I made the following post to the Pupman Tesla Coil mailing list on March 8, 2018:

If you want a truly fascinating coil design with groundbreaking potential, try building a magnifier with three tertiary coils on a common grounded frame. From my decades of studying Tesla literature, this is how Tesla built the flying triangle, which we black projects have since perfected. In the 1990s, there was more Tesla information on the Internet and BBS forums, which has since disappeared. One such report was of Tesla having built a model flying triangle configuration in his lab.
 
There is one primary and secondary coil, which drives three tertiary coils. All are grounded to a single aluminum frame, which is not in contact with Earth's ground. The tertiary coils are each 1/3 out of phase with each other and have variable inductance or variable capacitance to adjust the resonance finely.
 
The three tertiary coils develop a rotating magnetic field around the entire coil setup, creating a space bubble. The space in this macro rotating magnetic field becomes gravitationally separated from the space around it. By changing the characteristics of the rotating magnetic field space bubble, you can build a free-moving vehicle that can navigate through space with reduced gravitational influence from the Earth. The orientation of the tertiary coils concerning the Earth's ground plane keeps the system from tumbling. With the tertiary coils perpendicular to the Earth's ground plane, the rotating magnetic field orientation will also have an axis perpendicular to the Earth's ground plane.
 
I believe Tesla's first model was an open frame. The rotating magnetic field space bubble will exist whether the frame is open or completely enclosed around the Tesla coil system. However, a closed frame system should be more stable, as the conductive frame will give the rotating magnetic field space bubble a more reliable structure.
 
I have been planning this for years but have not yet put it together. The key component of this system will be the design of the tertiary coils to be in 1/3 phase with each other and have a controllable variable inductance or controllable variable capacitance with just the right range of adjustment. 
 
I followed up with the following comment:
 
Thanks, Jim, for the link to Antonio's work. This just clarified for me how the three tertiary coils should be tuned. A tertiary coil would be way out of tune with the resonating primary and secondary power supply if tuned to 1/3 wavelength. Instead, there should be three quarter-wave steps and a missing step, such that the tertiary coils would fire X-X-X-O, or 1/4, 1/2, 3/4, 0. This makes sense since a magnetic field, whether rotating or not, is asymmetrical. 
 
And more than just the magnetic field is at play here. Tertiary coils act strongly on the electrostatic field and the magnetic field. They are pushing electrons and ions. When three tertiary coils are mounted to a common ground and tuned to produce maximum potential in succession, they will push the ions circularly and perpendicular to the axis of the frame. This is what creates a rotating magnetic field plasma. The plasma will likely be double-layered, with negative ions moving in one direction and positive ions moving in the opposite direction.
 
The resulting plasma is the space bubble that surrounds the frame and coils. Naturally, tuning aims to minimize streamer production and keep as much energy as possible within the system.
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doublecoilnew01

bipolarcone01

The above pictures are of a double-coned coil I acquired on eBay. The seller purchased it from the estate of a deceased FBI agent.  One of the bidders, who owns a similar coil without wires, informed me that it was designed by Nikola Tesla himself. The wooden frame he owns was given to his father by Nikola Tesla as payment (Tesla had no money at the time). 

Each cone is 6" in diameter and 6" in height.  Each cone has approx—127 ft of wire.  The end-to-end inductance of the secondary is 2.36mH.  The quarter wavelength frequency calculates to 1.937MHz for a straight solenoid, but this coil resonates at about 1.12MHz as determined by a frequency counter and oscilloscope. 

The two cones are connected in the middle such that the entire length is one wire.  There is no tapping point between the two coils.  Due to age and wear, I had to replace the copper primary, but I am keeping the old copper tubing to verify the coil's age.  This coil was likely built in the early 1900s and is identical in layout to Tesla's patent schematics from the late 1890s. 

Rumor has it that this coil exhibits antigravity properties.  I have not seen antigravity effects when applying a standard spark gap discharge to the primary.

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Frequency 

Angular frequency is a cycle of repetition and refers to the angles covered by a frequency.   Thus angular frequency is equal to:

APM MO1

A bicycle wheel turning at five cycles per second will scan an angle of 10π radians per second.  Angular frequency is in units of radians per second.  

