https://htyp.org/mw/api.php?action=feedcontributions&user=24.23.229.100&feedformat=atomHTYP - User contributions [en]2024-03-28T11:05:29ZUser contributionsMediaWiki 1.35.0https://htyp.org/mw/index.php?title=dollar_a_gallon_gasoline&diff=10075dollar a gallon gasoline2008-08-06T18:40:05Z<p>24.23.229.100: /* Why gasoline? */</p>
<hr />
<div>Demand for petroleum products is growing while existing fields are declining. If it is not already here, peak oil is not far off. <br />
<br />
One way of engineering, especially for very large markets, is "design to cost."<br />
<br />
What would it take to make dollar a gallon, possibly carbon neutral, synthetic gasoline?<br />
<br />
==Why gasoline?==<br />
<br />
Hydrogen and gasoline are energy storage media, like batteries but much higher performance. In the case of current gasoline the energy was stored in the hydrocarbons a long time ago. Unlike batteries, one of the reacting chemical (oxygen) comes from the air.<br />
<br />
Hydrogen is widely considered a future fuel. It has serious drawback in that it either has to be stored liquid or under high pressure, or absorbed as in hydrides. All of these are low density.<br />
<br />
The hydrocarbons that make up gasoline, diesel, jet fuel, etc. are energy dense liquids at normal temperatures and pressures. There is a vast technology base and infrastructure behind them.<br />
<br />
As we run out of hydrocarbons, some other primary energy source will have to replace oil. However, if we have such an energy source, we can make hydrocarbons. All it takes is vast amounts of low cost energy.<br />
<br />
==Making synthetic hydrocarbons==<br />
<br />
Sasol's Fischer-Tropsch processes provides [http://www.sasol.com/sasol_internet/frontend/navigation.jsp;jsessionid=1QVOIKQA2FDMXG5N4EZSFEQ?navid=1600033&rootid=2] two ways to do this. The reaction converts syngas to synthetic oil. Syngas is carbon monoxide and hydrogen usually made by burning coal with limited oxygen and water.<br />
<br />
Mining old landfills and feeding them into plasma gasifiers can also make syngas. [http://www.plascoenergygroup.com/] More carbon would come from coal, biomass or even separating CO2 from air and reducing it to carbon monoxide with hydrogen. The water gas reaction, H2O + C--> H2 + CO makes syngas. It's endothermic at 131 kj/mol, about 11 kj/g or 11 mj/kg. A kWh is 3.6 mj so the reaction uses three kWh/kg of carbon or three MWh/t. The best way may be to heat coal in steam with an electric arc to the point the ash forms a melt.<br />
<br />
Coal fired power plants will be idled in the first few years by space based solar power.<br />
They are valuable rebuilt as coal to syngas plants or as coal to synthetic oil. They would pump the resultant synthetic oil into the nearest crude oil pipeline or the syngas into a re purposed gas pipeline. The hydrogen content makes this a bit questionable, but until the much safer natural gas displaced it in the 1950s, syngas with its poisonous carbon monoxide was distributed in iron pipes and used in homes.<br />
<br />
Fischer-Tropsch process needs twice that much H2, 2H2 + C0 --> (CH2)x + H2O. Making electrolytic hydrogen takes about 48 kWh/kg or 48 MWh/t. One sixth of a ton of hydrogen would take eight MWh, for 11 MWh/t of input carbon. This would result in 14/12th of a ton of oil or about 9.4 MWh/t or 1.3 MWh per barrel of oil. Processing 100 tons of carbon an hour, such a plant would draw 1100 MW and produce 730 bbl/hour or 17,500 bbl/day. This may sound like a lot, but it would take 20 converted power plants of this size to feed ExxonMobil's 350,000-bbl/day refinery at Beaumont, TX. It would take over a thousand of them to make the 20 million barrels per day of oil we now use. There are already power lines from these plants that could be used to send power to them.<br />
<br />
An alternative reaction is C + H2 --> (CH2)x where a ton of carbon and 1/6th ton of H2 are reacted with heat and pressure. This takes eight MWh/t of carbon, 6.9 MWh/ton of oil, or .95 MWh per bbl.<br />
<br />
These are worse case numbers since all coal has some hydrogen.<br />
<br />
==Cost==<br />
<br />
At a penny a kWh, a MWh is $10. Therefore, the direct energy cost would be $13 per bbl and perhaps $2 for pumps and other equipment.<br />
<br />
Coal ranges from $15/ton to $150/ton. Figured at $70/ton of carbon, synthetic oil would cost about $25/bbl for energy and carbon plus the capital charge for the synthetic oil plants.<br />
<br />
Sasol's most recent plant at Qatar cost $30,000 per bbl/day (note 1) for an oil synthesis unit fed with natural gas and the refinery to sort out the products. A modified power plant heating coal in steam with electricity should be less complicated and while it could turn out local diesel, it would probably just put the whole output into a crude oil pipeline to take advantage of existing refining infrastructure. If the power plant conversion cost $30,000/bbl/day, the capital cost would under $10/bbl (ten year write off at $3000/year, 300+ days/year.) So before making a profit on the oil, a power plant converted into a coal to oil plant would make synthetic oil for upper limit of $35 a barrel. Fed to existing refineries, gasoline from $35/bbl oil would be about a dollar a gallon.<br />
<br />
Fischer-Tropsch process converts cleaned syngas to a mix of hydrocarbons. This process has to clean out all the sulfur out before the syngas goes into the reactor or the sulfur poisons the catalyst. The reactions don't produce any carbon dioxide at the plant; the trains, aircraft, ships, trucks, farming tractors and personal transport release the CO2. Eventually (hundreds of years) the plants will have to make do with biomass (turning all the carbon into liquid fuels), or even pull C02 from the air. The process does reduce carbon dioxide emissions by about half because the power plants no longer produce any.<br />
<br />
If all 1.3 billion tons of coal per year the US burns in power plants became synthetic oil, the rate would about 120,000 t/hr of carbon or about 21 million barrels of synthetic oil per day, equal to current consumption. The conversion plants would draw 1300 GW. That is 2.6 years of power sat production at 500 GW/year.<br />
<br />
If a plant can buy penny kWh electricity, then on an industrial scale it should make dollar a gallon synthetic gasoline.<br />
<br />
Electricity, even in industrial quantities, is at least five times too expensive for this and we want *renewable* which makes solar the energy source of choice. Can we get solar power into this price range?<br />
<br />
Next http://htyp.org/Penny_a_kW<br />
<br />
(Note 1) "Sasol's first international joint venture, a factory in Qatar that turns natural gas into liquid fuel, cost $1 billion, or about $30,000 per barrel of capacity. According to Sasol CEO Pat Davies, that's twice as much as a more conventional oil refinery costs. "</div>24.23.229.100https://htyp.org/mw/index.php?title=DTC&diff=10073DTC2008-08-06T18:18:08Z<p>24.23.229.100: New page: ==Design to cost== "Design to cost is a management strategy and supporting methodologies to achieve an affordable product by treating target cost as an independent design parameter that n...</p>
<hr />
<div>==Design to cost==<br />
<br />
"Design to cost is a management strategy and supporting methodologies to achieve an affordable product by treating target cost as an independent design parameter that needs to be achieved during the development of a product." [[http://www.npd-solutions.com/dtc.html]]<br />
<br />
This was applied to the dollar a gallon project. [[http://htyp.org/Dollar_a_gallon_gasoline]]</div>24.23.229.100https://htyp.org/mw/index.php?title=dollar_a_gallon_gasoline&diff=10066dollar a gallon gasoline2008-08-05T22:17:07Z<p>24.23.229.100: /* Why gasoline? */</p>
<hr />
<div>Demand for petroleum products is growing while existing fields are declining. If it is not already here, peak oil is not far off. <br />
<br />
One way of engineering, especially for very large markets, is "design to cost."<br />
<br />
What would it take to make dollar a gallon, possibly carbon neutral, synthetic gasoline?<br />
<br />
==Why gasoline?==<br />
<br />
Hydrogen and gasoline are energy storage media, like batteries but much higher performance. In the case of current gasoline the energy was stored in the hydrocarbons a long time ago. Unlike batteries, most of the reacting chemical (oxygen) comes from the air.<br />
<br />
Hydrogen is widely considered a future fuel. It has serious drawback in that it either has to be stored liquid or under high pressure, or absorbed as in hydrides. All of these are low density.<br />
<br />
The hydrocarbons that make up gasoline, diesel, jet fuel, etc. are energy dense liquids at normal temperatures and pressures. There is a vast technology base and infrastructure behind them.<br />
<br />
As we run out of hydrocarbons, some other primary energy source will have to replace oil. However, if we have such an energy source, we can make hydrocarbons. All it takes is vast amounts of low cost energy.<br />
<br />
==Making synthetic hydrocarbons==<br />
<br />
Sasol's Fischer-Tropsch processes provides [http://www.sasol.com/sasol_internet/frontend/navigation.jsp;jsessionid=1QVOIKQA2FDMXG5N4EZSFEQ?navid=1600033&rootid=2] two ways to do this. The reaction converts syngas to synthetic oil. Syngas is carbon monoxide and hydrogen usually made by burning coal with limited oxygen and water.<br />
<br />
Mining old landfills and feeding them into plasma gasifiers can also make syngas. [http://www.plascoenergygroup.com/] More carbon would come from coal, biomass or even separating CO2 from air and reducing it to carbon monoxide with hydrogen. The water gas reaction, H2O + C--> H2 + CO makes syngas. It's endothermic at 131 kj/mol, about 11 kj/g or 11 mj/kg. A kWh is 3.6 mj so the reaction uses three kWh/kg of carbon or three MWh/t. The best way may be to heat coal in steam with an electric arc to the point the ash forms a melt.<br />
<br />
Coal fired power plants will be idled in the first few years by space based solar power.<br />
They are valuable rebuilt as coal to syngas plants or as coal to synthetic oil. They would pump the resultant synthetic oil into the nearest crude oil pipeline or the syngas into a re purposed gas pipeline. The hydrogen content makes this a bit questionable, but until the much safer natural gas displaced it in the 1950s, syngas with its poisonous carbon monoxide was distributed in iron pipes and used in homes.<br />
<br />
