At 2:33 PM 4/4/5, John Berry wrote:
>Horace, thank you for your detailed analysis.
>The reason I was asking was because I thought that if the forces are as
>Grassmann insists are perpendicular then removing the battery and
>instead using high frequency alternating current in what is now an open
>circuit should give rise to thrust.
>
>-------------------------------------------------------------------------
>+ ~ -
>I
>I
>-------------------------------------------------------------------------
>- ~ +
>
>The force on the I's would be perpendicular with no force on any other
>segment.
>However with further thought, the only way the above would fail to
>generate thrust is if the forces are as Ampere claims (longitudinal)
>without any displacement current in the vacuum between the two rails.
>
>Even if Ampere is correct as long as there is displacement current the
>magnetic force from the vacuum displacement current would push on the
>rail in a longitudinal manner.
>
>So Newtons law would survive as the equal and opposite force would be
>placed on the vacuum (aether).
>
>If Grassmann is correct it doesn't matter if displacement current exists
>or not.
>
>
>
>
>
>/
> /
> /
> /
>------------------------------------------------------------------------/
>I
>I
>------------------------------------------------------------------------\
> \
> \
> \
>
>\
>
>By having the conductors diverge a bit more thrust might be created, but
>clearly the angle shown here is too steep.
>Clearly I keep the 'rails' close and parallel to increase capacitance, I
>thought of increasing capacitance by adding capacitor plates to the
>rails (the two plates would of course remain the same distance apart as
>the rails) but realized as the currents branch out in the plates counter
>forces would be created, however if the whole thing were made of the
>same thickness that objection would be removed.
>So wide ribbon would be the best material to use.
Plenty of things, including patents and published experiments have been
done along the above lines. Sorry, but I don't have time to look anything
up at the monent, but the vortex archives are full of this stuff. Again I
don't now of anything resulting in a successful product, so it all seems to
fall into the category of wishful thinking. The minute you accept Grassman
all kinds of perpetual motion things are possible including the Marinov
motor. Just for fun I've attached an old post of mine along those lines.
Virtual currents appear to close the gap just as effectively as real
currents. Virtual currents arise between capacitor elements (plates) -
they are equivalent to the currrent which would be required to generate the
B between the plates that arises due to the changing E between the plates.
If I correctly recall some work I did along those lines the net force from
the virtual current actually resides in the plate conductors due to the
effects of the B on the real currents in the plates, even though the force
mimics exactly the force which would be created on the non-existant virtual
current which closes the plate gap. An exception must be made for fields
that radiate away fromthe plates which carry photon momentum and energy.
Here's the old post on Grassman and Marinov stuff:
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Marinov's Longitudinal Force
An Analysis from a Design Standpoint
Horace Heffner - 3/23/98
The following is an attempt to analyze Marinov's law from a design
standpoint. The objective is to extract an expression for Marinov's
longitudinal force that may be useful to form longitudinal force
accelerator design concepts,and to briefly consider some design
consequences. An alternate objective was to derive an absurdity and thus
disprove Marinov's derivation, however that has not been sufficiently
achieved. Some unusual consequences have been derived that raise some
doubts, however. Any assistance in finding my errors or an error of
Marinov's would be appreciated.
It seems desirable to find the longitudinal component directly from the
Marinov formula (see equation (2) of quoted excerpt from Marinov's article
appended below):
Fm = (u0 q q')/(8 Pi r^3) {V'*R)V + (V*R)V' - 2(V*V')R} (1)
or more simply, substituting k = (u0 q q')/(8 Pi r^3):
Fm = k {V'*R)V + (V*R)V' - 2(V*V')R} (2)
Here Fm, V, V' and R are all vectors. Since I personally find it difficult
to visualize the above, converting everything into the longitudinal
components also has the advantage to me of eliminating the vectors. The
original text by Marinov, defining the above equation, is included at the
end of this post for the sake of clarity.
In the above equation * means dot product, an operation on two vectors.
