflective film on substrate may be utilized.
Hub
Figure 7 Heliostat Sub Unit Detail
Wind LoadsInner strip with greater surface area = 1152 m^2 = 12,672 ft^2Compiled with F = S x 0.004 x MPH^2 Zone AS = Sq Ft of strip Need to determine/quantify benefit of tie downs/vortex shedding.
Force( lbs/strip )
Wind Speed 25 MPH 50 MPH 75 MPH 100 MPH
Orientation
Edge on to wind
792 3,168 7,128 12,672
22.5 degree 12,123 48,490 109,102 193,960
45 degree 22,398 89,590 201,578 358,360
At max operational wind speed of 35mph:Edge on Force in lbs 1,55222.5 degree face 23,76045 degree face 43,899
Figure 8
Expected wind loads without use of wind - mitigating hardware.
Cable Tension and Rotational Arm Force Calculations
Tension Calculations Approximate
Inner strip 1120 m^2 reflective area @ 20 kg/m = 22,400 Kg strip weight22,400 Kg / 200 m strip length = 112 Kg/m, Cable sag = 20 m, Cable half length = 100 m
Cable Tension at midpoint = 112Kg/m x 100^2 = 28,000 Kg20 m x 2
Cable Tension at endpoints =
[ ( 28,000Kg^2 ) + ( 112^2 Kg/m x 100^2 m ) ] ^ 0.5 = 30,156.9 Kg
30,156.9 Kg x 2.2 = 66,345 lbs = 67 kips
Lighter weight outer strip tension made equal to 67 kips by reducing cable sag.
Rotational Arm Calculations Approximate
Arm length = 4.5 m = 180”, rotating about midpoint. Unsupported length = 90”Force at end of unsupported arm = 70 kips, Use HSS 8” x 14” x 0.625” wall
Deflection = 0.73”, Bending stress = 57 kips, weight = 1404 lbs x $1.1 = $1,544 cost
Post calcs and Costs:
Post length 6.5m (21.66’), 2.5m foundation/concrete with 4m unsupported. Post strip load 67 Kips with 1.69 safety factor. Post style plate girder with plates or HSS with plates. HSS: 2 each, 20”x12”x0.625”x 21.66’length at 127 lbs/foot 5,507 lbs Plates 0.5”x1m, 500lbs each, 2 total 1,000 lbs
Total steel post lbs 6,507 lbs
6,507 lbs x $1.25 Steel cost per post $8,134 Foundation drilled with concrete 8.3’ x $350/ft $2,905
Total installed post $11,039 Rotational arm avg. per post ($1544x8)/5posts $ 2,470
Total Post and Rotational arm $13,509 times 75 posts per field x 75
Total Collecting Field Post Cost $1,013,175
Anchors 30 (100 Kip), 60 tie downs $ 90,000
Total Field heliostat ready cost $1,103,175
Cost per Square Meter $1,103,175 / 59,520m2 = $18.53/m2
Heliostat Costs $/m^2
Mirror module and truss ( From Sandia SAND2007-3293 ) x 1.13 CPI to 2015 $27.96Axle 2” SCH 40, 19.6’ x 3.6 lb/ft x $1.19 per lb / 64m^2 $ 1.31Drive, Linear Act 3000 lb thrust 18” throw $100, 6” gear and case $50 $ 2.342 Pillow bearing 2” and clamps $ 1.00Steel cable 24,000m/59520 m^2 x $8.36/m ( 1 1/8”, 130 kips ) $ 3.37Control wifi inclinometer $75/64m^2 $ 1.17
Total Heliostat Cost $ 37.15
Heliostat Ganging Costs
Control: 2 wifi inclinometers $350/992m^2 $ 0.35Actuators: 2 for rotational arms $2000/992m^2 $2.02Installation Strip: Clamps to cables, cables to arms and heliostats to cables Cost $6,800 per strip, $6800 / 992 m^2 = $6.85Total Strip Cost $ 9.22
Total Costs $/m^2Heliostats $ 37.15Posts $ 18.53Heliostat Ganging $ 9.22Profit/OVHD 15% $ 9.72
Total Collecting Field Cost $ 74.62/ m^2Cost Penalty for Flat Land Applications: $12.00 to $14.00 per m^2
Cost penalty for flatter terrain application calculated with the following parameters:
Increase post height to 7.5 m to accommodate cable sag.
