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Thread: Warp Speed would be fatal

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    Warp Speed would be fatal

    Travelling near the speed of light would be a fatal enterprise.
    ---------------------------------------------------------------


    Is there friction in space? It was a question that physicist William Edelstein has been pondering since his son was about 10-years-old.
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    Link to the article:


    http://www.thestar.com/news/sciencet...eed-would-kill

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    That conclusion is correct if one assumes no shielding. But one can calculate how much shielding is necessary to protect against interstellar-medium particles.

    I'll estimate for several speeds:

    1. 100 km/s = 0.0003 c - a little over the velocity scatter of neighboring stars
    2. 10,000 km/s = 0.03 c - plausible maximum for nuclear-energy propulsion
    3. 210,000 km/s = 0.71 c - kinetic energy = rest-mass energy
    4. 0.995 c - kinetic energy = 10 * rest-mass energy


    The interstellar medium has a density of about 1 atom/cm3, and one can use that to estimate how many electrons, protons, and helium nuclei collide with the spacecraft as it travels.

    Using various sources for various materials' stopping power - Stopping power (particle radiation) - Wikipedia, the free encyclopedia and Stopping-Power and Range Tables: Electrons, Protons, Helium Ions - I can calculate how far they will penetrate. I'll use (energy)/(stopping power) as an estimate of the distance.

    I'll also use some common materials. Water can serve as a proxy for human flesh, and silicon dioxide for rocky materials.

    Electrons: 0.03 eV, 300 eV, 0.5 MeV, 5 MeV

    For the first two cases, the electrons will stop in less than a micron of just about any solid material. The electrons travel farther in the last two cases.

    In liquid water: 0.24 cm, 2.5 cm
    In silicon dioxide: 0.11 cm, 1.1 cm
    In iron: 0.04 cm, 0.4 cm

    So electrons will not be a problem.

    Protons are another story. Their energies are 50 eV, 0.5 MeV, 0.9 GeV, 9 GeV

    The first case is insignificant, so I'll find the results for the other three.
    In liquid water: 13 microns, 4.1 m, 44 m
    In silicon dioxide: 7 microns, 1.9 m, 20 m
    In iron: 3 microns, 0.74 m, 7.5 m

    The numbers are similar for helium-4 nuclei. Note how "normal" wall thickness will suffice for nonrelativistic interstellar travel.

    -

    Now for ionizing-radiation doses in the unshielded case for speeds approaching c. One has to be careful in one's calculation of the particle flux, since time as well as space are relative. In particular, the particle flux per unit area is

    (number density)*(relativistic gamma factor)*(velocity)

    Doing the calculations in the relativistic cases yields radiation does of 11 and 101 gray/s, and using the Q factor for protons (5) yields about 50 and 500 sievert/s.

    Being exposed to 100 sievert will cause any of us to die within a few days, so one will need a LOT of shielding. How much can be estimated with the US Nuclear Regulatory Commission's permitted upper limit for radiation dose: about 0.05 sievert/year for adults. This is a reduction by a factor off about 3*1010 for v = 0.71 c, or 24 e-folding distances. For v = 0.995 c, that's 26 e-folding distances.

    That means you'll need 20 m of iron for v = 0.71 c and 200 m of that substance for v = 0.995 c. For silicon dioxide, it's 50 m and 500 m, while for water, it's 100 m and 1000 m (1 km!).

    -

    Radiation-hardened electronic components can survive much more, of course - spacecraft at Jupiter must survive as much as 200 sievert/day. That will allow the shielding thickness to be reduced by a factor of 2, to about 10 to 12 e-folding distances.

    So relativistic interstellar spaceflight will require huge amounts of shielding, even when using rad-hard electronic components.

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    There's a reason why the Enterprise warps with the shields up
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    Navigational shields, yes.. "regular" sheilds, no. At least not in what I remember.

