3. Aerodynamic loads
The tube passes through the troposphere into the stratosphere, and will occasionally encounter the jet stream. The aerodynamic load for a length L immersed in a jet stream of speed v = 50 m/sec is
where we have taken L = 1 km as the jet stream depth, CD = 1 and a = 1103 gm/cm3 for the upper troposphere. It may be possible to reduce this load by a factor 2{3 if the tube is aerodynamically shaped with a \weather vane" to turn it into the wind. In addition, we have made the very conservative assumption that the tube has a constant diameter. In fact, the portion at jet stream altitudes may be a few times narrower because of the higher density there (we have tacitly assumed the gas in the tube to be in pressure equilibrium with the ambient air), reducing the aerodynamic load in proportion. The cross-section required to bear this load in tension is 50 CD=S cm2. The weight of a tube of length Lt = 50 km is then
Of course, the previous calculation is not self-consistent. The tube must bear its own weight as well as that of any aerodynamic load. We could solve the self-consistent equation, but instead make the following qualitative points:
1. The balloon must support a load 1012 dyne.
2. It is essential that the along-axis tensile strength of the tube material be O(10) Kbar.
3. Minimizing CD by aerodynamic shaping and optimal orientation of the tube has large benets.
We conclude that the chimney may be feasible, but involves signicant technical risks in material and aerodynamic performance.
E. Photophoresis
Photophoresis (lift provided by asymmetric surface properties of a small oriented particle not in thermal equilibrium with its gaseous environment) has been suggested as an explanation of the presence of tropospheric soot in the stratosphere20,21. Keith22 has suggested its application to deliberately engineered aerosols for the purpose of geoengineering. Photophoresis requires a signicant temperature dierence between the particle and the gas, particles of low density, and particles with an asymmetric thermal accommodation coecient and an oset between their center of mass and center of drag.
Pueschel, et al.21 found that \ uy" soot aggregates with mean densities of a few tenths of a gm/cm3 could, if suciently asymmetric, have sucient diurnally averaged photophoretic lift to overcome gravity. However, the particles required to increase the Earth's albedo must not (unlike soot) absorb a signicant amount of Solar radiation, and are expected to have higher densities (1.8 gm/cm3 for sulfuric acid, and somewhat greater for other materials). Sulfuric acid aerosols would be spherical liquid drops without any surface asymmetry or oset between their centers of gravity and of drag. Net photophoretic lift appears unlikely for aerosols produced by the processes of Section IV.
Carefully engineered particles22 might do much better. However, their scattering properties are not likely to be a great improvement over those of mineral or liquid particles of similar dimensions, so for them to be useful it must be possible to fabricate and disperse them in megaton quantities at reasonable cost.
F. Choice of Lofting Mechanism
Two of the lofting concepts considered, rockets and guns, are technically mature and would only require engineering development. Rockets may be substantially cheaper. Chimneys would require extensive research and development, and it is dicult to estimate their cost. Photophoresis raises major questions of the ability to engineer and mass-produce suitable particles that do not absorb visible light but have sucient photophoretic lift to loft them into the stratosphere.
VII. BALLOONS
Balloons have at least three potential applications in geoengineering.
1. A means of carrying material to stratospheric altitude. The material might be a gas (such as a hydride precursor of aerosols) lling the balloon itself, or in a vessel hanging from the balloon.
2. A source of lift for a chimney, as discussed in VI D.
3. As re ective objects that themselves modify the Earth's albedo..
These three applications require dierent kinds of balloons meeting dierent technical criteria. They are best considered according to their required lifetimes rather than according to their application.
A. Short-lived balloons
The buoyancy of a balloon in pressure equilibrium with the ambient air is
where Ma, a and Ta are the mass, molecular weight and temperature of the displaced air and Mb, b and Tb are the mass, molecular weight and temperature of the gas lling the balloon. Because if Ta = Tb B is independent of altitude (equivalently, independent of atmospheric pressure) such a balloon has no equilibrium height. If B exceeds the load it will rise indenitely, until (if open at the bottom) it spills lifting gas, or (if closed) it bursts from internal overpressure once the skin expands to its maximum volume. If B is less than the load it sinks to the surface of the Earth.