Decrease strip length to 100 m.
Maintain cable tension and array geometry.
Possible Site Locations
Several possible site locations were investigated utilizing topographical information generated
by the USGS and Google Earth. Sites were chosen to be similar in characteristic to the idealized
array presented above. Sites incorporated ganged heliostat lengths of 125 m to 275 m. Reflector
area expected to be 25% of Site area. High insolation areas of the U.S., with suitable terrain,
offer multiple GWE potential. Reflector area of larger surrounding field expected to be 5% of
Field area. This may be substantially increased by using taller posts over flatter terrain, although
at a cost penalty. Three sites are presented:
Site E - Yellow Highlighted Area (25% heliostat density), located just East of Bullhead City, AZ 847m x 373m 10 to 15 MW
Many suitable areas surround Site E. With a 5% heliostat density and an efficiency of 17%, this field has a 500MWPotential ( 2 – 3 towers).
Site F - Gray Highlighted Area (25% heliostat density), located just South of Bullhead City, AZ 943 m x 250 m, 10 to 12MW
Many suitable areas surround Site F. With a 5% heliostat density and an efficiency of 17%, this field has a 350MWPotential ( 2 – 3 towers).
Site B - Gray Highlighted Area( 25% heliostat density), located just North West of Searchlight, NV 1327 m x 314 m, 15 to 20MW
Many suitable areas surround Site B. With a 5% heliostat density and an efficiency of 17%, this field has a 200MWPotential ( 2 towers).
Skysun Intellectual Property
Skysun, LLC holds one granted patent, US 8,609,979 and three provisional patents pending.
Skysun wishes to thank attorneys Cynthia Murphy and Ray Weber for their dedication in
promoting and protecting this technology.
Alternative Configurations
The ganged methodology described above details an economical means of proper reflector
orientation for Power Tower or Beam Down applications. As such, each reflector facet’s normal
axis was not coincident with the solar point. However, the methodology may be used to orient
each of the ganged reflector’s normal axes to be generally coincident with the solar point. Such
a configuration may be utilized for PV or HCPV applications. For example, a ganged strip
carrying PV modules could be oriented with long axis in the North/South and a rise in grade to
the North (for Northern hemispheric applications). Two actuators controlling ganged rotational
movement would decrease diurnal cosine loss, decrease support structure cost and allow for
dense packing of modules upon the ganged strip. By utilizing both ganged rotational and
individual module rotational control (akin to the prototypes described above) the many modules
normal axes may be aligned to be coincident with the solar point. For greater accuracy cable
tensioning control (described in the earlier development of the LCCC prototype) may be
reintroduced to satisfy acceptance angles demanded by HCPV. This application would decrease
support structure cost.
Another application of the methodology’s ability to orient modules normal to the solar point
would utilize condensing and collimating optics in place of the PV or HCPV modules. For a
Cassegrain example, a concave reflective primary reflects to a convex fixed secondary. The
collimated output would pass through a hole in the primary to a tertiary reflector. The dual axis
actuated tertiary directs the concentrated output beam to a receiver. Many such concentrating
heliostats would be placed on a single ganged heliostat strip. Many strips would work in unison.
Additional reflections will decrease efficiency. Optical alignment and maintenance will likely
present challenges. This “Beam To” design, although substantially more complex, eliminates the
need for a tower by placing the receiver at or near ground level. Suitable collecting field
geometry would create increased flux density, implying a smaller receiver cavity. Supporting
structure cost would decrease and tower associated glare would be mitigated. Initial alignment
testing of this method using the LCCC prototype demonstrated that an accuracy of 1 to 2 degrees
is readily achievable across the ganged heliostat. As described earlier, the three heliostats
utilized were located at the ends and middle of a ganged heliostat strip of 24 heliostats (7.75 m
long). See Figure 9.
“Beam to” Type Ganged HeliostatOne of many similarheliostats shown. Allheliostats share SolarNormal Axis diurnally.Multiple ganged heliostats may becombined. Receiver may be located at or near ground level.
