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Shown in Figure 12 are the results of film stress on the reflected image. All measurements are performed on 1m reflectors using the sun as the source, concentration ratios are considerable higher at larger apertures. The highest concentration ratios measured were on the 600 psi film stress reflector which had the narrowest and highest intensity image. The 350 psi film stress reflector had a more diffuse and lower intensity reflection, with the 100 psi film stress reflector lower still. Note, however, that in the 100 psi case the maximum intensities are lower but further away from the target center they are higher. The light concentrated by the lower film stress reflector is a lower overall intensity but scattered over a larger area. Increasing film stress pulls out wrinkles in the material and results in a more specular reflection.
Many reflector configurations were tested. Other than pressure
effects there are the effects of material wrinkling and the canopy.
Shown in Figure 13 are some of the configuration effects. The
highest intensities measured are just below 400 suns for the 600
psi unwrinkled reflector. The next highest intensities measured
(of around 360 suns) were for the same reflector but in a deliberately
wrinkled state. The reflector was folded in a manner representative
of a packaged reflector and stored in a compressed state overnight.
The effect, not surprisingly, is to scatter the image somewhat.
The effect of the canopy is quite pronounced and significantly
reduces the concentration ratios. Interestingly, the image passed
through the canopy is not scattered very much and still falls
in a 1" radius of the target center. The image is very attenuated
with much of the light completely reflected away from the target.
The effect of wrinkling with the canopy is similar to that measured
without the canopy, and not a large effect.
Correlating all canopy data the losses are much higher than expected. A correlation of all known canopy effects results in a two-pass canopy transmission of only 62% or a one pass of %79. The effect is similar for all film stresses and configurations. The measured transmissivity of the canopy was 90%. The canopy has seams which doubles up the material in a few areas. Accounting for the seams results in an overall transmissivity of 88.2%. The transmissivity of the Mylar canopy film is also a function of the incident angle of the light ray. When a light ray hits the canopy at a very oblique angle more energy is reflected away, this effect is quite pronounced around the edge of the reflector where the incident angles are quite large. A second scattering of light could be caused by wrinkles in the canopy itself. It is believed the losses are attributable to synergism between these two factors.
RAY TRACING
The main goal of the Power Antenna program is a system study to optimize the reflector configuration. Since we are unable to ground test the large aperture (6m) reflectors it is important to utilize the solar test data to calibrate our ray-tracing techniques. In this way we can develop credible optical performance estimates for larger reflectors.
In order to model the surface errors associated with wrinkling, a mathematical technique was incorporated into the ray tracing code. While the code is calculating what direction an incident light ray will be reflected a slight error is introduced using a "Monte Carlo" statistical technique. The error is in two parts, the magnitude of the direction error, and the direction of the error. An RMS slope error of s milli-radians means that the angle q the reflected ray makes with the "errorless" reflector direction has an average value of zero (along the errorless direction) and a standard deviation of s The angle q is assumed to be Gaussian-distributed. On the other hand, the azimuth angle around the "errorless direction" on the reflected ray may take is taken to be uniformly distributed. The direction of the error is assigned randomly; the result is the error cone shown in Figure 15.
The measured reflector surfaces from the V-stars testing was input into the ray tracing code as was the measured surface reflectivity parameters. RTRACE5, another L'Garde design code, was run with different levels of slope errors in order to calibrate the local slope errors. Some results of this analysis are shown in Figure 16 for the 600 psi film stress case. The measured test data is shown as the solid black line. Ray tracing runs of various slope errors were conducted and plotted. As can be seen the measured data most closely resembles the 2.0 mrad slope error case, interpolating we find a 2.2 mrad slope error. In this way we can determine the proper slope error as a function of film stress.
This analysis was conducted for the other film stresses and the results shown in Figure 17. At the lower film stresses the slope errors are quite high as expected. The wrinkled material has a higher slope error than the unwrinkled material. As the film stress is increased however, the slope error decreases. At 600 psi most of the wrinkling is pulled out of the material. The slope error at this point comes from the actual surface roughness of the metalization the global error in the reflector fabrication.
