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ШРЬАТАВШ FOAM-RIGIDIZED APPROACH TO SOLAR CONCENTRATORS Robert lymari* and James E. Houmard/ Goodyear Aircraft Corporation, Akron, Ohio Abstract

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Robert lymari* and James E. Houmard/

Goodyear Aircraft Corporation, Akron, Ohio Abstract

Inflatable, foam-rigidized solar concentrators that can be packaged in lightweight, small-volume units for launching in- to orbit and can be deployed to huge, efficient, long-life energy collection systems in space hold promise for providing power to operate a multitude of systems in both manned and un- manned vehicles* Goodyear Aircraib Corporation (GAC), under

subcontract to Sundstrand Aviation Division, Sundstrand Corp- oration, Denver, Colo«, has developed such solar concentrators for the Air Force Advanced Solar Turbo Electric Conversion

(ASTEC) system« Results of development, model fabrication, testing, and analytical and theoretical studies to date are described in this report« It is expected that a flight pro- totype suitable for integration with an ASTEC system for tests in space will be ready in 1965* Systems for space deployment and rigidization have been developed and tested« Inflatable, foam-rigidized concentrators can be built by use of proved fabrication techniques from commercially available materials«

No major breakthroughs will be required«

Introduction

The increased interest in solar energy collection systems for aerospace applications is a logical result of urgent re- quirements for efficient, reliable, power sources that can be orbited by existing or near-future launch vehicles« Such power systems are needed to operate electrical, communications life support, propulsion, and a multitude of other systems in

Presented at the ARS Space Power Systems Conference, Santa Monica, California, September 25-28, 1962«

"x"Project Engineer, Astronautics Design, Space Systems Divi- sion; presently Research Specialist, North American Aviation, Columbus, Ohio«

/Senior Stress Engineer, Structural Analysis, Aeromechanics Technology Division«

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both manned and unmanned vehicles» Solar concentrators cap- "

i t a l i z e on a natural source of energy. Inflatable, foam- rigidized concentrators add to t h i s prime advantage a high de- ployed-to-packaged volumetric r a t i o , light weighty and excel- lent potential for long-time, reliable , service-free operation in the space environment« Fig, 1 gives the weights and pack- aged volumes for various diameters of inflatable-rigidized solar concentrators using presently available materials and fabrication techniques» Improvements in weights and volumes are possible with advance materials and fabrication methods,

The i n f l a t a b l e , foam-rigidized solar concentrators conceived by Goodyear Aircraft Corporation are made up entirely of com- mercially available materials. Gores of l^ylar film thinly coated with hi^ily-reflective aluminum are seamed together and tailored to take a specific shape under pressure. This alum- inized l·lylar mirror and a loose backflap jacket are attached to a metal hub to form a balloon, or pocket. The concentrator i s equipped with specially designed and built inflation and polyurethane foam-mixing and generating devices,

Once the balloon i s inflated to the proper proportions, the generator releases foam into the backflap jacket and over the back of the Mylar mirror, which maintains the desired configur- ation under gas pressure. Mien the foam has been distributed properly and hardened and the balloon covering has burned off, the orbiting concentrator i s ready for operation. Complete processes for the fabrication of such units as well as for i t s deployment and rigidization in space are being developed and t e s t e d ,

Goodyear Aircraft's current efforts on solar concentrators are in support of the Advanced Solar Turbo Electric Conversion system, a 1^-kw space power system being b u i l t for the Air Force by Sundstrand Corporation, Denver, Colo, As Sundstrand*s subcontractor, GAC has b u i l t and t e s t e d several models of the parabolic mirror. Two 2-ft-diaitu models were built for de- ployment t e s t s in an evacuated environment. The 10-ft-diam unit shown in Fig, 2 was built to demonstrate geometric accuracy,

These and concurrent in-house efforts demonstrated the feas- i b i l i t y of the inflated, foam-rigidized solar concoitrator concept for the fabrication of large units and established the suitability of the selected materials for use in space. Work on a full-scale (UU,^-ft-diam) ground t e s t model has been started on the tool shown in Fig, 3. Scheduled for delivery early in I963, this concentrator will be used in ASTEC system

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integration tests* The ultimate objective of GACTs efforts is the delivery of a flight prototype concentrator for actual or- bital testing in 1$6$.