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    Yes, should have mentioned that. They're still shields, used for exactly the reason mentioned in the OP.
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    Quote Originally Posted by HenrikOlsen View Post
    There's a reason why the Enterprise warps with the shields up
    Quote Originally Posted by Christopher Ferro View Post
    Navigational shields, yes.. "regular" sheilds, no. At least not in what I remember.
    They have force-field shielding against weapons, though it wasn't addressed how they go through interstellar space.

    I will concede a problem with my modeling of the charged particles' attenuation at relatively low energies. I'd assumed pure collision, when in fact, these charged particles get dragged by the electric charges in the medium. This makes them slow down steadily, producing a Bragg peak - Wikipedia, the free encyclopedia. So the penetration distances will be about what I'd calculated, but without the exponential factors of 10-12 or 24-26.

    However, collision with nuclei starts becoming significant for spacecraft velocities above 10,000 km/s or so. The incoming protons and helium nuclei start knocking out parts of the shielding-material nuclei, including neutrons. It's been hard for me to find good numbers on how many neutrons will be produced, and what the reaction cross-sections of energetic ones are, despite looking in places like Brookhaven National Lab's National Nuclear Data Center.

    In my v = 0.71 c case, the incoming nuclei have kinetic energies greater than the binding energies of most nuclei, even the heaviest ones. They will cause the shielding-material nuclei to disintegrate into much smaller nuclei.

    So past v = 10,000 km/s, the oncoming nuclei will produce a flux of neutrons that's not much less than the flux of incoming nuclei.

    When they get below a few MeV kinetic energy, they will not cause many nuclear reactions, and to shield against them, one must slow them down. The best substance for that is hydrogen, because a proton has close to the same mass as a neutron, meaning that it will remove the most kinetic energy when it collides. Molecular hydrogen is not very easy to store, since it boils at about 20 K. However, it's much easier to store water or hydrocarbons, like blocks of wax. One will need an amount of it comparable to the amount of shielding around a nuclear-reactor core, which is at least a few meters.

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    Quote Originally Posted by lpetrich View Post
    They have force-field shielding against weapons, though it wasn't addressed how they go through interstellar space.
    The "shields" that Kirk refers to when he says "raise the shields" are the defensive shields. The "navigational shields" are suppossed to be separate and protect the ship during navigation. They are always on when the ship is manuvering. No specific order for them is usually given.

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    How about a magnetic field to deflect the protons? Given the known kinetic energy values, how strong would such a field have to be?

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    Turning to magnetic-field shelding, magnetic fields will work on ionized atoms but not for neutral ones.

    Charged particles can go into orbit around magnetic-field lines, and the radius of their orbit is called the gyroradius or Larmor radius.

    gyroradius = 3.3 m * (momentum)/((electric-charge)*(magnetic-field))

    where the momentum is in units of 1 GeV/c, the electric charge in units of the elementary charge, and the magnetic field in units of tesla (104 gauss).

    To avoid consuming a lot of power, one ought to use superconducting electromagnets. They can go up to 20 tesla, which should be more than enough to stop ionized interstellar medium in even the worst case I've considered. Electrons have a momentum of 5.6 MeV/c and a gyroradius of 1 mm, while protons have a momentum of 10 GeV/c and a gyroradius of 1.7 m, which are much smaller than the likely size of an interstellar spacecraft.

    -

    Neutral atoms are another story. One can calculate the magnetic field necessary to create Lorentz forces great enough to strip electrons from nuclei, and it is very high: about 104 tesla.

    Its energy density is about 3*1013 joules/m3, which translates into a similar value for the pressure -- 3*1013 pascal or 3*108 bar. If the field is made by an electromagnet, then the current-carrying coils would be subject to this pressure. By comparison, the greatest yield strengths are about a few times 109 pascal, and a diamond anvil cell can go up to 3*1011 pascal.

    So an electromagnet with the necessary field strength would blow itself apart, and it would also get fried by its current.

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    http://en.wikipedia.org/wiki/Warp_drive
    "Warp drive is a faster-than-light (FTL) propulsion system in the setting of many science fiction works, most notably Star Trek. A spacecraft equipped with a warp drive may travel at velocities greater than that of light by many orders of magnitude, while circumventing the relativistic problem of time dilation."

