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brianok
2010-Feb-20, 07:11 AM
Travelling near the speed of light would be a fatal enterprise.
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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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http://www.thestar.com/news/sciencetech/article/768378--star-trek-s-warp-speed-would-kill

lpetrich
2010-Feb-20, 11:38 AM
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:

100 km/s = 0.0003 c - a little over the velocity scatter of neighboring stars
10,000 km/s = 0.03 c - plausible maximum for nuclear-energy propulsion
210,000 km/s = 0.71 c - kinetic energy = rest-mass energy
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 (http://en.wikipedia.org/wiki/Stopping_power_(particle_radiation)) and Stopping-Power and Range Tables: Electrons, Protons, Helium Ions (http://physics.nist.gov/PhysRefData/Star/Text/contents.html) - 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.

HenrikOlsen
2010-Feb-20, 03:56 PM
There's a reason why the Enterprise warps with the shields up:)

CJSF
2010-Feb-20, 06:08 PM
Navigational shields, yes.. "regular" sheilds, no. At least not in what I remember.

CJSF

HenrikOlsen
2010-Feb-20, 11:10 PM
Yes, should have mentioned that. They're still shields, used for exactly the reason mentioned in the OP.

lpetrich
2010-Feb-21, 05:27 AM
There's a reason why the Enterprise warps with the shields up:)

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 (http://en.wikipedia.org/wiki/Bragg_peak). 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 (http://www.nndc.bnl.gov/).

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.

Bearded One
2010-Feb-21, 07:10 AM
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.

baric
2010-Feb-21, 07:18 PM
http://www.stardestroyer.net/mrwong/wiki/index.php/Deflector_dish

eburacum45
2010-Feb-22, 12:47 AM
How about a magnetic field to deflect the protons? Given the known kinetic energy values, how strong would such a field have to be?

lpetrich
2010-Feb-22, 10:48 AM
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 (http://en.wikipedia.org/wiki/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 (http://en.wikipedia.org/wiki/Yield_strength) are about a few times 109 pascal, and a diamond anvil cell (http://en.wikipedia.org/wiki/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.

noncryptic
2010-Feb-22, 02:34 PM
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.

Amber Robot
2010-Feb-22, 02:43 PM
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.

lpetrich
2010-Feb-22, 08:52 PM
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 (http://en.wikipedia.org/wiki/Abundances_of_the_elements_(data_page)#Sun_and_sol ar_system) Those abundances are listed as by mole fraction, that is, by relative number of atoms.

From Interstellar Dust Grain Sputtering (http://www.tlchm.bris.ac.uk/~paulmay/spacdust/spacdust.htm), 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 (http://csep10.phys.utk.edu/astr162/lect/milkyway/ism.html), "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

eburacum45
2010-Feb-22, 10:43 PM
"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.

IsaacKuo
2010-Feb-22, 10:55 PM
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.

Jens
2010-Feb-23, 02:55 AM
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.

Atraveller
2010-Feb-23, 06:19 AM
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.)

eburacum45
2010-Feb-23, 12:57 PM
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.

IsaacKuo
2010-Feb-23, 04:41 PM
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.

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.

eburacum45
2010-Feb-23, 09:52 PM
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.

IsaacKuo
2010-Feb-23, 10:19 PM
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.

HenrikOlsen
2010-Feb-23, 10:42 PM
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.

Atraveller
2010-Feb-24, 01:07 AM
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.

lpetrich
2010-Feb-24, 10:32 AM
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 (http://en.wikipedia.org/wiki/Bulk_modulus) (for compression in all directions):
Glass: 45 GPa
Steel: 160 GPa
Diamond: 442 GPa

The shear modulus (http://en.wikipedia.org/wiki/Shear_modulus):
Glass: 26.2 GPa
Steel: 79.3 GPa
Diamond: 478 GPa

Young's modulus (http://en.wikipedia.org/wiki/Young%27s_modulus) (for compression in one direction):
Glass: 70 GPa
Steel: 200 GPa
Diamond: 1220 GPa

Yield strength (http://en.wikipedia.org/wiki/Yield_strength) and tensile strength (http://en.wikipedia.org/wiki/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.

eburacum45
2010-Feb-24, 12:40 PM
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.

kzb
2010-Feb-24, 06:37 PM
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.

kzb
2010-Feb-25, 06:44 PM
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?

