coils ...
@ jeanna
I think your intuition is right-on-the-money.
One odd thing about Hendershot's circuit (actually in the
Barry Hilton book there are several alternative circuits),
Hendershot may have wound his current path unconventionally
through his 5:1 transformers. These are standard off-the-shelf
guys extracted from TV or something.
On the 120V side there would be lots of turns around an iron
core ... making for an inductance that could well be up
in the Henries.
His circuit is so weird it might be difficult to do conventional
circuit analysis on it ... unless your good at that (unlike me I'm afraid).
There is mutual inductance all over the place here...
I too have the feeling that he is exploiting LARGE inductances
by simply hooking all these coils up in series essentially. His 40 MFD
and 80 MFD do something clever as well.
In the circuit I'm experimenting, which is essentially half of
Hendershot dual-coil arrangement, I can see pulses from a relay -- which
amount to just high-voltage spikes really, turned into a SQUARE wave ...
as if they were run through a flip-flop. This done with passive
components ... coils ... capacitors ... no diodes ... no transistors.
Its mind bending.
I had this thought before ... but last night got this thought again
after studying the Hendershot material.
The thought was ...
"Why did Hendershot select 5 15/16 inches for the diameter of his coil?"
This bothered me because Hubbard too, who used PHI in his coil designed,
came up with a radius for his first prototype that was a similar diameter.
I have to assume that Hendershot used some sort of math to come up
with this radius ... because it is so specific ... and so unusual.
Its not a standard coffee-can size ... I don't think.
In fiddling with the numbers, I came up with this ... using a very
Hubbard-ish approach:
Start from 60Hz.
Take it up a power of two until your in the 2Ghz range.
60 * 2^25 = 2.013266 GHz
That is your standing wave that will appear on the top of your
cylinder.
Ok ... now compute how much distance that is using speed-of-light
equal to 299792458 meters/sec.
I get the value in inches to be 5.862540. The dowels were .125 inches,
so add one half that ... twice ... yielding: 5.98754.
Take the fractional part .98754 and multiply by 16 to get it in 16ths ..
and truncate: 5 15/16 ... viola!!
Better still, I wanted to check this line of reasoning ... so I thought
to myself:
"How did he come up with 14 turns for L1 ... which is clearly the
coil that when combined with 7.8nF ... TUNES a special frequency?"
"So is that special frequency also a power-of-two harmonic of
2.013266 GHz derived above?"
60 Hz * 2^12 = 245760 Hz (well below AM dial).
What value of inductance would be needed to resonate at
245760 Hz if the capacitor is 7.8nF?
Answer: 53.768017 uH (assuming AIR-COIL)
Now the question is...
"How many turns on a coil form that has diameter 5 15/16 would
be needed of 28 AWG wire to achieve 53.768017 uH?"
Hendershot would have had the Wheeler forumla if he looked
that up in some Radio Engineer book.
Solving for N (number of turns), given:
L = 53.768uH, D = 5.9375 in, H approx .33 inch (a guess)
results in
***** 14 turns *****
which is the correct answer!!!
This is either an amazing coincidence ... or the very math
Hendershot used.
Caveat: The Wheeler formula is only accurate for when
H > .4 * D which is NOT the case above. This cylinder coil
has a height far too small for that formula to predict accurately
the inductance. However, I'm not bothered by that too much
because Hendershot was interviewed and stated that
sometimes he needed to REMOVE wire since he wrapped
the coil (presumably this last coil L1) ... with too much wire.
So that little TWEAK to get it working might be a clue
that this last coil requires a bit of guess work due
to the inaccuracy of the Wheeler formula.
If all of the above math is correct and was used ... then
Hendershot derived his coil dimensions in a similar way to how
Hubbard did it.
Certainly they would have the Wheeler formula in common...
but the bit about a standing wave across the top of the cylinder
is a very ANTENNA-like calculation ... not normally done for coils ...
except for perhaps TESLA COILS!!!.
