In other thread superluminal mentioned “ the anti-gravitational Shield”. We all have read a lot about such a shield in many fantastic novels, sow in movies and TV programs … Antigravitational, anti-missile, anti-bullet, anti-gamma-ray , anti-cosmic-ray etc, etc… I asked superL to start thread about those shields, but he had a little interest on it. So, let us prove to him that issue is interesting enough….
My question to all: does somebody know how such shields should be organized according to our current knowledge of Nature? The subject of this thread is concerning to the physics of (separately!)
1. Anti-gravitational shield;
2. Anti-bullet shield;
3. Anti-charged-particle shield;
4. Anti-gamma-ray shield.
Any projects? Any theories? Any thoughts?

Anti-Grav: Probably not possible. Would require the mass-energy equivalent of the object you were trying to shield against. (actually, create a counter gravitational well, exactly opposing the other one).

Anti-Bullet: Probably not possible. Would require the inter-atomic forces within matter to somehow be present and coherent without the matter...

Anti-charged-particle: A powerful magnetic field.

Anti-gamma-ray: A big slab of lead.

Superl,
Your almost instant answer has shown that we have to detail our “specification”:
1. The attack can be done from any direction;
2. There is not a lot of time to prepare shield, it should get in state “ready to shield” fast enough;
3. It should not accumulate the energy of attacked weapon in form that itself will become a dangerous circumstance.

BTW, I like your proposal 4. It fingers at very realistic way to the effective and optimal solution. The details will form whole intrigue of the concrete projects…

Ok. Lets work on the anti-grav. What do we want it to do? You talk of an attack. Some kind of weapon. What am I defending against?

superluminal,
I do not know why writers reffer sometimes to anti-gravity shield: may be to avoid to be swallowed by a black-hole? Or for sake of sudden escape of enemies at orbiting some new star or planet? Honestly saying I do not read scifi, I hear it time-by-time from my sons...

I do read scifi and there are not too many references to a "gravity shield". Mostly they are talking about anti-gravity devices that let you float free within a gravity field. The only thing I have ever thought of that would do this is a device that would somehow "flatten out" the spacetime curvature around the device. I think of it as a "Gravity Planer".

So, we certainly need some ideas about
2. Anti-bullet shield;
3. Anti-charged-particle shield;
Simple statements like "Anti-charged-particle: A powerful magnetic field" definitely does not explains any concrete design (construction) or configuration of shield. More specifics are needed.
And how about anti-missle shield? How to avoid impacts with missles? (except simple launching of anti-missle rockets or sooting anti-bullet ... bullets)
Are there concrete physical processes or fields that can, in principle, help us to avoid to be stroken by missles, rockets, charged particles, etc?
In other words, can idea of considering shields be put in practice anytime in future?

An interesting thread and not as silly as it seems.....

Anti gravity, as in defy gravity by de-sequencing the alternating field patterns of the object you wish to defy gravity.

Anti missile, desequencing the alternating field patterns to remove the weight value of the missile thus rendering it inert.

Anti charged particle shield works on similar grounds. sequencing the alternation of a given space so that it repels the value of the charged particle.


hmmm...simple really..... :D

The difference is that I am asking to put real phenomena of physics with real calculations in base of any "verbal" shield, and you are creating one more "verbal" shield.
For instance, superL suggested using magnetic field to protect body against falling of the charged particles on it. Can you calculate what configuration of field and what magnitude of the magnetic field we need in this project? After getting of those answers, can you design any schematics of a corresponding shield and devices that can provide this kind shield?

Well QQ has started it there, because you will need the general idea before you start working on calculations.
I however do not wish to claim that he has the right general concept :) nor do i wish to defy him.

Yuriy, word of advice. The magnetic field that SuperL suggested, i find that to be very "layman-ish". Will the next thing be a really strong magnetic pull that "absorbs" all light so that you can create a totally stealthy aircraft or something? There are major problems with this kind of practical application and it should stay in your dreams, of course it is fine to start with it but you will get disappointed later on.
You seem to advocate "real calculations" but my advice is to actually have a workable theory before you start with a practical theory.