Atraveller
2010-Feb-26, 06:09 AM
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.

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?

kzb
2010-Feb-26, 12:36 PM
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.

lpetrich
2010-Feb-26, 03:51 PM
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 (http://www.sdplastics.com/peek.html)

That plastic is PEEK: polyether ether ketone (http://en.wikipedia.org/wiki/PEEK), 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.

IsaacKuo
2010-Feb-26, 04:05 PM
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.
As I had noted before, such geometries are not needed. It doesn't matter what shape is hit--the resulting particles will be scattered away at severe angles.

What would be the products of the collisions in a Hydrogen cloud? How could these results be deflected?
Mostly nuclei and electrons, with extremely rare neutrons. Any incoming nucleus which collides with one of the cloud's nuclei will get scattered off in random directions. The probability of heading toward the starship depends on the size of the profile of the starship when viewed from the distance of the cloud.

Any incoming nucleus which does not directly collide with a nucleus will continue on almost a straight line with practically no deflection. The sideways impulse from having its electron yanked away will be orders of magnitude less significant than its own relativistic velocity.

In any case, all of these charged particles can be deflected away from the starship with its magnetic field.

It's best to slow down charged particles slowly with low-z materials.
It's even better to not slowing them down, using a magnetic field to deflect them without any loss of shield mass.

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?
If we assume the use of a magnetic field, then the ideal "thickness" of the shield is only one atom, or a few atoms. That would imply that the balloon's mass is so great that you needn't bother with the hydrogen filling at all. This reduces the "balloon" solution down to that of a "foil" shield.

kzb
2010-Feb-26, 04:44 PM
On the plus side, the local bubble mass density is only 1 atom per 10 cm^-3, so that would be a factor of 10 lower energy deposition rate.

At 0.71c, we then have 8kW per sq metre, only about 6 times direct sunshine at distance of Earth from sun.

kzb
2010-Feb-27, 05:59 PM
I've thought of something else about the radiation shield and heat deposition. The calculation by Ipetrich assumes all energy deposited a massive shield would by turned to heat.

I think it is plausible that a significant fraction of the energy would leave the site in the form of high-energy gamma rays, bremstahlung and neutrons. These would be emitted in all directions from the shield under bombardment by relativistic protons (but certain directions would be favoured).

This means two things, first, the heating effect might not be as large as calculated above, and two, any shield is better placed a considerable distance in front of the vessel, to reduce the dose from secondary gamma rays and scattered particles.

lpetrich
2010-Feb-27, 09:00 PM
However, one will have to find the mean free paths and stopping distances of the various forms of secondary radiation that you describe.

For gamma rays, I've found NIST: X-Ray Mass Attenuation Coefficients (http://physics.nist.gov/PhysRefData/XrayMassCoef/cover.html) -- goes up to 100 MeV.

For 10-MeV gamma rays:

Water - 45 cm
Silica - 20 cm
Iron - 4 cm

Less energetic ones travel shorter distances.

For 10-MeV neutrons, I find from EXFOR/CSISRS: Experimental Nuclear Reaction Data (http://www.nndc.bnl.gov/exfor/exfor00.htm)
Water - 7 cm
Silica - 5 cm
Iron - 4 cm

Less energetic ones also travel shorter distances before being scattered or absorbed.

Jerry
2010-Feb-28, 04:29 AM
We have never detected anything moving faster than the speed of light, so if we assume such travel is possible and occurs on a regular bases, we should also assume everything traveling at warp speeds does not interact with anything traveling less than the speed of sound.

So now the only problems are finding places to accelerate to above and below the speed of light where there is no matter in the sub-light speed path; and a way to accelerate to faster than the speed of light, which is no small matter...

[insert new physics here]

kzb
2010-Mar-01, 01:03 PM
Should this thread not be moved to "Space Exploration" ?