Fischer-Tropsch process needs twice that much H2, 2H2 + C0 --> (CH2)x + H2O. Making electrolytic hydrogen takes about 48 kWh/kg or 48 MWh/t. One sixth of a ton of hydrogen would take eight MWh, for 11 MWh/t of input carbon. This would result in 14/12th of a ton of oil or about 9.4 MWh/t or 1.3 MWh per barrel of oil. Processing 100 tons of carbon an hour, such a plant would draw 1100 MW and produce 730 bbl/hour or 17,500 bbl/day. This may sound like a lot, but it would take 20 converted power plants of this size to feed ExxonMobil's 350,000-bbl/day refinery at Beaumont, TX. It would take over a thousand of them to make the 20 million barrels per day of oil we now use. There are already power lines from these plants that could be used to send power to them.<br />
<br />
An alternative reaction is C + H2 --> (CH2)x where a ton of carbon and 1/6th ton of H2 are reacted with heat and pressure. This takes eight MWh/t of carbon, 6.9 MWh/ton of oil, or .95 MWh per bbl.<br />
<br />
These are worse case numbers since all coal has some hydrogen.<br />
<br />
==Cost==<br />
<br />
At a penny a kWh, a MWh is $10. Therefore, the direct energy cost would be $13 per bbl and perhaps $2 for pumps and other equipment.<br />
<br />
Coal ranges from $15/ton to $150/ton. Figured at $70/ton of carbon, synthetic oil would cost about $25/bbl for energy and carbon plus the capital charge for the synthetic oil plants.<br />
<br />
Sasol's most recent plant at Qatar cost $30,000 per bbl/day (note 1) for an oil synthesis unit fed with natural gas and the refinery to sort out the products. A modified power plant heating coal in steam with electricity should be less complicated and while it could turn out local diesel, it would probably just put the whole output into a crude oil pipeline to take advantage of existing refining infrastructure. If the power plant conversion cost $30,000/bbl/day, the capital cost would under $10/bbl (ten year write off at $3000/year, 300+ days/year.) So before making a profit on the oil, a power plant converted into a coal to oil plant would make synthetic oil for upper limit of $35 a barrel. Fed to existing refineries, gasoline from $35/bbl oil would be about a dollar a gallon.<br />
<br />
Fischer-Tropsch process converts cleaned syngas to a mix of hydrocarbons. This process has to clean out all the sulfur out before the syngas goes into the reactor or the sulfur poisons the catalyst. The reactions don't produce any carbon dioxide at the plant; the trains, aircraft, ships, trucks, farming tractors and personal transport release the CO2. Eventually (hundreds of years) the plants will have to make do with biomass (turning all the carbon into liquid fuels), or even pull C02 from the air. The process does reduce carbon dioxide emissions by about half because the power plants no longer produce any.<br />
<br />
If all 1.3 billion tons of coal per year the US burns in power plants became synthetic oil, the rate would about 120,000 t/hr of carbon or about 21 million barrels of synthetic oil per day, equal to current consumption. The conversion plants would draw 1300 GW. That is 2.6 years of power sat production at 500 GW/year.<br />
<br />
If a plant can buy penny kWh electricity, then on an industrial scale it should make dollar a gallon synthetic gasoline.<br />
<br />
Electricity, even in industrial quantities, is at least five times too expensive for this and we want *renewable* which makes solar the energy source of choice. Can we get solar power into this price range?<br />
<br />
Next http://htyp.org/Penny_a_kW<br />
<br />
(Note 1) "Sasol's first international joint venture, a factory in Qatar that turns natural gas into liquid fuel, cost $1 billion, or about $30,000 per barrel of capacity. According to Sasol CEO Pat Davies, that's twice as much as a more conventional oil refinery costs. "</div>24.23.229.100https://htyp.org/mw/index.php?title=dollar_a_gallon_gasoline&diff=10063dollar a gallon gasoline2008-08-04T16:00:14Z<p>24.23.229.100: /* Making synthetic hydrocarbons */</p>
<hr />
<div>Demand for petroleum products is growing while existing fields are declining. If it is not already here, peak oil is not far off. <br />
<br />
One way of engineering, especially for very large markets, is "design to cost."<br />
<br />
What would it take to make dollar a gallon, possibly carbon neutral, synthetic gasoline?<br />
<br />
==Why gasoline?==<br />
<br />
Hydrogen and gasoline are energy storage media, like batteries but much higher performance. In the case of current gasoline the energy was stored in the hydrocarbons a long time ago. Unlike batteries, most of the reacting chemical (oxygen) comes from the air.<br />
<br />
Hydrogen is widely considered a future fuel. It has serious drawback in that it either has to be stored liquid or under high pressure, or absorbed as in hydrides. All of these are low density.<br />
<br />
The hydrocarbons that make up gasoline, diesel, jet fuel, etc. are energy dense liquids at normal temperatures and pressures. There is a vast technology base and infrastructure behind them.<br />
<br />
As we run out of hydrocarbons, (peak oil) some other primary energy source will have to replace oil. However, if we have such an energy source, we can make hydrocarbons. All it takes is vast amounts of low cost energy.<br />
<br />
==Making synthetic hydrocarbons==<br />
<br />
Sasol's Fischer-Tropsch processes provides [http://www.sasol.com/sasol_internet/frontend/navigation.jsp;jsessionid=1QVOIKQA2FDMXG5N4EZSFEQ?navid=1600033&rootid=2] two ways to do this. The reaction converts syngas to synthetic oil. Syngas is carbon monoxide and hydrogen usually made by burning coal with limited oxygen and water.<br />
<br />
Mining old landfills and feeding them into plasma gasifiers can also make syngas. [http://www.plascoenergygroup.com/] More carbon would come from coal, biomass or even separating CO2 from air and reducing it to carbon monoxide with hydrogen. The water gas reaction, H2O + C--> H2 + CO makes syngas. It's endothermic at 131 kj/mol, about 11 kj/g or 11 mj/kg. A kWh is 3.6 mj so the reaction uses three kWh/kg of carbon or three MWh/t. The best way may be to heat coal in steam with an electric arc to the point the ash forms a melt.<br />
<br />
Coal fired power plants will be idled in the first few years by space based solar power.<br />
They are valuable rebuilt as coal to syngas plants or as coal to synthetic oil. They would pump the resultant synthetic oil into the nearest crude oil pipeline or the syngas into a re purposed gas pipeline. The hydrogen content makes this a bit questionable, but until the much safer natural gas displaced it in the 1950s, syngas with its poisonous carbon monoxide was distributed in iron pipes and used in homes.<br />
<br />
Fischer-Tropsch process needs twice that much H2, 2H2 + C0 --> (CH2)x + H2O. Making electrolytic hydrogen takes about 48 kWh/kg or 48 MWh/t. One sixth of a ton of hydrogen would take eight MWh, for 11 MWh/t of input carbon. This would result in 14/12th of a ton of oil or about 9.4 MWh/t or 1.3 MWh per barrel of oil. Processing 100 tons of carbon an hour, such a plant would draw 1100 MW and produce 730 bbl/hour or 17,500 bbl/day. This may sound like a lot, but it would take 20 converted power plants of this size to feed ExxonMobil's 350,000-bbl/day refinery at Beaumont, TX. It would take over a thousand of them to make the 20 million barrels per day of oil we now use. There are already power lines from these plants that could be used to send power to them.<br />
<br />
An alternative reaction is C + H2 --> (CH2)x where a ton of carbon and 1/6th ton of H2 are reacted with heat and pressure. This takes eight MWh/t of carbon, 6.9 MWh/ton of oil, or .95 MWh per bbl.<br />
<br />
These are worse case numbers since all coal has some hydrogen.<br />
<br />
==Cost==<br />
<br />
At a penny a kWh, a MWh is $10. Therefore, the direct energy cost would be $13 per bbl and perhaps $2 for pumps and other equipment.<br />
<br />
Coal ranges from $15/ton to $150/ton. Figured at $70/ton of carbon, synthetic oil would cost about $25/bbl for energy and carbon plus the capital charge for the synthetic oil plants.<br />
<br />
Sasol's most recent plant at Qatar cost $30,000 per bbl/day (note 1) for an oil synthesis unit fed with natural gas and the refinery to sort out the products. A modified power plant heating coal in steam with electricity should be less complicated and while it could turn out local diesel, it would probably just put the whole output into a crude oil pipeline to take advantage of existing refining infrastructure. If the power plant conversion cost $30,000/bbl/day, the capital cost would under $10/bbl (ten year write off at $3000/year, 300+ days/year.) So before making a profit on the oil, a power plant converted into a coal to oil plant would make synthetic oil for upper limit of $35 a barrel. Fed to existing refineries, gasoline from $35/bbl oil would be about a dollar a gallon.<br />
<br />
Fischer-Tropsch process converts cleaned syngas to a mix of hydrocarbons. This process has to clean out all the sulfur out before the syngas goes into the reactor or the sulfur poisons the catalyst. The reactions don't produce any carbon dioxide at the plant; the trains, aircraft, ships, trucks, farming tractors and personal transport release the CO2. Eventually (hundreds of years) the plants will have to make do with biomass (turning all the carbon into liquid fuels), or even pull C02 from the air. The process does reduce carbon dioxide emissions by about half because the power plants no longer produce any.<br />
<br />
If all 1.3 billion tons of coal per year the US burns in power plants became synthetic oil, the rate would about 120,000 t/hr of carbon or about 21 million barrels of synthetic oil per day, equal to current consumption. The conversion plants would draw 1300 GW. That is 2.6 years of power sat production at 500 GW/year.<br />
<br />
If a plant can buy penny kWh electricity, then on an industrial scale it should make dollar a gallon synthetic gasoline.<br />
<br />
Electricity, even in industrial quantities, is at least five times too expensive for this and we want *renewable* which makes solar the energy source of choice. Can we get solar power into this price range?<br />
<br />
Next http://htyp.org/Penny_a_kW<br />
<br />
(Note 1) "Sasol's first international joint venture, a factory in Qatar that turns natural gas into liquid fuel, cost $1 billion, or about $30,000 per barrel of capacity. According to Sasol CEO Pat Davies, that's twice as much as a more conventional oil refinery costs. "</div>24.23.229.100https://htyp.org/mw/index.php?title=Hundred_dollars_a_kg&diff=10057Hundred dollars a kg2008-08-03T14:35:44Z<p>24.23.229.100: /* How much lifted to GEO */</p>
<hr />
<div>To sum up what's gone before:<br />
<br />
To solve the energy crisis using space-based solar power, replacement power needs to come on line at a rate of 400-500 GW/year. That replaces about 6 million barrels of oil a day each year over the next 50 years. To make liquid fuels at a dollar a gallon out of electricity requires that the electricity cost be around a penny a kWh. To make penny a kWh requires lift cost to GEO of $100 or less<br />
<br />
