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The largest naval artillery shell that could be fired in the twentieth century weighed 1510 kg using the 18 inch (0.457 m) barrel designed for HMS Furious in the First World War . The size of the gun was effectively limited by the size of the ship needed to support it; the barrel itself weighed 151 tonnes and had a very complex form of construction. Such guns had a muzzle velocity of 738ms−1 and a horizontal range of about 37 km. Air drag (FD =(1/2)CDrv2A) is significant; equating the change in kinetic and potential energy with the frictional drag for a shell moving vertically gives
The drag coefficient for a streamlined projectile is reasonably constant in the subsonic and trans-sonic regions at around CD =0.5 and if it is assumed that air density decreases linearly with altitude from 1.2 to 0.1 kgm−3 at 20 km, then a simple numerical integration shows that if a 1510 kg shell were fired vertically it would need to have a muzzle velocity of about 800ms−1 (Mach 2.6) just to reach 20 km. Smaller or heavier shells travel further.
It is assumed here that a similar gun, firing a 1500 kg shell, of which 800 kg is the aerosol payload, could be (re)developed relatively easily, and that it could be mounted on land, or on a specialized barge. The shells would need to be robust in order to withstand the accelerations when firing, and they would have to be intelligent to disperse the payload at the right time: requirements that might be difficult to achieve simultaneously. To lift 10 million tonnes p.a. would require 12.5 million shots a year. Inflation-adjusted estimates based on  for a slightly smaller shell give a 2009 cost of £15 000 per shot, or about £200 billion for shells per year. Gun barrels would need to be replaced at least every 3000 shots, because of wear and the effects of the very hot gases, at a cost of £1 million per barrel, and this rate of replacement assumes that relatively low accuracy is required for stratospheric lofting. Total annual expenditure on barrels would therefore be about £4.2 billion.
At a firing rate of 5 shots per hour, with continuous firing throughout the year, some 290 barrels would be required at any one time, and each barrel would need replacing every 25 days. There would be large setup costs but these would be small by comparison with the annual cost of shells (£200 billion) and barrels (£4 billion).
These cost estimates may be considered too high because no account has been made that the shell price might be expected to reduce given the scale of the operation but this will be offset by the environmental costs associated with recovery and clean up of the spent shells. There would probably be public opposition to the establishment of such a large arsenal of ‘weapons’, and this option has been classified with a moderate environmental and moderate social cost. Although a system such as this would make use of 100-year-old technologies, there remain difficulties of making large gun barrels to withstand the very high pressures from the propellant, and it is probable that it would take many years and a large investment in heavy manufacturing facilities before an artillery system could be deployed.
Missiles differ from artillery in that they possess their own means of propulsion and guidance. There is no longer a need for the gun barrels that made up a large proportion of the cost of the artillery option. (i) Single-use missiles ‘Battlefield range ballistic missiles’ (BRBMs) such as the Pakistani Hatf-1
have a range of 70 km, a weight of 1500 kg and a payload of 500 kg [http:// www.fas.org/nuke/guide/pakistan/missile/hatf-1.htm, date accessed: 31 October 2010]. If this could be modified without incurring too much expense to yield a stratospheric rocket with a weight of approximately 2000 kg capable of lofting 1 tonne of aerosols into the stratosphere, delivering 10 million tonnes of aerosols per year would require 10 million flights per year. If particles are dispersed explosively and missiles are not retrieved, then this is also the annual number of rockets required. As a possible point of reference for the price, a sophisticated longrange cruise missile such as the Tomahawk has a unit cost of around £300 000 [http://www.fas.org/man/dod-101/sys/smart/bgm-109.htm, date accessed: 31 October 2010], thus one might assume that the short range, technologically less complex missiles required for stratospheric lofting might be procurable at a far reduced unit cost of £20 000. To inject the required amount of aerosol into the stratosphere would therefore cost 2 × 104 × 107 =£200 billion annually.
The technology is available today, but the systems are complex, so it is assumed that it would take several years before production could be increased sufficiently for such a system to be deployed effectively. There would also be significant pollution from the exhaust gases, and expended missile casings. As with artillery, it is to be expected that there would be public objections to the significant expansion in the production of war-like systems, resulting in a classification of high environmental and moderate social impact.
The cost of missiles can be significantly reduced if individual missiles are reused, in which case they would have to make a controlled landing. They would thus need to be powered after dispersing the payload so might be much more closely based on cruise missiles or a new generation of high performance UAVs. They would be expected to carry a more sophisticated particle dispersion technology and a landing mechanism, potentially doubling the unit cost to £40 000. In addition, individual missiles would need to be refuelled before each flight. If, as with balloons, one assumes 20 flights a year for each missile, then once retrieval and refuelling have been taken into account, about 500 000 missiles would be required. The initial expenditure on missiles would be £20 billion, onetenth of the cost of one-shot missiles. However, the lifetime of the missiles can be expected to be of the order of one year, so this is probably also the annual replacement cost.