    Imo that's a bit silly because once time dilation can be circumvented, there is no need to go FTL in order to get where you want to go in a really short time. 0.999c or thereabout would do just fine.

    But my point is this:

    "warp drive technology creates an artificial "bubble" of normal space-time that surrounds the spacecraft"

    So "hydrogen atoms would seem to reach a staggering 7 teraelectron volts" is a non-issue.

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    Quote Originally Posted by lpetrich View Post
    The interstellar medium has a density of about 1 atom/cm3, and one can use that to estimate how many electrons, protons, and helium nuclei collide with the spacecraft as it travels.
    What about dust?

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    I'll now consider interstellar dust. One can estimate upper limits by treating nearly all of the heavier elements as condensed in dust grains.

    I'll use the Solar System's element abundances as a reference: 3 Sun and solar system Those abundances are listed as by mole fraction, that is, by relative number of atoms.

    From Interstellar Dust Grain Sputtering, interstellar dust grains are mostly composed of silica (SiO2), magnesium and iron silicates ((Mg,Fe)2SiO4, etc.), amorphous carbon, and water ice.

    From The Interstellar Medium, "Interstellar dust grains are typically a fraction of a micron across (approximately the wavelength of blue light), irregularly shaped, and composed of carbon and/or silicates." That wavelength is 0.475 microns.

    Water-ice grains: 2*109 molecules, 4*10-13 grains/cm3
    Carbon grains: 7*109 atoms, 5*10-14 grains/cm3
    Silica grains: 2*109 atoms, 2*10-14 grains/cm3

    I'll use an abundance of about 10-13 grains/cm3 and an average density of about 1.5 g/cm3, yielding an average grain mass of about 10-13 g.

    A square meter of forward-facing surface will thus collide with about 3*109 grains/parsec, or about 3*10-4 grams/parsec. That means that it will accrete about a micron of interstellar dust per parsec, or about a centimeter or so when traveling the length of our Galaxy.


    I'll now consider what happens when a dust grain hits such a surface. When it hits, it creates a shock wave that vaporizes not only it but also some of the material it hits. One can estimate how much will be vaporized with the help of the materials' heats of vaporization, including heating to boiling. For iron, that is about 7700 joules/gram or 980 joules/cm3.

    Approximate excavation depth (vaporized volume)1/3:
    At 100 km/s, 8.0 microns
    At 10,000 km/s, 0.18 mm / 180 microns
    At 0.71 c (g = 2), 2.1 mm
    At 0.995 c (g = 10), 4.5 mm

    At 10,000 km/s, this estimated depth is still less than the penetration distances of the individual nuclei, meaning that this approximation continues to be reasonable.

    But at relativistic speeds, this depth will be less than the penetration distances of the individual nuclei, meaning that they will excavate thin holes with radii of about 0.1 mm.

    The total depth excavated per parsec is:
    At 100 km/s, 1.5 microns
    At 10,000 km/s, 1.8 cm
    At 0.71 c (g = 2), 28 m
    At 0.995 c (g = 10), 270 m

    So one would need a LOT of shielding to protect against interstellar dust.

    Some abundances:
    • Hydrogen: 28,000
    • Helium: 2,700
    • Carbon: 10
    • Nitrogen: 3.1
    • Oxygen: 24
    • Sodium: 0.06
    • Magnesium: 1.0
    • Aluminum: 0.083
    • Silicon: 1 (reference value)
    • Phosphorus: 0.009
    • Sulfur: 0.45
    • Potassium: 0.0037
    • Calcium: 0.064
    • Iron: 0.9

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    Quote Originally Posted by noncryptic View Post

    "warp drive technology creates an artificial "bubble" of normal space-time that surrounds the spacecraft"

    So "hydrogen atoms would seem to reach a staggering 7 teraelectron volts" is a non-issue.
    True enough. The Alcubierre drive as described would encapsulate the ship in a bubble of space-time which would not allow any particles in or out, so the ship would be safe from the interstellar medium.

    It would also be blind.