Significant results of development, model fabrication, tests, and theoretical and analytical studies to date are reviewed in the following discussion.

Materials

There has been considerable concern that polymers may d i s - t i l l in space. Theoretical calculations of the vapor pressure of what probably i s the lowest molecular weight found in Mylar indicate t h a t , at a temperature of 125°C, the film vapor pres-

sure will be about 10~40 m Hg. The concern for polymer sol- u b i l i t y , therefore, i s unwarranted»1 Mylar and polyurethane foams have been exposed to a high vacuum {$ x 10-7 mm Hg) for a continuous period of llj.19 hr (about 60 days) at normal temp- eratures. The resultant loss in weight was l e s s than 0.1$.

Tests also have been conducted to determine the effect of u l t r a v i o l e t radiation on the weight and mechanical properties of the candidate materials in a vacuum (£ x 10""7 mm Hg). Uh- coated Mylar, as would be expected, degraded considerably and l o s t 91$ of i t s tensile strength when exposed 60 days to u l t r a - violet radiation of about the same magnitude as that found in

space. However, the same material, coated with a 500-A thick- ness of vacuum-deposited aluminum showed only a ]\1% loss of u l - timate t e n s i l e strength, a 1.$% gain in yield strength, and an 11$ loss of tensile modulus. Polyurethane foam was found to be exceptionally stable under the same conditions. Since a space concaitrator can be designed as a Mylar-foam sandwich, with the film stressed well below i t s yield point, the loss

of t e n s i l e strength i s not significant.

Model Fabrication

Paraboloidal mirrors of the inflatable-rigidized concept are built by the accurate construction of a form on which f l a t sores are patterned t o f i t the specific configuration (see Fig. 3)# The gores then are seamed together and the double curvature i s established by internal air pressure. Fig. k shows an inflated lij-ft-diam membrane ready for application of rigidizing foam, which w i l l be diverted outside the 10-ft-diam concentrator rim» The foam i s poured onto the Mylar side of the vacuum-met alized film (through the center metal hub) in

successive layers. Some cure time i s allowed between applica- tions. A rigid metal backup structure, secured to the hub and

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encapsulated in the foam layers, is needed to maintain an accurate shape in the gravitational field (1 g) to which the ground test unit will be exposed« A space concentrator will differ only in detail,

Current efforts are concentrated on the spheroid inflation vessel shown in Fig« 5« It was fabricated on a hemispheroid tool consisting of 2-ft-diam parabolic gores placed tangent to the gores of a Ц-ft-diam hemisphere« The two identically

shaped halves were seamed at the equator (on this tool) before the model was inflated« Note the foam-retaining jacket (or backflap) of clear Mylar which contains the foam in the vacuum and zero-g environment« Several models of this size have been packaged and deployed successfully in a vacuum chamber in a manner similar to that illustrated in Fig« 6«

Factors Affecting Accuracy

If the reflector is initially patterned as a perfect para- boloid, it will not take this shape perfectly on deployment«

Fortunately, the deformations are not excessive and can be predetermined« The shape that will yield the desired para- boloidal surface can be derived by applying the principle of

superposition with reversed sign to the predetermined deforma- tions«

Generally, deformations fall into two categories: those re- sulting from fabrication and those resulting from effects of the operational environment« Possible problem areas con- sidered during these programs are listed below:

I) Ground deformation factors A) Fabrication

1) Inflation pressure deflections 2) Film and wet foam weight

3) Foam exothermic heat

k) Foam shrinkage on solidification 5) Inflation pressure release

6) Reactions from handling (turnover), sectioning, transportation, erection B) Operation