Although BRBMs generally use solid rocket fuel the price of jet fuel is used here as a first approximation. If 1000 kg of a missile weighing 2000 kg is fuel, and the price of jet fuel is £0.42 kg−1 [http://www.iata.org/whatwedo/economics/fuel_monitor/Pages/index.aspx, date accessed: 7 July 2010], then the fuel cost for 10 million flights per year is £4.2 billion. Total costs are thus of the order of £25 billion p.a. As with single-use missiles, the technology largely exists today, although the rate of production would need scaling up very rapidly, and there would be the same concerns about exhaust gases. Overall, retrievable missiles are classified with a lower environmental impact than single use missiles with a comparable social impact.
(f ) Electrical systems
Electrical technology has developed to the extent that it is now feasible to use it to accelerate an object to the speeds needed by weapons. For stratospheric injection, the projectile would not need to be steered, so the system could be a fixed-axis device mounted inside a shaft in the ground, either vertically or, more probably, slightly inclined towards an area where the debris could safely fall. The naval gun discussed above achieves a muzzle velocity of 800ms−1 with 1800 g acceleration in an 18m barrel, whereas if the system consisted of a 1km long tube in the ground, the acceleration would reduce to about 35 g, which would then allow a much lighter casing to be used. Two technologies can be considered—railguns and coilguns.
Railguns are under development for use as weapons [http://en.wikipedia.org/wiki/Railgun, date accessed: 31 October 2010]. Two rails carry a large current that passes through the projectile; the interaction between these currents generates a propulsive force. In essence, it is a conventional electric motor with a single winding. The requirement for electrical contact between the rails and the projectile would lead to friction and wear, especially for systems such as those envisaged here that will be fired frequently. The very high current would also cause heating within the projectile, which would almost certainly impose constraints on the type of payload.
A railgun can provide energies of the order of 50MJ and seems feasible for SRM operations in the near future [http://www.defenseindustrydaily.com/bae-produ cing-scaleddown-rail-gun-naval-weapon-01986, date accessed: 31 October 2010] but the use of coilguns presents a more suitable alternative and for this reason the railgun option has not been costed.
Coilguns use linear motor technology [http://en.wikipedia.org/wiki/Coilgun, date accessed: 31 October 2010]. By surrounding a tube with a series of annular coils that are switched on and off in sequence, a ferromagnetic projectile can be accelerated. As for the railgun, lower accelerations are experienced if the tube is very long. Long tubes mean that less steel is needed both to provide electromagnetic coupling and to resist the inertial forces, but more material is required for the tube and more coils are needed. One of the most significant design considerations for such a gun would be the difficulty of switching the coils on and off fast enough.
If it is assumed that the projectiles are of a similar weight to the artillery shells discussed above (1500 kg), but with only 250 kg of steel and 1250 kg of payload, then 8 million shots will be needed each year or about 1000 shots an hour. Each shell would contain less steel but, unlike conventional guns where the barrel is rifled to make the shell spin to achieve stability, it is probable that the projectiles would have to be provided with deployable fins, adding to the cost. It is assumed that each shell would be cheaper than an artillery shell at about £10 000, which would give an annual cost of £80 billion. Without the need to constrain very hot high-pressure gases, the lifetime of the tubes is expected to be much longer than that of conventional gun barrels. If each gun can be fired once every 5 min, only about 80 coilguns would be needed. If it is assumed that each tube is mounted in a separate shaft drilled into the ground that costs £10 million to build, with another £10 million for the electrical equipment, then the capital cost is under £2 billion.
The kinetic energy of each 1500 kg shell at the muzzle velocity of 800ms−1 is 480MJ giving a total annual energy requirement of about 4 × 1015 J. As a rough guideline, consumer electricity prices in July 2010 were around £0.1 per kWh or £3 × 10−8 per J, giving total annual energy costs of £120 million. If the efficiency of the coilgun is 20 per cent, this would entail annual costs of £0.6 billion, which is small by comparison with the cost of the projectiles.
The overall costs are thus £2 billion setup costs plus £80 billion p.a., mainly for the shells themselves. The use of fins opens the possibility of making a reusable system, since it is conceivable that the shells could be programmed to glide back unpowered to a landing site downrange. This would significantly add to the cost and complexity of the system but would save on the number of shells that would be needed. The recovery option has not been costed because of the large number of unknown factors, but as with balloons it is expected that recovery will be a substantial contribution to the overall cost. It is assumed here that it would take about 10 years to develop a working system and to construct the required infrastructure, and there would be pollution issues associated with the spentcasings falling back to Earth. These systems have been classified as having a moderate environmental impact as a result, but a low social impact.
(g) High altitude airships
Airships have the advantage, over free-flying balloons, of being powered and able (weather permitting) to navigate back to given launch points. In 2006, Lockheed Martin was granted a $150 million contract by the US Army to construct high altitude airships capable of reaching the stratosphere for battlefield surveillance purposes [http://www.defenseindustrydaily.com/lockheedwins- 1492m-contract-for-high-altitude-airship-updated-01607, date accessed: 31 October 2010] but the project was delayed in 2008, before being re-launched in 2010 [http://remixxworld.blogspot.com/2010/09/lockheed-martins-highaltitude- airship.html, date accessed: 31 October 2010]. These airships are designed to loiter for long periods in the relatively low wind speeds at 20km (compared with the higher wind speeds at lower altitudes) rather than shuttling up and down frequently. Basing costs on such a design probably gives a lower bound on the cost of an aerosol deployment system. The prospective cost per unit has been estimated at ‘tens of millions of dollars’, so £6 million is assumed here [http://www.usatoday.com/tech/science/space/2005-07-05-air-force-balloons_x.htm, date accessed: 31 October 2010].