    But Star Trek warps must work on a different principle, since they have deflector shields, which presumably do project forward of the ship for some reason. I suspect Federation vessels do not use Alcubierre warps, at least not as currently understood.

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    Quote Originally Posted by lpetrich View Post
    Turning to magnetic-field shelding, magnetic fields will work on ionized atoms but not for neutral ones.
    The key is to convert those neutral atoms into ionized atoms. All you need is a thin "physical shield", which might be anything from a thin sheet of foil to a spray of dust particles ahead of the starship to a puff of cold gas. After this thin shield strips the electrons from the incoming matter, the starship's magnetic field will do the rest.

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    Quote Originally Posted by eburacum45 View Post
    But Star Trek warps must work on a different principle, since they have deflector shields, which presumably do project forward of the ship for some reason. I suspect Federation vessels do not use Alcubierre warps, at least not as currently understood.
    I suspect they are fictional devices, and thus don't have to obey the laws of physics.
    As above, so below

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    Perhaps this questions is invalid, but what about considering geometries?

    Perhaps combining several strategies -
    in stages:

    1. a thin film as suggested by IsaacKuo

    2. A geometric shield (I'm invisioning a long conical shape to deflect particles, or give them some slight lateral movement - at .995c this might be a very long and delicate structure - might be impractical)

    3. a magnetic field - to accelerate the lateral movement

    4. a thick physical shield (very large water tanks might be the logical choice since there would be a large requirement for water anyway.)

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    Quote Originally Posted by IsaacKuo View Post
    The key is to convert those neutral atoms into ionized atoms. All you need is a thin "physical shield", which might be anything from a thin sheet of foil to a spray of dust particles ahead of the starship to a puff of cold gas. After this thin shield strips the electrons from the incoming matter, the starship's magnetic field will do the rest.
    I think the thin shield would evaporate before too many light years have passed, if the impact of dust particles and neutral atoms has any effect on it. Perhaps the shield could be continually replaced, like a gigantic roller blind.

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    Quote Originally Posted by Atraveller View Post
    1. a thin film as suggested by IsaacKuo

    2. A geometric shield (I'm invisioning a long conical shape to deflect particles, or give them some slight lateral movement - at .995c this might be a very long and delicate structure - might be impractical)

    3. a magnetic field - to accelerate the lateral movement

    4. a thick physical shield (very large water tanks might be the logical choice since there would be a large requirement for water anyway.)
    There's no need for a geometric shield to produce lateral movement. With collisions at these speeds, the incoming particle won't merely be slowed down--it will splash if it hits anything. Think of the nuclei involved as billiard balls. If there's a collision, it's not going to just keep on going straight with a lower speed. It'll bounce off at an angle.

    Of course, nuclei are small things, and the shield I propose should ideally be thin enough that nuclei collisions are the exception rather than the rule. The purpose of the shield is only to ionize the incoming. For this, a "thickness" of just one atom is enough--just thick enough to ensure that the electron shells collide (much bigger than the nuclei).

    At that point, the magnetic field is sufficient to provide protection. The starship's superconducting magnetic loop protects a donut shaped region around it.

    That said, an extra layer of radiation shielding may be desirable to protect human crew. While nuclei collisions are ideally avoided, some collisions will take place and these might result in some neutrons. The neutrons would not be deflected by the magnetic field. Of course, these neutrons will be spalling off at all sorts of angles, so only a tiny fraction would hit the starship.

    It depends on the specifics of the starship, its payload, and medical technology...I think that generally the neutrons will not be a problem. If they are, then an aneutronic ionization shield may be desirable. This could be a cold puff of hydrogen or a cloud of electrons.
    Quote Originally Posted by eburacum45 View Post
    I think the thin shield would evaporate before too many light years have passed, if the impact of dust particles and neutral atoms has any effect on it. Perhaps the shield could be continually replaced, like a gigantic roller blind.
    The thin shield would require periodic or continuous replenishment/replacement. Assuming the shield is kept down to, say a thousand atoms thick, on average, then the supply requirements for a human lifetime scale trip is very low.

