Another proposal to create the lightweight, kilometers high vacuum shroud for a large ground-based telescope.
I had thought that the shroud would be lightweight because the formulas for the thickness of a vacuum chamber would be almost the same as the formulas for the thickness of a pressure chamber. The only difference I thought would be you would use the strength in compression of the material in the formula rather than the strength in tension. But then the formula for a pressure vessel says that the thickness to size ratio equals the inner pressure to be contained to the materials tensional strength ratio. So if your material had a tensional strength of 10,000 bar, within the range of common materials, and the pressure inside was only 1 bar higher than the outside, your pressure vessel would only have to be 1/10,000th as thick as it is wide. So a 100 meter wide pressure vessel would only have to be 1 cm thick. So I thought that vacuum vessels would be analogous. So if the
*compressional* strength was 10,000 bar you would likewise need a 1/10,000th as thick a wall as the vessel diameter for the pressure 1 bar on the outside and 0 bar on the inside. However, I found that the engineering for vacuum vessels is more complicated than this. (For instance, try to find a single formula for the thickness of a vacuum vessel on the web!) A key problem for such vessels is actually buckling of the structure. From looking at various examples made from steel, an approximate rule of thumb is that you need a thickness of 1/100th that of the diameter of the vessel. So for a shroud 100 meter across you would need a thickness of 1 meter. This would result in a prohibitive mass for the shroud kilometers high. So to get the thickness back to as low as it is for pressure vessels why not turn it into a problem in tension? I'm suggesting making the shroud of a high tensional strength material (or fabric) stretched over a frame. This is how I'm envisioning it:Hyperboloid of one sheet.
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There would be many of these sheets repeating up the length of the shroud, each sheet supported by rings at its top and bottom. Then the resistance to the outside pressure will be provided by the material in
*tension*. As for buckling, the shape is already "buckled": the situation is analogous to that of the strength provided by a pyramid for a tall structure. It is the shape for maximal strength under compressional pressure of its own weight since that is the shape a structure will naturally fall into if it collapsed. I don't know that the hyperboloid is the shape of maximal tensional strength against buckling but I imagine it is similar. You would also need to calculate how far apart you would keep the equally spaced rings to support the hyperboloid sheets to have maximal strength at the lowest weight. I don't know the formula for calculating the thickness of the hyperboloid so I'll look at a simpler case. Imagine a frame in the shape of a vertical rectangular box, i.e., the edges only, no faces. On each vertical open face imagine a cylindrical surface, caved inward. The 1 bar outside pressure would be supported by these cylindrical surfaces. Then the thickness should be the same as the thickness of a cylindrical pressure vessel, with the pressure supported in tension. So a 10,000 bar tensional strength material at 100 meters across would require a 1 cm thickness. For the actual shape of maximal strength the thickness would be even lower.
Bob Clark
Robert Clark wrote:
Below is a proposal for an atmospheric envelope for ground-based
> telescopes that extends up to 100,000 ft. One method would be to use
> electrohydrodynamic propulsion (EHD) to support the structure. However,
> the requirement to hold out the external air may make the weight
> requirements prohibitive.
> Could you rotate the cylindical shroud about its vertical axis to
> provide outward pressure to support the pressure of the air? The
> initial energy to start the rotation for a structure miles high would
> be very large, but then only a relatively small energy would be needed
> to keep the rotation going due to losses from atmospheric pressure. >
>
> Bob Clark
>
>
> Robert Clark wrote:
> > Robert Clark wrote:
> > > J> > > > In message ,
> > > > Robert Clark writes
> > > > ...
> > > > > Is the interferometry that can be done with radio telescopes dependent
> > > > >on distance? That is, does being at longer distance make the accurate
> > > > >combining of the different signals more difficult? I know there have
> > > > >been successful experiments with one component of the array in orbit.
> > > > >Could we place one component on the Moon?
> > > > > Could we then detect Oort cloud comets at radio wavelengths? > > > > >
> > > >
> > > > Comets don't radiate at those frequencies - or indeed any others; they
> > > > just reflect. Anyway, an interferometer isn't very sensitive; it just
> > > > has much better resolution.
> > > > An Earth/Moon interferometer has certainly been proposed, though - look
> > > > at , for
> > > > instance.
> > > > There was a proposal to use the Hubble Space Telescope to look for Oort
> > > > clouds around novae. The idea was that the increase in radiation would
> > > > evaporate the comets and the spectrum of the resulting water vapour and
> > > > other gases would be detectable.
> > >
> > >
> > > Yes, but comets do have a thermal emission which does extend into
> > > radio wavelengths. This report on the planned uses of the Square
> > > Kilometer Array suggests large Kuiper belt objects could be detected at
> > > 100 AU:
> > >
> > > Kuiper Belt Objects.
> > > "In spite of their large numbers, KBOs are faint, difficult sources,
> > > and it will be especially troublesome at visible and infrared
> > > wavelengths to find members of the outer Kuiper belt, beyond 50 AU. The > > >
> > > brightness of reflected sunlight drops off with distance d as d-4,
> > > making objects in the outer belt 5 magnitudes fainter than comparable
> > > inner belt objects. Similarly, the low temperature of the KBOs,
> > > dropping from around 40 K in the inner belt to only 20 K in the outer
> > > belt, means that the thermal emission does not start to dominate the
> > > reflected sunlight until far-infrared wavelengths.