When a cycle completes, it does so in a given period of time.  The period of time to complete a cycle is the reciprocal of the frequency:

APM MO2

A bicycle wheel turning at five cycles per second will have a period of 1/5 second.  Or in other words, the time it takes to turn the wheel once at five cycles per second will be 1/5 second.

Not all cycles are stationary and go in circles.  Quite often, a cycle is associated with a velocity.  As a bicycle wheel turns and completes one cycle, the bike rider will travel a distance.  This distance is called the "wavelength" when applied to photons.  The distance the bicycle rider will travel will depend on its velocity per frequency:

APM MO3

So if the rider travels five feet per second, and the wheel turns at five cycles per second, then the rider has traveled one foot (the bicycle would be very small!).  

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David Thomson's Coil Formula

As is explained in the Aether Physics Model, Coulomb's constant is equal to:

\(k_{C} = \frac{c \cdot Cd \cdot \mu_{0}}{\epsilon_{0}}\)

From this, inductance can be defined as:

induct2(1.2)

In equation (1.2) 1 meter equals 1 Henry.  .003 meter equals 3 mH, and so on.  The relationship of length to inductance is clearly shown by Coulomb's constant.  Wheeler's formula (for the inductance of an air core solenoid coil) outputs inductance in thousand inches. 

induct4(1.3)

where N is the number of turns, R is the radius in inches, and H is the length of windings in inches.

Equation (1.3) outputs in length, just what Coulomb's constant formula requires.  So if the units of Wheeler's formula are converted to meters and the two formulas are combined, then:

induct5(1.4)

And this can be simplified to:

induct6(1.5)

The values and units generated in equation (1.5) are accurate to the same degree as Wheeler's formula for inductance since it incorporates Wheeler's formula unchanged.  The exact value of Cd is equal to:

induct7(1.6)

the values are Coulomb's constant, light speed, permeability, and permittivity.

A practical simplification of the formula (1.5) is:

induct8(1.7)

where the value N is a number, R and H are in inches, and the result is in Henry.

If you use MathCAD or another program, which automatically converts inches to meters, then use equation (1.8):

induct9(1.8)

If you're looking for an inductance formula where the input is in meters instead of inches, you can use this formula:

induct10(1.9)

Formula (1.9) can be used for solenoid or flat spiral coils.  For flat spiral coils, use the average R radius and the coil windings width for H.  Both R and H are in meters.  N is the number of turns.

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pulsegraphic02

Pulse Graphic

In the above pulse graphic, two radiating circles expand outward and toward each other and then contract while moving away from each other. The movement scans an area representing the pulse.  Visualize the area between opposing pairs of circles as the surface of an imaginary cylinder (not shown, but inferred.)  The area of the cylinder is equal to the total power of the field in a Tesla coil.

We visualize this mathematically by looking at the electric and magnetic fields of the electromagnetic pulse for the case of a flat spiral coil. 

Electric field strength is

ε = E / d Volts per meter

E is the potential in Volts, and d is the distance between two potentials.  Similarly, the magnetic field strength is -

H = Fm / l   Ampere turns per meter

where l is the length of the field line and magnetomotive force Fm is -

Fm = I × N   Ampere-turns 

The formula for calculating the length of wire in a flat spiral coil is -

l = 2π x Ravg x N

Where l is the length of the wire, Ravg is the average radius of the coil, and N is the number of turns.  Thus

N / l = 1 / (2π x Ravg)

and

H = I / 2π x Ravg

To get the total field power -

Pf = ε x H or

Pf = V x I / 2π x Ravg x d   Watts per cylinder

As inferred in the diagram above, 2π x Ravg x d is a cylinder. 

From this, the nature of longitudinal waves in a flat spiral coil can be understood.  The longitudinal wave is represented by the current and circumference of the radius.  It is clear the longitudinal component of the flat spiral coil remains in the coil at all times.  In actuality, the full length of the flat spiral secondary fills up with a charge, much like a hose fills up with water.  The "crest" of the hose's water wave corresponds with the wave's longitudinal "head."  Each time the head of the wave makes one full circle, it would appear from a radius perspective that a beat had occurred in the expansion of the wave from its center toward the outer winding.