1) Tracking - accelerations, varying attitude 2) Aerodynamic

3) Thermal conditions II) Space deformation factors

A) Fabrication

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1) Inflation pressure deflections 2) Foam pressure

3) Foam exothermic heat plus radiant energy 10 Foam shrinkage on solidification

5>) Inflation pressure release B) Operation

1) Reactions from attached system component 2) Aerodynamic loads

3) Solar pressure k) Magnetic forces

5) Micrometeoroid impacts 6) Thermal conditions

Only deformations resulting from fabrication are of particular interest in the ground environment» The ground operational deformations can be reduced satisfactorily by straightforward structural design» Once the desired shape has been rigidized, it can be maintained indefinitely by providing a sufficiently rigid backup structure»

The effects of film and the weight of the first layer of wet foam act parallel to the gravity fie Id j inflation pressure acts normal to the concentrator surface» The resulting effect is small and can be corrected at the concentrator rim by a slight increase in inflation pressure» Since no backflap is required to retain the foam on the ground, foam pressure de- formation and any significant effects of foam shrinkage are eliminated«, Moreover, foam exothermic heat of reaction can be controlled by selection of the proper formulation so that the ultimate Mylar temperature can be held below the limits at which a significant change in the physical properties of the film occurs» Finally, the effects of inflation pressure release can be controlled by the rigid backup structure»

The first major step in the erection of an inflatable, foam rigidized solar concaitrator is the inflation of the para- boloidal mirror and its auxiliary sphere with gas» Effects of inflation pressure on concentrator shape are identical in both the space and ground environments» The methods of analysis that were used to determine the membrane stresses and deflections of the paraboloid when subjected to inflation pressures are summarized below»

Membrane Stresses

It is common practice to define a particular paraboloid (such as that shown in Fig» 7) by the rim diameter, D, and the

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rim a n g l e , / 3 . From the p o l a r equation with the o r i g i n a t the f o c a l p o i n t , t h e rim i s defined by

R = 2 f / ( 1 + cos/3) (1) where R i s the r a d i u s to t h e rijn and f i s the f o c a l l e n g t h .

In terms of t h e rim diameter,

f = ( D / 4 ) ( l + cos/3) csc£ (2) The r i s e of t h e p a r a b o l o i d , a s d e t e m i n e d fï>om F i g . 7 and Eq.

( 2 ) , i s

Уо = ( D / 4 ) ( 1 - c o s j 8 ) csc/3 (3) The equation of the meridian curve of t h e p a r a b o l o i d in C a r t e -

sian c o o r d i n a t e s i s

4fy = x2 (U)

and t h e slope i s

d y / d x = x / 2 f (£) where f is as given by Eq. (2).

The principal radii of curvature, />1 and p2^ are in the meri- dian plane and the plane perpendicular to the meridian plane, respectively; p2 is determined easily from geometry since the center lies on the axis of the paraboloid. Then, from Fig. 7

p2 - X CSC(£ (6)

where ^ , the parameter angle shown, i s r e l a t e d t o t h e slope of t h e p a r a b o l o i d as f o l l o w s :

tan<£ = dy/dx = x / 2 f (7) S u b s t i t u t i n g the expression f o r x , from Eq. ( 7 ) , i n t o Eq. (6)

y i e l d s t h e d e s i r e d e x p r e s s i o n for p<i*

p2-~ 2f seccf> (8)

The conventional expression for the meridian radius of cur- vature is

Г o 3 / 2

, JilifZífüÜ] (

9

)

d^y/dxz

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Differentiating Eq. (£) and substituting the re suit , along with Eq, (7)j for the proper expressions in Eq, (9) yields

/o1 = 2f sec3<£ (10)

Since the principal radii of curvature have been determined, the corresponding membrane stresses, f^ and ±2» c a n be found»