The payload of each airship (150m in length with a diameter of 46 m) is only 2 tonnes, so to loft 10 million tonnes of aerosols requires 5 million flights each year. If each airship is capable of performing two flights per day, including ascent, dispersal, descent and refuelling, then 7000 vessels are required, amounting to an initial £42 billion for airships. Very extensive ground handling facilities would be required, for which a similar amount probably needs to be added. Each airship carries around 135 000m3 of helium xxxxxxxxxxxxxxxxxxxxxxxxxxx (chosen for safety purposes) for buoyancy [http://www.globalsecurity.org/intell/systems/haa.htm, date accessed: 31 October 2010]. In order to return to the ground after dispersing 2 tonnes of aerosol the airship will need to discard 2 tonnes worth of lift and this is most easily achieved by dumping roughly 20 per cent of the helium in the airship. At a crude helium price of £1500 per million m3 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx [http://www.blm.gov/pgdata/etc/medialib/blm/nm/programs/0/helium_docs.Par.50876.File.dat/FY2011 Posted Price final.pdf, date accessed: 31 October 2010], £40 is required on each balloon per flight, amounting to £200 million for 5 million flights. However, there are significant concerns about the rate at which helium supplies are being depleted  and the cost is unlikely to remain so low for long. If each airship is designed to remain in the air for a year that gives a lifetime of approximately 9000 flight hours. If, as with multiple balloons, the average flight time is around 3 h and two flights are performed each day that gives a lifetime of 3000 flights a ship, or around 4 years. If the fleet is renewed at this frequency, the average annualized replacement cost would be about £10 billion.
The total is therefore about £80 billion startup costs, plus about £11 billion p.a. It is assumed that this project would take 10–20 years to reach practicality as a delivery system, and the side effects would be relatively small, apart from the significant amount of helium jettisoned during descent, giving a low social
and environmental impact.
(h) Mixing aerosols into the fuel supplies of commercial flights
It has been suggested that sulphur compounds could be added to the fuel on commercial airliners to permit the deployment of albedoenhancing aerosols without needing to expend large amounts of additional energy and resources on specifically constructed aerosol lofting mechanisms
[http://groups.google.com/ group/geoengineering/web/jet-fuel-additive, date accessed: 31 October 2010]. Commercial airliners only reach the stratosphere when flying over the poles. Elsewhere, the tropopause is above normal flight levels.
No modifications to the aircraft would be necessary and aerosols could be dispersed as part of jet engine exhaust. The practicality of such a scheme hinges on the amount of aerosol that could be delivered. There are four polar flight routes over the North Pole and none over the South Pole, accommodating about10 000 cross-polar flights per year [http://www.icao.int/icao/en/assembl/a36/wp/wp144_en.pdf, date accessed: 31 October 2010; http://travel.usatoday.com/flights/legacy/item.aspx?ak=68495594.blog&type=blog, date accessed: 31 October 2010]. Most of these flights operate between the eastern United States and eastern Asia, corresponding to a distance of roughly 10 000 km. A Boeing 747 consumes some 17.5 l of fuel per km [http://www-personal.umich.edu/∼murty/planetravel2/planetravel2.html, date accessed: 31 October 2010] corresponding to 175 000 l or 140 tonnes. Assuming that 5 per cent of this fuel payload could be allocated to transporting SO2 aerosols then this accounts for only about 70 000 tonnes of SO2 per year, or around 0.7 per cent of the necessary 10 million tonnes required. In addition, as discussed earlier, aerosols injected at the poles are believed to be much less effective for SRM than aerosol injection at mid-latitudes.
Figure 7. Tethered balloon concept. SO2 flow of 96kgs−1 or approximately 2 500 000 t yr−1, per pipe and balloon system. Pipe: 200mm o.d., 100mm i.d., 21.5km length.
(i) Balloon-supported high-pressure pipes
Pumping precursors to aerosols such as H2S or SO2 via a pipe elevated by a balloon or aerostat or has been suggested by a number of authors . The concept that is described here was developed in 2009 by one of us and has been refined with the help of the co-authors: a large high-altitude balloon or aerostat located at around 20km altitude of sufficient size can provide enough lift to support its own weight as well as the weight of a fibre-reinforced pipe, lifting devices intermittently spaced along the tether, and the weight of the fluid being pumped through the pipe  (figure 7).
The balloon system has a low cost and only moderate difficulty of manufacture, provided structural and stability considerations are satisfied. Some degree of streamlining can also be considered, but this is outside the scope of the current work.
However, the pipe needs considerable additional lift from aerodynamic surfaces providing a high lift to drag ratio. These need to be attached at a variety of altitudes to prevent the pipe from having too great an inclination to the vertical when exposed to jet streams and also to ensure suitable launch and recovery trajectories (see the forthcoming sections).
The analysis below is similar to that of Badesha et al. , where the wind profile was shown to be the most significant design driver for both the balloon size and tether tensions, and hence cost. Others also mention wind but do not factor its significant effect in their detailed analysis .