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    Quote Originally Posted by IsaacKuo View Post

    The thin shield would require periodic or continuous replenishment/replacement. Assuming the shield is kept down to, say a thousand atoms thick, on average, then the supply requirements for a human lifetime scale trip is very low.
    That depends on the velocity. lpetrich calculated that a shield would evaporate quite rapidly at 0.71c and even more rapidly at 0.995c. I can't imagine a thin shield would last very long without replacement at those speeds, even though it does seem a good idea.

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    Quote Originally Posted by eburacum45 View Post
    That depends on the velocity. lpetrich calculated that a shield would evaporate quite rapidly at 0.71c and even more rapidly at 0.995c. I can't imagine a thin shield would last very long without replacement at those speeds, even though it does seem a good idea.
    There's no contradiction. If you put up a "thick" shield, then each incoming atom will have a chance to knock out a whole bunch of atoms. But if the shield is thin, then an incoming atom will only knock out perhaps a thousand atoms or less. The thin shield does not stop the incoming atom, but rather merely ionizes it. Under ideal conditions, you only lose atoms 1 for 1 for the incoming atoms. Assuming ideal conditions seems implausible, of course.

    With the thin shield, very little energy is absorbed so erosion is mitigated. Even so, the thin shield does erode and periodic replacement/replenishment is needed.

    To minimize mass loss, you want to keep the shield thin and replace/replenish as necessary. The obvious alternative strategy is to simply stack all of the replacements together and deploy them all at once at the start of the journey. However, this strategy is flawed because it gives an incoming atom the chance to erode all of the stacked shields rather than just the one which is deployed. In fact, the erosion rate is increased even more because each impact event results in a "cone of destruction"...the shields behind the first one will suffer even more erosion than the first one.

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    Quote Originally Posted by noncryptic View Post
    Imo that's a bit silly because once time dilation can be circumvented, there is no need to go FTL in order to get where you want to go in a really short time. 0.999c or thereabout would do just fine.
    Except that not only would it take 5 years getting to the nearest star, it would feel like 5 years. Beating time dilation actually makes things worse.


    Clarke solved the problem of hitting stuff with a massive ablative shield of water ice in one of his novels.
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    Quote Originally Posted by eburacum45 View Post
    That depends on the velocity. lpetrich calculated that a shield would evaporate quite rapidly at 0.71c and even more rapidly at 0.995c. I can't imagine a thin shield would last very long without replacement at those speeds, even though it does seem a good idea.
    Perhaps it has already been suggested, but what about spraying a thin cloud of hydrogen ahead of the vessel?

    As the cloud was thined out by the incoming atoms you could easily replenish. And since it would be hydrogen, there would be very few neutrons involved.

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    The geometric shield would not work - an oncoming macroscopic object would not bounce or slide off of it, but instead would create a crater in it. To see why, let us consider what happens in a collision. The oncoming particle compresses the shield when it strikes that shield, and much of its kinetic energy becomes compression of both itself and the neighboring bit of shield. Compression energy density is comparable to the resulting pressure, and may conveniently be expressed in pressure units.

    To estimate how much the shield material will get compressed, we consider its compressibility, which is roughly the amount of pressure needed to compress or shear by some amount comparable to the material's size. It is expressed in various ways, like the bulk modulus, the shear modulus, Young's modulus, etc.

    So if a material is subject to a pressure more than its bulk modulus, it will get very seriously deformed. It will be able to recover from this deformation if it was subjected to a pressure less than its "yield strength", which is often much smaller than the bulk and shear moduli.

    In my four cases and a density of 2 g/cm3,

    At 100 km/s, 1013 J/m3 = 104 gigapascals = 102 megabars
    At 10,000 km/s, 1017 J/m3 = 108 gigapascals = 106 megabars
    At 0.71 c (g = 2), 2*1020 J/m3 = 2*1011 gigapascals = 2*109 megabars
    At 0.995 c (g = 10), 2*1021 J/m3 = 2*1012 gigapascals = 2*1010 megabars

    While for a familiar sort of velocity,

    At 1 m/s, 103 J/m3 = 10-6 gigapascals = 103 pascals = 10-8 megabars = 10-2 bars

    Let us now turn to the properties of various shield materials. Glass I'll use as a proxy for rocky materials. Diamond I'll use as a best case.