In practice, the altitude of a pressure-equilibrium balloon, such as those used to loft scientic payloads to the stratosphere, is controlled by dumping ballast. If the lling gas were always in thermal equilibrium with the air it would remain at a constant altitude indenitely, once enough ballast had been dumped (or gas spilled) that the lift equals the load. But because of the diurnal variation in Solar heating of the skin (and advective heat transport to the lling gas) Ta=Tb varies and ballast or gas must be expended daily. As a result, pressure-equilibrium balloons have ight durations of O(10) days, except during polar summer and winter (\midnight Sun" or \noontime night") when there is no diurnal Solar heating cycle. Somewhat longer durations may be obtained if they are made of material that is less absorbing of Solar near-infrared radiation than polyethylene, in order to reduce the magnitude of their diurnal temperature swings, if they are baed inside to reduce transport of heat from the skin, or if they are aluminized to re ect sunlight.
These balloons must be in pressure equilibrium with the ambient air because they are made of very weak material (typically 0.8 mil polyethylene, with a tensile strength of 300 bars and even lower yield threshold, so that a 100 m radius balloon begins plastic ow at an overpressure of . 100 dyne/cm2, about 104 bar or about 102 of a oat pressure of 10 mbar at about 1200000. Such a balloon is very cheap and light, and they have been used to loft scientic payloads for many years.
1. Delivery vehicles
Short-lived balloons are satisfactory if the goal is only to deliver materials to the stratosphere. Gaseous material may either be mixed with hydrogen or helium as the lifting gas, or (if liquid or solid) may be suspended from the balloon, as are scientic payloads. Volatile materials (such as the precursor hydrides we have considered) are better carried as gases to take advantage of their buoyancy which, at least partially, osets their weight. This also avoids the need to lift the parasitic weight of a cryogenic or pressurized container. Balloon delivery of materials has been considered and rejected on the grounds that the number of balloons is excessive and that the large number of expended balloons falling to the Earth would pose an unacceptable risk to the environment2. Balloons that failed to vent or burst in the planned location might also pose a risk to aviation upon their unpredictable descent. These objections are dicult to evaluate.
A typical scientic balloon operation may cost several hundred thousand dollars, and lofts a payload of order a ton, suggesting a cost per unit mass perhaps 1{10 times that of artillery lofting. The launch of such a balloon is a tricky operation that depends on favorable weather (low wind) at the launch site.
B. Long-lived balloons
If we wish to use a balloon to support a chimney, or to eect a long-term reduction in the Earth's albedo, we must avoid daily expenditure of lift gas or ballast. The solution to this problem is an overpressure balloon, whose volume is essentially independent of its temperature. The concept is old, but its realization has depended on the development of better materials17,18.
1. Lift
To provide 1012 dynes of lift at the 30 mbar level requires a volume of about 2 1013 cm3, or a radius rb 170 m. The overpressure P it must support is a fraction fvar (the fractional diurnal temperature variation) of ambient, or 104 dyne/cm2. The required wall thickness is
The ratio of the weight Wskin of its skin to its buoyant lift is then
where we have taken a temperature of 250K, skin = 1:5 gm/cm3, fvar = 0:3 and H2 as the lling gas. The importance of the material strength is evident. For example, Mylar has an ultimate tensile strength of 1.5 Kbar23, which gives Wskin=B 0:3, so the requirement to contain the overpressure of large temperature swings would exact a large price in a Mylar balloon's lifting capability. The materials discussed in VID are much stronger, but their behavior when used to make membranes subject to isotropic tension must be understood.