Using the above procedure and test data the ray tracing code has been calibrated to reproduce the measured intensities of inflatable reflectors at different film stresses. The technique will now be used to predict the performance of larger reflectors. Future analysis will assume that though the aperture of the reflector will be increased significantly the local surface errors will not scale but will remain the same, only a function of material and film stress. L'Garde's experience with many reflectors over the years shows this to be true. The wrinkling of the films appears similar regardless of the size of the reflector. Most of the wrinkling occurs during handling of the material and construction of the reflector though some is a function of the packaging concept. The packaging concept will vary with configuration. The Power Antennas were wrinkled using a generic packaging described in the Solar Testing Data Analysis section and therefore represent a deployed on-orbit configuration.
SYSTEM STUDY
The Jovian rendezvous mission was chosen as the design point for optimization. This complemented work conducted under the JPL Gossamer Spacecraft program, which conducted a conceptual design of the configuration during 1997. The Power Antenna optimization is more generic and not as mission specific as the Gossamer Spacecraft project. It is intended chiefly to explore the design sensitivities of the key Power Antenna variables and not to specifically refine a particular mission and bus. However, to confine the design space to a manageable effort the Jovian rendezvous mission was selected. Where possible any synergism between the two programs has been exploited.
The following mission assumptions were used in calculating
the masses of the three Power Antenna study configurations. The
main requirement in the Power Antenna is the generation of 75
watts of electricity when the antenna is oriented toward the sun.
The reflector is not deployed until fairly close to the Jovian
orbit. This assumption was made to be consistent with the mission
assumptions made during JPL's Gossamer Spacecraft program and
to reduce the complexity of de-focusing the PV array to reduce
intensities closer to sun. The mission duration is 12 months after
the antenna is inflated. The spacecraft is assumed to be in a
sleep state during the flight from Earth to Jupiter powered by
batteries and possibly a small PV array mounted directly to the
spacecraft. The antenna will be deployed before orbital insertion
to provide power and communication for the insertion itself and
must withstand the associated forces. Should the forces be higher
it is possible to re-inflate the structure briefly to reinforce
it for known high load conditions. This, however, is not explored
here. The insertion forces are assumed to be 0.05 g's axial to
the antenna centerline with ±10 degree thrust vectoring
of the nozzle.
Configuration/Deployment
The structural concept is shown in Figure 18, though the dimensions have changed slightly. A circular tube or torus made up of segments of straight tubes supports the lenticular. The torus is attached to the spacecraft by three struts spaced evenly around the circumference of the torus.
It is not practical to use a constantly inflated structure for
the main structural members of the Power Antenna. In time leaks
can develop, and with high internal pressure a tremendous amount
of make-up gas would be required to replenish the lost inflatant.
Instead a rigidization scheme is used so that the structure can
support itself without internal pressure. A rigidizable structure
would be deployed using pressurized gas, once it has reached its
final geometry it becomes rigid and internal pressure is no longer
required.
For deep space missions L'Garde has developed a practical rigidization scheme known as sub Tg (glass transition temperature) rigidization. The structure material is composed of a specially designed elastomeric compound with a Tg well below that of the on-orbit equilibrium temperature of the structure. Prior to deployment the packaged assembly will be at or near the equilibrium temperature of the spacecraft which is generally higher than the deployed equilibrium temperature due to internal electronics and control systems. The material is chosen so that the Tg will be below that of the spacecraft temperature, so the structure will be in its pliable softened state while stowed. The structure is then inflated to reach its final geometry and the pressure is held until the structure cools and becomes rigid. Once the structure is rigidized the pressure is no longer required for strength. Care must be taken not to allow the intense concentrated solar energy from the reflector to wander onto the cold rigidized structure as temporary local "softening" can occur. The possibility of thermal excursions can be minimized through the use of MLI around the cold rigidized structural elements.
The canister and deployment systems are based on the JPL Gossamer Spacecraft program. A picture of the canister concept is shown in Figure 19. This particular canister was designed for a 9m reflector with 300 psi film stress so the tanks are larger than expected. For the 6.7m class reflector however the basic canister design is valid. The L'Garde Deployment Devices (LDDs) deploy the struts in a controlled manner. The three struts are deployed at equal rates, once the struts are fully deployed the torus is inflated and finally the lenticular is brought to it's inflation pressure.