    The bulk modulus (for compression in all directions):
    Glass: 45 GPa
    Steel: 160 GPa
    Diamond: 442 GPa

    The shear modulus:
    Glass: 26.2 GPa
    Steel: 79.3 GPa
    Diamond: 478 GPa

    Young's modulus (for compression in one direction):
    Glass: 70 GPa
    Steel: 200 GPa
    Diamond: 1220 GPa

    Yield strength and tensile strength:
    Glass: 0.05 GPa (compression ultimate strength)
    Steel: 0.25 - 0.69 GPa
    Diamond: (can't find a number)

    Silicon carbide: 3.44 GPa (ultimate; chemically similar to diamond)
    Kevlar: 3.62 GPa (ultimate; degrades above 500 C)
    Carbon fiber: 5.65 GPa (ultimate)

    So even the strongest materials will not survive 100-km/s impacts -- it's difficult even for 1-km/s ones.

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    Quote Originally Posted by Atraveller View Post
    Perhaps it has already been suggested, but what about spraying a thin cloud of hydrogen ahead of the vessel?

    As the cloud was thinned out by the incoming atoms you could easily replenish. And since it would be hydrogen, there would be very few neutrons involved.
    That is similar to the method used in the Valkyrie design of interstellar craft, which maintains a cloud of particles in front, although I can't remember how it is maintained in a tight cloud.

    The trouble with a cloud of atoms or molecules is that it would expand and dissipate. Perhaps a cloud of small foil sails would be the best idea- when they wear away you could just send out some more.

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    Ipetrich well done for ploughing through all the calculations, but I can't help thinking you have over-extrapolated things.

    I find it difficult to believe high-energy protons and He-nuclei will travel through the many meters of dense materials you suggest unchanged. Surely they will cause nuclear reactions ?

    Don't forget our atmosphere is a very good shield against cosmic rays, even much higher energy particles than in question here interact with the atmosphere at high altitudes. Typically they cause showers of lower-energy particles, which are more easily shielded against.

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    I don't pretend to know much about it, but particle accelerators have a "beam dump", where the high energy beam can be directed in case of a fault:

    http://en.wikipedia.org/wiki/Beam_dump

    The LHC accelerates protons to 7TeV, or 7000GeV, considerably in excess of the 9GeV at 99.5% c. How are they shielded and what is the beam dump like there?

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    Quote Originally Posted by lpetrich View Post
    The geometric shield would not work
    So even the strongest materials will not survive 100-km/s impacts -- it's difficult even for 1-km/s ones.
    Ipetrich, I have to compliment you on some really impressive work.

    A couple of comments:

    understood that geometry would not deflect a macroscopic object (perhaps some sort of dynamic defense system would be required...) but I was proposing goemetries to deflect the results of the collisions.

    So - say there was a dynamic defense for anything larger than say 1 micron? (rail gun, laser, or some other focused energy device? would have to scan a long way ahead if travelling at .995c. But this would seem to be a tecnological problem to solve rather than a law of physics.)

    There would be a constantly replenished Hydrogen cloud sprayed in front of the vessel - which would be the first collision with smaller objects (ie less than 1 micron) and this cloud would be constantly expanding and disapating - as long as the .995c vessel wasn't accelerating.

    What would be the products of the collisions in a Hydrogen cloud? How could these results be deflected?

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    It's best to slow down charged particles slowly with low-z materials. These are also best for neutron shielding. Instead of a cloud of hydrogen (which would need constant replenishment), how about a large balloon of low-pressure hyrodrogen sent out in front of the craft when at cruise velocity?

    This is fired off to sit perhaps 1000'd of km in front of the vessel. It will be slowed down gradually by drag more than the vessel itself, so it will gradually re-approach the vessel during the voyage. However I'm sure this can be calculated for.