==How much lifted to GEO==<br />
<br />
Four hundred GW of power sats requires 800,000 tons per year lifted to GEO (perhaps twice that). At least there is economy of scale.<br />
<br />
Do we have to lift that much mass? No. Extra terrestrial resources are a better idea, but there isn't time to develop the space industry to tap them. The economic effects (including famines) of the developing energy crisis are so bad that the large scale production of SBSP needs to come on line by 2015 to avoid economic collapse. Expect ET resources to be exploited by 2025 with this much activity in space.<br />
<br />
This works out to lifting about 100 tons per hour. Will physics let us get under $100/kg? A moving cable space elevator only requires about 15 kWh to lift a kg from the surface of the earth to GEO. This is $1.50 at the high rate of 10 cents a kWh. Even if it cost $100 billion dollars to build, a capital cost of $10 billion a year lifting a billion kg is only ten dollars. Unfortunately we don't have the cable--yet.<br />
<br />
There are other choices but the ones further examined here are among rockets, lasers or some combination of them.<br />
<br />
==Rockets vs lasers==<br />
<br />
Rockets are good for high thrust, but the rocket equation is a hard taskmaster when you need delta V that is a multiple of the exhaust velocity.<br />
<br />
Lasers are not as well developed as rockets. They can get very high exhaust velocity, leading to small mass ratios, but they don't do very good for high thrust. Jordin Kare and others have been working for decades designing lasers to launch from the surface.<br />
<br />
Rockets to lift this much cargo would have to launch every hour, each rocket having a lift off mass of 6,000 tons to get 350 tons to LEO and 100 tons of that to GEO. The projected cost to GEO is around $500/kg. http://www.ilr.tu-berlin.de/koelle/Neptun/NEP2015.pdf<br />
<br />
The energy payback (for making fuel) is about 40 days. The cost of rockets is not in the fuel, but in the high cost of aerospace hardware and the rocket equation which dictates that even for the most energetic fuels only about one part in sixty is payload to GEO.<br />
<br />
The needed delta V LEO to GEO is about 4.1 km/sec. Using 10% of the LEO payload for reaction mass (35 tons) and a laser that provides a 40 km/sec exhaust velocity will produce about 4.2 km/sec delta V.<br />
<br />
(http://en.wikipedia.org/wiki/Rocket_equation )<br />
<br />
The power required for 1/20th g (.5 m/sec exp 2) is 1/2 x 350,000 kg x .5m/sec exp 2 x 40,000 m/sec = 3.5 GW<br />
<br />
Delta V changes require 4100 m/sec /0.5 m/sec exp 2, or 8200 sec or about 2.7 hours. I.e., 3.5 GW of laser power would raise eight loads a day from LEO to GEO. At 315 t each that is 2500 t/day, somewhat exceeding the 2200 t/day needed to install 400 GW per year.<br />
<br />
It also cuts the rocket launches from 24 to a more manageable but still excessive 7 or 8.<br />
<br />
A 3.5-GW space based laser built at GEO that massed 10,000 tons would cost $5 billion to lift by rockets and $35 billion for the laser. It can be expected to more than triple the yearly throughput to GEO, saving 2/3 of 0.8 billion kg x $500/kg or $267 billion a year in transport costs.<br />
<br />
Amortized at 10 percent, the additional lift from LEO to GEO would cost $4 billion/0.8 billion/kg or $5 per kg plus the lift to LEO.<br />
<br />
==Cost reduction==<br />
<br />
There is another way that cuts the liftoff mass by a factor of five compared to rockets.<br />
<br />
Injection to geosynchronous transfer orbit is 7.8 k/s (to LEO), 2.5 k/s (to GTO) plus 1.6k/sec to circularize at GEO, totaling 11.9 km/s. http://en.wikipedia.org/wiki/Delta-v_budget To get to LEO takes 796 s at 1g, 13.2 minutes. At one g 17.5 minutes for GTO, 14 minutes at 1.25 g, plus 2.2 minutes to circularize the orbit (1.6 km/s) at GEO. Assuming half payload and half reaction mass, 0.69 velocity ratio and 11.9 km/s delta v, then the average exhaust velocity needs to be a modest (for lasers) 17.2 km/s.<br />
<br />
Because the laser can be cycled close to 4 times an hour, the payload only needs to be 25 tons. Taking the midpoint (the exhaust velocity would be varied for constant thrust) the power required for 1.25 g (12.25 m/sec exp 2) is 1/2 x 37,500 kg x 12.25 m/sec exp 2 x 17,200 m/sec = 4 GW. In the context of building a GW of power satellite a day, this is a small piece of hardware. The choice of building the laser in space or on the ground has not been fully examined.<br />
<br />
The 50-ton payload-plus-reaction-mass has to hang in space long enough to be accelerated. This takes a modest mass ratio rocket.<br />
<br />
50 tons payload plus reaction mass for the laser. 16.5%<br />
<br />
50 tons rocket structure 16.5%<br />
<br />
200 tons propellant. 66%<br />
<br />
<br />
The rocket would lift off on two SSMEs (or similar), and if a zeroth turbofan stage was used, it would take eight 50-ton thrust engines, perhaps with afterburners. Simplifying operations, it goes straight up and lands back at the launching site. If the payload is oriented at right angles to vertical, we could avoid wasting time reorienting it for laser acceleration.<br />
<br />
This "little" rocket (about the mass of a 747) has a mass ratio of two and a delta V of 4 k/sec (less gravity loss and drag). The payload-plus-reaction-mass exits the atmosphere at 2.1 k/sec, goes up to 260 miles, falls to 150 miles before picking up orbital velocity and falls to 55 miles (picking up a little air drag) before losing downward velocity. It enters GTO 1000 seconds after launch. This is conservative, not accounting for the curvature of the earth.<br />
<br />
It masses 1/20th of a Neptune and (with the aid of the laser) delivers 1/4 as much payload per launch. One part in 12 (rather than one part in 60) is payload. To keep the laser busy and to meet the 100-ton per hour cargo requirement requires a launch every 15 minutes. This rate is common for airlines, but not for spacecraft.<br />
<br />
If the laser cost 40 billion dollars and was written off at 10% per year, the lift cost from sub orbital to GEO would be $4 billion /0.8 billion kg, $5/kg plus the sub orbital flight of perhaps $60/kg of payload. This meet the penny a kWh and dollar a gallon fuel goals.<br />
<br />
Energy payback is 8 days for the rocket fuel and 8 days for the laser. This is about 8.4% of the theoretical minimum for a space elevator.<br />
<br />
This is probably not the optimum design. A shorter "hang time," smaller payloads and higher but shorter acceleration may yield lower cost per kg. (It is possible that laser launch from the ground is the end point of this optimization.) However, the size of the largest part for a power satellite may limit the minimum size of rocket.</div>24.23.229.100https://htyp.org/mw/index.php?title=Hundred_dollars_a_kg&diff=10056Hundred dollars a kg2008-08-03T14:35:20Z<p>24.23.229.100: /* How much lifted to GEO */</p>
<hr />
<div>To sum up what's gone before:<br />
<br />
To solve the energy crisis using space-based solar power, replacement power needs to come on line at a rate of 400-500 GW/year. That replaces about 6 million barrels of oil a day each year over the next 50 years. To make liquid fuels at a dollar a gallon out of electricity requires that the electricity cost be around a penny a kWh. To make penny a kWh requires lift cost to GEO of $100 or less<br />
<br />
==How much lifted to GEO==<br />
<br />
Four hundred GW of power sats requires 800,000 tons per year lifted to GEO (perhaps twice that). At least there is economy of scale.<br />
<br />
Do we have to lift that much mass? No. Extra terrestrial resources are a better idea, but there isn't time to develop the space industry to tap them. The economic effects (including famines) of the developing energy crisis are so bad that the large scale production of SBSP needs to come on line by 2015 to avoid economic collapse. Expect ET resources to be exploited by 2025 with this much activity in space.<br />
<br />
This works out to lifting about 100 tons per hour. Will physics let us get under $100/kg? A moving cable space elevator only requires about 15 kWh to lift a kg from the surface of the earth to GEO. This is $1.50 at the high rate of 10 cents a kWh. Even if it cost $100 billion dollars to build, a capital cost of $10 billion a year lifting a billion kg is only ten dollars. Unfortunately we don't have the cable--yet.<br />
<br />
There are other choices bit the ones further examined here are among rockets, lasers or some combination of them.<br />
<br />
==Rockets vs lasers==<br />
<br />
Rockets are good for high thrust, but the rocket equation is a hard taskmaster when you need delta V that is a multiple of the exhaust velocity.<br />
<br />
Lasers are not as well developed as rockets. They can get very high exhaust velocity, leading to small mass ratios, but they don't do very good for high thrust. Jordin Kare and others have been working for decades designing lasers to launch from the surface.<br />
<br />
Rockets to lift this much cargo would have to launch every hour, each rocket having a lift off mass of 6,000 tons to get 350 tons to LEO and 100 tons of that to GEO. The projected cost to GEO is around $500/kg. http://www.ilr.tu-berlin.de/koelle/Neptun/NEP2015.pdf<br />
<br />
The energy payback (for making fuel) is about 40 days. The cost of rockets is not in the fuel, but in the high cost of aerospace hardware and the rocket equation which dictates that even for the most energetic fuels only about one part in sixty is payload to GEO.<br />
<br />
The needed delta V LEO to GEO is about 4.1 km/sec. Using 10% of the LEO payload for reaction mass (35 tons) and a laser that provides a 40 km/sec exhaust velocity will produce about 4.2 km/sec delta V.<br />
<br />
(http://en.wikipedia.org/wiki/Rocket_equation )<br />
<br />
The power required for 1/20th g (.5 m/sec exp 2) is 1/2 x 350,000 kg x .5m/sec exp 2 x 40,000 m/sec = 3.5 GW<br />
<br />
Delta V changes require 4100 m/sec /0.5 m/sec exp 2, or 8200 sec or about 2.7 hours. I.e., 3.5 GW of laser power would raise eight loads a day from LEO to GEO. At 315 t each that is 2500 t/day, somewhat exceeding the 2200 t/day needed to install 400 GW per year.<br />
<br />
It also cuts the rocket launches from 24 to a more manageable but still excessive 7 or 8.<br />
<br />
A 3.5-GW space based laser built at GEO that massed 10,000 tons would cost $5 billion to lift by rockets and $35 billion for the laser. It can be expected to more than triple the yearly throughput to GEO, saving 2/3 of 0.8 billion kg x $500/kg or $267 billion a year in transport costs.<br />
<br />
Amortized at 10 percent, the additional lift from LEO to GEO would cost $4 billion/0.8 billion/kg or $5 per kg plus the lift to LEO.<br />
<br />
==Cost reduction==<br />
<br />