Thanks Ipetrich for all the work you are putting in. This is such an important topic for interstellar filght you would think it would get more attention.

Anyway, I am convinced the high energy protons and other nuclei would interact with the shielding material in relatively short path lengths. My reason for believing this is because the atmosphere shields us from such particles, even at high altitudes. I think there must be something left out of your calculation where you arrived at meters of iron being necessary.

The short path lengths means most of the secondary particles and gamma rays would also be produced at relatively low depths. Especially if the shield was made of low-z materials, the gamma rays and bremstrahlung could escape the immediate scene. A significant fraction of the gammas and photons could be emitted back in front of the shield. This carries away energy that would otherwise heat the shield.

Here's another thing for you to calculate :) There is clearly significant drag at relativistic speeds: how much thrust per square meter of frontal area would be needed to keep a constant velocity (ie compensate for the drag) ?

lpetrich
2010-Mar-01, 02:54 PM
Our atmosphere is not as thin as it looks. It has a column density equal to that of 10 m / 32 ft of water, and its ability to stop incoming ionizing radiation is similar.

As to cosmic rays, I haven't found good numbers on how many primary protons reach the surface, so I can't make a proper comparison.

Above the atmosphere, the protons' peak intensity is at 0.3 GeV, and their integrated intensity goes as (energy)-1.7.

I turned to the NIST tables, and I found that air has a stopping power of 2 MeV * cm2/g for proton energies of 1 to 10 GeV. Our atmosphere has a column density of about 1000 g/cm2, giving it a stopping power of 2 GeV for vertically-arriving protons. So I estimate that only about 1/70 of the incident protons make it to the surface.

Cosmic ray - Wikipedia (http://en.wikipedia.org/wiki/Cosmic_ray)
Particle Data Group review of Cosmic Rays (http://pdg.lbl.gov/2008/reviews/cosmicrayrpp.pdf)
Cosmic Rays (http://hyperphysics.phy-astr.gsu.edu/HBASE/astro/cosmic.html)

-

I now turn to what may be called interstellar-medium accretion drag. The interstellar mass density is about 2*10-24 g/cm3 for 1 atom/cm3.

This adds up to about 6*10-6 g/cm2/parsec, meaning that 1 parsec of travel adds the mass of 6*10-6 cm of water to the forward surfaces. For the size of our Galaxy, about 30 kiloparsecs, this becomes the mass of 0.2 cm of water.

Thus, interstellar accretion drag is insignificant.

kzb
2010-Mar-01, 06:29 PM
The accretion drag might be tiny, but I am thinking of momentum loss.

If the heat production rate is as great as you calculate, that adds up to a substantial braking effort. The loss-rate of vessel kinetic energy will equal the heat production rate (neglecting the energy loss mechanisms I mentioned, and assuming the vessel is in coasting mode).

What you've done with the cosmic rays and the atmosphere isn't the issue. I am saying I think there is something missing from your model, precisely because it IS a better shield for high energy charged particles than is calculated from the NIST tables.

If this were not the case, cosmic rays of greater than 2GeV would reach the surface. But I don't think they do?

lpetrich
2010-Mar-02, 08:37 AM
On cosmic rays, I'd have to do a lot of reading in the appropriate literature to resolve this issue. Perhaps we could find some physicist who is knowledgable about cosmic-ray interactions with our atmosphere.

Turning to reradiation reaction, as it may be called, I shall now calculate it. I'll work in the spaceship's frame, and set c = 1.

The forward momentum imparted by a colliding particle with mass m is

- m*g*v

where g is the relativistic gamma factor, g = (1-v2)-1/2

Its kinetic energy is m*(g-1)

It gets reradiated as heat, with a forward focusing factor f:
Perfect forward: 1
Isotropic in forward directions: 1/2
Perfect isotropic: 0
Isotropic in backward direction: -1/2
Perfect backward: -1

The forward momentum it imparts by departing is
- m*(g-1)*f

Thus, the total over the incoming momentum is

1 + (1 - 1/g)*v*f

For v << 1, it is

1 + (1/2)*v*f

with a limit of 1

For g >> 1, it is

1 + (1 - 1/g)*f

with a limit of 1 + f

So in the worst case (g >> 1, f = 1), the accretion drag would be muliplied by 2.

kzb
2010-Mar-02, 12:22 PM
But in post #30 above, at 0.71c, you have the kinetic energy dissipating at 80kW per sq meter of frontal area.

