Solar-pumped laser power transmission, a way to dramatically decrease launch costs?
in [Physics]
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From: William Mook on 16 Feb 2010 13:30 On Feb 15, 7:52 pm, "Scott M. Kozel" <koze...(a)comcast.net> wrote: > William Mook <mokmedi...(a)gmail.com> wrote: > > > "Scott M. Kozel" <koze...(a)comcast.net> > > > > That is the velocity you would have to attain. > > > BASIC ASTROGATION > > > The vis-viva equation gives you the velocity of an object in an orbit; > > Interesting calculations snipped ... > > I can see that you have put a lot of thought into this ... one > question, what is temperature at 2 million miles from the Sun? > > Mercury at 35 million miles is about 800 degrees F on the surface at > the equator, hot enough to melt lead. Its a problem of heat balance. Since we're in vacuum we transfer everything - or nearly so given corona discharge - by radiation. The radiation 3.5 million km from the sun is (150/3.5)^2 = (42.857)^2 = 1,836.8 times as intense as it is here on Earth (above the atmosphere) which is 1,380 watts/m2. Which is 2.53 million watts per square meter. A perfectly black film would absorb all that and heat up until the radiant heat balanced the incoming radiation. This is given by Stephan Boltzmann relation which is a function of temperature. Since a film has 2x the area (front and back) we take 2.53 MW and divide by 2 (a sphere would have 4x the projected circular area) and set it equal to the fourth power of temperature (in Kelvins) j = rho * T^4 = 2,530,000 / 2 = 5.67e-8 * T^4 rearranging T = (2,530,000 / 2 / 5.67e-8)^(1/4) = 2,172.3 K Which carbon could withstand. Here's an interesting tid-bit. 35 million miles is 16.1x the distance of 3.5 million km. So, the energy flux is 1/259th at Mercury than the satellite. A sphere is 4x the area of the disc it's shadow projects. So, heat flux is 1/518th what we just calculated. So we take the 1/4 power of this figure and find that the average temperature of Mercury if it were a perfectly absorbing body is 21% of the figure above, or 456.2 K (361.5 F) Actual temperatures on Mercury range from 90 to 700 K (â183 °C to 427 °C, â297 °F to 801 °F), which agree with this heat balance calculation - which is the mean temperature adjusted for reflectivity (mean temperature of 400 K and albedo is 0.12) so, this is pretty powerful stuff. Suppose we have 98% reflective film only 2% of the energy would get into the film. Then the temperature would be 816.9 K at 3.5 million km and 171.5 K at Mercury's orbit - which is quite cold. Films that are 99.99% reflective have been made http://www.sciencemag.org/cgi/content/abstract/287/5462/2451 So, even at 3.5 million km - with the right engineering - we can keep things at reasonable temperatures. Now, if we're using refrigerators we can keep stuff cooler than that - if the radiators are hotter than that - we have plenty of power. There are several possibilities. The system I'm working on converts solar photons to laser photons at 55% efficient. 25% of all solar photons are reflected, so 75% of that remains. 30% of the energy is used on board for refrigeration and 55% of the remainder ends up radiated away as laser energy. The rest ends up radiated away as heat. So, the heat balance is 2,530,000 Watts/m2 coming in 632,500 Watts/m2 reflected away (producing controlled thrust) 678,562 Watts/m2 radiated away as laser energy (also producing thrust). Leaving 609,469 Watts/m2 per side - radiated away as heat (also controlled to produce thrust effects) This means the radiators must be at T = (609,469/5.67e-8)^(1/4) = 1,810.7 K About the meltping point of iron, well below the melting point of ASTM