| Rama The Power of the Sun Rama is the name of a Hindu divinity. It is also the name given to the giant alien spaceship in Sir Clarke's novels. When I realized that the Sun radiates 3.8E26 watts and that a one million ton ship accelerated to 66% c required: KE= 0.5( 1,000,000,000 kg.)(200,000,000 m/s)^2 = 2E25 joules or correcting for relativity: KE= {1,000,000,000 kg.}{3E8 m/s SQRD}{[1/SQRT (1- 0.66^2/1)]-1} = 3E25 joules It became clear that the Sun radiated enough energy every second to propell twelve starships amassing one million tons each to 2/3 the speed of light! Just harnessing a fraction of the Sun's energy would be necessary to propell interstellar ships. If a ship accelerates at one G for 236 days it will reach 66% c. Dividing the total amount of energy required to drive the ship up to speed by the number of seconds in 236 days we find that a power level of 1.47E18 watts or just 0.0000000039 of the Sun's energy would be needed to drive the ship. If we envision a solar collector system, propulsion beams and mag-sail combination with an overall efficiency of just 1% we only need to build a solar panel station with an area of 0.00000039 of any spherical area surrounding the Sun. The closer we are to the Sun the smaller the solar collectors and the more intense the light. At 10 million miles the collector would have an area of about 534 million square miles or about 23,110 miles by 23,110 miles. Or there could be one hundred of them about 2300 miles by 2300 miles in dimension. At the distance of Venus the collector would be about 240,000 miles by 240,000 miles. Such a device at the Venus-Sun L1 point could also cool Venus down. I then envisioned a pair of Dyson shells hovering above and below the solar equator, similar to those envisioned by Marshall Savage in his book The Millenial Project that could collect 10% of the Sun's energy and a total system efficieny of 10%. This would generate 3.8E24 watts. That would be enough to accelerate 2,585,000 ships amassing a million tons each to 66% c in 236 days! At this point I envisioned the grandiose 2.5 gigaton Rama class Star Carrier made not by aliens but by man and woman. About 1000 of these Rama sized vessels could be propelled every year. The other 129 days would be devoted to maintenance and repair of the solar collectors and propulsion beams. Since the beams would fire in opposing directions to stay on station we could actually launch only half as many starships but this is still incredible! The propulsion beams would harvest solar wind gases with magnetic scoops and fire jets of plasma to propell the mag-sailing starships. |
| Star Carriers A six kilometer wide sphere with a cosmic ray shield consisting of water and hydrogen impregnated carbon nanotubes at three tons per square meter would have a shield mass of 340,000,000 tons. The Rama Star Carrier might have three of these hulls with a total mass of roughly one billion tons and the other 1.5 billion tons would be devoted to decks, machinery, the mag-sail loop, fusion generators, etc. The interior volume of the three spheres would be 340 billion cubic meters. That would give 10 million passengers 33,900 cubic meters of living room each or a space about ten feet high and 340 feet square. Since private cabins and suites would be much smaller, lots of room would be available for public areas like restaurants, gymns, swimming pools and simulated outdoors decks with gardens, ponds, etc. A five to ten year trip in Rama would be very comfortable. A smaller Star Carrier or Siva class vehicle with three spheres 3 km. diameter would have a shield mass of about 85 million tons and a total mass of perhaps 250 million tons. These are only estimations. It could carry about 400,000 people with the same amount of living room as a Rama carrier. The ship would amass a tenth as much and carry only four percent as many passengers, so we can see that there are economies of scale due to the fact that the surface area of a sphere goes up to the square of the radius and the volume to the cube of the radius. Since the mass of the cosmic ray shield is directly related to the surface area because it doesn't have to get any thicker a larger sphere has a better surface/shield mass to interior volume ratio. The shield is the single most massive component of the vessel. If we build single large spheres instead of three smaller spheres things would work out better, but three hulls allow for redundancy in case one hull is irreparably damaged. Reality Check This is all an exercise in the imagination and some basic math. Could an advanced civilization of genetically enhanced humans with AI super computers and robot worker armies about one thousand years from today actually build such things? Assuming that they would want to and that money is no object thanks to vast wealth produced by robots the construction of the Dyson shells, after Dr. Freeman Dyson who envisioned spherical solar collectors surrounding entire stars, would require mining a large numer of asteroids and much of the planet Mercury! If 1000 Ramas carry 10 billion people every year to nearby stars (don't ask me how I came up with 900 Ramas and nine billion people earlier as indicated on other pages! A simple error.) then a trillion people can go star faring in a century. Life spans will reach at least 100 years someday, possibly longer, but will there be trillions of people in the solar system? When do we stop populating? That's a philosophical/social issue and I won't bother with that here. I see no reason to populate most of the galaxy and the population of the Earth is already to large. Rugged pioneers will someday colonize Mars and some will build space colonies. Some will even live on the moons of outer