Anti-bullet shield :

http://www.electron.de/bilder/sb25.jpg

Anti-Missile :

http://www.cheniere.org/images/weapons/ABMdef2sm.jpg

another anti-missile system :

http://us.news2.yimg.com/us.yimg.com/p/afp/20040324/capt.sge.awh33.240304095209.photo00.default-384x265.jpg



Anti-gravitational shield :

A lots of them Here (http://www.crank.net)

Dilbert, everneo (BTW, everneo, I like your post!),
of course, if we will respond on post like this one in manned as QQ did we never will consider any physical problem scientifically (remember the name of our Forum - word "frontier" is figuring there!).
So let me formulate the one of problem in this (http://www.sciforums.com/attachment.php?attachmentid=3848&stc=1) way.
Do we have a proper answer?

you could use Reactionary armor

Yuriy, you could make a vest out of it and try it on :p

Dilbert,
you are right, especially if bullet's speed is 290000km/sec...
(remember: we are in "Stars Wars" zone?)

You could have the bullets pass through a spray of highly charged particles, thus giving each bullet a high electric charge, followed by an intense magnetic field oriented such that the bullets would be deflected away from the target.

Dilbert wrote:

Yuriy, word of advice. The magnetic field that SuperL suggested, i find that to be very "layman-ish". Will the next thing be a really strong magnetic pull that "absorbs" all light so that you can create a totally stealthy aircraft or something?

Dilbert, are you aware that a magnetic field is exactly what protects the earth from bombardment by a deadly wind of charged solar particles?

You could have the bullets pass through a spray of highly charged particles, thus giving each bullet a high electric charge, followed by an intense magnetic field oriented such that the bullets would be deflected away from the target.

OH MY GOD,
how can you even say something like that and refer to practical application.

Dilbert, are you aware that a magnetic field is exactly what protects the earth from bombardment by a deadly wind of charged solar particles?


Sure, but i failed to see your point.

It's an idea. In engineering you start with a fundamental concept and refine it. What is your background? You sound confused.

Yuriy,

Why do crackpots always try to ruin our fun?

I assumed this was to be a fun and exploratory thread on how you might begin to approach these ideas.

it's an idea

what a statement.
In my kind of engineering you do not have ideas, you have workable theories, preferebly even prototypes. Otherwise they would be laughing at you.

But ill leave you and Yuriy alone. Perhaps i am too harsh, i should probably not expect more from mere mortals.

A self admitted asshole. How refreshing.

superluminal,
1. You still can not adopt the fact that Freedom of Speech inevitably provides a couple of clowns at any funerals, a couple of weepers at any wedding and a couple of cranks in any scientific Forum. Consider it as a price for having this freedom...
2. Idea is good but ultimately unpractical one. If you estimate what this "charging” blanket should be and what configuration and power in what volume the magnetic field should have you will come to the very unrealistic numbers. But such estimation by itself will be very useful for any curious in physics…

Clearly it is impractical under ordinary circumstances, but someone mentioned "star-wars" and attacks form energy weapons... So, if I have a space battle cruiser, and a matter-antimatter power source, I can direct a stream of charged particles at any incoming projectile weapons, and deflect them with the magnetic field surrounding my ship. Might even be less energy intensive than destroying them outright. Then I can go on to defeat the rest of the evil galactic empire.

Were you looking for practical solutions to these shielding questions?

SuperL,
even in "Stars Wars" zone we should have some edges of fantasy. Let us imagine that calculative estimation of your project would require energy equal to the energy ... a Galactic. Would you say: "I still am in Stars Wars zone"? No, my friend, you will be out of this zone, you will be somewhere in "Gods Wars" zone. So, be realistic ... resident of Stars Wars zone! Do some estimation...

Are you talking about teh classic shields usewd inthese sci fi scenes. LIke the legendary force fields of "Lost in space" a barrier of 2 dimensional thickness that effects that which attempts to penetrate it?

are you wishing to describe a shield that is similar to a glass partition or window?

Ok Yuriy. What is this thread about anyway?

Let's see... Hmmm

a 1Kg kinetic energy weapon fired at about one tenth c...

Ke = 0.5mv^2 = 0.5*1*(300e5)^2

Ke = 4.5e^14 Joules = 4.5e^20 ergs

The amount of energy stored in a magnetic field is given, in ergs/cc, by B^2/8 x pi where B is in gauss units. I'm not going near the complexities of estimating the force necessary to deflect the projectile over a distance D, or the amount of charge on the projectile.