There is another way that cuts the liftoff mass by a factor of five compared to rockets.<br />
<br />
Injection to geosynchronous transfer orbit is 7.8 k/s (to LEO), 2.5 k/s (to GTO) plus 1.6k/sec to circularize at GEO, totaling 11.9 km/s. http://en.wikipedia.org/wiki/Delta-v_budget To get to LEO takes 796 s at 1g, 13.2 minutes. At one g 17.5 minutes for GTO, 14 minutes at 1.25 g, plus 2.2 minutes to circularize the orbit (1.6 km/s) at GEO. Assuming half payload and half reaction mass, 0.69 velocity ratio and 11.9 km/s delta v, then the average exhaust velocity needs to be a modest (for lasers) 17.2 km/s.<br />
<br />
Because the laser can be cycled close to 4 times an hour, the payload only needs to be 25 tons. Taking the midpoint (the exhaust velocity would be varied for constant thrust) the power required for 1.25 g (12.25 m/sec exp 2) is 1/2 x 37,500 kg x 12.25 m/sec exp 2 x 17,200 m/sec = 4 GW. In the context of building a GW of power satellite a day, this is a small piece of hardware. The choice of building the laser in space or on the ground has not been fully examined.<br />
<br />
The 50-ton payload-plus-reaction-mass has to hang in space long enough to be accelerated. This takes a modest mass ratio rocket.<br />
<br />
50 tons payload plus reaction mass for the laser. 16.5%<br />
<br />
50 tons rocket structure 16.5%<br />
<br />
200 tons propellant. 66%<br />
<br />
<br />
The rocket would lift off on two SSMEs (or similar), and if a zeroth turbofan stage was used, it would take eight 50-ton thrust engines, perhaps with afterburners. Simplifying operations, it goes straight up and lands back at the launching site. If the payload is oriented at right angles to vertical, we could avoid wasting time reorienting it for laser acceleration.<br />
<br />
This "little" rocket (about the mass of a 747) has a mass ratio of two and a delta V of 4 k/sec (less gravity loss and drag). The payload-plus-reaction-mass exits the atmosphere at 2.1 k/sec, goes up to 260 miles, falls to 150 miles before picking up orbital velocity and falls to 55 miles (picking up a little air drag) before losing downward velocity. It enters GTO 1000 seconds after launch. This is conservative, not accounting for the curvature of the earth.<br />
<br />
It masses 1/20th of a Neptune and (with the aid of the laser) delivers 1/4 as much payload per launch. One part in 12 (rather than one part in 60) is payload. To keep the laser busy and to meet the 100-ton per hour cargo requirement requires a launch every 15 minutes. This rate is common for airlines, but not for spacecraft.<br />
<br />
If the laser cost 40 billion dollars and was written off at 10% per year, the lift cost from sub orbital to GEO would be $4 billion /0.8 billion kg, $5/kg plus the sub orbital flight of perhaps $60/kg of payload. This meet the penny a kWh and dollar a gallon fuel goals.<br />
<br />
Energy payback is 8 days for the rocket fuel and 8 days for the laser. This is about 8.4% of the theoretical minimum for a space elevator.<br />
<br />
This is probably not the optimum design. A shorter "hang time," smaller payloads and higher but shorter acceleration may yield lower cost per kg. (It is possible that laser launch from the ground is the end point of this optimization.) However, the size of the largest part for a power satellite may limit the minimum size of rocket.</div>24.23.229.100https://htyp.org/mw/index.php?title=Hundred_dollars_a_kg&diff=10055Hundred dollars a kg2008-08-03T14:32:21Z<p>24.23.229.100: /* Cost reduction */</p>
<hr />
<div>To sum up what's gone before:<br />
<br />
To solve the energy crisis using space-based solar power, replacement power needs to come on line at a rate of 400-500 GW/year. That replaces about 6 million barrels of oil a day each year over the next 50 years. To make liquid fuels at a dollar a gallon out of electricity requires that the electricity cost be around a penny a kWh. To make penny a kWh requires lift cost to GEO of $100 or less<br />
<br />
==How much lifted to GEO==<br />
<br />
Four hundred GW of power sats requires 800,000 tons per year lifted to GEO (perhaps twice that). At least there is economy of scale.<br />
<br />
Do we have to lift that much mass? No. Extra terrestrial resources are a better idea, but there isn't time to develop the space industry to tap them. The economic effects (including famines) of the developing energy crisis are so bad that the large scale production of SBSP needs to come on line by 2015 to avoid economic collapse. Expect ET resources to be exploited by 2025 with this much activity in space.<br />
<br />
This works out to lifting about 100 tons per hour. Will physics let us get under $100/kg? A moving cable space elevator only requires about 15 kWh to lift a kg from the surface of the earth to GEO. This is $1.50 at the high rate of 10 cents a kWh. Even if it cost $100 billion dollars to build, a capital cost of $10 billion a year lifting a billion kg is only ten dollars. Unfortunately we don't have the cable--yet.<br />
<br />
The choices further examined here are among rockets, lasers or some combination of them.<br />
<br />
==Rockets vs lasers==<br />
<br />
Rockets are good for high thrust, but the rocket equation is a hard taskmaster when you need delta V that is a multiple of the exhaust velocity.<br />
<br />
Lasers are not as well developed as rockets. They can get very high exhaust velocity, leading to small mass ratios, but they don't do very good for high thrust. Jordin Kare and others have been working for decades designing lasers to launch from the surface.<br />
<br />
Rockets to lift this much cargo would have to launch every hour, each rocket having a lift off mass of 6,000 tons to get 350 tons to LEO and 100 tons of that to GEO. The projected cost to GEO is around $500/kg. http://www.ilr.tu-berlin.de/koelle/Neptun/NEP2015.pdf<br />
<br />
The energy payback (for making fuel) is about 40 days. The cost of rockets is not in the fuel, but in the high cost of aerospace hardware and the rocket equation which dictates that even for the most energetic fuels only about one part in sixty is payload to GEO.<br />
<br />
The needed delta V LEO to GEO is about 4.1 km/sec. Using 10% of the LEO payload for reaction mass (35 tons) and a laser that provides a 40 km/sec exhaust velocity will produce about 4.2 km/sec delta V.<br />
<br />
(http://en.wikipedia.org/wiki/Rocket_equation )<br />
<br />
The power required for 1/20th g (.5 m/sec exp 2) is 1/2 x 350,000 kg x .5m/sec exp 2 x 40,000 m/sec = 3.5 GW<br />
<br />
Delta V changes require 4100 m/sec /0.5 m/sec exp 2, or 8200 sec or about 2.7 hours. I.e., 3.5 GW of laser power would raise eight loads a day from LEO to GEO. At 315 t each that is 2500 t/day, somewhat exceeding the 2200 t/day needed to install 400 GW per year.<br />
<br />
It also cuts the rocket launches from 24 to a more manageable but still excessive 7 or 8.<br />
<br />
A 3.5-GW space based laser built at GEO that massed 10,000 tons would cost $5 billion to lift by rockets and $35 billion for the laser. It can be expected to more than triple the yearly throughput to GEO, saving 2/3 of 0.8 billion kg x $500/kg or $267 billion a year in transport costs.<br />
<br />
Amortized at 10 percent, the additional lift from LEO to GEO would cost $4 billion/0.8 billion/kg or $5 per kg plus the lift to LEO.<br />
<br />
==Cost reduction==<br />
<br />
There is another way that cuts the liftoff mass by a factor of five compared to rockets.<br />
<br />
Injection to geosynchronous transfer orbit is 7.8 k/s (to LEO), 2.5 k/s (to GTO) plus 1.6k/sec to circularize at GEO, totaling 11.9 km/s. http://en.wikipedia.org/wiki/Delta-v_budget To get to LEO takes 796 s at 1g, 13.2 minutes. At one g 17.5 minutes for GTO, 14 minutes at 1.25 g, plus 2.2 minutes to circularize the orbit (1.6 km/s) at GEO. Assuming half payload and half reaction mass, 0.69 velocity ratio and 11.9 km/s delta v, then the average exhaust velocity needs to be a modest (for lasers) 17.2 km/s.<br />
<br />
Because the laser can be cycled close to 4 times an hour, the payload only needs to be 25 tons. Taking the midpoint (the exhaust velocity would be varied for constant thrust) the power required for 1.25 g (12.25 m/sec exp 2) is 1/2 x 37,500 kg x 12.25 m/sec exp 2 x 17,200 m/sec = 4 GW. In the context of building a GW of power satellite a day, this is a small piece of hardware. The choice of building the laser in space or on the ground has not been fully examined.<br />
<br />
The 50-ton payload-plus-reaction-mass has to hang in space long enough to be accelerated. This takes a modest mass ratio rocket.<br />
<br />
50 tons payload plus reaction mass for the laser. 16.5%<br />
<br />
50 tons rocket structure 16.5%<br />
<br />
200 tons propellant. 66%<br />
<br />
<br />
The rocket would lift off on two SSMEs (or similar), and if a zeroth turbofan stage was used, it would take eight 50-ton thrust engines, perhaps with afterburners. Simplifying operations, it goes straight up and lands back at the launching site. If the payload is oriented at right angles to vertical, we could avoid wasting time reorienting it for laser acceleration.<br />
<br />
This "little" rocket (about the mass of a 747) has a mass ratio of two and a delta V of 4 k/sec (less gravity loss and drag). The payload-plus-reaction-mass exits the atmosphere at 2.1 k/sec, goes up to 260 miles, falls to 150 miles before picking up orbital velocity and falls to 55 miles (picking up a little air drag) before losing downward velocity. It enters GTO 1000 seconds after launch. This is conservative, not accounting for the curvature of the earth.<br />
<br />
It masses 1/20th of a Neptune and (with the aid of the laser) delivers 1/4 as much payload per launch. One part in 12 (rather than one part in 60) is payload. To keep the laser busy and to meet the 100-ton per hour cargo requirement requires a launch every 15 minutes. This rate is common for airlines, but not for spacecraft.<br />
<br />
If the laser cost 40 billion dollars and was written off at 10% per year, the lift cost from sub orbital to GEO would be $4 billion /0.8 billion kg, $5/kg plus the sub orbital flight of perhaps $60/kg of payload. This meet the penny a kWh and dollar a gallon fuel goals.<br />
<br />
Energy payback is 8 days for the rocket fuel and 8 days for the laser. This is about 8.4% of the theoretical minimum for a space elevator.<br />
<br />
This is probably not the optimum design. A shorter "hang time," smaller payloads and higher but shorter acceleration may yield lower cost per kg. (It is possible that laser launch from the ground is the end point of this optimization.) However, the size of the largest part for a power satellite may limit the minimum size of rocket.</div>24.23.229.100https://htyp.org/mw/index.php?title=Hundred_dollars_a_kg&diff=10054Hundred dollars a kg2008-08-03T07:11:44Z<p>24.23.229.100: /* Rockets vs lasers */</p>
<hr />