planets or in space colonies orbiting those worlds rotating to produce Earth normal "artificial gravity" and some will even venture into the Oort Cloud purely for adventure and freedom. Perhaps there will be a slowly expanding human population in space that spreads out amongst the comets and worlds of nearby stars. People with lifespans of several centuries will not be stopped by the light barrier or travel at 50% to 66% of light speed. If hibernation or cryostassis is possible their range of travel in space will go beyond the nearby stars within 20 light years. Humans may be exceeded by androids with quantumn computer brains storing information in the molecular structure of matter someday. These androids might have "life spans" of over a thousand years with regular maintenance! If we can create new life biologically, why can't we create new life technologically? Could we even comprehend the mystery of consciousness and transfer our minds into superior android bodies? If we can discover the mystery of the soul, which some of us think has something to do with the complex patterns of electrical energy in the brain and the RNA molecules of the neurons and some deeper mystery of physics involving the storage of these energies in the higher dimensions of quantumn mechanical micro-space is it not beleivable that we would also develop an understanding of inertia, gravity, the forces of nature and time that allows us to transcend all barriers of time and space to create spaceships that can go anywhere in the universe? Giant space arks and propulsion beams would be as primitive as balloons compared to super-sonic aircraft, or worse, mere ox carts! It is probable that I am like a 17th century dreamer who forsees enormous balloons with wooden gondolas the size of sailing ships riding the winds across the Atlantic to the New World! I don't claim to be a better prophet than Cyrano de Bergerac was with his fanciful methods of travel to the Moon! However, this is all done for fun and within the limits of today's phsyics and forseeable technology. Cyrano's flock of birds or rising dew would never reach the Moon, but beamrider mag-sail ships could reach far into space. |
| Downsizing Mega-scale Engineering Downsizing my vision makes it more realistic. Let's dispense with the Dyson shells and 2.5 gigaton vessels. A 500 meter diameter Bernal Sphere would have a shield mass of 2,350,000 tons and four would have a total mass of about 10 million tons. The ship or Star Carrier as I like to call these monsters would have a total mass (estimated) of about 25 million tons when everything (machinery, decks, powerplant, mag-sail) is included. Only 2000 people could fit into each sphere if given 33,900 cubic meters each, but O'Neill put 10,000 colonists in his Bernal sphere so I will give this smaller Rama 40,000 passengers. We will have to generate 3.675E19 watts to propell the vessel up to 66% c in 236 days. Stopping is no problem; we just use a mag-sail brake charged up by the ship's powerplants. We will only need to collect 0.0000000967 of the Sun's energy to drive this ship filled with scientists, colonists and ambassadors to another solar system. At Mercury's distance from the Sun we will need a solar collector 41,000 miles by 41,000 miles. If we have a total efficiency of only 1% ( silicon solar panels are only 15% efficient, power transmission and particle beams will be somewhat inefficient at no better than 50% because they must fire opposing beams to stay on station, the mag-sail will be 95% efficient like an electric motor we hope) we need one hundred of these constructs. This is still fantastic, but given that we think we can build space colonies on up to the size of Island 3 in about 200 years and space elevators, it's not to far fetched for a civilization 1000 years from today. In space there really is no limit to how large a structure can be. Tidal forces, the effects of gravity from othe planets, flexing of the structure, would all have to be allowed for. Perhaps these solar collectors would be cellular like Marshall Savage's power bubbles and be built up on cell at a time. They could be connected by super strong C60 (buckminsterfullerene) cables and beams or some material similar to spider silk. Parts of the structures above and below the center of mass would want to move to opposite positions as the structure revolved around the Sun, so perhaps they would rotate slowly like a wheel along a circle. They could have mag-sails operating in reverse to overcome the solar wind and they would be located in the Mercury-Sun L5, L4 and L3 regions in halo orbits. A Better Way? What if we use another principle? Could we build solar powered particle beams to drive mag-sailed chunks of iron amassing a few tons up to high fractions of light speed and slam them into comets or asteroids or even each other to create mini-black holes by the intense impact compression shocks? We could "feed" matter into these and as it spirals in it would generate energy and jets of plasma would be spewed from the accretion disks of these spinning charged objects that could be channelled with magnetic focusing tubes to form the propulsion beams. Fusion converts about 0.7% mass to energy and a black hole can convert 6% to 40% mass to energy. Since we need 3.675E19 watts we would have to feed 1,020 kg. of mass into the mini-BH every second at 40% efficiency. 