Originally posted by jeanna
View Post
I think your intuition is right-on-the-money.
One odd thing about Hendershot's circuit (actually in the
Barry Hilton book there are several alternative circuits),
Hendershot may have wound his current path unconventionally
through his 5:1 transformers. These are standard off-the-shelf
guys extracted from TV or something.
On the 120V side there would be lots of turns around an iron
core ... making for an inductance that could well be up
in the Henries.
His circuit is so weird it might be difficult to do conventional
circuit analysis on it ... unless your good at that (unlike me I'm afraid).
There is mutual inductance all over the place here...
I too have the feeling that he is exploiting LARGE inductances
by simply hooking all these coils up in series essentially. His 40 MFD
and 80 MFD do something clever as well.
In the circuit I'm experimenting, which is essentially half of
Hendershot dual-coil arrangement, I can see pulses from a relay -- which
amount to just high-voltage spikes really, turned into a SQUARE wave ...
as if they were run through a flip-flop. This done with passive
components ... coils ... capacitors ... no diodes ... no transistors.
Its mind bending.
I had this thought before ... but last night got this thought again
after studying the Hendershot material.
The thought was ...
"Why did Hendershot select 5 15/16 inches for the diameter of his coil?"
This bothered me because Hubbard too, who used PHI in his coil designed,
came up with a radius for his first prototype that was a similar diameter.
I have to assume that Hendershot used some sort of math to come up
with this radius ... because it is so specific ... and so unusual.
Its not a standard coffee-can size ... I don't think.
In fiddling with the numbers, I came up with this ... using a very
Hubbard-ish approach:
Start from 60Hz.
Take it up a power of two until your in the 2Ghz range.
60 * 2^25 = 2.013266 GHz
That is your standing wave that will appear on the top of your
cylinder.
Ok ... now compute how much distance that is using speed-of-light
equal to 299792458 meters/sec.
I get the value in inches to be 5.862540. The dowels were .125 inches,
so add one half that ... twice ... yielding: 5.98754.
Take the fractional part .98754 and multiply by 16 to get it in 16ths ..
and truncate: 5 15/16 ... viola!!
Better still, I wanted to check this line of reasoning ... so I thought
to myself:
"How did he come up with 14 turns for L1 ... which is clearly the
coil that when combined with 7.8nF ... TUNES a special frequency?"
"So is that special frequency also a power-of-two harmonic of
2.013266 GHz derived above?"
60 Hz * 2^12 = 245760 Hz (well below AM dial).
What value of inductance would be needed to resonate at
245760 Hz if the capacitor is 7.8nF?
Answer: 53.768017 uH (assuming AIR-COIL)
Now the question is...
"How many turns on a coil form that has diameter 5 15/16 would
be needed of 28 AWG wire to achieve 53.768017 uH?"
Hendershot would have had the Wheeler forumla if he looked
that up in some Radio Engineer book.
Solving for N (number of turns), given:
L = 53.768uH, D = 5.9375 in, H approx .33 inch (a guess)
results in
***** 14 turns *****
which is the correct answer!!!
This is either an amazing coincidence ... or the very math
Hendershot used.
Caveat: The Wheeler formula is only accurate for when
H > .4 * D which is NOT the case above. This cylinder coil
has a height far too small for that formula to predict accurately
the inductance. However, I'm not bothered by that too much
because Hendershot was interviewed and stated that
sometimes he needed to REMOVE wire since he wrapped
the coil (presumably this last coil L1) ... with too much wire.
So that little TWEAK to get it working might be a clue
that this last coil requires a bit of guess work due
to the inaccuracy of the Wheeler formula.
If all of the above math is correct and was used ... then
Hendershot derived his coil dimensions in a similar way to how
Hubbard did it.
Certainly they would have the Wheeler formula in common...
but the bit about a standing wave across the top of the cylinder
is a very ANTENNA-like calculation ... not normally done for coils ...
except for perhaps TESLA COILS!!!.
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