For the sake of convenience and to avoid the use of Greek letters for
angles, let us denote the cosine of the angle between two vectors V and V'
as cos(V,V'). If we denote the length of a vector V by |V|, then we have
the definition of the dot product being given by:
V*V' = |V| |V'| cos(V,V') (3)
Applying (3) to (2) we have:
Fm = k { [ |V'| |R| cos(V',R) ] V
+ [ |V| |R| cos(V,R) ] V'
-2[ |V| |V'| cos(V,V') ] R } (4)
Now, the magnitude of vector V in the V direction is |V|. The magnitude of
the component of V' in the direction of V is cos(V,V') |V'|. Similarly the
magnitude of the component of R in the direction of V is cos(V,R) |R|.
Substituting into (4) to get the component of each term in the V direction,
i.e. the longitudinal direction, we then get an equation for the scalar
longitudinal force component Fl:
Fl = k { |V'| |R| cos(V',R) |V|
+ |V| |R| cos(V,R) cos(V,V') |V'|
-2|V| |V'| cos(V,V') cos(V,R) |R| } (5)
Fl = k |V| |V'| |R| {cos(V',R) + cos(V,R) cos(V,V')
-2 cos(V,V') cos(V,R) } (6)
Noting that |R| = r, simplifying (6) we have:
Fl = (u0 q q')/(8 Pi r^2) |V| |V'| {cos(V',R) - cos(V,R) cos(V,V')} (7)
It is now clear that the key to understanding Marinov's longitudinal force
lies in the understanding of the dimensionless scalar term:
h = {cos(V',R) - cos(V,R) cos(V,V')} (8)
because given scalar speeds v, v' of two charges q and q' at scalar
distance r we have from (7) and (8):
Fl = v v' (h u0 q q')/(8 Pi r^2) (9)
Note that -2 < h < 2.
Equation (9) may be useful for a finite element analysis, and converts
readily into a form for current segment (ilB) analysis. Equation (9) seems
to indicate that Marinov's longitudinal force can be related almost purely
to the electrostatic attraction of the two charges, q and q'!
Knowing the identity:
u0 e0 = 1/c^2 (10)
we have:
u0 = 1/(c^2 e0) (11)
Substituting (11) into (9):
Fl = v v' (h 1/(c^2 e0) q q')/(8 Pi r^2) (12)
Recalling that the scalar force between two charges is:
Fe = (q1 q2)/(4Pi e0 r^2) (13)
We can rearrange (9) to show the scalar longitudinal force Fl in terms of Fe:
Fl = (v v' h/2)/c^2 (q1 q2)/(4Pi e0 r^2) (14)
Fl = (h v v')/2c^2 Fe (15)
It is important to recall that the vector longitudinal force was defined to
be in the direction of V, by definition of "longitudinal".
The units of Fe clearly represent a force (the electrostatic force), so the
term (h v v')/2c^2 in (15) should be dimensionless, which it clearly is.
At least the units appear to be correct.
This is a really bizarre notion of reality, that a longitudinal force
exists and is a function of the electrostatic force and velocity vectors
relative to the frame of reference where energy is extracted. Due to the
critical energy producing regions being at velocities near c, a
relativistic analysis is warranted. However, it is believed that practical
use may be made of devices operating at 0.1 c. It is possible such a force
has not been readily observed or identified because it is so small unless
both v and v' are near c, and q' is large.
Given only the dimensionless directional scalar term:
h = {cos(V',R) - cos(V,R) cos(V,V')} (8)
and the scalar longitudinal force Fl in terms of the scalar electrostatic
force Fe:
Fl = (h v v')/2c^2 Fe (15)
and knowing, -2 < h < 2, we can readily see that increasing v is
beneficial, but is bounded by c, the speed of light, so the majority of the
remaining limitation on Fl is the ratio v'/c. This sets an upper limit on
the size of the longitudinal force at v'/c Fe, which means the primary
limit to the force magnitude from a permanent magnet is determined by the
speed of the permanent magnet's orbital electrons v'.