The Gossamer Spacecraft Power Antenna deployment sequence is shown in Figure 20. The deployment is initiated on the left with the jettisoning of the canister lid. The lid can be hinged if required. The next picture in the sequence shows the LDDs deploying the struts. Note the torus and lenticular are still uninflated and suspended between the extending struts. The next picture shows the struts at full deployment and the torus partially inflated. The lenticular is still not inflated. Finally the deployment is complete with the inflation of the lenticular.
System Study
The following parameters were traded off for the optimization process, film stress of the reflector membrane, aperture size, and the size of the PV array. Also optimized, are the structural considerations such as torus and strut tube diameter and material thicknesses. Mission parameters such as the loads and accelerations are fixed.
Initially the aperture was sized based on the spacecraft power requirement of 75 watts of electrical power. The optical losses shown in Table 1 were accounted for in the aperture sizing. The Sun's output at Earth's orbit is 1353 watts/m2. At Jupiter's orbit, 5.2 AU away from the Sun, the flux is 50.04 watts/m2. Assuming the losses shown below and the further assumption that about 60% of the energy concentrated by the concentrator will fall on and be usable by the PV array, the total efficiency expected is about 4.77%. To achieve a 75 watt output from the PV array with these efficiencies we need a concentrator with a 33.5 m2 aperture or 6.5m diameter. It should be noted that this is only the first iteration and that the reflector will be sized again based on the results of this analysis.
A technique was developed to analyze PV arrays at different
focal planes. Ray-tracing was conducted for each configuration
at many focal planes. The technique analyzed each focal plane
and chose the plane with the smallest yet most even and diffuse
intensity distribution, this plane yielded the lightest and most
efficient PV array design and location
Study Results
Ray tracing was conducted on the three configurations and the power generation performance was estimated. For each configuration to generate the required 75 watts of on-orbit power the aperture required was 6.7m. An unexpected result of the study was that the power generation is insensitive to the film stress. As the film stress is reduced the concentrated image becomes larger and requires a larger PV array to capture the energy. Some light is scattered by the increased wrinkling but the overall diffusing of the image leaves the PV array illuminated in an even and diffuse manner.
L'Garde has developed a tool to conduct preliminary mass estimates of candidate configurations. This tool was utilized in estimating the masses of the three 6.73m Power Antenna study configurations. The tool sized structural features like torus and strut diameters based on film stress and expected loadings and accelerations. These estimates are based on analytical calculations and compiled L'Garde test data of similar structures and configurations. Further configuration components such as the canister, inflation system, and other equipment masses are based on required packaging volumes, required inflation gas, and empirical data on similar configurations. The results from the sizing analysis are shown in Table 2 and Table 3. The predicted surface precisions for the 100, 350, and 900 psi 6.73m aperture reflectors are 1.9mm, 1.4mm, and 1.3mm RMS respectively. These conservative surface precision estimates are based on extrapolations from the 1m test reflectors. A constructed 6.7m aperture is expected to be about 1mm RMS.
The reflector and canopy masses are insensitive to internal pressure, as the membranes are the same for all configurations. A large change in mass is noted in the torus, as the increased internal pressure results directly in compressive loads in the torus (Table 3 right side). The torus tube diameter must be increased to withstand the added loads. The material properties of the cold rigidized structure are derived from L'Garde test data and theory. The struts are also effected by the internal pressure in that they must support the added mass of the torus both in compression and bending during orbital maneuvering.
The masses of the Inflatant and tanks are, as expected, a strong function of internal pressures. The leak rate of the gas due to micrometeoroid damage is a strong function of the internal pressure. The make-up gas masses are calculated using two L'Garde codes, ROID and GAS. ROID, given the expected micrometeoroid flux (in our case a flux similar to Earth's geosynchronous orbit was applied) and the geometry of the reflector, calculates the area of the holes caused by the micrometeoroids as a function of time on orbit. ROID uses data gathered on film damage during impact tests of small particles on thin membranes to calculate the effect of the micrometeoroid flux on the lenticular. The particles tested represent the size and velocities of micrometeoroids found on orbit. Once the size and number of the holes generated on orbit are calculated as a function of time, GAS calculates how much gas will leak from the reflector given the specified internal pressure. Once the mass of the make-up gas is calculated a tank mass is estimated using the most efficient composite tanks available. The results are the make-up gas and tank masses shown in Table 3.