If t is the membrane thickness and p is "the inflation pressure, the meridional stress, f^, is found by considering the equi- librium of a portion of the paraboloid above the plane de- fined by the angle, fi9 From Fig* 8, for equilibrium,

2 7 T X t f1 Sin</> = Р 7 Г Х2

and

f1 = ( px/2t) cscc/> (11)

or, substituting for x firom Eq. (7)j

f1 = ( p / t ) f ьесф (12)

The hoop stress, Í2, is given by the well-known membrane equation:^

V ^ + V ^ * P

/f

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By substituting the expressions for/o^ and p2 used in Eqs*

(10) and (8) and by using Eq0 (12),

f2= f1 ( 2 - с о з 2 ф ) ( Щ )

or, on substituting "the solution for f^ from Eq, (12),

f2 = ( p / t ) f (2-cos2c/>) sec(£ (15)

Membrane Deflections

The membrane deflections of an inflated concentrator can be determined by considering an element of a p a r a l l e l c i r c l e cut from a body of revolution of constant thickness* The d i s - placement of the element resulting from internal pressure is as showi by the dotted l i n e in Elg. (?)• Upward deflections

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(v), growth in radius (u), and clockwise rotations (O) are taken as positive.

The strain in tiie hoop direction i s equal t o the r a d i a l s t r a i n ; that i s ,

2 = u/x (16)

From Hooke!s law (for an isotropic material),

€ l = ( 1 / E ) ( f1 - / i f2) (17) and

2= ( l / E K f g - ^ ) (18)

•where E i s the modulus of e l a s t i c i t y and /л i s Poisson!s r a t i o . By equating Eqs. (16) and (18), the desired expression for the r a d i a l deflection -where the stresses f^ and £2 are given by Eqs. (12) and (1$) i s obtained, as follows:

u = ( x / E ) ( f2- / t f1) = ( x / E ) U (2 -fJL- cos2 ф ) (19)

Rewriting Eq. (19) in terms of / and substituting the ex- pression for f i used in Eq. (12) yields

u = ( 2 p / E t ) f2 [ ( 2 - / i ) s e c ^ - l ] s i n £ (20)

The v e r t i c a l deflection, v, i s not so easily obtained. Prom Pig, 99 the following equations may be derived readily:

dx = ds соБф (21)

d's = ds ( 1 + € i ) (22) u + du + ds cosc/> = d's cos ( ф - 9 ) + u (23)

v-hds sin<£ = v t dv + d's sin( ф - 6 ) (2k)

By substituting the expressions for ds and d's from Eqs.

(21) and (22) for those used in Eqs. (23) and (2k) 9

du/dx = ( 1 - €1) 5есф c o s ( £ - 0 ) - 1 (25)

and

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dv/dx = \опф - ( 1 + € j ) $есф sin( ф-9) (26)

Differentiating Eq. (7) gives dx - 2f sec2 /i d/, and by sub- s t i t u t i n g t h i s for the expression used in Eq. (26), the dif- f e r e n t i a l equation for the v e r t i c a l deflection becomes

dv/d</>= 2f [tan<£ - ( 1 + € ^ sec<£ sin ( ф - 9 )]sec2(£ (27)

For the 2-ffc and 10-ft solar concentrators, i t was found that sufficient accuracy could be obtained by using an approximate expression for v* If the angular r o t a t i o n , 9, in Eq. (27) i s zero (a contradiction but also used by Timoshenko2), the equa- tion can be integrated to yield

\/ ^ - 2 f € i sec2<£ + Ci (28)

Or, on substituting the expression for €]_ from Eq. (17) along with the stresses from (12) and (1Ц),

pf sec^A / ч

v ^ ( 1 - 2/1+ /t cos2<£) + C l (2?)