Type A314 Martensitic stainless steel. Tungsten, Diamond, and carbon fibers are very strong still at this temperature. Drexler's discussion of nanoscale technology involving diamond structures is important here. Even so, MEMS scale refrigerators made of processed CVD diamond structures will work at these temperatures with radiators of stainless steel or chemical vapor deposition diamond. Here's a list of materials that are solid at this temperature, and their alloys are also interesting to check into. 21 Scandium Sc 1,539 °C (1,812 K) 69 Thulium Tm 1,545 °C (1,818 K) 46 Palladium Pd 1,552 °C (1,825 K) 91 Protactinium Pa 1,600 °C (1,870 K) 98 Californium Cf 1,652 °C (1,925 K) 22 Titanium Ti 1,660 °C (1,930 K) 71 Lutetium Lu 1,663 °C (1,936 K) 90 Thorium Th 1,755 °C (2,028 K) 78 Platinum Pt 1,772 °C (2,045 K) 40 Zirconium Zr 1,852 °C (2,125 K) 24 Chromium Cr 1,857 °C (2,130 K) 23 Vanadium V 1,902 °C (2,175 K) 45 Rhodium Rh 1,966 °C (2,239 K) 43 Technetium Tc 2,200 °C (2,470 K) 72 Hafnium Hf 2,227 °C (2,500 K) 44 Ruthenium Ru 2,250 °C (2,520 K) 5 Boron B 2,300 °C (2,570 K) 77 Iridium Ir 2,443 °C (2,716 K) 41 Niobium Nb 2,468 °C (2,741 K) 42 Molybdenum Mo 2,617 °C (2,890 K) 73 Tantalum Ta 2,996 °C (3,269 K) 76 Osmium Os 3,027 °C (3,300 K) 75 Rhenium Re 3,180 °C (3,450 K) 74 Tungsten W 3,422 °C (3,695 K) 6 Carbon (diamond) C 3,550 °C (3,820 K) 6 Carbon (graphite) C 3,675 °C (3,948 K)â 569,250 Watts/m2 used on board (primarily for refrigeration)
From: William Mook on 16 Feb 2010 13:34 On Feb 15, 10:52 pm, "Scott M. Kozel" <koze...(a)comcast.net> wrote: > OM <o...(a)sci.space.history> wrote: > > > "Scott M. Kozel" <koze...(a)comcast.net> wrote: > > > >I can see that you have put a lot of thought into this > > > ...Most of it the result of years of substance abuse, especially > > sniffing paint fumes from a paper bag while high on really poorly made > > acid. > > I asked about the temperature at 2 million miles from the Sun, because > I wonder if there is any substance that would not melt if that close. > > Mercury at 35 million miles is 800 F ... at 2 million miles it might > be hot enough to melt tungsten ... i.e. a satellite would melt or > maybe even vaporize long before it got that close. > > "The metal with the highest melting point is tungsten (W) at 3410 > degrees Celcius (6170 degrees Fahrenheit). However, technically Carbon > has a higher melting point, though not under normal atmospheric > conditions. This is because it sublimates (turns directly from a solid > to a gas) at 6740 degrees Fahrenheit under normal circumstances." > > http://wiki.answers.com/Q/What_metal_element_has_the_highest_melting_... > ...... > > "The Sun is the most prominent feature in our solar system. It is the > largest object and contains approximately 98% of the total solar > system mass. One hundred and nine Earths would be required to fit > across the Sun's disk, and its interior could hold over 1.3 million > Earths. The Sun's outer visible layer is called the photosphere and > has a temperature of 6,000°C (11,000°F). This layer has a mottled > appearance due to the turbulent eruptions of energy at the surface." > > http://www.solarviews.com/eng/sun.htm > > The Sun itself has a diameter of 0.84 million miles. Its a process of heat balance. Radiant energy in - radiant energy out. Stephan-Boltzmann says what the temperature has to be. A perfectly absorbing film would heat up to temperatures carbon and tungsten would remain viable structural materials. A perfectly absorbing sphere would be a slightly less temperature (the 1/4 power of 1/2) - unless there were a plane of spheres spread at the same radius - then it would approach the film temperature.