Optical testing shows that the size and mass of the PV array necessary to collect the required 75 watts is inversely affected by the internal pressure, the effect was included in the system study. Thus, the lower film stresses have larger arrays and an associated mass penalty. The array sizes were based on the PV array design philosophy documented in the previous section. The masses were estimated by assuming a 0.94 kg/m2 areal density of the array. This density is based on other work L'Garde has conducted into deep space probes. The mass estimate is for a 4 mil thick crystalline silicon cell with 3 mils of cover glass to protect it from the space environment. The estimate also includes adhesives and connections. It is assumed the cells are mounted directly to the spacecraft and need no further substrates. Certainly, more detailed design work must be conducted to fully define the array concept, however this simple design philosophy captures the mass sensitivities between the various configurations.
SUMMARY AND CONCLUSIONS
During the SBIR Phase II of the Power Antenna program L'Garde has conducted a detailed study of the issues concerning the design and performance of the Power Antenna concept. Key parameters influencing the concept design were identified and quantified through testing and analysis.
Much design information resulted during the optical testing of the reflectors and subsequent data analysis. Reduction of internal pressure in the lenticular results in diffusing the projected image. This diffusion stems from increased surface wrinkling in the reflector material. The diffusion enlarges the image but does not scatter much light off the target, as expected. By enlarging the target region slightly, most of the incident light can still be captured. This conclusion was further confirmed by the system study, which showed a pronounced insensitivity to the reduction in film stress. Had the optical energy been severely scattered it would have missed even an enlarged target altogether and rendered the configuration less efficient.
Optical losses through the canopy were larger than predicted. A two-pass transmission through the canopy was estimated at 81% (90%2) yet a survey of the optical test data yielded a two-pass transmissivity of 63% less than expected and a significant system loss. The effect is believed to be due to high incidence angles of the incoming and reflected light rays. These losses were carried into the system study for conservatism but it is firmly believed the canopy performance can be improved through the use of anti-reflective coatings.
Calibration of the ray tracing methods to enhance accuracy proved to work very well. The simple wrinkle error model documented above was able to match the test data with surprising accuracy. The effects of thermal gradients on the reflector surface precision were not evaluated during the system study and that these effects can adversely influence optical performance. Thermal gradients, however, can be significantly reduced through the use of thermal coatings, and that conservatism in the surface precision predictions will accommodate these effects.
An RF analysis not documented in this paper was conducted that showed all reflectors exceeded the required 48.7dB gain, for good uplink/downlink with Earth, with some margin.
Results of the solar testing system study validate our prediction that the lightest system masses occur at the lowest film stress configurations. In fact dropping the reflector film stress from 600 to 100 psi can cut the system weight almost in half yet still produce the same power output. This is due in no small part to the use of a PV array as the energy conversion method. The diffusion of the image with reduced lenticular pressures eminently complements the PV requirement of a homogeneous luminous intensity profile.
The generic Jovian mission resulted in a Power Antenna subsystem mass of only 21.9kg. well within the realm of the micro-spacecraft arena, able to benefit most from its economies. This low mass yields a power density of 3.42 watts/kg. A state-of-the-art Earth orbiting system yields 100 watt/kg. of solar power. That same system in a Jovian orbit, assuming it retains its conversion efficiencies at the reduced temperatures and light intensities would yield about 3.7 watts/kg. The power antenna compares well to this performance, particularly when it includes a large aperture high gain antenna shown to exceed mission requirements.
The low cost, light weight, reliable, and environmentally benign Power Antenna concept, concurrently providing high bandwidth communications, reliable space power and thermal energy, make this an eminently enabling technology in the field of deep space probes and interplanetary travel. This new technology will allow the space community to meet the challenge of reducing mass, volume, and most importantly, the price of spacecraft and launch vehicles of the future.
ACKNOWLEDGEMENTS
The authors are indebted to Bill Nesmith of JPL, the SBIR technical monitor, for his overall guidance of the program and his expertise in the field of space power. Also, to Dr. Joel Sercel and the JPL Gossamer Spacecraft team for their enthusiasm and involvement.
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