The highest coefficient of power (COP) implementation then is a
longitudinal force accelerator using magnetic "coils" made from coiled long
mean free path discharge tubes. Since the path of the accelerated
particles might be naturally spiraled by local magnetic fields, the
accelerator portion of the device might be made in a coil as well, and the
geometry of this coil such that the electrons in the field driver coils are
accelerated by the accelerator coil electrons. The distinction then
between driver coils and accelerator coils might become dissolved, thus
creating a single fully auto-actuated accelerator.
One implication of the above is that there may exist a self-sustaining or
self enhancing discharge geometry to explian ball lightning.
If Marinov's equation is correct:
Fm = (u0 q q')/(8 Pi r^3) {V'*R)V + (V*R)V' - 2(V*V')R} (1)
and my derivation of that:
h = {cos(V',R) - cos(V,R) cos(V,V')} (8)
Fl = (h v v')/2c^2 Fe (15)
is correct, then one design influence is that what happens in wires is of
almost no consequence to a near light speed longitudinal force accelerator.
For this reason, it should be possible to build and test the longitudinal
force (LF) principle derived here using segments constructed from evacuated
tubes. Such accelerator tube segments could be hooked up in parallel or in
series, as it does not matter what happens in the adjoining circuitry,
except for the beam guiding influence of the magnetic fields. The segments
can be assembled in any geometry of utility and could all be linear tubes.
It is possible to make a kind of LF accelerator erector set from evacuated
glass or quartz envelope tube diodes. At last Ampere's isolated current
segment can have a reality of a kind, at least in regards to energy
conservation, or non-conservation.
In that longitudinal force is proportional to velocity v, the free energy
imparted is at least proportional to the average force squared. This
implies that a near lightspeed current device compared to a current in wire
driven device should produce a factor of about 10^20 more free energy. The
longitudinal force is similarly symmetrically proportional to the
energizing coil electron velocity v', so large gains are feasible there as
well. As the velocities v and v' approach c, the factor (h v v')/2c^2
approaches unity, and the longitudinal force on an accelerated particle in
the generator approaches the enormous summation of the combination of
electrostatic potential energy between the accelerating particle and every
energizing particle. Note that this is a volume effect, unlike surface
charge forces utilized in a van deGraff accelerator. Because Fl is a
function of both speeds v and v', the positive nuclei in permanent magnets,
for example, have no effect, because for them v' = 0, yet all the charges
with unbalanced motion, those responsible for B, are active in the
longitudinal force on every accelerated particle.
If all the above conclusions are correct, an unlimited, non-polluting, and
enormously robust and portable source of power is potentially available
from a longitudinal force based accelerator.
Let us see if we can now glean some understanding of the scalar term:
h = {cos(V',R) - cos(V,R) cos(V,V')} (8)
so it can be applied to the longitudinal force equation:
Fl = v v' (h u0 q q')/(8 Pi r^2) (9)
repeated over a volume of a magnet, for example, to evaluate the force on a
particle in the vicinity. If a convenient path can be found then a test
can be devised.
Let us assume we have a cubical magnet volume aligned to the x y and z
axes, consisting of atoms all magnetically aligned in the x direction. If
we want to analyze the longitudinal force on a particle in space near the
magnet at point p with velocity V, we then can partition the magnet into
small cubic segments and compute the Fl at p for each magnet segment and
sum them. For each segment we have a vector R from p to the segment. We
can use q' as the sum of charges of electrons aligned with B in the
segment. Atoms are small, so the lateral motion of the electrons, changing
R slightly as V' changes direction, can be ignored.
To account for electron orbiting in the magnet, we need to sum (integrate)
the force Fl for each V' over all the 360 degrees of rotation about the
local B vector that is performed by each of the electrons in our charge q'.
For this reason, it would be convenient to look at the special case where
V is aligned with B, so every V' is purpendicular to V and we thus have
cos(V,V') = 0.
When:
cos(V,V') = 0 for every V' (16)
we have:
cos(V,R) cos(V,V') = 0 for every V' (17)
however, if every R is approximately aligned with B, then also:
cos(V',R) ~ 1.0 for every V' (18)
thus:
h ~ 1.0 (19)
for every segment in the example magnet.