The constant of integration, C]_, i s given from the boundary condition that v = 0 at / = 0. Then, сд_ = (p/Et)f2(l - p), and the deflection i s

V ^ ( p f2/ E t ) [ ( 1 -fJL) " ( I - 2 / I + /X С052ф) (30)

зес3ф]

Deflections u and v Eqs* (20) and (29) are plotted as the ddjuensionless parajreters Etu/2pf2 and Etv/2pf2 vs the angle / and the radius x in Fig* 10« This i l l u s t r a t i o n i s for a Poisson r a t i o , \L - l/U and for 10-ft-diam models with no central hubs*

The approximation for v e r t i c a l deflection, obtained as just shown, proved inaccurate for the ljlui>-ft solar concentrator currently being built* The exact expression Eq* (27) was numerically integrated* To f a c i l i t a t e t h i s integration, the rotation, 9, was f i r s t determined point by point along the meridian* Differentiating Eq. (20), with respect to / , yields

ću/сф = ( 2 p / E t ) f2[ ( 2 - ^ ) Бес2ф (Бес2ф + 1ап2ф)- \]соьф (31)

Since, by differentiating Eq. (7). dx * 2f sec2 /i d/rf, Eq. (25) may be written

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du/d<£= 2f [( 1 + 6 ^ ъесф cos ( ф - 0 ) - i ] зес2ф (32)

The desired rotation i s then given by equating the right-hand sides of Eqs. (31) and (32) and simplifying to yield

( p f / E t ) [( 2 - a ) ( 2 - c o s2A ) - c o s ^ l + cos(b

с о 5 ( ф - 0 ) = != ™ (33) 1+€ 1

where € ]_ i s given by Hooke's law Eq. (17)

Deflections u and v, as determined from Eqs» (19) and (27) for the 14l*5-ft solar concentrator, are shown in Fig» 11. They are valid only for the specific pressure and material proper- t i e s shown since the exact solution i s nonlinear (as compared with the l i n e a r , approximate solution)» The Fig» 11 conditions are for a concentrator with an 8-fb-diam central hub; thus, de- flections are referenced to the edge of the hub»

Effects of Hub Restraint

The horizontal deflections, иь, resultjjig from the r e s t r a i n t of the rigid hub, were approximated by considering the region around the hub as a thick ring subjected to a r a d i a l com- pression, ръ, applied around the inner radius, хь» For the UUei-ft model, Xfc, = Ij. f t , which was considered a good approxi- mation since the paraboloids were very shallow; the I|lu5>-ft model has a slope of only 0»10l| ft per foot at the hub radius.

The resulting deflections then were given by use of Eq. (207) in Timoshenko's Strength of M a t e r i a l s ^ which (for these

applications) resolved t o

ub= ( xb/ x ) ( ub)x = b (3U)

where (ub)x e b is the deflection of the free paraboloid (no hub) at the hub radius. Vertical deflections were ref- erenced to the edge of the hub by subtracting the deflection of the free paraboloid at the hub radius from all other vertical deflections»

Space Deformation Factors

Application of the membrane analytical results separately to the sphere and the paraboloid revealed a discrepancy between the deflections of the sphere and the paraboloid at the

juncture of the two surfaces» Only a minor distortion results,

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however, and if the juncture is outside the reflecting area of the concentrator, the effect can be neglected.

When the pressure is released, the stresses on the para- boloidal surface tend to curl the coicoitrator in toward the center. To analyze the effects of this warpage, the concen- trator is treated as a rigid shell composed of two skins and a foam core of variable thickness« The metal hub restrains the shell deflection, but its affect is assumed to be small.

The exothermic heat of foaming coupled with the radiant energy encountered in space may effect stresses or strains in the film. Foam shrinkage during curing also must be considered.

VJhile the pressure, temperature, and shrinkage of the foam as functions of time are not completely known, they can be de- termined by tests in a space chamber. Resulting data will permit analytical predictions of foaming effects by methods

similar to those developed to determine pressure release de- formations.