<div>To sum up what's gone before:<br />
<br />
To solve the energy crisis using space-based solar power, replacement power needs to come on line at a rate of 400-500 GW/year. That replaces about 6 million barrels of oil a day each year over the next 50 years. To make liquid fuels at a dollar a gallon out of electricity requires that the electricity cost be around a penny a kWh. To make penny a kWh requires lift cost to GEO of $100 or less<br />
<br />
==How much lifted to GEO==<br />
<br />
Four hundred GW of power sats requires 800,000 tons per year lifted to GEO (perhaps twice that). At least there is economy of scale.<br />
<br />
Do we have to lift that much mass? No. Extra terrestrial resources are a better idea, but there isn't time to develop the space industry to tap them. The economic effects (including famines) of the developing energy crisis are so bad that the large scale production of SBSP needs to come on line by 2015 to avoid economic collapse. Expect ET resources to be exploited by 2025 with this much activity in space.<br />
<br />
This works out to lifting about 100 tons per hour. Will physics let us get under $100/kg? A moving cable space elevator only requires about 15 kWh to lift a kg from the surface of the earth to GEO. This is $1.50 at the high rate of 10 cents a kWh. Even if it cost $100 billion dollars to build, a capital cost of $10 billion a year lifting a billion kg is only ten dollars. Unfortunately we don't have the cable--yet.<br />
<br />
The choices further examined here are among rockets, lasers or some combination of them.<br />
<br />
==Rockets vs lasers==<br />
<br />
Rockets are good for high thrust, but the rocket equation is a hard taskmaster when you need delta V that is a multiple of the exhaust velocity.<br />
<br />
Lasers are not as well developed as rockets. They can get very high exhaust velocity, leading to small mass ratios, but they don't do very good for high thrust. Jordin Kare and others have been working for decades designing lasers to launch from the surface.<br />
<br />
Rockets to lift this much cargo would have to launch every hour, each rocket having a lift off mass of 6,000 tons to get 350 tons to LEO and 100 tons of that to GEO. The projected cost to GEO is around $500/kg. http://www.ilr.tu-berlin.de/koelle/Neptun/NEP2015.pdf<br />
<br />
The energy payback (for making fuel) is about 40 days. The cost of rockets is not in the fuel, but in the high cost of aerospace hardware and the rocket equation which dictates that even for the most energetic fuels only about one part in sixty is payload to GEO.<br />
<br />
The needed delta V LEO to GEO is about 4.1 km/sec. Using 10% of the LEO payload for reaction mass (35 tons) and a laser that provides a 40 km/sec exhaust velocity will produce about 4.2 km/sec delta V.<br />
<br />
(http://en.wikipedia.org/wiki/Rocket_equation )<br />
<br />
The power required for 1/20th g (.5 m/sec exp 2) is 1/2 x 350,000 kg x .5m/sec exp 2 x 40,000 m/sec = 3.5 GW<br />
<br />
Delta V changes require 4100 m/sec /0.5 m/sec exp 2, or 8200 sec or about 2.7 hours. I.e., 3.5 GW of laser power would raise eight loads a day from LEO to GEO. At 315 t each that is 2500 t/day, somewhat exceeding the 2200 t/day needed to install 400 GW per year.<br />
<br />
It also cuts the rocket launches from 24 to a more manageable but still excessive 7 or 8.<br />
<br />
A 3.5-GW space based laser built at GEO that massed 10,000 tons would cost $5 billion to lift by rockets and $35 billion for the laser. It can be expected to more than triple the yearly throughput to GEO, saving 2/3 of 0.8 billion kg x $500/kg or $267 billion a year in transport costs.<br />
<br />
Amortized at 10 percent, the additional lift from LEO to GEO would cost $4 billion/0.8 billion/kg or $5 per kg plus the lift to LEO.<br />
<br />
==Cost reduction==<br />
<br />
There is another way that cuts the liftoff mass by a factor of five compared to rockets.<br />
<br />
Injection to geosynchronous transfer orbit is 7.8 k/s (to LEO), 2.5 k/s (to GTO) plus 1.6k/sec to circularize at GEO, totaling 11.9 km/s. http://en.wikipedia.org/wiki/Delta-v_budget To get to LEO takes 796 s at 1g, 13.2 minutes. At one g 17.5 minutes for GTO, 14 minutes at 1.25 g, plus 2.2 minutes to circularize the orbit (1.6 km/s) at GEO. Assuming half payload and half reaction mass, 0.69 velocity ratio and 11.9 km/s delta v, then the average exhaust velocity needs to be a modest (for lasers) 17.2 km/s.<br />
<br />
Because the laser can be cycled close to 4 times an hour, the payload only needs to be 25 tons. Taking the midpoint (the exhaust velocity would be varied for constant thrust) the power required for 1.25 g (12.25 m/sec exp 2) is 1/2 x 37,500 kg x 12.25 m/sec exp 2 x 17,200 m/sec = 4 GW. In the context of building a GW of power satellite a day, this is a small piece of hardware. The choice of building the laser in space or on the ground has not been fully examined.<br />
<br />
The 50-ton payload-plus-reaction-mass has to hang in space long enough to be accelerated. This takes a modest mass ratio rocket.<br />
<br />
50 tons payload plus reaction mass for the laser. 16.5%<br />
<br />
50 tons rocket structure 16.5%<br />
<br />
200 tons propellant. 66%<br />
<br />
<br />
The rocket would lift off on two SSMEs, and if a zeroth turbofan stage was used, it would take eight 50-ton thrust engines, perhaps with afterburners. Simplifying operations, it goes straight up and lands back at the launching site. If the payload is oriented at right angles to vertical, we could avoid wasting time reorienting it for laser acceleration.<br />
<br />
This "little" rocket has a mass ratio of two and a delta V of 4 k/sec (less gravity loss and drag). The payload-plus-reaction-mass exits the atmosphere at 2.1 k/sec, goes up to 260 miles, falls to 150 miles before picking up orbital velocity and falls to 55 miles (picking up a little air drag) before losing downward velocity. It enters GTO 1000 seconds after launch. This is conservative, not accounting for the curvature of the earth.<br />
<br />
It masses 1/20th of a Neptune and (with the aid of the laser) delivers 1/4 as much payload per launch. One part in 12 (rather than one part in 60) is payload. To keep the laser busy and to meet the 100-ton per hour cargo requirement requires a launch every 15 minutes. This rate is common for airlines, but not for spacecraft.<br />
<br />
If the laser cost 80 billion dollars and was written off at 10% per year, the lift cost from sub orbital to GEO would be $8 billion /0.8 billion kg, $10/kg plus the sub orbital flight of perhaps $60/kg of payload. This meet the penny a kWh and dollar a gallon fuel goals.<br />
<br />
Energy payback is 8 days for the rocket fuel and 16 days for the laser. This is about 5.6%% of the theoretical minimum for a space elevator.<br />
<br />
This is probably not the optimum design. A shorter "hang time," smaller payloads and higher but shorter acceleration may yield lower cost per kg. (It is possible that laser launch from the ground is the end point of this optimization.) However, the size of the largest part for a power satellite may limit the minimum size of rocket.</div>24.23.229.100https://htyp.org/mw/index.php?title=Hundred_dollars_a_kg&diff=10053Hundred dollars a kg2008-08-03T07:00:35Z<p>24.23.229.100: /* Rockets vs lasers */</p>
<hr />
<div>To sum up what's gone before:<br />
<br />
To solve the energy crisis using space-based solar power, replacement power needs to come on line at a rate of 400-500 GW/year. That replaces about 6 million barrels of oil a day each year over the next 50 years. To make liquid fuels at a dollar a gallon out of electricity requires that the electricity cost be around a penny a kWh. To make penny a kWh requires lift cost to GEO of $100 or less<br />
<br />
==How much lifted to GEO==<br />
<br />
Four hundred GW of power sats requires 800,000 tons per year lifted to GEO (perhaps twice that). At least there is economy of scale.<br />
<br />
Do we have to lift that much mass? No. Extra terrestrial resources are a better idea, but there isn't time to develop the space industry to tap them. The economic effects (including famines) of the developing energy crisis are so bad that the large scale production of SBSP needs to come on line by 2015 to avoid economic collapse. Expect ET resources to be exploited by 2025 with this much activity in space.<br />
<br />
This works out to lifting about 100 tons per hour. Will physics let us get under $100/kg? A moving cable space elevator only requires about 15 kWh to lift a kg from the surface of the earth to GEO. This is $1.50 at the high rate of 10 cents a kWh. Even if it cost $100 billion dollars to build, a capital cost of $10 billion a year lifting a billion kg is only ten dollars. Unfortunately we don't have the cable--yet.<br />
<br />
The choices further examined here are among rockets, lasers or some combination of them.<br />
<br />
==Rockets vs lasers==<br />
<br />
Rockets are good for high thrust, but the rocket equation is a hard taskmaster when you need delta V that is a multiple of the exhaust velocity.<br />
<br />
Lasers are not as well developed as rockets. They can get very high exhaust velocity, leading to small mass ratios, but they don't do very good for high thrust. Jordin Kare and others have been working for decades designing lasers to launch from the surface.<br />
<br />
Rockets to lift this much cargo would have to launch every hour, each rocket having a lift off mass of 6,000 tons to get 350 tons to LEO and 100 tons of that to GEO. The projected cost to GEO is around $500/kg. http://www.ilr.tu-berlin.de/koelle/Neptun/NEP2015.pdf<br />
<br />
The energy payback (for making fuel) is about 40 days. The cost of rockets is not in the fuel, but in the high cost of aerospace hardware and the rocket equation which dictates that even for the most energetic fuels only about one part in sixty is payload to GEO.<br />
<br />
The needed delta V LEO to GEO is about 4.1 km/sec. Using 10% of the LEO payload for reaction mass (35 tons) and a laser that provides a 40 km/sec exhaust velocity will produce about 4.2 km/sec delta V.<br />
<br />
(http://en.wikipedia.org/wiki/Rocket_equation )<br />
<br />
The power required for 1/20th g (.5 m/sec exp 2) is 1/2 x 350,000 kg x .5m/sec exp 2 x 40,000 m/sec = 3.5 GW<br />
<br />
Delta V changes require 4100 m/sec /0.5 m/sec exp 2, or 8200 sec or about 2.7 hours. I.e., 3.5 GW of laser power would raise eight loads a day from LEO to GEO. At 315 t each that is 2500 t/day, somewhat exceeding the 2200 t/day needed to install 400 GW per year.<br />
<br />
It also cuts the rocket launches from 24 to a more manageable but still excessive 7 or 8.<br />
<br />
A 3.5-GW space based laser built at GEO that massed 10,000 tons would cost $5 billion to lift by rockets and $35 billion for the laser. It can be expected to more than triple the yearly throughput to GEO, saving 2/3 of 0.8 billion kg x $500/kg or $267 billion a year in transport costs.<br />