I've not done the calcs myself obviously but this must translate into a substantial brake. That amount of drag I bet is comparable to a car (automobile) travelling in the atmosphere at say 70mph.

lpetrich
2010-Mar-02, 12:51 PM
One little problem: how much momentum is in a photon with some energy. It's

Momentum = energy/c

That makes the force 2.7*10-4 newtons/m2

Adding it up over a year of travel gives a momentum per unit area of 8.4*103 kg m/s / m2

But a gram per square centimeter is 10 kg/m2, and its momentum at 0.71 c is 4.3*109 kg m/s / m2

The ratio of those two momenta is 2*10-6 -- tiny.

kzb
2010-Mar-02, 06:27 PM
I'm not looking at this from the point of view of momentum of emitted heat radiation. I am saying that at 0.71c, if your previous heat generation calc is correct, the kinetic energy loss rate is substantial at 80kW m^-2.

If you calc the kinetic energy of say a 100 tonne vessel at 0.71c, it should be possible to find what the velocity loss is in a small time interval (say 1 second).

If this does not square up with your previous calcs I think it shows there is something wrong somewhere.

astromark
2010-Mar-03, 05:42 AM
Oh my god...:o: its the end of sanity as I new it... The mathmaticle madness is taking over the internety thingie:) :eh: Sorry if thats a tad offensive., Its a point of view.

Calculations of mass and momentum and calculations of energy transfer inputs required...Its all to much for my burned out old brain to get to grips with...

What I can see and understand completely is this... That in the Gene Rhodenbury conceived television series it was important to have the fictional ability to be some place else very quickly... "Make it so Data"... and they did. Zwish>>>

The point obviously is that in reality we know it just can not be that simple.
Energy requirements to protect the ship are excessive if not seemingly impossible.
I will however stop short of suggesting that velocity greater than c. will never be possible. I might think that. I can not know it to be so... mark.

Atraveller
2010-Mar-03, 06:04 AM
I'm not looking at this from the point of view of momentum of emitted heat radiation. I am saying that at 0.71c, if your previous heat generation calc is correct, the kinetic energy loss rate is substantial at 80kW m^-2.

If you calc the kinetic energy of say a 100 tonne vessel at 0.71c, it should be possible to find what the velocity loss is in a small time interval (say 1 second).

If this does not square up with your previous calcs I think it shows there is something wrong somewhere.

Just a random thought - going with the magnetic field diverter - what if the diverter not only moved particles out of the path of the vessel, but also accelerated those particles behind the vessel - you would not only overcome the drag, but might actually end up with a net acceleration.

This assumes ofcourse we have some virtually endless souce of energy :doh: but then we are travelling in a vessel at 0.995c so of course we have endless energy...

Atraveller
2010-Mar-03, 06:10 AM
Sorry, but I just realized that I was describing a variant of the Bussard Ramjet...

Bussard Ramjet (http://en.wikipedia.org/wiki/Hydrogen_ramscoop)

Is there nothing new under the sun?

lpetrich
2010-Mar-03, 01:12 PM
kzb, the calculation is E-Z.

The kinetic energy is (g-1)*m*c2, and for 100 metric tons and v = 0.71 c, it is 9*1021 joules.

astromark
2010-Mar-03, 07:03 PM
The statement, That warp speed would be fatal is in it's self, a mistake.
What is warp speed. Where on the scale of things I understand does it sit ?
Can I have multiples of it ?
How does it compare to the absolute velocity of light in a vacuum ?
Looking fleetingly at my own vacuum cleaner and wondering if it knows the secret it holds...:)and how do you converse with such ? I need a knowledgeable maths wizo.., to expel these demons...forever.