A design altitude of around 20km was chosen to be just within the stratosphere, above the tropopause, in near-equatorial regions, allowing the majority of the material injected to circulate within the stratosphere and not immediately be lost to the troposphere. A higher altitude might be preferable to reduce losses further but a far larger balloon would be required to provide the necessary lift. The other great advantage of the 20km altitude is that the wind strengths are at their lowest at this altitude, typically being of the order of 20ms−1 or less (see figure 1). However, the balloon needs to tolerate winds whose mean velocity is as much as 45ms−1 at this altitude (P. Davidson 2010, personal communication). The wind speeds in figure 1 are taken from the ERA database and do not reflect short
duration (2 min or more) gust speeds. These must be taken into account to prevent ‘blow-over’: in this scenario, the wind load on tether and balloon is sufficient to cause the balloon to be dragged sideways and downwards, leading to a pronounced fall in altitude of the balloon. This can drag the balloon into the higher wind speeds encountered at lower altitudes resulting in balloon failure. A wind speed of 55ms−1 (continuous + 20%) has been used for ‘semi-static’ design purposes to prevent blow-over. For blow-over calculations, only winds of duration of at least 2 min need be considered to generate sufficient changes of height. Two minutes at approximately 45ms−1 implies a vertical or horizontal eddy size of at least 5 km, which is unlikely at an altitude of 20 km, if the balloon is sited away from large mountain ranges.
Still shorter time-constant transient gusts must be considered in analyses of the dynamics of the system, and when ensuring the structural integrity of the tether and the balloon. Analyses for balloons at 6 km altitude suggest that stress peaks show relatively modest transients [38,39]. Extension of this analysis to 20km will require some additional turbulence data for suitable sites. Predictions have been made about the response to severe turbulence of a smaller diameter tethered balloon at 20km altitude for a thunderstorm propagating across the system with a core updraft and microburst. A benign balloon temporal response is reported, with the tether length scale (diameter) reacting to a comparatively narrow part of the turbulence energy spectrum that has very little energy. The model used
101 nodes to represent the balloon and tether, and a time duration of 2000 s with a time step of 0.01 s .
Balloon launch and recovery present particular problems for a tethered balloon. Free-flying balloons move with the wind in ascent or descent and are only affected by variations with a length scale similar to the balloon diameter, but a tethered balloon is subject to cross winds (with a maximum dynamic load at around 10km altitude), so the balloon surface must be under tension from the launch level to operating altitude, to avoid the possibility of waves developing on its surface that could tear the fabric.
A conventional ballonet arrangement allows an internal air-filled balloon to be deflated on ascent and inflated by fans (which must be powered) on descent to accommodate a factor of 14 volume change in the lifting gas between 20km altitude and ground level. This restricts the maximum rate of descent because of limitations on fan size and power. A similar problem has been described in trajectory simulation of the descent of a tethered balloon .
Another issue is that of vortex-induced oscillations of tethered balloons in directions both inline and transverse to the flow . The drag on the balloon is less significant than the tether drag, and furthermore active oscillation control may be possible both with control surfaces on the tether and adjacent to the balloon.
Twisting and kinking of the tether have been raised as potential issues with variable wind direction and speed over the height of the tether. For kinking to occur, the longitudinal tension in the tether would need to fall transiently to zero which is not what is observed in the analyses described above. Three thousand barrage balloons in the Second World War were successfully deployed in the most turbulent part of the lower atmosphere over the UK alone. This gives encouragement that such issues will not give material problems.
The particle injection does not need to be continuous, allowing operation for between 200 and 300 days of the year, given that the time constants of the upper atmosphere are of the order of 1–2 years (as seen with the Mt Pinatubo eruption). Jet streams occur at an altitude of around 10 (±3)km and the design accommodates a peak jet stream velocity of around 95ms−1 with 55ms−1 winds at 20km in the same direction. The maximum pipe angle under these conditions is between 10◦ and 35◦ to the vertical, so the tether length needs to be around 21.5 km. A large tethered balloon would best be deployed from a ship or an island, or possibly in desert regions with low population densities but with good rail transport links.
Siting considerations (leaving aside political questions) should preferably be in equatorial regions, with dry tropospheric conditions for at least six months of the year, leading to low lightning frequencies and minimal icing potential. Tether surfaces that are hydrophobic may also help in this regard. The vertical altitude over which ice can build up if suitable locations are chosen is likely to be small (approx. 2 km) compared with the tether length (approx. 20 km), with typical lapse rates of 6K per thousand metres.
The tether acts both as a tension element and as a pipe carrying liquid at very high pressures. It thus has to withstand very high longitudinal tensile stresses and very high hoop stresses. Aramid fibres appear to be the most probable candidate materials from which to fabricate the tether. They are made on an industrial scale by a number of manufacturers; world production is of the order of 30 000 tonnes annually. They have a short-term strength of about 2700MPa, and a density of 1440 kgm−3, giving a free length (the length of itself that it will support) of about 190 km, which at first sight appears more than adequate. However, aramid fibres are susceptible to creep rupture, which is a thermally activated process  and allowance must be made for a 60 per cent fill factor, the weight of the product being delivered, fibres to resist the high hydrostatic pressures in the pipe, possible temperature effects from the product and from the environment, the need to anchor the tether, and a safety factor. A design stress of 750MPa has been used here . Although aramids are suited to this application, their capabilities will be pushed to the limit. A potentially much stronger alternative is PBO  with an allowable design stress of around 1500MPa, and it has been successfully anchored, in the same way as aramids, without the use of resin. Such a doubling of design stress would allow the balloon volume to be halved. However, there are no published data on its creep and creep-rupture properties, which are currently being studied. Neither aramids nor PBO can carry axial compression since they form kink bands (essentially buckles at the sub-filament scale), which is another reason why the tether should be designed to be under tension at all times.
