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Application of Space to the Electric Dimensional Relations
Application of Space to the Electric Dimensional Relations
In order to gain an understanding of the electric field of induction a concept of the distribution of this induction in the dimension of space must be developed. An example is a 200 mile long power line. It has a span of 600 feet between towers. This is a 230 kilovolt, 60 cycle/sec, 3 phase line. It can be shown that for each span of line between supporting structures there exist an electro-motive force, E, in Volts, this in series along this span, and a displacement current, I, in Amperes, this in shunt along this span. The series E.M.F., and the shunt displacement of each span compound with each successive span. The total E.M.F. and total displacement for the entire length, 200 miles, of the line is found by integrating over the total number of spans. However, this integrated value is not given by the simple addition of the individual E.M.F.s and displacements developed by each of the individual spans. Here we find an exponential function of space determines the relation between the individual values, and the total values of E.M.F. and displacement. These considerations are developed by Carl P. Steinmetz in his “Theory and Calculation of Transient Electric Phenomena” book, in particular the chapter on “Transients in Space.”
The general problem of the representation in space is given by the introductory part of “Transients in Space” and also by Ernst Guillimen in the introductory chapters in his “Communications Networks” vol. 2. Read these, they are a most important study. These writings form the basis for the theories of electrical engineering utilized today.
The metrical dimension of space is most often considered as a VOLUME, this representing an enclosed quantity of space. This space is filled with something substansive, often which must be paid for, such as a gallon of milk. The milk is the substantial dimension, the “throw away” gallon container is the metrical dimension. In general, this volume of space is considered a cubic quantity, or boundary, this such as a cubic foot, cubic yard, cubic centimetre, and etc. It is habitual to express a volume in cubic terms, this in three mutually perpendicular co-ordinates, wrongly called “dimensions.” It is also habitual to express electric relations in the same manner, a corner of a cube, such as Psi, Phi, and Q. This now is three dimensional, a 3D relation, since Psi, Phi, and Q are dimensions. The cubic relation itself has no substansive dimensions, it is only the metrical dimension of space expressed by a group of three mutually perpendicular co-ordinates. This is important.
It is given here that a one centimetre cube is the elemental unit of the dimension of space, a volume of one cubic cm. This is about the size of a common sugar cube, but instead of sugar, this cube is filled with electric induction. It is a cube of electricity. What exists outside the boundaries of this cube is for now unknown, it is excluded by the boundaries. For most of the examples that follow, all space is filled with 10-C transformer oil, the dielectric. All boundaries enclosing, or dividing, this space are sheet copper, the metallic. Here given is the metallic-dielectric geometry, such as a power transformer, or a static condenser, two fundamental apparatus in electrical work.
In the case of the 200 mile long A.C. power line the basic element of space is the span. This is first order space. Here it is given as per 600 feet, this now a unit value. It now equals one, one span. This unit value is known as a differential element, it is indivisible, the smallest “line on the ruler.” It relates to the Newton-Leibnitz concept of the infinitesimal.
It is considered that cubic, or third order space, is the most general expression of space, a metrical dimension. Since the ordinary transformers and condensers utilized in power engineering are of considerable volume, it is then allowable to consider one cubic cm. as a differential element, that is, an infinitesimal quantity if space. Taking the, one cubic cm. of space, as a unit value, gives the differential element of the metrical dimension of space. It is hereby about the size of a sugar cube, but filled with 10-C oil. Hence the VOLUME is given as ONE cubic cm., the AREA as ONE square cm., the DISTANCE as ONE cm., the SPAN as ONE per cm., the DENSITY as ONE per square cm., and the CONCENTRATION as ONE per cubic cm., all faces, corners, spacings, and etc. of this unit cube are ONE. Hence our differential, indivisible, element of the metrical dimension of space. All orders, or powers, of this space equals one, one squared is one, one cubed is one, and etc. All are one.
This may just as well have been a cubic yard, or a cubic nanometre. The consideration of “unit value” is to reduce the size to the point to which there is no distinguishable variation of the substansive dimension with respect to the unit of the metrical dimension of space. It is then a space scalar condition, no variation in space. For example, consider the 200 mile long A.C. power line. It has a propagation velocity very near that of light. For a frequency of 60 cycles per second, this gives the wavelength as 2880 miles in length. The total distance of this line is 200 miles, this a significant fraction of a quarter wave or an impedance to admittance transformation. However the per 600 feet of a span is an infinitesimal fraction of the quarter wave distance. Hence the distance between towers, the spans, serve as the differential element. It is then 600 feet is of unit value, indivisible. There are no intervening towers.