The answers in a questions and answers forum should be understandable by at the least the people whom read it. The fog descends on most of the mathematics I see in the posts above... I have very little idea of any reality as such (g-1)*m*c* and forever and ever.... By the way,. The answer to my question is NO.
The reality is that we need to find a other method other than velocity to beat the fact that its un attainable for objects of any substance to get to velocity c.

Atraveller
2010-Mar-04, 05:31 AM
The statement, That warp speed would be fatal is in it's self, a mistake.

Interesting we all knew what was meant by the OP.

But true - Wiki (the source of all knowledge) defines Warp Speed as a Faster Than Light speed. The concept of "Warping space" to allow FTL travel was an early artifice of Science fiction - arguably and loosely based on some form of Einstein-Rosen bridge...

Warp Speed (http://en.wikipedia.org/wiki/Warp_speed)

Einstein-Rosen bridge (http://en.wikipedia.org/wiki/Worm_hole)

What we have been discussing is more of a conventional sub-luminal speed - or light fractional speed.

We need new physics... Where is negative mass when you need it?

Jens
2010-Mar-04, 09:53 AM
What we have been discussing is more of a conventional sub-luminal speed - or light fractional speed.

Sorry in advance for a geeky question. I wonder if you can use "warp" when discussing subluminal speed? It's possible to say "mach 0.7", so I wonder if it's possible to say "warp 0.7," or does "warp" require superluminal speed before it even starts to be a measure?

kzb
2010-Mar-04, 12:36 PM
Jens, according to my Star Trek Techical Manual, Warp 1 does indeed correspond to light speed, however, warp 2 is NOT X2 light speed, it is closer to X10. Each warp factor is a several times increase on the previous, but it explains that a X10 rate of progression quickly makes the galaxy too small for the Star Trek format. Hence later warp factors are not X10 the previous ones.

Non-integral warp speeds, eg warp 1.6, are permitted, but often it will be more energy efficient to move up to the next integral warp factor. A bit like changing gear in a car: it will be more efficient to change up to 5th and travel at 40mph rather than travel at 35mph in 4th.

It makes no mention of sub-warp 1 (ie subluminal) velocities. I do not know if you can use warp drive for subluminal velocities such as 0.7c. That is an interesting question, but I have never heard either Kirk or Picard order a less-than-one warp factor. This makes me think it is not possible.

kzb
2010-Mar-04, 12:40 PM
Actually I should add for the purists, warp 1 is not exactly light speed. There is some quantum tunneling going on that allows the vessel to cross the speed of light without actually travelling exactly at it at any point.

lpetrich
2010-Mar-05, 03:28 PM
How does it compare to the absolute velocity of light in a vacuum ?
It's not very clearly stated, but I recall from somewhere v = c*w3 - the cube of the warp factor w.

I'm not going to try to disentangle it any further.

The fog descends on most of the mathematics I see in the posts above... I have very little idea of any reality as such (g-1)*m*c* and forever and ever....
astromark, why is mathematics so horrible to you?

I wanted to show how I got my results, so that you people can see how I did it, and maybe learn even more.

Sorry in advance for a geeky question. I wonder if you can use "warp" when discussing subluminal speed?
I think that it may be possible, even if it's not used very much.

Non-integral warp speeds, eg warp 1.6, are permitted, but often it will be more energy efficient to move up to the next integral warp factor. A bit like changing gear in a car: it will be more efficient to change up to 5th and travel at 40mph rather than travel at 35mph in 4th.
Seems like it's a quirk of the warp drive rather than the mechanics of FTL travel.

It makes no mention of sub-warp 1 (ie subluminal) velocities. I do not know if you can use warp drive for subluminal velocities such as 0.7c. That is an interesting question, but I have never heard either Kirk or Picard order a less-than-one warp factor. This makes me think it is not possible.
I think that that's because there's usually no need to go subluminal, except near a planet. Some Solar-System times when traveling at c:

Earth to Moon: 1.3 seconds
Saturn to Titan: 4.1 seconds
Sun to Earth: 8.3 minutes
Sun to Saturn: 1.3 hours

mahesh
2010-Mar-05, 04:22 PM
http://www.trishbennett.net/jtk/episodes/enemywithin/enemy277.JPG

...Seems like it's a quirk of the warp drive rather than the mechanics of FTL travel...

ahem...couldn't resist, cap'n ...sorry...cough cough ...

kzb
2010-Mar-05, 04:57 PM
I think that that's because there's usually no need to go subluminal, except near a planet.