<br />
Amortized at 10 percent, the additional lift from LEO to GEO would cost $4 billion/0.8 billion/kg or $5 per kg plus the lift to LEO.<br />
<br />
There is another way that cuts the liftoff mass by a factor of five compared to rockets.<br />
<br />
Injection to geosynchronous transfer orbit is 7.8 k/s (to LEO), 2.5 k/s (to GTO) plus 1.6k/sec to circularize at GEO, totaling 11.9 km/s. http://en.wikipedia.org/wiki/Delta-v_budget To get to LEO takes 796 s at 1g, 13.2 minutes. At one g 17.5 minutes for GTO, 14 minutes at 1.25 g, plus 2.2 minutes to circularize the orbit (1.6 km/s) at GEO. Assuming half payload and half reaction mass, 0.69 velocity ratio and 11.9 km/s delta v, then the average exhaust velocity needs to be a modest (for lasers) 17.2 km/s.<br />
<br />
Because the laser can be cycled close to 4 times an hour, the payload only needs to be 25 tons. Taking the midpoint (the exhaust velocity would be varied for constant thrust) the power required for 1.25 g (12.25 m/sec exp 2) is 1/2 x 37,500 kg x 12.25 m/sec exp 2 x 17,200 m/sec = 4 GW. In the context of building a GW of power satellite a day, this is a small piece of hardware. The choice of building the laser in space or on the ground has not been fully examined.<br />
<br />
The 50-ton payload-plus-reaction-mass has to hang in space long enough to be accelerated. This takes a modest mass ratio rocket.<br />
<br />
50 tons payload plus reaction mass for the laser. 16.5%<br />
<br />
50 tons rocket structure 16.5%<br />
<br />
200 tons propellant. 66%<br />
<br />
<br />
The rocket would lift off on two SSMEs, and if a zeroth turbofan stage was used, it would take eight 50-ton thrust engines, perhaps with afterburners. Simplifying operations, it goes straight up and lands back at the launching site. If the payload is oriented at right angles to vertical, we could avoid wasting time reorienting it for laser acceleration.<br />
<br />
This "little" rocket has a mass ratio of two and a delta V of 4 k/sec (less gravity loss and drag). The payload-plus-reaction-mass exits the atmosphere at 2.1 k/sec, goes up to 260 miles, falls to 150 miles before picking up orbital velocity and falls to 55 miles (picking up a little air drag) before losing downward velocity. It enters GTO 1000 seconds after launch. This is conservative, not accounting for the curvature of the earth.<br />
<br />
It masses 1/20th of a Neptune and (with the aid of the laser) delivers 1/4 as much payload per launch. One part in 12 (rather than one part in 60) is payload. To keep the laser busy and to meet the 100-ton per hour cargo requirement requires a launch every 15 minutes. This rate is common for airlines, but not for spacecraft.<br />
<br />
If the laser cost 80 billion dollars and was written off at 10% per year, the lift cost from sub orbital to GEO would be $8 billion /0.8 billion kg, $10/kg plus the sub orbital flight of perhaps $60/kg of payload. This meet the penny a kWh and dollar a gallon fuel goals.<br />
<br />
Energy payback is 8 days for the rocket fuel and 16 days for the laser. This is about 5.6%% of the theoretical minimum for a space elevator.<br />
<br />
This is probably not the optimum design. A shorter "hang time," smaller payloads and higher but shorter acceleration may yield lower cost per kg. (It is possible that laser launch from the ground is the end point of this optimization.) However, the size of the largest part for a power satellite may limit the minimum size of rocket.</div>24.23.229.100https://htyp.org/mw/index.php?title=Hundred_dollars_a_kg&diff=10052Hundred dollars a kg2008-08-03T06:37:12Z<p>24.23.229.100: /* Rockets vs lasers */</p>
<hr />
<div>To sum up what's gone before:<br />
<br />
To solve the energy crisis using space-based solar power, replacement power needs to come on line at a rate of 400-500 GW/year. That replaces about 6 million barrels of oil a day each year over the next 50 years. To make liquid fuels at a dollar a gallon out of electricity requires that the electricity cost be around a penny a kWh. To make penny a kWh requires lift cost to GEO of $100 or less<br />
<br />
==How much lifted to GEO==<br />
<br />
Four hundred GW of power sats requires 800,000 tons per year lifted to GEO (perhaps twice that). At least there is economy of scale.<br />
<br />
Do we have to lift that much mass? No. Extra terrestrial resources are a better idea, but there isn't time to develop the space industry to tap them. The economic effects (including famines) of the developing energy crisis are so bad that the large scale production of SBSP needs to come on line by 2015 to avoid economic collapse. Expect ET resources to be exploited by 2025 with this much activity in space.<br />
<br />
This works out to lifting about 100 tons per hour. Will physics let us get under $100/kg? A moving cable space elevator only requires about 15 kWh to lift a kg from the surface of the earth to GEO. This is $1.50 at the high rate of 10 cents a kWh. Even if it cost $100 billion dollars to build, a capital cost of $10 billion a year lifting a billion kg is only ten dollars. Unfortunately we don't have the cable--yet.<br />
<br />
The choices further examined here are among rockets, lasers or some combination of them.<br />
<br />
==Rockets vs lasers==<br />
<br />
Rockets are good for high thrust, but the rocket equation is a hard taskmaster when you need delta V that is a multiple of the exhaust velocity.<br />
<br />
Lasers are not as well developed as rockets. They can get very high exhaust velocity, leading to small mass ratios, but they don't do very good for high thrust. Jordin Kare and others have been working for decades designing lasers to launch from the surface.<br />
<br />
Rockets to lift this much cargo would have to launch every hour, each rocket having a lift off mass of 6,000 tons to get 350 tons to LEO and 100 tons of that to GEO. The projected cost is around $500/kg. http://www.ilr.tu-berlin.de/koelle/Neptun/NEP2015.pdf<br />
<br />
The energy payback (for making fuel) is about 40 days. The cost of rockets is not in the fuel, but in the high cost of aerospace hardware and the rocket equation which dictates that even for the most energetic fuels only about one part in sixty is payload to GEO.<br />
<br />
The needed delta V LEO to GEO is about 4.1 km/sec. Using 10% of the LEO payload for reaction mass (35 tons) and a laser that provides a 40 km/sec exhaust velocity will produce about 4.2 km/sec delta V.<br />
<br />
(http://en.wikipedia.org/wiki/Rocket_equation )<br />
<br />
The power required for 1/20th g (.5 m/sec exp 2) is 1/2 x 350,000 kg x .5m/sec exp 2 x 40,000 m/sec = 3.5 GW<br />
<br />
Delta V changes require 4100 m/sec /0.5 m/sec exp 2, or 8200 sec or about 2.7 hours. I.e., 3.5 GW of laser power would raise eight loads a day from LEO to GEO. At 315 t each that is 2500 t/day, somewhat exceeding the 2200 t/day needed to install 400 GW per year.<br />
<br />
It also cuts the rocket launches from 24 to a more manageable but still excessive 7 or 8.<br />
<br />
A 3.5-GW space based laser built at GEO that massed 10,000 tons would cost $5 billion to lift by rockets and $35 billion for the laser. It can be expected to more than triple the yearly throughput to GEO, saving 2/3 of 0.8 billion kg x $500/kg or $267 billion a year in transport costs.<br />
<br />
Amortized at 10 percent, the additional lift from LEO to GEO would cost $4 billion/0.8 billion/kg or $5 per kg plus the lift to LEO.<br />
<br />
There is another way that cuts the liftoff mass by a factor of five compared to rockets.<br />
<br />
Injection to geosynchronous transfer orbit is 7.8 k/s (to LEO), 2.5 k/s (to GTO) plus 1.6k/sec to circularize at GEO, totaling 11.9 km/s. http://en.wikipedia.org/wiki/Delta-v_budget To get to LEO takes 796 s at 1g, 13.2 minutes. At one g 17.5 minutes for GTO, 14 minutes at 1.25 g, plus 2.2 minutes to circularize the orbit (1.6 km/s) at GEO. Assuming half payload and half reaction mass, 0.69 velocity ratio and 11.9 km/s delta v, then the average exhaust velocity needs to be a modest (for lasers) 17.2 km/s.<br />
<br />
Because the laser can be cycled close to 4 times an hour, the payload only needs to be 25 tons. Taking the midpoint (the exhaust velocity would be varied for constant thrust) the power required for 1.25 g (12.25 m/sec exp 2) is 1/2 x 37,500 kg x 12.25 m/sec exp 2 x 17,200 m/sec = 4 GW. In the context of building a GW of power satellite a day, this is a small piece of hardware. The choice of building the laser in space or on the ground has not been fully examined.<br />
<br />
The 50-ton payload-plus-reaction-mass has to hang in space long enough to be accelerated. This takes a modest mass ratio rocket.<br />
<br />
50 tons payload plus reaction mass for the laser. 16.5%<br />
<br />
50 tons rocket structure 16.5%<br />
<br />
200 tons propellant. 66%<br />
<br />
<br />
The rocket would lift off on two SSMEs, and if a zeroth turbofan stage was used, it would take eight 50-ton thrust engines, perhaps with afterburners. Simplifying operations, it goes straight up and lands back at the launching site. If the payload is oriented at right angles to vertical, we could avoid wasting time reorienting it for laser acceleration.<br />
<br />
This "little" rocket has a mass ratio of two and a delta V of 4 k/sec (less gravity loss and drag). The payload-plus-reaction-mass exits the atmosphere at 2.1 k/sec, goes up to 260 miles, falls to 150 miles before picking up orbital velocity and falls to 55 miles (picking up a little air drag) before losing downward velocity. It enters GTO 1000 seconds after launch. This is conservative, not accounting for the curvature of the earth.<br />
<br />
It masses 1/20th of a Neptune and (with the aid of the laser) delivers 1/4 as much payload per launch. One part in 12 (rather than one part in 60) is payload. To keep the laser busy and to meet the 100-ton per hour cargo requirement requires a launch every 15 minutes. This rate is common for airlines, but not for spacecraft.<br />
<br />
If the laser cost 80 billion dollars and was written off at 10% per year, the lift cost from sub orbital to GEO would be $8 billion /0.8 billion kg, $10/kg plus the sub orbital flight of perhaps $60/kg of payload. This meet the penny a kWh and dollar a gallon fuel goals.<br />
<br />
Energy payback is 8 days for the rocket fuel and 16 days for the laser. This is about 5.6%% of the theoretical minimum for a space elevator.<br />
<br />
This is probably not the optimum design. A shorter "hang time," smaller payloads and higher but shorter acceleration may yield lower cost per kg. (It is possible that laser launch from the ground is the end point of this optimization.) However, the size of the largest part for a power satellite may limit the minimum size of rocket.</div>24.23.229.100https://htyp.org/mw/index.php?title=Hundred_dollars_a_kg&diff=10051Hundred dollars a kg2008-08-03T06:36:15Z<p>24.23.229.100: /* How much lifted to GEO */</p>