So, just as a real rough estimate of magnetic field requirements equivalent to the energy in the projectile... Hmmm:

B = sqrt(E*8/pi) = sqrt(4.5e^20*8/pi) = 3.38e10 Gauss

So, some sunspot fields can be 10000 Gauss. Hmmm. My idea just might take the entire energy output of a star. Or more. Rats.

QQ,

Good question. Yuriy?

Another obvious point to consider is that if you intend to deflect or repell a force an object must provide an appropriate counter force. The police vest for example may stop a bullet from penetrating but only if it desperses the force in such a way that the man wearing the vest is thrown of his feet backwards so that the bullets energy is despersed in a more safe fashion.

An anti missile field would have to either counter that force with another force or remove the inertia, kinetics from that missile.

A magnetic field could repell but the magnet must absorb the vectored energy of the object it is deflecting.

The alternative is to render the missile inert or take away it's inertia, weight or what ever you wish to call it so that it's mass is no longer acting on the field.

An anti gravity field that stops a falling object would have the same result if the objects attraction via gravity remains the same so to produce a field that forces the object to defy gravity is needed.

There is a hypothesis that I am currently working on that deals with de-synchronising the alternating energy of an object that allows gravity to become repulsive....In other words changing the timing of the alternating charges of an object.

SuperL,
Much, much better! Now you are trying to talk as scifi, not a simple fiction!
What I mean is any method to shield "the cosmic vehicle" due to real processes known for the contemporary Physics. One of such project you already have suggested (I do not ythink you have developed it deep enough, but suggestion is valid). I hope, you will finish estimation of this project on a good level and will teach all of us what it really will take to build the magnetic shield...

Any other projects?

a good scenario to start with would simply be the generation of a so called "Plasma" window that acts as a barrier to air, just like a normal glass window.

QQ,
be more specific, please...

Yuriy,

If you have a specific idea for this thread could you please state it? You mention shielding a "cosmic vehicle" Are we talking about practical ways to protect high speed spacecraft from micrometeroids, cosmic rays, and charged particle radiation?

I'm getting a little confused...

And from attacks of enemies...
Of course, I have some idea for sake of which I started this thread. Of course, this idea is to attract your attention to some very interesting physical phenomenon. Of course, I will tell you it. But before that, let us discuss all possibilities; let us listen all proposals... Is it wrong?

With the window idea the difficulty is in creating a field that takes the place of the glass that is able to effect orthogonal deflections on objects of mass, using only massless fields or energies.

say we errect two parallel posts with a separation of one metre. The posts are one meter high. We have a meter square window. One post could be consisdered as a negative pole and the other considered as the positive pole.

The question is how can this plane of field deflect objects of mass attemting to penetrate it?

One way that I can see this happening is simply to disintergrate the object of mass so that it becomes a part of that field. The field converts the mass to it's energy.

The other is to render the objects of mass as inert so that they can not penertrate the field because thay have no vector energy.
Obvously the later option is better than the first.

So really the question comes down to inertia if I am not mistaken, and how to alter the inertia of an object fo mass so that it does what you want it to.

We know I guess that when an object is in a gravity well it's inertia conforms to that gravity well. IN other words the object is showing the effects of that gravity well.
So to effect the inertia of an object the attraction to gravities must be mitigated.

Now of course we have no technologies at this stage that can alter the inertia of an object so that an object of mass has only a psuedo mass and not real mass [or ambient mass]

So a "plasma" window would need to effect the air wishing to pass though it's space by elliminating the inertia of that air that comes into contact with it.

Sorry if my terminology is incorrect.

"Is it wrong?" Not at all.

Yuriy, I have an idea.

I will throw certain weapons at you. You can describe what happens to the projectile, particle beam, laser, or whatever. From your description we will try to deduce your method of defense.

Or is this an insane idea???

Going to bed now. Nighty-night.

Ke = 4.5e^14 Joules = 4.5e^20 ergs
B = sqrt(E*8/pi) = sqrt(4.5e^20*8/pi) = 3.38e10 Gauss

My idea just might take the entire energy output of a star. Or more. Rats.

According to google, 4.5e14 Joules = 4.5e21 ergs. So the B would be sqrt(10)=~3 times bigger. Make it 3 stars :D

Not trying to be a smartass, I'm just pointing it out.