Alternative materials have been considered. Carbon fibres have strength comparable to that of aramids, and can be stiffer, but they are always used with resin (thus adding about 30% to the weight of the tether) and are difficult to anchor . Their use would also make the tether electrically conducting. A lightning strike passing down the tether might destroy it. Another alternative would be ultra high modulus polyethylene (UHMPE) fibres, which are widely used in the marine industries for ropes and cables, and have the advantage of being cheap. But they have the disadvantage that they creep which discounts their use in a pressure pipe.
The design pressure of 6000 bar allows all pumping requirements to be satisfied at ground level. The pumping power is determined by the hydrostatic head (of the order of 3000 bar) and additional frictional pressure drop, which for a low total system cost (pump + pipe + balloon) design is comparable to but lower than the hydrostatic head. With a mean supercritical SO2 density of around 1400 kgm−3 throughout the pipe, and a maximum velocity inside the pipe of under 9ms−1, the frictional pressure drop is in the region of 2000 bar, leaving a maximum total operating pressure at the pipe base of less than 6000 bar. Water-jet pumps at 6000 bar, with a capacity of around 7 l min−1, have a cost of around £70 000 (manufacturer’s quotation, 2011), compared with the required flow of the order of 4000 l min−1, but a scale-up in flow rate of the order of 10–100 seems entirely practical even if this requires a number of parallel pumps. If high pressure positive displacement pumps have a cost versus capacity exponent of around 0.65, 25 pumps with a capacity of 160 l min−1 will cost around £630 000 each, and the whole pump assembly will cost around £16 million. Tripling this cost to allow for different materials and ground level pipe work gives a cost per installation of around £50 million or £200 million for the four installations.
As a cross-check, these numbers were compared with American data. The capital cost for a 4000 bar, 100 hp (75 kW) water-jet pump with all infrastructure is $62 500 [http://news.directindustry.com/press/jet-edge/jet-edge-introduceslow-cost-100hp-waterjet-pump-11866-333796.html, date accessed: 31 October 2010]. Scaling up using a 0.65 power rule gives the cost of a 6MW pump as (6/0.074)0.65 × $62 500=$1 million each. Ten of these would be needed in each location. So, for four locations, the cost would be $40 million. Allowing for more sophisticated technology than simple water pumps might cost 200 per cent more, suggesting a total capital of £75 million for the pumps for all four locations.
The energy required to lift the materials is only greater than the thermodynamic minimum to the extent that the design incurs frictional pressure drop, pump inefficiencies and dispersion power requirements. It is thus unlikely to be bettered by any design that involves high-speed delivery (artillery, rockets, etc.) or the use of intermittent carriers such as weather balloons or jet aircraft, where the additional payloads to be carried to altitude, or the energy costs of throwing away the carrier gases (either H2 or He) are relatively prohibitive. For a pipe the pumping power is given by 500 × 106 (Pa) × (100 (kg s−1)/1400 (kgm−3))/0.6 (60% efficiency)=60MW. Assuming power costs of £0.1kWh−1 and with an 85 per cent motor efficiency, the cost is about £7000 h−1.
A tether of outer diameter (o.d.) 200mm with an inner diameter (i.d.) of 100mm would weigh around 800 tonnes (with a composite density of 1600 kgm−3 and with an additional weight of fluid of around 250 tonnes). The sales price of aramid fibres is currently in the range $20–$30 kg−1, so assuming a fabricated cost of around $40 kg−1 and a tether length of 21.5km the cost of each tether would be in the range of £18 million.
Lifting devices comparable to small gliders attached to the tether mostly at between 7 and 13km in altitude dramatically reduce the size of the tether and balloon system. Approximately 4200m2 of wing area is needed with an associated cost (based on quoted prices for small commercial gliders) of £9 million. Previous studies have considered smaller pipes for a ‘slurry system’ of 40mm o.d. and 20mm i.d. (for liquid), or 210mm o.d. and 200mm i.d. (for gas) . The cost comparisons are very different from those calculated here. A material cost for pipes is given as $2.5 million, which seems reasonable, but a development cost of $10 billion, just for the pipes, is used in their cost estimates which seems excessively high. Those figures were based on the assumption that a balloon system would be as complex as a deep-water offshore oil production platform, which seems unreasonable. Many different manufacturers are already making pipes of 5–20 cm diameter for use as undersea fibre optic cable runs, umbilical systems for offshore oil and gas production or distributed district heating systems. Individual pipe runs can be many kilometres long. Based on manufacturers’ quotations to the authors, and taking a conservative estimate that the facility costs are proportional to the volume of pipe produced, suggests a plant cost of about £40 million. The marginal material cost of the tethers would be around £10 million each; assuming seven tethers would be needed for development, with a development personnel cost of 20 staff for five years at an all-in cost of £200 000 per person year including equipment and facilities (£20 million) would make a total of £130 million. Allowing development and facility costs of the order of £130 million to £250 million would seem to be adequate.