2. Baloon Albedo
It is also possible to consider using balloons themselves to increase the albedo of the Earth if they are coated with a material with high re ectivity7. The obvious choice is vapordeposited aluminum, Aluminized plastic lms are widely used in applications ranging from insulation (where the aluminum layer inhibits radiative transport of heat) to space ight. A layer of 300 A of aluminum is sucient to re
ect most incident Solar visible and nearinfrared radiation, while transmitting most of the upwelling mid-infrared radiation of the Earth.
The minimum size of such a balloon is set by the requirement that the aluminum, which contributes negligibly to its strength, have a weight small compared to that of the underlying plastic. This implies r & 0:3. The thinnest plastic lms of which we are aware are 0:9 thick. The lms used in Solar sail experiments have been either 5 Mylar or 7:5 Kapton. We do not know how thin lms can be made from the high-strength materials discussed in Section VI D. For P = 104 dyne/cm2, r = 2 106S = r 1 S 200 cm, assuming the balloon is designed to minimize Wskin=B. Smaller balloons are possible (letting S be the maximum achieved tensile stress in the skin, rather than the material's limiting stress), but the minimum radius for which the buoyancy is positive is about 5{10 cm.
Unless there is a breakthrough in making and handling ultra-thin lms, the minimum diameter of an overpressure balloon will be 10{20 cm. Its mass would be 0:5 gm. Although very light, it would be large and very strong. A rain of such balloons that have reached the end of their lives would be a signicant hazard to wildlife and conceivably to aviation.
VIII. RESEARCH PROGRAM
This report has discussed a number of questions involving aerosol properties (entirely apart from our understanding of climate, either natural or subject to anthropogenic forcing) that must be answered before it can be known if aerosol mitigation of the thermal eects of increasing atmospheric CO2 is feasible. We list a number of issues in basic science, each of which needs both theoretical and experimental investigation:
1. Chemical kinetics of oxidation of gaseous hydride precursors
2. Physical kinetics of aerosol aggregation
3. Aerodynamics and aeroelasticity of chimneys and balloons
4. Properties of candidate chimney and balloon materials
5. Stratospheric transport aerosols
(a) Wind elds
(b) Turbulent diusion
(c) Photophoresis
(d) Sedimentation
6. Engineered aerosols
7. Side eects of anthropogenic stratospheric aerosols
(a) Stratospheric chemistry (ozone depletion?, etc.)
(b) Ecological consequences of increased diuse (scattered) radiation ux
(c) Tropospheric and terrestrial eects of precipitated aerosols
In addition, there are many engineering design issues that must be addressed before any aerosol climate modication plan can be developed. We believe the basic science questions should be answered rst, so that the engineering eorts can be directed in a most productive manner.
Work performed under the auspicies of the Novim Foundation. I thank the Kavli Institute of Theoretical Physics at the University of California, Santa Barbara, for hospitality.
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24 The equilibrium degree of hydration depends on the activity (fugacity) of water vapor, equivalent to relative humidity5,6. This particular composition is not a stoichiometrically dened compound, but rather a representative concentration, 84% by mass of H2SO4, of sulfuric acid aerosol in the stratosphere.
25 For macroscopic objects half the scattering is into forward angles O(=(d)) and is not readily observed, so we are familiar with the geometric cross-section only.
26 As evidenced by the lightning that accompanies volcanic eruptions.
27 The rst number is the barrel length in units of the caliber.
28 Given these arguments, why have militaries mostly used guns, except at very long ranges? The reasons are: 1. Rockets require sophisticated technology to guide them to a target, while guns are simply pointed (allowing for gravity, air drag and wind). 2. A gun-launched projectile has its full velocity out of the muzzle, while a rocket may not have a lethal impact, and may even be so slow as to be avoidable by the target, until a substantial distance from its launch. None of these arguments apply to geoengineering
29 A tube would be required because if the energy injected in the tropopause's Brunt-Visala time ( 30 sec) is less than tens of megatons, any unconned tropospheric injection would mix in the troposphere and not reach the stratosphere. Volcanoes are suciently energetic to avoid this, but continual injection is not.
Quelle: http://arxiv.org/pdf/0906.5307v1.pdf
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