Your'e right of course. I'm going to run out of stars :(

An interesting thread and not as silly as it seems.....

Anti gravity, as in defy gravity by de-sequencing the alternating field patterns of the object you wish to defy gravity.

Anti missile, desequencing the alternating field patterns to remove the weight value of the missile thus rendering it inert.
What is the type of missle?
heat seeking - divert heat exhaust in direction least likely to be incoming direction of heat seeking missile, emit heated flares approximating the target's heat emission signature (false target signature)..
laser guided - avoid laser signal from reflecting from target with dense laser beam absorbing smoke;emit false laser signal to confuse missle target on reflected laser beam.
inertially guided missle - small disruptive nuclear blasts to give high energy short wave length, concentrated energy of EM pulse to disrupt missle eloctronics and inertial guidance functions.
charged particle "missile" - to divert incomiong beam with some counter emission of radiation would require complex tageting system and beam design (I wouldn't do this). Charged particle ordnance is target specific so design potential target shield that charged beam is deflected over area greater than cross section area of beam.

========> /
========> /
========> \
========> \
Above: charged particle beam impingingi on target surface.
ballistic missiles - basic intelligence and counter intelligence to hide location of target, if a military target - large scale civilian targets (cities) is another story. Some were taught to react to an imminent nuclear ballistic missile attack as follows:
While in a sitting position bend as far forward as possible while arching your head downward as far as you are able, then kiss your ass goodby.

Geistkiesel


.

So, its time to start talking about real physical concepts of shields, that indeed can protect a given body (especially – the space ships, from attacks of possible cosmic enemies and (what is much more realistic) from the contra-flowing dust, rocks, etc at speedy motion of our space ship.
1. The general principles of such shield are very clear. The most important for us should be the following one: all what we should do is to provide change the trajectory of the contra-moving particle to force it to miss our ship. In the professional language it sounds like that: we should provide the conditions of a scattering of contra-moving particle on our ship. Following this general principle, we will come to the conclusion that our shield should create the additional transversal (i.e. normal to the direction of our own motion, our course) velocity of each contra-moving particle (body). Therefore, shield should create some transversal force acting on contra-moving bodies. The all set of the constructive parameters of shield will depend upon laws that regulate motion of bodies at action of the external force. And here we should take into account the existing huge difference between Classic Mechanics and SRT Mechanics.
2. Let me tell you about one of such huge difference that, unfortunately, never was touched in our Forum, where the majority of posts are about (mostly against) SRT.
The first of all let me remind you one of the most useful consequence of the Newton’s 2 law, that is used very often at the concrete solution of the concrete mechanical problems.
dP /dt = F
shows, that is the driven force F has no component in some direction, lets call it the normal to F direction, then the momentum, P = mV, in that directions remains unchanged, i. e.
dPn /dt = 0, or Pn = const.
and acting force F is changing only the momentum of body in direction longitudinal to force’s direction, i.e.

dP||/dt = F

In other words, in Classic Mechanics we have the law of conservation of the velocity of body in the directions normal to the direction of acting force.
It means that designing our shield by laws of the classic mechanics, we should always keep in mind that any transversal force acting on the contra-moving particle can not change its velocity directed right on us, V||. This force will create the transversal velocity, Vn, what will force body to scatter aside of us (hopefully!), but it will not change the relative velocity of the approaching of body to us!

Absolutely another situation we have in the case of SRT Mechanics: there is no law of conservation of the velocity of body in the directions normal to the direction of acting force.
It means that in SRT any action of any driven force leads to the increasing (decreasing) of body’s velocity in longitudinal to this force direction and to the simultaneous decreasing (increasing) of this body’s velocity in the normal to this force directions. It means that no one body approaching to the rested center of shield-field with velocity Vo can not come closer then some specific distance Ro(Vo).

To understand the origins of this purely relativistic effect, let us recall that momentum P actually is
P = MoV/√(1-V²/c²) ,
where V = √(Vn² +V||²) and V = Vn + V||.

So, the conservation of the transversal (to the force!) momentum,
Pn = MoVn/√(1-V²/c²), can be provided only if

MoVn/√(1-V²/c²) = const, what means that

Vn(t) = Vn(0)* √(1-V²(t)/c²)/√(1-V²(0)/c²)

i.e. Vn decreases if V|| increases and Vn increases if V|| decreases.