3.675E19j = m in kg. (3E8 m/s)^2 m=408 kg. at 40% efficiency 408 kg./0.4= 1,020 kg. In 236 days we have to supply 20,800,000 metric tons of matter. That's about the mass of a small comet one third of a kilometer in diameter. The mass that isn't converted to energy becomes super hot plasma that forms the propulsion beam. We might also harvest solar wind gases with a magnetic scoop of enormous size. The propulsion beam device itself would consist of superconducting magnetic coils several kilometers long and several kilometers wide. The mini-BH would be contained in a spherical magnetic containment of similar dimension at the heart of the beam projector. This would be of open cage design to let stray radiation escape into space. The magnetic containment structure of the mini-BH would be many kilometers in diameter and contain a cooling jacket of liquid metal or water like an enormous fusion reactor. Hot gas from the jacket would drive turbogenerators that energize electron beams which neutralize the protons and alpha particles jetting from the focusing tubes. Power would also be used to run the cooling systems that keep the superconducting coils cold. This would be an incredible engineering project but it seems to be more realistic than Dyson shells 20 million miles wide capturing 10% of the Suns energy or 100 giant solar collectors. This interstellar engine would be as large as an O'Neill space colony and similarly massive, but it doesn't have to go anywhere. The machine would be built to last for centuries in the vacuum of outer space, if it doesn't vaporize itself with all that radiation!!! |
| The Mag-Sail According to Dr. Robert Zubrin, from his article "The Magnetic Sail" found in Islands in the Sky pg. 206, ed. Stanley Schimdt and R. Zubrin, Wiley Popular Science:1996, the acceleration imparted by a mag-sail is given by: D/M= 0.6(up^2V^4Rm/I)^0.333(J/pm) V= 5*10^5 m/s the solar wind speed p= (8.35*10^-21 kg/m^3)/Rs^2 density of the solar plasma wind where Rs is the distance from the Sun in A.U. J/pm= (2*10^6 amp-m/kg) the current to mass density of the sail u= 4pi*10^-7 N/A^2 Rm= radius of mag-sail in km I= mag-sail loop current in kilo amps Let's assume that plasma beam is as dense as the solar wind at 1 A.U. Or p= (8.35*10^-21 kg/m^3) The velocity of the plasma beam we will make 2E8 m/s or 66%c Let's make the sail 1000 km in diameter or Rm= 500 km. We'll make I= 50 kA This give us: D/M= 0.6{(1.256E-6)(8.35E-21)^2(2E8)^4(500)/50}^0.333(2E6) = 67.8 m/s^2 If the wire is 2.52mm in diameter it only amasses 78 metric tons ( 5000 kg./ m^3) (4.985E-6 m^2)( 10E10 A/m^2) = 50 kA 10E10 A/m^2 is the current capacity of the superconducting cable to cable cross section area If the sail is to accelerate the ship at 9.8 m/s^2 it must have a wieght factor of 6.92 and the ship's mass is only 462 tons (462+78)/78= 6.92 We need a bigger mag-sail! Maybe a denser plasma beam also. Keeping u, p^2 and V^4 equal we get 1.4E-13 Let's try a 40,000 km diameter mag-sail carrying 100,000 kA Since (100,000,000 A)/( 10E10 A/m^2) = 0.01 m^2, the cross sectional area of the cable and it's circumference is 125,600,000 meters we find it has a volume of 1,256,000 cubic meters and a mass of 6,280,000 tons at 5000 kg./m^3 for YBCO. D/M = 0.6 {(1.4E-13)(20,000)/100,000}^0.333(2E6) = 36.5 m/s^2 W= 36.5/9.8 = 3.722 because we want 1G, thus (6,280,000+17,000,000)/6,280,000)=3.7 and our STAR CARRIER's total mass is about 23.3 million tons. We estimated earlier that the 40,000 passenger vessel had 10 million tons of shielding and a total mass of about 25 million tons. In this case the vessel has a 6.28 million ton mag-sail cable and a total mass of about 23.3 million tons leaving 17 million tons for the ship itself of which 10 million tons is the cosmic ray shield and seven million tons remain for everything else. Seems plausible for an advanced civilization. The shield is the heaviest part of the ship followed by the mag-sail cable. If the propulsion beam density is increased or its velocity increased, the ship will accelerate faster but we don't want to accelerate faster than 1G, so the mag-sail could be reduced in mass and the ship's mass increased. If the beam density is doubled to 1.67E-20 kg.m^3 we find that the sail accelerates at 57.9 m/s^2. W=5.9 The ship itself can amass 30.7 million tons or a total of 37 million tons with the 40,000 km. diameter mag-sail carrying a current of 100,000 kA. The ship proper to mag-sail cable ratio is about 5 to 1. At half the beam density as in the earlier case the ship to cable mass ratio was 2.7 to 1. We get a lot more ship for the same mag-sail if the propulsion beam density is increased. Since the velocity of the plasma beam increase the acceleration of the sail to the fourth power, by increasing the beam speed from 66%c to 80% c the acceleartion is 46.5 m/s^2 at a density equal to that of the solar wind at 1 A.U. and W= 4.75 Thus the vessel amasses 23.5 million tons with the 6.28 million ton cable with this modest increase in beam speed. Of course, increasing beam speed will require much more energy since KE=(mV^2)/2 and mass increases significantly at these relativistic velocities. How fast and how dense would the jets of plasma from our artificial miniature black holes be? Could they reach near light speed? If so, would the matter fed into the "hole" increase in mass relativistically so that the beam density also increases for vast improvements in our starship's performance? |
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| A 25 million ton+ mag-sailing Star Carrier uses fusion power plants that "burn" deuterium and helium 3 or helium 3+helium 3 for electrical power generation necessary for all onboard systems, energizing the mag-sail and powering the lasers. The power plants when turbogenerators, compressors, waste heat radiators and other components are included generate a whopping 500 kWe to 1000 kWe per kilogram of system mass. Advanced materials and technology are used to achieve this. Hundreds of units provide power but not all are active at all times. Some are back-ups. |