<hr />
<div>To sum up what's gone before:<br />
<br />
To solve the energy crisis using space-based solar power, replacement power needs to come on line at a rate of 400-500 GW/year. That replaces about 6 million barrels of oil a day each year over the next 50 years. To make liquid fuels at a dollar a gallon out of electricity requires that the electricity cost be around a penny a kWh. To make penny a kWh requires lift cost to GEO of $100 or less<br />
<br />
==How much lifted to GEO==<br />
<br />
Four hundred GW of power sats requires 800,000 tons per year lifted to GEO (perhaps twice that). At least there is economy of scale.<br />
<br />
Do we have to lift that much mass? No. Extra terrestrial resources are a better idea, but there isn't time to develop the space industry to tap them. The economic effects (including famines) of the developing energy crisis are so bad that the large scale production of SBSP needs to come on line by 2015 to avoid economic collapse. Expect ET resources to be exploited by 2025 with this much activity in space.<br />
<br />
This works out to lifting about 100 tons per hour. Will physics let us get under $100/kg? A moving cable space elevator only requires about 15 kWh to lift a kg from the surface of the earth to GEO. This is $1.50 at the high rate of 10 cents a kWh. Even if it cost $100 billion dollars to build, a capital cost of $10 billion a year lifting a billion kg is only ten dollars. Unfortunately we don't have the cable--yet.<br />
<br />
The choices further examined here are among rockets, lasers or some combination of them.<br />
<br />
==Rockets vs lasers==<br />
<br />
Rockets are good for high thrust, but the rocket equation is a hard taskmaster when you need delta V that is a multiple of the exhaust velocity.<br />
<br />
Lasers are not as well developed as rockets. They can get very high exhaust velocity, leading to small mass ratios, but they don't do very good for high thrust. Jordin Kare and others have been working for decades designing lasers to launch from the surface.<br />
<br />
Rockets to lift this much cargo would have to launch every hour, each rocket having a lift off mass of 6,000 tons to get 350 tons to LEO and 100 tons of that to GEO. The projected cost is around $500/kg. http://www.ilr.tu-berlin.de/koelle/Neptun/NEP2015.pdf<br />
<br />
The energy payback (for making fuel) is about 40 days. The cost of rockets is not in the fuel, but in the high cost of aerospace hardware and the rocket equation which dictates that even for the most energetic fuels only about one part in sixty is payload to GEO.<br />
<br />
The needed delta V LEO to GEO is about 4.1 km/sec. Using 10% of the LEO payload for reaction mass (35 tons) and a laser that provides a 40 km/sec exhaust velocity will produce about 4.2 km/sec delta V.<br />
<br />
(http://en.wikipedia.org/wiki/Rocket_equation )<br />
<br />
The power required for 1/20th g (.5 m/sec exp 2) is 1/2 x 350,000 kg x .5m/sec exp 2 x 40,000 m/sec = 3.5 GW<br />
<br />
Delta V changes require 4100 m/sec /0.5 m/sec exp 2, or 8200 sec or about 2.7 hours. I.e., 3.5 GW of laser power would raise eight loads a day from LEO to GEO. At 315 t each that is 2500 t/day, somewhat exceeding the 2200 t/day needed to install 400 GW per year.<br />
<br />
It also cuts the rocket launches from 24 to a more manageable but still excessive 7 or 8.<br />
<br />
A 3.5-GW space based laser built at GEO that massed 10,000 tons would cost $5 billion to lift by rockets and $35 billion for the laser. It can be expected to more than triple the yearly throughput to GEO, saving 2/3 of 0.8 billion kg x $500/kg or $267 billion a year in transport costs.<br />
<br />
Amortized at 10 percent, the additional lift from LEO to GEO would cost $4 billion/0.8 billion/kg or $5 per kg plus the lift to LEO.<br />
<br />
There is another way that cuts the liftoff mass by a factor of five compared to rockets.<br />
<br />
Injection to geosynchronous transfer orbit is 7.8 k/s (to LEO), 2.5 k/s (to GTO) plus 1.6k/sec to circularize at GEO, totaling 11.9 km/s. http://en.wikipedia.org/wiki/Delta-v_budget To get to LEO takes 796 s at 1g, 13.2 minutes. At one g 17.5 minutes for GTO, 14 minutes at 1.25 g, plus 2.2 minutes to circularize the orbit (1.6 km/s) at GEO. Assuming half payload and half reaction mass, 0.69 velocity ratio and 11.9 km/s delta v, then the average exhaust velocity needs to be a modest (for lasers) 17.2 km/s.<br />
<br />
Because the laser can be cycled close to 4 times an hour, the payload only needs to be 25 tons. Taking the midpoint (the exhaust velocity would be varied for constant thrust) the power required for 1.25 g (12.25 m/sec exp 2) is 1/2 x 37,500 kg x 12.25 m/sec exp 2 x 17,200 m/sec = 4 GW. In the context of building a GW of power satellite a day, this is a small piece of hardware. The choice of building the laser in space or on the ground has not been fully examined.<br />
<br />
The 50-ton payload-plus-reaction-mass has to hang in space long enough to be accelerated. This takes a modest mass ratio rocket.<br />
<br />
50 tons payload plus reaction mass for the laser. 16.5%<br />
50 tons rocket structure 16.5%<br />
200 tons propellant. 66%<br />
<br />
The rocket would lift off on two SSMEs, and if a zeroth turbofan stage was used, it would take eight 50-ton thrust engines, perhaps with afterburners. Simplifying operations, it goes straight up and lands back at the launching site. If the payload is oriented at right angles to vertical, we could avoid wasting time reorienting it for laser acceleration.<br />
<br />
This "little" rocket has a mass ratio of two and a delta V of 4 k/sec (less gravity loss and drag). The payload-plus-reaction-mass exits the atmosphere at 2.1 k/sec, goes up to 260 miles, falls to 150 miles before picking up orbital velocity and falls to 55 miles (picking up a little air drag) before losing downward velocity. It enters GTO 1000 seconds after launch. This is conservative, not accounting for the curvature of the earth.<br />
<br />
It masses 1/20th of a Neptune and (with the aid of the laser) delivers 1/4 as much payload per launch. One part in 12 (rather than one part in 60) is payload. To keep the laser busy and to meet the 100-ton per hour cargo requirement requires a launch every 15 minutes. This rate is common for airlines, but not for spacecraft.<br />
<br />
If the laser cost 80 billion dollars and was written off at 10% per year, the lift cost from sub orbital to GEO would be $8 billion /0.8 billion kg, $10/kg plus the sub orbital flight of perhaps $60/kg of payload. This meet the penny a kWh and dollar a gallon fuel goals.<br />
<br />
Energy payback is 8 days for the rocket fuel and 16 days for the laser. This is about 5.6%% of the theoretical minimum for a space elevator.<br />
<br />
This is probably not the optimum design. A shorter "hang time," smaller payloads and higher but shorter acceleration may yield lower cost per kg. (It is possible that laser launch from the ground is the end point of this optimization.) However, the size of the largest part for a power satellite may limit the minimum size of rocket.</div>24.23.229.100https://htyp.org/mw/index.php?title=Hundred_dollars_a_kg&diff=10050Hundred dollars a kg2008-08-03T06:29:17Z<p>24.23.229.100: /* How much lifted to GEO */</p>
<hr />
<div>To sum up what's gone before:<br />
<br />
To solve the energy crisis using space-based solar power, replacement power needs to come on line at a rate of 400-500 GW/year. That replaces about 6 million barrels of oil a day each year over the next 50 years. To make liquid fuels at a dollar a gallon out of electricity requires that the electricity cost be around a penny a kWh. To make penny a kWh requires lift cost to GEO of $100 or less<br />
<br />
==How much lifted to GEO==<br />
<br />
Four hundred GW of power sats requires 800,000 tons per year lifted to GEO (perhaps twice that). At least there is economy of scale.<br />
<br />
Do we have to lift that much mass? No. Extra terrestrial resources are a better idea, but there isn't time to develop the space industry to tap them. The economic effects (including famines) of the developing energy crisis are so bad that the large scale production of SBSP needs to come on line by 2015 to avoid economic collapse. Expect ET resources to be exploited by 2025 with this much activity in space.<br />
<br />
This works out to lifting about 100 tons per hour. Will physics let us get under $100/kg? A moving cable space elevator only requires about 15 kWh to lift a kg from the surface of the earth to GEO. This is $1.50 at the high rate of 10 cents a kWh. Even if it cost $100 billion dollars to build, a capital cost of $10 billion a year lifting a billion kg is only ten dollars. Unfortunately we don't have the cable--yet.<br />
<br />
The choices further examined here are among rockets, lasers or some combination of them.<br />
<br />
Rockets are good for high thrust, but the rocket equation is a hard taskmaster when you need delta V that is a multiple of the exhaust velocity.<br />
<br />
Lasers are not as well developed as rockets. They can get very high exhaust velocity, leading to small mass ratios, but they don't do very good for high thrust. Jordin Kare and others have been working for decades designing lasers to launch from the surface.<br />
<br />
Rockets to lift this much cargo would have to launch every hour, each rocket having a lift off mass of 6,000 tons to get 350 tons to LEO and 100 tons of that to GEO. The projected cost is around $500/kg. http://www.ilr.tu-berlin.de/koelle/Neptun/NEP2015.pdf<br />
<br />
The energy payback (for making fuel) is about 40 days. The cost of rockets is not in the fuel, but in the high cost of aerospace hardware and the rocket equation which dictates that even for the most energetic fuels only about one part in sixty is payload to GEO.<br />
<br />
The needed delta V LEO to GEO is about 4.1 km/sec. Using 10% of the LEO payload for reaction mass (35 tons) and a laser that provides a 40 km/sec exhaust velocity will produce about 4.2 km/sec delta V.<br />
<br />
(http://en.wikipedia.org/wiki/Rocket_equation )<br />
<br />
The power required for 1/20th g (.5 m/sec exp 2) is 1/2 x 350,000 kg x .5m/sec exp 2 x 40,000 m/sec = 3.5 GW<br />
<br />
Delta V changes require 4100 m/sec /0.5 m/sec exp 2, or 8200 sec or about 2.7 hours. I.e., 3.5 GW of laser power would raise eight loads a day from LEO to GEO. At 315 t each that is 2500 t/day, somewhat exceeding the 2200 t/day needed to install 400 GW per year.<br />
<br />
It also cuts the rocket launches from 24 to a more manageable but still excessive 7 or 8.<br />
<br />