If you will cogitate on this fact, you will see that:
 Effective power-shield can be design as some dipole-type field with dipole axis oriented by a nornal to (or along?) the course of ship
 At relativistic speeds this shield is much more effective than at non-relativistic speeds.
 At relativistic speeds there is no problem with providing of reliable scattering conditions: all contra-moving particles will be unable to reach ship.

Any reader now can easily solve the problem of motion of relativistic particle in the uniform transversal fiiled of force and find out what is the minimal distance that this particle can approach to the origin of coordinates.

Any questions?

So, its time to start talking about real physical concepts of shields, that indeed can protect a given body (especially – the space ships, from attacks of possible cosmic enemies and (what is much more realistic) from the contra-flowing dust, rocks, etc at speedy motion of our space ship.
1. The general principles of such shield are very clear. The most important for us should be the following one: all what we should do is to provide change the trajectory of the contra-moving particle to force it to miss our ship. In the professional language it sounds like that: we should provide the conditions of a scattering of contra-moving particle on our ship. Following this general principle, we will come to the conclusion that our shield should create the additional transversal (i.e. normal to the direction of our own motion, our course) velocity of each contra-moving particle (body). Therefore, shield should create some transversal force acting on contra-moving bodies. The all set of the constructive parameters of shield will depend upon laws that regulate motion of bodies at action of the external force. And here we should take into account the existing huge difference between Classic Mechanics and SRT Mechanics.
2. Let me tell you about one of such huge difference that, unfortunately, never was touched in our Forum, where the majority of posts are about (mostly against) SRT.
The first of all let me remind you one of the most useful consequence of the Newton’s 2 law, that is used very often at the concrete solution of the concrete mechanical problems.
dP /dt = F
shows, that is the driven force F has no component in some direction, lets call it the normal to F direction, then the momentum, P = mV, in that directions remains unchanged, i. e.
dPn /dt = 0, or Pn = const.
and acting force F is changing only the momentum of body in direction longitudinal to force’s direction, i.e.

dP|| = F

In other words, in Classic Mechanics we have the law of conservation of the velocity of body in the directions normal to the direction of acting force.
It means that designing our shield by laws of the classic mechanics, we should always keep in mind that any transversal force acting on the contra-moving particle can not change its velocity directed right on us, V||. This force will create the transversal velocity, Vn, what will force body to scatter aside of us (hopefully!), but it will not change the relative velocity of the approaching of body to us!

Absolutely another situation we have in the case of SRT Mechanics: there is no law of conservation of the velocity of body in the directions normal to the direction of acting force.
It means that in SRT any action of any driven force leads to the increasing (decreasing) of body’s velocity in longitudinal to this force direction and to the simultaneous decreasing (increasing) of this body’s velocity in the normal to this force directions. It means that no one body approaching to the rested center of shield-field with velocity Vo can not come closer then some specific distance Ro(Vo).

To understand the origins of this purely relativistic effect, let us recall that momentum P actually is
P = MoV/√(1-V²/c²) ,
where V = √(Vn² +V||²) and V = Vn + V||.

So, the conservation of the transversal (to the force!) momentum,
Pn = MoVn/√(1-V²/c²), can be provided only if

MoVn/√(1-V²/c²) = const, what means that

Vn(t) = Vn(0)* √(1-V²(t)/c²)/√(1-V²(0)/c²)

i.e. Vn decreases if V|| increases and Vn increases if V|| decreases.

If you will cogitate on this fact, you will see that:
 Effective power-shield can be design as some dipole-type field with dipole axis oriented along course of ship
 At relativistic speeds this shield is much more effective than at non-relativistic speeds.
 At relativistic speeds there is no problem with providing of reliable scattering conditions: all contra-moving particles will be unable to reach ship.

Any reader now can easily solve the problem of motion of relativistic particle in the uniform transversal fiiled of force and find out what is the minimal distance that this particle can approach to the origin of coordinates.

Any questions?

Only the obvious question of which formula does one use for ??? (http://www.sciforums.com/attachment.php?attachmentid=3881&stc=1)

Comment: So you would not even provide for a backup system just in case SRT proves as impotent as described on this forum?

Geistkiesel

Yuriy,

With all due respect (to your last post), so what?

