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