From: William Mook on 16 Feb 2010 13:40 On Feb 16, 3:12 am, Pat Flannery <flan...(a)daktel.com> wrote: > Scott M. Kozel wrote: > > > Mercury at 35 million miles is 800 F ... at 2 million miles it might > > be hot enough to melt tungsten ... i.e. a satellite would melt or > > maybe even vaporize long before it got that close. > > The radiation flux at that distance is going to be ferocious also. > You would be well inside the Sun's corona, and the first time a major > flare erupted underneath it it would be like sticking it inside of a > nuclear reactor. > At least as of 2008, JPL was planning to send a spacecraft to 4.1 > million miles from the Sun's surface, and just designing that was > driving them nuts:http://www.astronomy.com/asy/default.aspx?c=a&id=6917 > > > "The metal with the highest melting point is tungsten (W) at 3410 > > degrees Celcius (6170 degrees Fahrenheit). However, technically Carbon > > has a higher melting point, though not under normal atmospheric > > conditions. This is because it sublimates (turns directly from a solid > > to a gas) at 6740 degrees Fahrenheit under normal circumstances." > > Temperature at 4.1 million miles is 2,160F according to the above > article, so assuming halving the distance increases the temperature four > times over (I think that's how it works, though the large solar radius > may screw this up; it's going to at least double) that makes the temp it > could be facing over 8,000 F. > So unless you are building it out of Larry Niven's Puppeteer Hull > Metal... another problem at this distance is that you aren't going to be > orbiting it in vacuum, but rather in the very thin superheated gas of > its outer atmosphere. That's going to generate drag on the solar array, > and given its extremely high orbital velocity it's probably going to end > up falling into the Sun in fairly short order. > > Pat A perfectly black film would have that temperature. One that reflected a lot of energy would not. Its a process of heat balance. Heat in versus heat out. What does the temperature have to be to get the heat out in a vacuum? Stephan Boltzman gives the answer. Yes, halving the distance doubles the energy, and raises the temperature. How much? You must take the 1/4 power of two to get the fourth root of 2 to find its 19% higher in Kelvins - since its related to absolute zero - fahrenheit and celsius are not so you can't use them in Stephan-Boltzmann. Which is the temperature I quoted in another post for a perfectly black body. Of course you won't have a perfectly black body. You'll have efficient mirrors. 25% of the energy is reflected straight away. 30% is used internally and must be disposed of. The remaining energy 55% of that is radiated away as laser energy - the balance must be added to the first part and radiated away. At 3.5 million km you'd have a system that has radiators that must operate between 1,600 K and 1,800 K - which is perfectly feasible.
From: William Mook on 16 Feb 2010 14:41 On Feb 16, 6:55 am, Pat Flannery <flan...(a)daktel.com> wrote: > Fred J. McCall wrote: > > : > > > No. You've engineered a vehicle when you can take your data package, > > hand it to a bunch of metal benders, and get back a working vehicle > > that performs approximately as you claimed it would. > > > You're not even close. > > Consider the plumbing on all those tiny engines at the base of its three > stages sometime; that's going to probably weigh a bit, isn't it? :-D > When Henry Spencer was discussing his 100+ RL-10 engined SSTO design, I > tried to figure out how to do the plumbing to all of those also, and it > was no treat from the weight point of view either. > Where exactly are the turbopumps on Mook's design? You sure can't see > them in the drawings. > > Pat This is a sound consideration. Its the subject of some patent activity. When the patent application is published I will talk about it.
From: William Mook on 16 Feb 2010 14:55
On Feb 15, 10:57 pm, Pat Flannery <flan...(a)daktel.com> wrote: > Scott M. Kozel wrote: > > I can see that you have put a lot of thought into this ... one > > question, what is temperature at 2 million miles from the Sun? > > > Mercury at 35 million miles is about 800 degrees F on the surface at > > the equator, hot enough to melt lead. > > (Note to self - don't use solder on near-sun solar power gatherer.) :-) > > Pat At least not anywhere exposed to sunlight. |