As an engineer, what you have described is meaningless speculation. You have stated one simple obvious effect that all high school students are familiar with:

...the law of conservation of the velocity of body in the directions normal to the direction of acting force.


and some not at all obvious relativistic effects.

You want to talk about realistic shields, so do so.

Please describe the "dipole" field generator that will do this, and the shape of the field generated.

Thank you.

SuperL,
Sometime I really do not understand you.
My post was not about
the law of conservation of the velocity of body in the directions normal to the direction of acting force
but about
there is no law of conservation of the velocity of body in the directions normal to the direction of acting force in SRT
Look on this picture (http://www.sciforums.com/attachment.php?attachmentid=3884&stc=1) and you will recognize what an advantage it gives for shield we are talking about!
“Field generator” is very simple – some powerful and very productive charger. It could be placed anywhere, for instance – inside body (ship). Dipole you can see in this picture (http://www.sciforums.com/attachment.php?attachmentid=3885&stc=1).
So, show how good engineer you are – develop this scheme!

Yuriy,
Most times I do not understand you! :p

This looks very similar to my original particle charger/magnetic field gizmo.

Still pondering your curve.

SuperL,
the point is not in design (I am sure, you will create any design that will be needed) but is showing that SRT formulas define design, which is absolutely another then the one that the Classic formulas require! It will be the difference like betweew sub - and suoper-sonic jets: absolutely another shapes! SRT will be seen in shape of shield!

Phase 1 - Set some limits

Given:
- Maximum relative velocity between ship and particle = 0.5c = 150e6m/s
- Particles can get no closer than 10m to hull

***************************
Calculate maximum mass particle our ship's hull can tolerate:

A typical bullet weighs 100g (.1Kg)
Muzzle velocity = 366m/s

So,
Ke = 1/2(.1)(366^2) = 6700 Joules

So, I will say, for arguments sake, our hull can absorb 7000J without damage.

Therefore, at 0.5c we can admit a particle with a relativistic mass no larger than:

m = 2(Ke)/(v^2) = 2(7000)/(150e6^2) = 6.22e-13Kg
***************************
I find indications that interstellar dust particles are estimated to be on the order of 10 picograms(10e-12g) or 1e-14Kg.

In this case we do not even need a shield. However, lets say we want to deflect even these small particles.

So, the transverse force required will be:

F = pi(1e-14)(300e6)(150e6)/(2 * 10) = 71N

So far so good? Please check my numbers.

71N seems like a completely reasonable and do-able number if one were to actually build such a thing.

superluminal,
Now you are talking as … an engineer, not as a curious layman! And I like it very much!
So, let’s speak as the engineers….
1. Your way is very good and I am ready to follow it. But this problem is a little tricky and we should be careful. My experience tells me that for a good start we should solve this problem in simple configurations of the homogeneous force. Let me do it for us, because I know how to handle such stuff better than you do…
Let us solve the SRT problem #1: particle moves with velocity Vo along X-axis and penetrates into area X>0 where we have the field of a homogeneous force (Fx = 0, Fy = F). What trajectory the particle will have at X>0? (This problem is solved in my lecture on SRT Mechanics in volume #7 of “The Scientific Notes”, but it is useful to repeat the solution right here). The velocity Vx(t) can be found just from momentum conversation law:
[Ax and Ay mean x and y components of vector A; Ft is a product of F and time t]

mVx(t)/√(1- Vx²(t)/c²- Vy²(t)/c²) = const = mVo/√(1- Vo²/c²)

from which we have:

Vx(t) = Vo√(1- Vy²(t)/c²)………………….(1)

The velocity Vy(t) can be found from the Newtons 2 law:

d[mVy(t)/ √(1- Vy²(t)/c²) – Vx²(t)/c²)]/dt = F

what easily can be integrated and gives (at initial condition Vy(0) = 0):

Vy(t) = c (Ft/mc) √(1- Vy²(t)/c²) – Vx²(t)/c²)

After substituting here of (1), we easily will find:

Vy(t) = [c (Ft/mc) √(1- Vo²/c²]/√ [1+ (Ft/mc)²(1- Vo²/c²)]……..(2)

And returning it in (1), we will get

Vx(t) = Vo/√ [1+ (Ft/mc)²(1- Vo²/c²)]…………………………..(3)

Now we can find out trajectory of particle of mass m in the field of a homogeneous force F.