> > > "By contrast, the SKA operating at 20 GHz will be almost ideally suited > > >
> > > to study KBOs. The linear scale which the SKA will resolve at a
> > > distance of 40 AU is 200 km. After an 8 hour integration it should be
> > > possible to achieve a 5 [sigma] detection on a 120 km object, as shown
> > > in Table 3.1. Even at a distance of 100 AU, the smallest detectable
> > > object would be 350 km in diameter, and there may be many of these
> > > objects if their size distribution is similar to that which we have
> > > measured on the inner edge of the belt. If self-gravitating clusters of > > >
> > > KBOs exist, capable of generating clumps of dust emission such as are
> > > seen around other stars, the SKA may be the tool required to find > > > them."
> > >
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> >
> > The recently discovered Kuiper belt object Sedna at around 90AU (it
> > > has a highly eccentric orbit) and 1200 km across for instance would be
> > > detected by the SKA. However, at best if you were detecting internal
> > > heat the radiated energy would be smaller by a factor of 100^2 = 10,000
> > > times at 10,000 AU than at 100 AU. So you would need a radio telescope
> > > 100 kilometers across rather than the 1 kilometer across equivalent
> > > collecting area of the SKA. At worst if this thermal emission is only
> > > solar generated, it would be smaller by a factor of 100^4 = 10,000,000
> > > and you would need a telescope 10,000 km across.
> > > That there is or has been internal radiogenic heating in comets has
> > > been supported by some studies:
> > >
> > > Radioactive Heating of Porous Comet Nuclei.
> > > D. Prialnik and M. Podolak
> > > Icarus
> > > Volume 117, Issue 2 , October 1995, Pages 420-430
> > >
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> >
> > > Some scientists have even argued the amount of this heating at least
> > > early on in the Solar Systems history may have been enough to provide
> > > comets with liquid water interiors.
> > >
> > > Interestingly a report in Nature last year supports the idea of
> > > radiogenic heating in deep Kuiper belt objects:
> > >
> > > Chilly Quaoar had a warmer past.
> > > Mark Peplow
> > > Crystalline ice suggests remote object has radioactive interior.
> > >
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> >
> > > It will be interesting to find out if Sedna which is even further out
> > > than Quaoar also has this crystalline ice on its surface.
> > >
> >
> > It *may* be that detecting them with the planned 100 meter
> > optical/infrared telescopes is feasible. David Jewitt co-discover of
> > the crystalline ice on Quaoar believes the internal heating creating
> > this form of ice is still active:
> >
> > Crystalline Ice on Kuiper Belt Object (50000) Quaoar.
> > David Jewitt (University of Hawaii) and Jane Luu (Lincoln Laboratory, > > MIT)
> >
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>
> > Then this is likely to be the case also with other Kuiper belt and
> > Oort cloud objects, Sedna for instance. Sedna was detected with just a
> > 1.2 meter telescope at 90 AU. Then *if* internal heating can allow Oort
> > cloud objects to maintain a similar surface temperature despite being
> > 100 times further away from the Sun, a 100 meter telescope could detect
> > similar sized objects at around 10,000 AU.
> > The temperature required for forming the crystalline ice is above 110
> > K. The researchers theorize internal heating allows it to form
> > subsurface then outgassing, cryovolcanism or impacts brings it to the
> > surface. If this is an ongoing process then given the trillions of Oort
> > cloud objects it may be we could observe this warmer ice during the
> > process of it coming to the surface at 110 K for some comets.
> >
> > As to creating the 100 meter or larger optical telescope I suggest the
> > method of liquid mirror telescopes with the addition of an atmospheric
> > shroud to retain mesospheric pressures through a column above the > > telescope:
> >
> > Newsgroups: sci.astro, sci.physics, sci.engr.mech, sci.space.policy
> > From: "Robert Clark"
> > Date: 29 Apr 2005 09:55:15 -0700
> > Local: Fri,Apr 29 2005 12:55 pm
> > Subject: An atmospheric envelope for ground-based telescopes.
> >
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>
> > Note that liquid mirror telescopes can cost 1/100th the cost of a
> > similarly sized solid mirror telescope. Then such a telescope itself
> > might only be $10 million rather than the $1 billion projected for a
> > usual 100 meter telescope. This would allow very many to be built at
> > different sites and latitudes, markedly increasing the total collecting
> > area for astronomical observations.
> > The method suggested for keeping the shroud erect was through
> > pressurized fluid providing thrust, but a more easy to implement method
> > may be electrohydrodynamic propulsion (EHD):
> >
> > Newsgroups: sci.astro, sci.space.policy, sci.physics,
> > sci.electronics.design, sci.electronics.misc
> > From: "Robert Clark"
> > Date: 17 May 2005 12:53:31 -0700
> > Local: Tues,May 17 2005 3:53 pm
> > Subject: Long cables to power "ioncraft" to orbit?
> >
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>
> > There was debate on this thread about whether this method would work
> > for generating thrust at high velocity. However, the method is
> > well-established for operating at low speeds, which is all that would
> > be required for erecting and maintaining the shroud at altitude.
> > Two factors that need to be calculated are the mass of the shroud
> > required to keep a near vacuum from sea level up to approx. 100,000 ft.
> > over a 100 meter diameter, and the electrical energy cost for raising
> > this mass and keeping it aloft.
> > Note that the efficiency of this propulsion method as measured by the
> > ratio of weight lifted (grams) to electrical power required (watts) is
> > proportional to the air pressure, so more power would be required at
> > high altitudes. However, the reduced pressure means the required
> > thickness of the shroud could be reduced at high altitudes so less
> > weight would need to be supported at high altitudes and so less power.
> > Then the result may be equal amount of power is required even at high > > altitudes.
> >
> >
> > Bob Clark