    The balloon could be quite flimsy construction, therefore quite lightweight. Could also be sausage or zeppelin shaped to give a longer path length in the direction of travel, and contain a compressed gas container to replenish hydrogen as necessary.

    Protons etc would interact with the hydrogen and result in larger quantities of lower-energy particles. Dust grains would cause micro-punctures in the balloon, hence hydrogen leakage. Perhaps some ultra-lightweight self-sealing balloon material could be invented.

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    I'm flattered.

    Beam dumps are designed to dissipate heat as efficiently as possible while having simple designs. So with that in mind, I'll calculate the amount of energy that gets dumped into the forward shielding.

    Dust has insignificant mass, so I'll concern myself with the hydrogen and helium. The kinetic-energy flux is

    relativistic: n*m*c2*g*(g-1)*v
    Newtonian limit: (1/2)*n*m*v3

    The interstellar-medium mass density, n*m here, is 2*10-24 grams/cm3

    I also worked out the Stefan-Boltzmann equilibrium temperature, assuming that the shield surface is where the heat would be radiated from, and also that it is a perfect radiator.

    Doing the calculations,

    v = 100 km/s -- 1.05*10-6 joules/m2/s -- 2.07 K
    v = 10,000 km/s -- 1.05 joules/m2/s -- 65.6 K
    v = 0.71 c; g = 2 -- 8.00*104 joules/m2/s -- 1090 K
    v = 0.995 c; g = 10 -- 5.04*106 joules/m2/s -- 3070 K

    So unless the interstellar medium can be deflected from the shield, it will get HOT. Bear in mind that the temperature goes as (energy-emission)1/4. This means that an increase in 100 of the radiating area, by radiators along the sides of the spaceship, will produce a temperature drop of a factor of 3.

    For the highest velocity that I have been analyzing, one would need some very refractory material, and the first one that comes to my mind is the element tungsten, which has one of the highest boiling points of any of the elements. Working out the penetration depth for it gives 4 meters.

    However, tungsten is not a very common element; there are about 8 million silicon atoms for each tungsten atom in the Solar System, while there are only 1.1 silicon atoms per iron atom.

    -

    I now turn to the question of a hydrogen balloon.

    Such a balloon may be difficult to maintain; one has to keep it from leaking or getting punctured. However, there is an alternative: using much more refractory substances that are nevertheless rich in hydrogen. Fortunately, there are some such substances that all of us are familiar with:

    Water: H2O - H is 2/3
    Hydrocarbons: {CH2} - best case: saturated and loopless - H is 2/3
    Biological materials: variable
    - Lipids: close to hydrocarbons - saturated: H is 2/3
    - Carbohydrates (sugar, starch, cellulose): {CH2O} - H is 1/2
    - Proteins - H is around 1/2
    - Bone (vertebrate) - H is 1/11
    Plastics and rubbers - H is 1/2 to 2/3

    We can set aside bone as being too much like rocky materials: silica and metal silicates.

    This leaves water and the organic compounds. Of these, water is the most chemically refractory, decomposing at temperatures over 2000 C. Next are the hydrocarbons, as is evident from their survival in rock strata over geological time. However, even they are not as chemically refractory as water; they decompose at temperatures of around 500 C.

    So we narrow the choices down to:

    Water
    Wax (long-chain hydrocarbons)
    Hydrocarbon plastics (polyethylene, etc.)

    -

    It's hard to find much on the radiation resistance of plastics, but one company claims that a plastic it makes can survive 109 rads or 107 gray of ionizing radiation without significant degradation:

    SAN DIEGO PLASTICS INC - PEEK PLASTIC, SHEET, ROD, TUBE AND FILM

    That plastic is PEEK: polyether ether ketone, and it is mostly hydrocarbon.

    At an exposure rate of 11 gray (v = 0.71 c) or 101 gray (v = 0.995 c), that plastic would reach its limit in 10 days in the first case, and 1 day in the second case.

    So I think that water is the best choice.

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