Of the loading conditions affecting the erected concentrator (listed under "Factors Affecting Accuracy," in a previous sec- tion) the most important from the structural viewpoint are probably the thermal conditions. Since the concentrator passes through the earth1 s shadow during its orbit, it may be exposed to the sun only part of the time. Thermal conditions are transient immediately after deployment, but eventually a stable thermal cycle is reached.

Temperature variations give rise both to thermal stresses and deflections. First, there will be a variation of tempera- ture from the face of the reflector to the back, which is al- ways in shade (although some heat reflected from the earth will strike it). Second, because the energy absorbed at a given point on the reflecting surface is a function of the angle of incidence of the sun's rays, there will be a radial temperature gradient over the face of the reflector. Third, as the reflector passes from sunlight to shade, or vice versa, a nonsymmetrical temperature distribution occurs.

Thermal stresses will occur when nonlinear gradients occur and, since a shell is a redundant structure, any gradient will produce a stress. Moreover, since the shell is of nonhomo- geneous (sandwich) construction, any temperature change also will cause a stress. Such thermal deformations may occur in any structure as a result of temperature variation and are especially important in aerospace applications since thqy dictate the limits of accuracy achievable.

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Evaluation Methods

Both thermal and optical methods^ were used t o evaluate the 10-ft solar concentrator. Each method acts as a check against the r e s u l t s obtained with the other. Thermal measurements are made of l ) the radiation intensity on the focal plane and 2) the t o t a l reflected energy. These methods are the most direct means of evaluating solar concentrator performance because they are related closely t o the basic function of the device.

Optical methods, including measurement of contour and concen- t r a t o r surface reflectance, are needed to provide detailed i n - formation on the deviation of the concentrator from a perfect paraboloid* Results are readily related to the t h e o r e t i c a l analysis of concentrator surface deformations» Furthermore, they serve as a very rapid quality t e s t for model development work.

Figure 12 shows a 10-ft-diam model mounted on a polar axis solar tracker* For thermal t e s t s , either a radiometer or various calorimeters (one of which i s shown in Fig. 12 i s mounted on the tracker. The radiation intensity was measured at various points in the focal region of t h i s concentrator with a water-cooled, Gardon f o i l radiometer that has an effective area of 0.001 sq i n . and a time constant of 0.01 sec. Figures 13 and ±k show the radiometer mounted on a water-cooled face plate located at the concentrator focal plane. The radiometer measures short pulses of intense

thermal radiation and i s particularly adaptable to continuous measurement of the high values encountered at the focus of a parabolic concentrator. Measurements were made in several radial directions to detect any non-symmetrical distributions.

Results of a radiation intensity survey are given in Figs, If? and 16. These t e s t s were performed with the instruments j u s t described. Results were converted to a space equivalent flux intensity of hX6 Btu/sq f t - h r . For the 10-ft concentra- t o r , the plane of maximum flux intensity i s approximately 2 in. farther from the mirror vertex than the theoretical focal plane (behind the focus). There i s also a slight r a d i a l dis- placement from the theoretical optical axis.

Concentrator efficiency was determined from t e s t s made by placing a variable-aperture, cold-wall calorimeter in the focal region of the 10-ft-diam concentrators. A typical calorimeter, as shown in Fig. 17, was used to determine the t o t a l energy available in the focal region. These data were obtained by simultaneous measurement of fluid-flow rate through the calorimeter and temperature r i s e in the f l u i d .

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The intensity of incident solar radiation during a l l the t h e r - mal t e s t s was measured with a normal-incident pyrheliometer.

The r e s u l t s of cold-wall calorimetry testing are shown in Fig. 18♦

Optical accuracy testing was conducted with the apparatus diagrammed ±n Fig. 19 • The five collimators, mounted on an arm, project a shaft coincident with the optical axis of the mirror« Light rays from each are projected p a r a l l e l to the optical axis and are reflected by the mirror toward the focal point of the collector. A glass indicator plate i s mounted on the same shaft» Five sets of concentric rings are drawn on the glass; each i s caitered where the light beam from the corresponding projector i n t e r s e c t s the plate "when i t i s r e - flected from a perfect parabolic surface toward the focal point. The displacement of the light beam from the center of the cone en t r i e - r i n g t a r g e t provides a measure of the geometric error.

