Curved Surface Thinsats

The first thinsats will probably be flat - this makes them easier to make on existing flat panel assembly lines. However, the substrates are engineering glass, molded from liquid glass, and they can be made with any shape.

If second generation thinsats are also uniformly thin, but have a spherical curvature like the surface of a lens, a few degrees of curvature can bring some significant advantages.

Advantage: Vibration/Flexing

A flat thinsat can vibrate or flex, like rolling a sheet of paper, at frequencies on the order of 1 Hertz. A curved thinsat can still flex, but the rolled surface has a much higher bending moment, which means the flex frequencies will be much higher as well. That means that bending force perturbations from turning on and off the electrochromic thrusters will cause less vibrations.

The thrusters will turn on and off slowly, perhaps 100 milliseconds from clear to reflective. The frequency spectrum of these slowly changing forces will drop off rapidly at higher frequencies - they will not deposit significant vibration energy at the higher resonant frequencies (hundreds of hertz? TBD) of a curved thinsat.

Glass is a pretty good resonator, as you know from running a wet finger around the edge of a wine glass. In a vacuum, without air to carry away sound, a wineglass may resonate for a long time. But glass is not completely elastic - nonlinearities and hysteresis in the material will eventually turn the vibration energy into heat. Faster resonances flex more often than slow ones, so we can expect that those resonances will dissipate faster.

Advantage???: Thermal expansion

If there is differential thermal expansion between the front and backside of a thinsat, it can curl as it moves into eclipse, and the temperature drops by almost 100C. While we can expect the curvature of a thinsat to change as well, a temperature change will not bend a thinsat in unpredictable ways, and probably won't change the radial symmetry. This needs more study - it is possible that the shape change could be worse. If so, we've eliminated this geometry, but learned an interesting way to build a thermostat spring or a temperature valve.

Advantage: Phased Array Endfire

The antenna arrays on a thinsat will be surrounded by a complex stew of conducting objects, especially the thin strips of solar cell that cover most of the surface. If a thinsat is absolutely flat, then endfire transmission - beams broadcast in the plane of the thinsat - will be difficult. Thinsats will have trouble talking to neighboring arrays in the noon orbital position. Thinsats will have trouble talking to some ground locations when they are between the 6 o'clock and 8 o'clock morning positions (and the 4'oclock and 6 o'clock afternoon orbit positions). And if we minimize night sky light pollution by orienting night-side thinsats edgewise to the day/night terminator on earth, then the terminator will get poor coverage from all night-side thinsats.

On the other hand, a slightly curved thinsat will always have some antennas exposed to edgewise targets. The coverage will not be good, but it will be better than an edgewise flat thinsat.

Advantage: Parabolic mirrors

We can have specialized thinsats working in groups, with many thinsats acting as a distributed parabolic receiver dish for a single thinsat in front of them. This will be good for radar reception, perhaps even optical imaging. Note that the off-axis curved thinsats will produce radial light pressure thrust, so we may need additional complications and optical reflectors to hold them in place relative to the rest of the array.

Advantage: Deployment

One of the problems with flat thinsats is deploying them in orbit - they will probably be somewhat "sticky" and not want to come apart. If we make the even and odd thinsats in a stack with slightly different curvatures, then their natural tendency is to spring apart, like this: (|(|(|(|(| in vacuum, while air pressure will tend to hold them together on the ground. We do not need much curvature difference to cause this to happen. Rather than need dispensing machinery, a thinsat launch stack will be naturally self-deploying.

Disadvantage? Design Complexity

A curved surface phased array is difficult to analyze with classic formulas and out-of-the-box opaque commercial software for phased array design. OTOH, it is just as amenable to numerical simulation as its flat cousins. The conductors and solar cells on the thinsat surface (flat or curved) will require numerical simulation anyway.

Accommodating Curvature in Manufacturing

One drawback of curved thinsats is that existing planar imaging systems won't work. However, large thinsat manufacturing volumes will soon justify the production of imagers with slight spherical distortion, designed to focus and project imaging patterns on a curved surface. Wafer chucks, photoresist spinners, silk-screen stencils, and other manufacturing tools can also be modified or produced specially for working with a standard curved surface.

This may actually feed back into manufacturing of everyday devices like laptop and smartphone/PDA screens. These devices use a lot of power for the backlight. If the solar cell lensing of thinsat glass is used on a complex screen, we can reduce the off-axis waste of light in these devices, saving power and increasing privacy.

• ... and if I just revealed a patentable and lucrative business idea, investors take note: pay the server sky team a lot of money, and we will only whisper such near-term ideas into your delicate shell-like ears. We have a lot more. A small fraction of our loyalty can be purchased with enough cash.

Analysis

Key words:

• shallow dome ( saucer dome )
• membrane analysis
• hoop stress

• Belleville springs

• http://www.physicsforums.com/showthread.php?t=526157

• Roark's formulas for stress and strain / Warren C. Young, Richard G. Budynas

• PSU TA658.3.G47 1984 Gere & Krawinkler Structural and Construction ...

• PSU TA660.S5 BS2 1983 Billington Thin Concrete Shell Structures

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