For that we should integrate (2) and (3) by t over interval [0, t] at initial conditions: Y(0) = 0 and X(0) = 0. The results are:

Y(t) = (mc²/F){√ [1+ (Ft/mc)²(1- Vo²/c²)] – 1}…………………..(4)
and
X(t) = (mcVo/F) arctan [(Ft/mc) √ (1- Vo²/c²)]…………………..(5)

Eliminating t from two last equations we will get the equation of trajectory:

Y(t) = (mc²/F){1/cos[(FX(t)/mcVo] – 1}…………………………(6)

As one can see from (5) [or from (6)] at t rushing to infinity X(t) is rushing to

Xo = πmcVo/2F ……………………………………………………(7)

and Y(t) goes to infinity.

This is a full solution of SRT problem #1: the body moving into a transversal field of uniform force.

2. Let us now solve the SRT problem #2: particle moves with velocity Vo along X-axis and penetrates into area X>0 where we have the field of a homogeneous force (Fx = - F, Fy = 0). What trajectory the particle will have at X>0?
The velocity Vy(t) can be found just from momentum conversation law:

mVy(t)/√(1- Vx²(t)/c²- Vy²(t)/c²) = const = 0
what immediately gives:

Vy(t) = 0 ……………………………………..(8)

The velocity Vx(t) can be found from the Newton 2 law:

d[mVx(t)/√(1– Vx²(t)/c²)]/dt = – F

what easily can be integrated at initial condition Vx(0) = Vo and gives:

Vx(t) = Vo – c (Ft/mc) √[1 – Vx²(t)/c²]………(9)

As this equation shows, at t equal to

to = mVo/F ……………………………………(10)

Vx(to) = 0

i.e. to is the time of a total vanishing of the initial velocity of a particle.
Resolving (9) in respect to Vx(t), one will have:

Vx(t) = {Vo – cZ(t)*√[1+ Z²(t) – Vo²/c²]}/[1+ Z²(t)]… ….(11)

where Z(t) = Ft/mc.

To find current X-coordinate of particle, we should integrate (11) by t over interval [0, t] at initial condition X(0) =0.
It is not an so easy task, but I am here just for that. And the answer is:

X(t) = (mcVo/F)*{arctan Z(t) + arctan[√[(c²/Vo²)(1+ Z²(t)) – 1]] –

– arctan√[(c²/Vo²) – 1] - (c/Vo)*√[1+ Z²(t) – Vo²/c²] +

+ (c/Vo)*√[1 – Vo²/c²]}….(12)

This is an exact solution of the SRT problem #2: the body moving into a field of the longitudinal decelerating uniform force.

At t = to it appears that Z(to) = Vo/c and we have:

X(to) = (mcVo/F)*{arctan(Vo/c) + arctan(c/Vo) –

– arctan √[(c²/Vo²) – 1] - c/Vo + (c/Vo)√[1 – Vo²/c²]}….(13)

3. And now comes the most important part of our model of shield.
If we compare X(to) from (7) (I will denote it as X1) with X(to) from (13) (I will denote it as X2), we will get:

R = X2/X1 = (2/pi){arctan U + arctan (1/U) –

– arctan [√(1/U² – 1)] - 1/U + (1/U)*√(1 – U²)}……………..(14)

The graph of this ratio vs. U = Vo/c is plotted in this picture (http://www.sciforums.com/attachment.php?attachmentid=3900&stc=1). As you see, X2 is less than X1 for any Vo. It means that method "to deflect particles" – is much less effective than proposal "to decelerate the same particles"!

But now about practical case. Who said that we should use "whole effect" to shield our ship? It will be very good if we … only deflect particles on such angle that they will have to miss our ship! It will take much less power of shielding field. We can find exact solution of this problem – the SRT problem #3 – too. This together with good schematics of shield and all major technical and technological solutions may represent a very sophisticated proposal as far as we can also add some effective configurations of the magnetostatic force too... Such a project will be accepted for Master Degree in any University in World! Dare to defense?

And this is for James R:

I guess now you see that you should not erase and should safe some posts in our Forum because of their originality and priority. I am absolutely sure, that if Superluminal will finish this project, he will be able to offer to NASA a very good tool of preserving of the space apparatus from the fluxes of the charged particles, at least! May be it will be effective against the "beam weapon" too...