A 3.5-GW space based laser built at GEO that massed 10,000 tons would cost $5 billion to lift by rockets and $35 billion for the laser. It can be expected to more than triple the yearly throughput to GEO, saving 2/3 of 0.8 billion kg x $500/kg or $267 billion a year in transport costs.<br />
<br />
Amortized at 10 percent, the additional lift from LEO to GEO would cost $4 billion/0.8 billion/kg or $5 per kg plus the lift to LEO.<br />
<br />
However, there is another way that cuts the liftoff mass by a factor of five compared to rockets.<br />
<br />
Injection to geosynchronous transfer orbit is 7.8 k/s (to LEO), 2.5 k/s (to GTO) plus 1.6k/sec to circularize at GEO, totaling 11.9 km/s. http://en.wikipedia.org/wiki/Delta-v_budget To get to LEO takes 796 s at 1g, 13.2 minutes. At one g 17.5 minutes for GTO, 14 minutes at 1.25 g, plus 2.2 minutes to circularize the orbit (1.6 km/s) at GEO. Assuming half payload and half reaction mass, 0.69 velocity ratio and 11.9 km/s delta v, then the average exhaust velocity needs to be a modest (for lasers) 17.2 km/s.<br />
<br />
Because the laser can be cycled close to 4 times an hour, the payload only needs to be 25 tons. Taking the midpoint (the exhaust velocity would be varied for constant thrust) the power required for 1.25 g (12.25 m/sec exp 2) is 1/2 x 37,500 kg x 12.25 m/sec exp 2 x 17,200 m/sec = 4 GW. In the context of building a GW of power satellite a day, this is a small piece of hardware. The choice of building the laser in space or on the ground has not been fully examined.<br />
<br />
The 50-ton payload-plus-reaction-mass has to hang in space long enough to be accelerated. This takes a modest mass ratio rocket.<br />
<br />
50 tons payload plus reaction mass for the laser. 16.5%<br />
50 tons rocket structure 16.5%<br />
200 tons propellant. 66%<br />
<br />
The rocket would lift off on two SSMEs, and if a zeroth turbofan stage was used, it would take eight 50-ton thrust engines, perhaps with afterburners. Simplifying operations, it goes straight up and lands back at the launching site. If the payload is oriented at right angles to vertical, we could avoid wasting time reorienting it for laser acceleration.<br />
<br />
This "little" rocket has a mass ratio of two and a delta V of 4 k/sec (less gravity loss and drag). The payload-plus-reaction-mass exits the atmosphere at 2.1 k/sec, goes up to 260 miles, falls to 150 miles before picking up orbital velocity and falls to 55 miles (picking up a little air drag) before losing downward velocity. It enters GTO 1000 seconds after launch. This is conservative, not accounting for the curvature of the earth.<br />
<br />
It masses 1/20th of a Neptune and (with the aid of the laser) delivers 1/4 as much payload per launch. One part in 12 (rather than one part in 60) is payload. To keep the laser busy and to meet the 100-ton per hour cargo requirement requires a launch every 15 minutes. This rate is common for airlines, but not for spacecraft.<br />
<br />
If the laser cost 80 billion dollars and was written off at 10% per year, the lift cost from sub orbital to GEO would be $8 billion /0.8 billion kg, $10/kg plus the sub orbital flight of perhaps $60/kg of payload. This meet the penny a kWh and dollar a gallon fuel goals.<br />
<br />
Energy payback is 8 days for the rocket fuel and 16 days for the laser. This is about 5.6%% of the theoretical minimum for a space elevator.<br />
<br />
This is probably not the optimum design. A shorter "hang time," smaller payloads and higher but shorter acceleration may yield lower cost per kg. (It is possible that laser launch from the ground is the end point of this optimization.) However, the size of the largest part for a power satellite may limit the minimum size of rocket.</div>24.23.229.100https://htyp.org/mw/index.php?title=Hundred_dollars_a_kg&diff=10046Hundred dollars a kg2008-08-03T01:12:38Z<p>24.23.229.100: /* How much lifted to GEO */</p>
<hr />
<div>To sum up what's gone before:<br />
<br />
To solve the energy crisis using space-based solar power, replacement power needs to come on line at a rate of 400-500 GW/year. That replaces about 6 million barrels of oil a day each year over the next 50 years. To make liquid fuels at a dollar a gallon out of electricity requires that the electricity cost be around a penny a kWh. To make penny a kWh requires lift cost to GEO of $100 or less<br />
<br />
==How much lifted to GEO==<br />
<br />
Four hundred GW of power sats requires 800,000 tons per year lifted to GEO (perhaps twice that). At least there is economy of scale.<br />
<br />
Do we have to lift that much mass? No. Extra terrestrial resources are a better idea, but there isn't time to develop the space industry to tap them. The economic effects (including famines) of the developing energy crisis are so bad that the large scale production of SBSP needs to come on line by 2015 to avoid economic collapse. ET resources be exploited by 2025 with this much activity in space.<br />
<br />
This works out to lifting 100 tons per hour. Will physics let us get under $100/kg? A moving cable space elevator only requires about 15 kWh to lift a kg from the surface of the earth to GEO. Even if it cost $100 billion dollars to build, a capital cost of $10 billion a year lifting a billion kg is only ten dollars. Unfortunately we don't have the cable--yet.<br />
<br />
The choices further examined here are among rockets, lasers or some combination of them.<br />
<br />
Rockets are good for high thrust, but the rocket equation is a hard taskmaster when you need delta V that is a multiple of the exhaust velocity.<br />
<br />
Lasers are not as well developed as rockets. They can get very high exhaust velocity, leading to small mass ratios, but they don't do very good for high thrust. Jordin Kare and others have been working for decades designng lasers to launch from the surface.<br />
<br />
Rockets to lift this much cargo would have to launch every hour, each rocket having a lift off mass of 6,000 tons to get 350 tons to LEO and 100 tons of that to GEO. The projected cost is around $500/kg. http://www.ilr.tu-berlin.de/koelle/Neptun/NEP2015.pdf<br />
<br />
The energy payback (for making fuel) is about 40 days. The cost of rockets is not in the fuel, but in the high cost of aerospace hardware and the rocket equation which dictates that even for the most energetic fuels only about one part in sixty is payload to GEO.<br />
<br />
The needed delta V LEO to GEO is about 4.1 km/sec. Using 10% of the LEO payload for reaction mass (35 tons) and a laser that provides a 40 km/sec exhaust velocity will produce about 4.2 km/sec delta V.<br />
<br />
(http://en.wikipedia.org/wiki/Rocket_equation )<br />
<br />
The power required for 1/20th g (.5 m/sec exp 2) is 1/2 x 350,000 kg x .5m/sec exp 2 x 40,000 m/sec = 3.5 GW<br />
<br />
Delta V changes require 4100 m/sec /0.5 m/sec exp 2, or 8200 sec or about 2.7 hours. I.e., 3.5 GW of laser power would raise eight loads a day from LEO to GEO. At 315 t each that is 2500 t/day, somewhat exceeding the 2200 t/day needed to install 400 GW per year.<br />
<br />
It also cuts the rocket launches from 24 to a more manageable but still excessive 7 or 8.<br />
<br />
A 3.5-GW space based laser built at GEO that massed 10,000 tons would cost $5 billion to lift by rockets and 35 billion for the laser. It can be expected to more than triple the yearly throughput to GEO, saving 2/3 of 0.8 billion kg x $500/kg or $267 billion a year in transport costs.<br />
<br />
Amortized at 10 percent, the additional lift from LEO to GEO would cost $4 billion/0.8 billion/kg or $5 per kg plus the lift to LEO.<br />
<br />
However, there is another way that cuts the liftoff mass by a factor of five.<br />
<br />
Injection to geosynchronous transfer orbit is 7.8 k/s (to LEO), 2.5 k/s (to GTO) plus 1.6k/sec to circularize at GEO, totaling 11.9 k/s. http://en.wikipedia.org/wiki/Delta-v_budget To get to LEO takes 796 s at 1g, 13.2 minutes. At one g 17.5 minutes for GTO, 14 minutes at 1.25 g, plus 2.2 minutes to circularize the orbit (1.6 k/s) at GEO. Assuming half payload and half reaction mass, 0.69 velocity ratio and 11.9 k/s delta v, then the average exhaust velocity needs to be a modest (for lasers) 13.2 k/s.<br />
<br />
Because the laser can be cycled close to 4 times an hour, the payload only needs to be 25 tons. Taking the midpoint (the exhaust velocity would be varied for constant thrust) the power required for 1.25 g (12.25 m/sec exp 2) is 1/2 x 37,500 kg x 12.25 m/sec exp 2 x 13,200 m/sec = 8 GW. In the context of building a GW of power sat a day, this is a small piece of hardware. The choice of building it in space or on the ground has not been fully examined.<br />
<br />
The 50-ton payload-plus-reaction-mass has to hang in space long enough to be accelerated. This takes a modest mass ratio rocket.<br />
<br />
50 tons payload plus reaction mass for the laser. 16.5%<br />
50 tons rocket structure 16.5%<br />
200 tons propellant. 66%<br />
<br />
The rocket would lift off on two SSMEs, and if a zeroth turbofan stage was used, it would take eight 50-ton thrust engines, perhaps with afterburners. Simplifying operations, it goes straight up and lands back at the launching site. If the payload is oriented at right angles to vertical, we could avoid wasting time reorienting it for laser acceleration.<br />
<br />
This "little" rocket has a mass ratio of two and a delta V of 4 k/sec (less gravity loss and drag). The payload-plus-reaction-mass exits the atmosphere at 2.1 k/sec, goes up to 260 miles, falls to 150 miles before picking up orbital velocity and falls to 55 miles (picking up a little air drag) before losing downward velocity. It enters GTO 1000 seconds after launch. This is conservative, not accounting for the curvature of the earth.<br />
<br />
It masses 1/20th of a Neptune and (with the aid of the laser) delivers 1/4 as much payload per launch. One part in 12 (rather than one part in 60) is payload. To keep the laser busy and to meet the 100-ton per hour cargo requirement requires a launch every 15 minutes. This rate is common for airlines, but not for spacecraft.<br />
<br />
If the laser cost 80 billion dollars and was written off at 10% per year, the lift cost from sub orbital to GEO would be $8 billion /0.8 billion kg, $10/kg plus the sub orbital flight of perhaps $60/kg of payload. This meet the penny a kWh and dollar a gallon fuel goals.<br />
<br />
Energy payback is 8 days for the rocket fuel and 16 days for the laser. This is about 5.6%% of the theoretical minimum for a space elevator.<br />
<br />
This is probably not the optimum design. A shorter "hang time," smaller payloads and higher but shorter acceleration may yield lower cost per kg. (It is possible that laser launch from the ground is the end point of this optimization.) However, the size of the largest part for a power satellite may limit the minimum size of rocket.</div>24.23.229.100