This implies that there exists a longtitudinal force even in a longitudinal
portion of a permanent magnetic field directly in front of a magnetic pole:
(e-)--Lf-> N---S <-Lf--(e-)
This also means that one possible test of this theory is to do calorimetry
on a diode tube both with and without a magnet near the collector plate
with a nearby magnetic pole facing the plate from the back side:
| |------------(-)
| |
| |
\/\/\/
------
|
------------- (+)
------
| N |
| |
| |
| |
| S |
------
One alternative is to form a ring of discharge tubes in plane XY and place
on the z axis the vertical tubes - over the center of the ring:
O -
|
|
O +
0---OO---O <---- ring of discharge tubes in plane xy
O +
|
|
O -
The discharge tubes could be connected in series. Wiring is not shown as
it is irrelevant to the longitudinal force for large high speed discharges.
Excess energy would show up primarily as heat and radiation at the +
terminals of the z axis tubes.
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MARINOV:ANNUS HORRIBILIS
The following is an excerpt from an ad by Marinov of the same title as
above. Bold letters (vectors) are changed here to capitals. The partial
derivative symbol is denoted here as @. Note however that the letter
capital S below is a scalar. Pi = 3.14159... and u0 is "mu sub zero."
There are some references here to photos which are not legible to me.
Marinov writes: "The Lorentz equation is wrong. If there are two electric
charges q, q' moving with velocities V, V' and the vector-distance from q'
to q is R, according to the Lorentz equation the force with which q'V' acts
on qV is given by the following Grassman formula:
Fg = (u0 q q')/(4 Pi r^3) {(V*R)V' - (V*V')R} (1)
Numerous experiments done by other authors (Hering's experiments are from
the beginning of the century!) and by me showed that the force acting on qV
can not only be transverse to its velocity, as required by (1), but also
longitudinal. Any rational man when seeing at least one falsifying
experiment rejects the respective formula (Popper), however for thousands
and thousands of Betonkoepfe even hundred experiments were not enough. In
the photograph there is one such falsifying experiment which (as well as
the other) can be carried out by children: A cylindrical magnet is cut
along one of its axial planes and the one half is turned up-down (the
magnetic forces themselves do the rotation). Around this magnet, there is
a trough filled with mercury in which the copper ring which can be seen at
right swims (the children take the salt solution and suspend the ring on
threads). After sending current of some tens of amperes from the battery
at left, which is regulated by the rheostat, the ring begins to rotate.
That's all!"
"The Lorentz-Marinov equation is the right one. As according to (1) Fg' is
not equal and oppositely directed to Fg, I obtained Marinov formula by the
most simple and natural symmetrization of (1) (take into account that R =
-R')
Fm = (Fg - Fg')/2
= (U0 q q')/(8 Pi r^3){V'*R)V + (V*R)V' - 2(V*V')R} (2)
Proceeding from (2) and assuming phi <> 0, @A/@t <> 0, I obtained the most
simple calculations that the force with which an electric system acts on a
test charge q moving with velocity V is
F/q = - grad phi - @A/@t + V x B + VS = Eior + V x B + VS (3)
where phi, A are the electric and magnetic potentials generated by the
system at the point of the charge's location, Bior = rotA is the Lorentz
magnetic intensity, Swhit = -divA/2 is the Whittaker magnetic intensity and
Bmar = -(u0/(8 Pi)) integral[ q'(V x V')(R*V)/ (v^2 r^3) ] (4)
Smar = -(u0/(8 Pi)) integral[ q'(V * V')(R*V)/ (v^2 r^3) ]
are the Marinov vector and scalar magnetic intensities. B = Bior + Bmar is
called the vector magnetic intensity and S = Swit + Smar is called the
scalar magnetic intensity, (3) is called the Lorentz-Marinov equation. If
neglecting the last term and under B we understand Bior, we obtain the
Lorentz equation which I call the Lorentz-Grassman equation. That's the
whole theory!"
Regards,
Horace Heffner