The balloon has to withstand gusts and is envisaged to be a pressurized balloon with an operating differential pressure of around 800Pa across the balloon envelope. Operating with pumpkin balloons might allow less fabric weight but such balloons have had launch issues, with large diameter balloons buckling at intermediate altitudes . A 375 mm balloon fabric wall thickness gives a low wall stress of 170Nm−2 with a balloon weight of 160 tonnes and a payload of 10 tonnes (in addition to the weight of the tether).
One of the most contentious aspects of this proposition is the development and costing of the very large balloon. McClellan et al.  make a comparison with an airship and arrive at a costing of around $400 million for a volume equivalent to that of a 300m diameter balloon. For four units using these costs there would be a capital outlay of $1.6 billion or £1 billion. However, an alternative strategy is to manufacture cheap balloons and not to re-use them after each deployment. That would obviate the need for expensive fan systems but could mean that descent would be uncontrolled. Simple high altitude balloons can be made in relatively cheap plant, essentially consisting of gore welding equipment, with the materials costs being simply those of the balloon fabric and the gondola.
Estimates of costs have been provided by a commercial balloon manufacturer. Fabric costs for material with a six month life at 20km and design stresses of 1500Nmm−1 are around £20m−2. Manufacturing costs are comparable with fabric costs. Adding a 50 per cent margin gives conservative manufactured costs of £60m−2. For a 315m diameter balloon with a surface area of around 300 000m2, the manufactured cost on this basis would be around £18 million. A comparable cost needs to be added for the ballonet, which has a similar amount of fabric, giving a total balloon cost of around £40 million.Alongside airships, this option has been classified as having a low environmental and social impact.
(i) Cost summary (excluding costs of aerosol and dispersal system)
The estimated costs for the balloon system are shown in table 2. It is assumed that each balloon will operate for 7000 hours per year, giving an electrical power cost of about £50 million per year per balloon. It is assumed that the balloon and tether will be replaced each year and that annual pump maintenance will cost 15 per cent of the pump capital cost, and the cost of providing the ships and maintaining the launch sites will be £100 million per year. Together these give a total operating cost of about £600 million per year.
Development costs are likely to be less than four years’ costs of a single station if infrastructure costs (ships) and SO2 or particle generation facilities are excluded, leaving a total for capital + development costs of £600 million. Extended discussion on siting and legal/governance issues might increase these
to £700 million but this may be a significant overestimate given the inherent simplicity of the design. Allowing between £700 million and £1000 million in development costs would seem to be adequate.
Such a sum would buy the plant to produce the tethers (£40 million), seven tethers (at £10 million each), seven assemblies of lifting devices (at £9 million each), seven large balloons (at £40 million each), a development, manufacturing, legal and management staff of 400 for 4 years (£320 million), and site facilities of £50 million.
If it were decided by a body, such as the Security Council of the UN, that SRM had to be introduced as a matter of extreme urgency, it is believed that this could be done within a period of 5 years and is the basis of the data point plotted in figure 8.
The facilities for manufacture of the tether already exist in the offshore industry, although some retooling would be necessary. Manufacturing facilities for balloons larger than any built so far would need to be established, and the balloons themselves tested, but this should just be a scale-up of existing technology. Parallel developments would need to be carried out for pumping and particle dispersal.
A more measured approach would however be highly desirable and might be spread over a generation. It would allow refinements of climate modelling, testing of the albedo effects and of the atmospheric chemistry impacts of the particles. It would allow testing of the actual delivery systems, first at low level, then at 20 km: in the first instance, nitrogen could be injected, followed later by injection of very limited amounts of particulate matter whose effects could be monitored by ground-based, aerial or satellite observation. Only if these tests worked, and then only if a supranational body such as the UN mandated the work, would prototype and production versions of the system be implemented.
Figure 8. Costs and development times (both on logarithmic scales) for various options, excluding cost of material to be dispersed. Costs are net present costs taking a 5% discount rate and amortizing over 10 years for the injection of 10 million tonnes p.a. into the stratosphere, to mitigate the temperature effects of a doubling of CO2 levels.
Were it found necessary to implement SRM climate remediation then the authors estimate that the research, development and governance process may take about 20 years with perhaps another 10–15 years for implementation in normal conditions. The basis for this estimate along with estimates of costs for each stage of the process are given in appendix A. These estimates are necessarily very approximate given the uncertainties of future global climate, economics and politics.
Appendix A shows an outline science and technology roadmap for developing not only the delivery technology but also the particle science and technology, the modelling of effect and some broad brush dialogue, communication, and governance issues. It should be noted that the cost estimates are dominated by the particle material costs if a manufactured particle (such as titanium dioxide) is used. These would be the same for all systems.
This delivery method has four main developmental issues:
— the size of the balloon (significantly larger than the world’s largest balloon to date, which had a diameter of 120 m),
— the manufacture of a reliable high pressure tether, — the need to ensure that no transient oscillations or dynamics compromise the integrity of the system, and
— the need to scale up pumping technology.