Figure 20 shows an apparatus t h a t was used successfully t o measure the optical accuracy of a 10-ft-diam mirror« The accuracy of t h i s method depends on the precision of the bear- ing and the r i g i d i t y of the s t r u c t u r e . For larger mirrors

(up t o £0 ft in diameter) , however, i t probably would be difficult to maintain the freedom from deflection required for accurate measurement.

The r e s u l t s of mirror surface tangential accuracy, measured in l/2-deg increments about the optical axis and for 5 r a d i i

(y) represaiting 3600 equal area samples, are given in Fig«

21. These r e s u l t s were obtained by numerical integration of the intensity contribution from each mirror surface point«

Conclusions

Work on inflatable, foam-rigidized solar concentrators has resulted in a device complete with systems for space deploy- ment and rigidization and compatible for integration with the ASTEC l5-kw space power system. A concentrator suitable for integration t e s t i n g with the ASTEC systan i s being produced.

Major r e s u l t s can be summarized as follows: l ) the materials selected have been demonstrated to be suitable for use in space through testing in vacuum and u l t r a v i o l e t radiation en- vironments; 2) concentrator fabrication processes and tech- niques have been proved through the construction of numerous models; 3) methods for deployment (inflation, r i g i d i z a t i o n , burnoff) have been tested; and k) optical and thermal t e s t s for accurate geometric measurement of concentrator accuracy

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have been devised and proved through use*

Past t e s t i n g has p i n p o i n t e d those a r e a s r e q u i r i n g concen- t r a t e d e f f o r t before ground performance can be d u p l i c a t e d or improved upon i n space* More e x t e n s i v e data must be obtained on p l a s t i c film and polyurethane foam p h y s i c a l c h a r a c t e r i s t i c s before p r e c i s e c o n c a i t r a t o r s can be p a t t e r n e d f o r o r b i t a l operation*

However, i t i s expected t h a t the r e q u i r e d improvements can be achieved by use of a v a i l a b l e m a t e r i a l s and proved f a b r i c a - t i o n techniques* No breakthroughs w i l l be required* Only i n t e n s i v e development and t e s t i n g y p r o p e r l y supported by t h e o r e t i c a l a n a l y s i s , are needed t o produce s a t i s f a c t o r y con- c e n t r a t o r s for i n f l a t i o n and r i g i d i z a t i o n i n space«

References

1 Snyder, C. E. and Cross, W. B . , "Theoretical and e x p e r i - mental e v a l u a t i o n of polymeric m a t e r i a l s for use i n a space environment," Wright Air Dev. Div* Tech. Rept* no* 60-773, p* 8Ц (November i 9 6 0 ) ; a l s o GER-1008I}., Goodyear A i r c r a f t Corporation, Akron, Ohio, Vol. I I , Appendix A (January 1961).

2 Timoshenko, S . , Theory of P l a t e s and S h e l l s (McGraw-Hill Book Co. I n c . , New York, 1959)* 2nd e d . , Chap. 1U.

3 Timoshenko, S . , Strength of M a t e r i a l s (D. Van Nostrand Co. I n c . , New York, 191$), 2nd e d . , Chap. 5 , Part I I .

h Jordan, R. C*, J o u r i l e s , N . , and Liu, B. Y. H . , "Methods of evaluating s o l a r c o n c e n t r a t o r s , "Opt. Soc. Am. Paper no*

FA-11 (October 20, 1961)3 a l s o GER-10513, Goodyear A i r c r a f t Corporation, Akron, Ohio (March 2 1 , I962)*

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0 10 MIRROR DIAMETER (FEET)

Fig. 1 Weight and packaged volume for various mirror sizes (current)