The sum of all circumferences of the radii of the coil (same as the total wire length of the coil)  is what I call the "stroke". 

curr = coulomb2 / sec

stroke = meter / coulomb2

velc = meter / sec

velc = curr x stroke

Where velc is the velocity of the total electron magnetic charge.

As the current flows through the flat spiral coil, the energy of each successive winding adds to the direction of the propagation of the pulse.  This is seen in the pulse model as the x-axis and the units are in meters per second, equal to the current time's stroke.  The potential in a flat spiral coil is not linear.  Just as the magnetic field is equal to current divided by 2π times the average radius, the electric field is equal to potential divided by the vertical distance between two opposite charges.  In a flat spiral coil oriented parallel to the earth's surface, a negative charge builds under the coil, and a positive charge builds above the coil. 

The free distance above and below the coil increases the energy potential and allows the energy to penetrate the permeability of the surrounding space. 

But since the flat spiral coil is a closed system of copper atoms, the charge reaches the end of the wire. Since the charge is practically incompressible, the charge momentum immediately reverses direction and heads for the center of the flat spiral coil.  At the maximum outer windings of the flat spiral coil, the cylinder defined by the total power of the electromagnetic field is spread out. Still, as the coil radius becomes minimum, the cylinder representing the total power would like to expand along the z-axis.  In a flat spiral coil, the z-axis is only one winding high. This causes the power at the center to have a high current and relatively low potential compared to a solenoid coil.

Due to the nature of the expanding cylinder of total field power, it can be seen that a flat spiral coil wound completely to the center of the coil will have the greatest effect on the voltage as the stroke will be the shortest and hence the current will be in its most dense state.  From the point of view of the total power output in the coil, the power will be mostly transferred to potential if the flat spiral coil is wound to the center.  But a flat spiral coil wound completely to the center of itself can only produce a high current rate because there is no distance along the z-axis for the voltage to travel in.  So to effect the most efficient and complete power transfer between current and voltage, a coil must be wound with a flat spiral secondary and tall solenoid secondary connected to each other.  This configuration is the ideal "magnifier" setup Nikola Tesla used in his World Transmitter System.

By placing a coil of a small radius and tall height in the center of the flat spiral coil, the optimum condition for transferring the energy of the declining radius is presented to the charge.  Now as the charge declines in radius and tends to increase in the distance from the coil, the distance of the charge will expand along the tall solenoid, and each successive turn will add to the potential, thus allowing the charge to penetrate the surrounding permeability with great force.

The momentum of the expanding potential is such that it has the force to induce movement into surrounding charged particles electrostatically.  This can cause radio waves. 

Per the Aether Physics Model, the rotational component of the flat spiral coil's current occurs as the head of the charge moves from the center winding to the outer winding and back. There is also a rotational component radiating from the wire's circumference. The solenoid between the top and lower winding further maintains the rotational component.  In effect, the cylinder defined by the total field power rotates as a single unit in one direction when the potential is declining and in the opposite direction when the potential is increasing.  It would follow that in certain cases, a spiral effect would be noticeable in the discharge of the upper solenoid terminal.  Several coilers have noticed such rotational effects.

In Tesla's Wardencliffe magnifier, the frequency of the flat spiral coil was tuned to the earth's resonant frequency.  The solenoid was wound to oscillate at many times the frequency of the earth such that it would generate high potential.  The high potential of the solenoid helped drive the current in the flat spiral coil, just as the current in the flat spiral coil helped drive the solenoid.  The high potential creates a strong electrostatic charge at the top of the coil and away from the ground. When the coil system is slightly detuned, the electrostatic charge oscillates up and down the coil and acts like an electrostatic pump. When the rising and falling electrostatic field equals the Earth's resonant frequency (Schumann resonance), the Earth's electrostatic field comes into resonance. This resonance of the electrostatic field made wireless power transmission possible.

Today, this wireless power transmission scheme is applied to computers, cell phones, and other devices with low power requirements.

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