It is believed, however, that all of these factors, although challenging, are at the edge of existing technology in one or more fields and can be overcome with suitable development resource. Consideration is being given to the possibility of using an aerodynamically shaped tether. Allowing for imperfections of manufacture, the drag coefficient for an aerodynamic tether would typically be a third to a fifth of that for a circular tether. Since the design case for the balloon is that it must generate enough lift to prevent blow-over by the wind forces on the tether, an aerodynamic tether with intermittent lifting surfaces has the potential to significantly reduce the size of the balloon by a factor of 2–3 in diameter. However, each balloon would then only support a smaller pipe so more balloons (by a factor of 15–20 times) would be needed. Such a design would allow smaller scale tests to be carried out more readily. A stratospheric injection system with eighty 125m diameter balloons rather than four 315m balloons could be envisaged for a full-scale system. The total tether and balloon fabric weights for the two systems would be comparable.
4. Comparing aerosol delivery technologies
It is now possible to compare the various options for delivering aerosols to the stratosphere. Table 3 shows a comparison of the systems discussed above in purely financial terms; the costs are taken from the discussion made earlier and then a net present cost has been calculated for establishing each technology and operating it for 10 years, taking a discount rate of 5 per cent. Allowing for differences in
the injection rate, the costs show good agreement with McClellan et al.  for the more limited number of technologies considered in that work, except for the tethered balloon. This difference can be explained by the much larger development costs suggested there, and the greater number of balloon systems. Table 4 shows non-financial aspects, including the time needed to set up the facility.
Figure 8 shows the time and cost data together. Rigid towers are extremely expensive mainly because of their very high initial cost, although their running costs would be low. And uniquely among the options they could allow manned access to a permanent dispersal facility at high altitude.
Single-use missiles, artillery and coilguns are all expensive, primarily because of the cost of the expendable delivery systems. It might well be possible, especially for coilguns where the accelerations during launch can be kept fairly modest, for the costs to be brought down if the delivery systems could be made to return autonomously to a landing facility.
Most of the other systems cluster around the middle of the figure, with the exception of the tethered balloon concept. It is worth reflecting on why this system is so cheap to ensure that no important factor is missing from the analysis.
Table 3. Summary of delivery technology costs. The initial procurement cost refers to the purchase price of capital necessary to begin delivery. In the case of technologies that involve fleets of delivery vehicles (e.g. planes, retrievable balloons, retrievable missiles) the cost of purchasing the initial fleet is taken. Single-use vehicles have procurement costs factored into operating cost. The net present cost is computed assuming a discount rate of 5% and covering a period of 10 years.
— The connection between the ground and the stratosphere, although permanent, is in tension and thus will tend to straighten, whereas the tower is in compression and tends to buckle. The lift for the supporting structure comes free, from the natural buoyancy of helium or hydrogen.
— Only the material to be dispensed at high altitude has to be lifted, and this is done by pumps at ground level. There are no casings to be manufactured, lifted, discarded or recovered.
— The accelerations during launch, pumping and recovery are all small, which means that the system can be made from lightweight materials.
All of these factors, taken together, mean that the system has the potential to have very much lower operating costs than the alternatives.
There is an additional advantage in that the system would remain in place more or less continuously. Unlike systems that have to dispense their payload in a very short time, the dispensing system can operate semi-continuously, and would not get thrown away after every shot. This opens the way to improving both the effectiveness of the dispersion techniques, and also the choice of particles to be dispensed.
There may be arguments against SRM of any kind, for instance that it does not directly retard ocean acidification, and there may be arguments against geoengineering itself. But while it is desirable that we work on reducing carbon emissions now, it would be prudent to have emergency systems in reserve as an insurance policy. We should design the emergency mechanism before we need it, so that it can be tested to make sure that it is safe to use.
After considering the various options for SRM by stratospheric particle injection, we suggest that a tethered balloon supporting a pressurized pipe is likely to be efficient, practical, controllable and much cheaper than any probable alternative.
A tethered balloon system might be used to deliver SRM, not just as an emergency measure, but also as part of a well-moderated and thoughtful process of climate control.
Peter Davidson is employed by Davidson Technology Limited which has a patent application pending regarding SRM technologies. Hugh Hunt and Chris Burgoyne are employed by the University of Cambridge. They provided consultancy services for Davidson Technology Limited in 2009, in their personal capacities, and were named as inventors on the patent application. All ownership and rights in the patent application reside with Davidson Technology Limited. Hugh Hunt and Chris Burgoyne are currently working on the SPICE project at the University of Cambridge which is funded by EPSRC and NERC. Matt Causier is a research student at the University of Cambridge also working on the SPICE project.
The work described here was partly funded by the Engineering and Physical Sciences Research Council, the Natural Environment Research Council and Davidson Technology. The authors would like to thank Tony Cox and Francis Pope (University of Cambridge), who provided input on the chemistry of the stratosphere, Don Grainger and Dan Peters (Universities of Oxford and Bristol), and John Temperley (Huntsman Tioxide) who provided input on scattering. In addition, Peter Braesicke and Richard McMahon (University of Cambridge), Matt Watson (University of Bristol), Olivier Boucher and Jim Haywood (Met Office) and Lesley Gray (University of Oxford) provided wind data and helpful comments on early versions of this paper. Hilary Costello and Kirsty Kuo (University of Cambridge) have also provided background work on balloon and tether dynamics, and with Jonathan Cooper (University of Liverpool) measurements of aerodynamic tether drag. David Loew (University of Cambridge) carried out calculations on some of the comparative systems.