Ganged HeliostatRotational Axis
HeliostatRotational Axis
Supporting Cables
Solar Normal Axis: Solar Point, Primary Normaland Secondary Normal
Dual Axis Actuated Tertiary
Figure 9 depicts a Cassegrain style “Beam To” heliostat. Collimating optics are not limited to
the above description.
A trough style application would place many parabolic troughs type reflectors, on a ganged
strip. As in the above PV example, this strip may only require actuation of the ganged rotational
motion (tensioning actuation may be combined for increased accuracy). The ganged rotational
motion would maintain the each trough’s normal axis to be coincident with the solar elevation.
In addition to utilizing rough terrain, this design would decrease support structure cost.
Although the methodologies presented are non-imaging systems, the accuracy may be
adequate for a reflective strip to perform as a primary in radio astronomy. Here, a reflective
surface carried by a deformable substrate replaces the many heliostats. The ganged rotational
and tensioning motions may be augmented with reflective strip vertical displacement, as
described for the initial LCCC prototype design, for improved surface accuracy. Such a primary
could have the equivalent of large objective diameter dimension and a surface suitable to provide
acceptable definition and gain.
The above illustrative examples are not to be construed as limiting in nature.
Additional Research Areas
System Automation with Feedback
Software Development
Tracking Accuracy
Accuracy Improvement with Wind - Mitigating Hardware
Heliostat power supply hardwire vs. PV
System Integration with Storage Capability
Optimal Field Layout
Conclusion
The methodologies described in this paper promise cost efficient CSP collector fields that can
utilize rough terrain. Rough terrain use reduces the infrastructure cost of the collecting field.
This reduced cost price point is expected to meet or best the DOE Sun Shot collecting field goal
of $75 per square meter installed. Due to shadowing constraints, optimal field size is likely to
be up to 25 MWE given the assumed 75 m tower height. A tower height of 150 m could scale in
excess of 100MWE. Multiple adjacent fields may be combined. Numerous potential sites exist
throughout the high insolation areas of the United States.
Skysun, LLC looks forward to addressing the challenges that lie ahead as we move forward to
the commercialization of this technology. Skysun, LLC welcomes partnering to advance these
concepts from vision to reality.
Acknowledgements
Skysun, LLC wishes to thank the following individuals and organizations:
GLIDE Innovation Fund JumpStart
NASA GRC TBEIC MAGNET
OAI LCCC SPI
Victor Weizer, NASA retired David Borton, RPI
Sean Milroy, CE Dave Heidenreich, ME
Chris Mather, EIN Cynthia Murphy, JD, ME
Al Hepp, NASA Paul Bartolotta, NASA
DeVon Griffin, NASA Dillon Morris, Xavier University
Brent Hartman, OAI Ray Weber, JD
Appendix
1. Dr. Paul Bartolotta’s summation of LCCC prototype oscillation characteristics:
1) Due to the high stiffness of the mirrors in relation to the lower stiffness of the cable-tube assembly there is no torsional modes to worry about just bending modes. The likelihood of the heliostat to swing in the wind is more likely than what happened in the Tacoma Bridge failure.
2) The modes to be concerned about are modes 1,2,3 only. The probability to excite the structure to modes 4 and higher is highly unlikely.
3) I used the vortex shedding calculator that Dennis Huff created for you and I created a new tab for you to use that plots out the shedding frequencies and compares them to a measured limit. As you can see at 2 MPH wind you’re close to the +10% limit of mode 3 frequency. At higher wind speeds you are nowhere near a limit therefore the probability of wind-induced oscillation of the structure is not likely.
4) For you to use the calculator for other larger structures, I would recommend not to change the Strouhal Number and the Kinematic Viscosity. Keep those the same.
5) If you do build a larger structure, you’ll have to change the diameter only and measure the natural frequency of the structure just like Trevor did last week.
6) So the bottom line is that wind-induced oscillation is not a problem for the present setup. As you scale up it probably won’t be an issue either since natural frequencies typically will decrease with increased mass and relative stiffness of the structure. However, I would still measure the natural frequencies to assure that your structure follows this trend.
End