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Fig. 2 Solar concentrator model (10-ft. diameter)

Fig. 3 Fabrication tool for large ground-test models

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TEN-FOOT MODEL READY FOR RISIDIZATION

Fig. k Inflated model before foaming

Fig. 5 Paraboloid with spheroid inflation vesselo (2-ffc- diameter model)

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SOLAR COLLECTOR

Fig, 6 Space deployment sequence

AXIS OF ROTATIONAL SYMMETRY

Fig, 7 Meridian curve of paraboloid

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u i u u n i u z^

V

Fig. 8 Paraboloid under internal pressure

Fig. 9 Geometry of surface element

(20)

RADIUS, v (INCHES) 0

8

6

2

•i r HORIZON v ^ V E R T I C A

♦ - MEMBRA

! 1

T A L D E F L E C T I L D E F L E C T I O N NE THICKNESS

—1 1 1

ON COMPONENT C O M P O N E N T

E = M E M B R A N E MODULUS OF E L A S T I C I T Y 0 = UNIFORM I N F L A T I O N PRESSURE f = F O C A L L E N G T H O F P A R A B O L O I D ( A ) = DIMENSIONLESS P A R A M E T E R , ^ - ~ - 2i f ( B ) " DIMENSIONLESS P A R A M E T E R , —^ ~

POISSON'S R A T I O . ,/ = 1 4 RIM A N G L E = 60 DEG

®^

_LjL—■

SLOPE ANGLE, u (DEGREES)

Fig. 10 Deflections of 10~ft model under uniform pressure

1

E = 600,000 PSI // = 0.3 T - 1 MIL P = l i x

F = 19.25 RIM ANGL

EDGE OF HUB

0"2PSI

FT E = 60 DEG

/ U

/ S

RADIUS (FEET)

Fig. 11 Deflections of i^o^-ft model under uniform pressure

(21)

F i g . 12 Model mounted on semiautomatic t r a c k e r

F i g . 13 Radiometer moimted on cooled face p l a t e (front view)

(22)

*Л»

'****«

Fig« lU Radiometer mounted on cooled face plate (rear view)

Fig» 15> Solar flux pattern (radial position)

(23)

Q 3 < O

1 1 1 - T r N O T E ;

P A T T E R N T A K E N A L O N G OPT

[ TOWA 1 V E R T

1

R D EX " *

: F

| w v

r

Í .'"

ROM E R T E X

]

1 1 I C A L AXIS

^ _ 5.155 I

L

i l T I O N A L O N G O P T I C A L AXIS (INCHES)

Fig* 16 Solar flux pattern (optical axis)

Fig. 17 Cold-wall calorimeter

(24)

CALORIMETER POSITION ON OPTICAL AXIS (INCHES)

Fig. 18 Collection efficiency of 10ft model

CONCENTRIC-RING TARGETS

PROJECTORS

F i g . 19 Draining of contour-measuring apparatus

(25)

/

шя

'X*

Fig. 20 Contois-measuring apparatus

o I

ч

<

IT a.

3

o Q

1

h

D

3

\

V

- — -"

\\ \

\ t

vy .^v

\

K E Y

f = 4.33 FT (THEORETICAL) MIRROR OUTSIDE DIAMETER - 10 FT MIRROR INSIDE DIAMETER = 2.5 FT

PERFECT REFLECTANCE FOCAL PLANE

— •— 1.5 IN.. FRONT OF FOCAL PLANE

— _ _ 1.5 |N.p BEHIND FOCAL PLANE

^\^^ > N LV > ^ . ^ . - > - ADIUS. « (INCHES)

Fig. 21 Theoretical intensity of 10-ft model

Ábra

Fig. 1 Weight and packaged volume for various mirror sizes  (current)
Fig. 2 Solar concentrator model (10-ft. diameter)
Fig. k Inflated model before foaming
Fig, 6 Space deployment sequence
+7

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