Appendix A. An outline science and technology roadmap for SRM climate remediation
1. Laboratory and concept development 3 years £2–3 million. Modelling of climate at approximately 50km horizontal cell size.
(a) Explore the potential feasibility of managing ozone destruction processes in laboratory experiments, particularly by keeping N2O5 and chlorate surface reactions to a minimum.
(b) Demonstrate coating technologies in the laboratory that allow the potential to achieve coatings that are stable for 3 years, that are non-toxic and allow for 6000 bar slurrying and dispersion.
(c) Demonstrate light scattering in the laboratory by suitably dispersed particles.
(d) Produce preliminary models of the impact on the flora and fauna of more diffuse light.
(e) Develop lower cost delivery technology: aerodynamic tether, vibration model, pumping concepts.
(f) Carry out public engagement at a modest level:
(i) communicate and discuss the scale of the problem,
(ii) discuss the concept of research to minimize the risk that we may have to carry out a ‘panic implementation’,
(iii) discuss the need to have a reversible intervention, and
(iv) discuss the strengths and weaknesses of the moral hazard argument.
(g) Examine the advantages and drawbacks of pre-made particulates in comparison with those created by slow hydrolysis of sulphates.
(h) Consider mechanisms that allow incremental testing of effect rather than a step change approach.
(i) Initiate a scientific, engineering and social debate on modelling needs and pace of implementation with a wide variety of stakeholders. Encourage dialogue with governments and nongovernmental organizations including environmental groups.
(j) Develop scale-up and testing scenarios, and initiate discussion on what tests need international agreement, e.g. would tests not resulting in measureable ground illumination or precipitation changes
over inhabited areas or areas of special scientific interest be routinely accepted?
2. Pre-trial development: injection of 100 tonne p.a. nitrogen at 20km altitude: approximately 3 years £6–10 million.
(a) Test pumping concepts, stabilization of tether, aerostat, launch and recovery steps.
(b) Develop modelling scenarios: computing power, measurement and science fundamentals.
(c) Continue laboratory work on phase 1 science + measurement techniques for operation off 20km platforms and identify other monitoring technologies suitable for observing the microphysics of plumes.
(d) Begin dialogue with UN to establish mandate for micro- and small-scale tests, governance and legal structure.
(e) Obtain buy-in to research from some mainstream environmental organizations: consider options to protect biodiversity.
3. Micro trials at 20km of 0.01 per cent full scale: 100 tonne p.a. or 2 tonne per week approximately 3 years £40–80 million, approximately £10–20 million p.a.
(a) Develop mandate for small-scale tests.
(b) Establish a climate remediation R&D centre on an ocean island with UN support, relatively near the equator.
(c) Test delivery technology, dispersion and pumping technology at a modest scale using a 150 000m3 aerostat.
(d) Check atmospheric chemistry and opacity of plume, approximately 50 miles downstream, with balloons, satellites and aircraft; continue laboratory R&D and development work.
(e) Check coating stability, local weather effects.
(f) Demonstrate a variety of observation technologies from 20km platforms.
(g) Computer model at approximately 10 times the resolution of 2011 capability with approximately 7 km horizontal cell size.
(h) Reaffirm environmental buy-in with preliminary field results. Further dialogue with disparate communities.
4. Mini tests at 20 km. One per cent full scale (10 000 tonne p.a. or 200 tonne per week): approximately 6 years £80 million p.a.
(a) With UN support, test effect of plume to 500–2000 miles lengths over oceans: atmospheric chemistry, solar scattering, precipitation.
(b) Implement five 20km altitude sampling points and three base stations.
(c) Monitor impact on a baseline series of ‘most sensitive areas’, e.g. South Asian monsoon, Sahel and Amazonian precipitation.
(d) Examine precipitation and vegetative impacts as well as microbiology under plume.
5. Five per cent scale at 20 km. 50 000 tonne p.a. £200 million p.a. approximately 6 years.
(a) With UN support, increase to just-detectable effects over whole planet.
(b) Monitor ozone levels and regional precipitation.
(c) Modelling to 100 times the resolution of current capability (approx.500m resolution).
6. Implementation only if mandated by UN Security Council. Allow four years to build facilities and then ramp up full implementation in 10 years. Cost approximately £500 million p.a. at the start, rising to £3 billion p.a. at the end (2011 prices) for complete scaled-up system, including the cost of a manufactured particle such as 1 Mt p.a. titanium dioxide (approx. 15% of current world production rates). It is assumed that costs of TiO2 are comparable to 2011 prices (around £2000 per tonne), but they could be lower because of the scale of the operation or higher because of an increased demand. At a rate of 2.5 Mt p.a., titanium dioxide costs would increase to £6–7 billion p.a. and would account for around 25 per cent of world titanium dioxide production but it is hoped that these rates would not be needed.
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