I think it goes deeper than that. Warp 1 corresponds to a single layer of the subspace warp field, and I think that layer is either established or not. It's either on or off. If it's on, it means you are travelling at c (or close to it).

The builders gave the Enterprise and similar vessels both impulse and warp drives. If warp drive could be used for sub-c manoevres I can't see the point of providing an impulse drive in addition to a warp drive. It would be a very expensive white elephant,

kzb
2010-Mar-07, 04:08 PM
Ipetrich wrote (some time back )

v = 0.71 c; g = 2

Is this actually true? The Lorentz factor is 1/[SQRT(1-(v/c)^2)]

So for g =2, you need 0.867c and not 0.71c as stated?

lpetrich
2010-Mar-08, 08:20 AM
Oops, you're right.

kzb
2010-Mar-08, 06:26 PM
AHA, have you done the same with the other g-factors?

I find protons at 0.995c are 8.4GeV, not 9GeV. I've not checked the others yet, I wish I had more spare time. Not much difference between 8.4 and 9GeV in any practical sense, but there might be a bigger relative error at lower g-factors, so there is more difference between your value and the real value for somewhat lower fractions of c.

kzb
2010-Mar-08, 06:42 PM
I find protons at 0.71c are 0.39GeV, not 0.9GeV. This should make the shielding requirements and the heat production a bit less severe at moderate v/c.

FarmMarsNow
2010-Mar-09, 04:07 AM
we should also assume everything traveling at warp speeds does not interact with anything traveling less than the speed of sound.
I was wondering about that. Does anyone know whether for an object to travel that fast it must behave more like a waveform than a solid?
Maybe stray neutrons and things would simply pass through a light-speed craft without interacting? The ship might act like a single, gigantic photon.

It seems to me, intuitively but not analytically, that a ship traveling at or above light speed would be like a giant photon or huge quantized energy packet that could only interact with an object of that same energy level or larger like an asteroid or planet. Also, someone told me that as you approach c, your density goes up sharply.

? :)

eburacum45
2010-Mar-09, 03:09 PM
There is no information available about the characteristics of superluminal (faster-than-light) travel, because it is almost certainly impossible.

Ipetrich has been calculating the effects of vaurious subluminal (slower-than-light) speeds, and in fact the original article was also concerned with subluminal speeds. FTL travel seems to be outlawed by the Universe on a very basic level, and for good reason.

99gecko
2010-Mar-09, 05:57 PM
I've often felt that due to the frail nature of our physical bodies, it would be more useful to find a means of bringing whatever distant objects we wish to interact/observe to us. That may be merely translating information about that which we wish to interact/observe into a medium that is FTL such as tachyons, and decoding it when it reaches us, and vice-versa. Observation as unidirectional interaction is the precursor to direct interaction. It's not hard to imagine a virtual visit in this regards without the need for expending vast quantities of unobtainable energy to do so.

Essentially this is how we have been exploring the universe outside of our own solar system to this point, except it has been subluminal. We just have to "tweak" the efficiency.

Excuse my ignorance if it has been suggested many times before, but I am new to this subject.

cheers.

FarmMarsNow
2010-Mar-09, 08:17 PM
in fact the original article was also concerned with subluminal speeds. FTL travel seems to be outlawed by the Universe on a very basic level, and for good reason.
That is disappointing a little bit, however it doesn't matter. We don't need to travel that fast, and it really isn't fast enough anyway. The distances are so great that even light speed is inconvenient for traveling around through space.

Jens
2010-Mar-10, 10:03 AM
Essentially this is how we have been exploring the universe outside of our own solar system to this point, except it has been subluminal.

Generally speaking, it has been neither subluminal nor superluminal. It has been precisely luminal, I believe.