No perceptible variation of the series E.M.F., E in Volts, or the shunt displacement, I in Amperes, exist along this 600 foot span of A.C. power line. Hereby it is said the E.M.F. per span, or the displacement per span. In the general case it is given as Volts per span and Amperes per span. These dimensional relations represent the voltage gradient and current gradient along the length of line. Dimensionally it is;
1) Volts per cm.
2) Ampere per cm.
It should be noted that this pair of gradients exist in space quadrature to the previous given gradients, the dielectric gradient, d, and the magnetic gradient, m. This is a fundamental relation in electro-magnetic induction and its propagation.
It can be seen that each span has a back E.M.F. in series with the power flow, and a displacement, or charging, current in shunt with the power flow. These are a consequence of the electric field of induction in a time rate of variation, the 60 cycle, or 377 radians per second. These are transmission impairments and give rise to a delay in propagation which progressively compounds down the line, from span to span. These differential elements, or spans, must be summed up, or INTEGRATED, in order to determine the total E.M.F., total displacement, and the total delay in propagation. This is not so easy of a task. Now for higher orders of space the situation is that order more difficult.
In the application of the metrical dimension of space to the substantial dimensions of electricity, the concept of magnetic inductance, and electro-static capacity, are utilized. Steinmetz, in his “Impulses, Waves, and Discharges”, established the inductance and the capacitance as the “Energy Storage” coefficients of the electric field of induction. It must be noted that here the term ELECTRIC FIELD is NOT the “electro-static” field, it is the union of the dielectric and magnetic fields of induction. Erase the “electric field” wording of the one wing parrot. These two distinct dimensional relations, the INDUCTANCE and the CAPACITANCE serve to define the ability of bounded to contain the electric field of induction, this field representing STORED ENERGY.
What follows here is the development of the properties related to the dielectric and magnetic fields and the interaction of these with the bounding metallic-dielectric geometry. Considerations involving energy will be arrived at later on. In this view inductance and capacitance now represent GEOMETRIC CO-EFFICIENTS, expressing the relation of the BOUNDING GEOMETRY with the fields of induction which it bounds. In essence inductance and capacitance are of a scalar form. Here enters the concepts of what is known as “radionics.” The inductance and capacitance each exist in distinction to the electricity itself. The inductance and capacitance ultimately serve as geometric expressions. This is important. Hereby they can be expressed as completely metrical dimensional relations, that is, having no substansive dimension.
We have of yet actually given the dimensional relations which make up inductance and capacitance. Further considerations involving the electric field have yet to be understood. Break, more to follow…
DE N6KPH
Application of Space to the Electric Dimensional Relations
In order to gain an understanding of the electric field of induction a concept of the distribution of this induction in the dimension of space must be developed. An example is a 200 mile long power line. It has a span of 600 feet between towers. This is a 230 kilovolt, 60 cycle/sec, 3 phase line. It can be shown that for each span of line between supporting structures there exist an electro-motive force, E, in Volts, this in series along this span, and a displacement current, I, in Amperes, this in shunt along this span. The series E.M.F., and the shunt displacement of each span compound with each successive span. The total E.M.F. and total displacement for the entire length, 200 miles, of the line is found by integrating over the total number of spans. However, this integrated value is not given by the simple addition of the individual E.M.F.s and displacements developed by each of the individual spans. Here we find an exponential function of space determines the relation between the individual values, and the total values of E.M.F. and displacement. These considerations are developed by Carl P. Steinmetz in his “Theory and Calculation of Transient Electric Phenomena” book, in particular the chapter on “Transients in Space.”
The general problem of the representation in space is given by the introductory part of “Transients in Space” and also by Ernst Guillimen in the introductory chapters in his “Communications Networks” vol. 2. Read these, they are a most important study. These writings form the basis for the theories of electrical engineering utilized today.
The metrical dimension of space is most often considered as a VOLUME, this representing an enclosed quantity of space. This space is filled with something substansive, often which must be paid for, such as a gallon of milk. The milk is the substantial dimension, the “throw away” gallon container is the metrical dimension. In general, this volume of space is considered a cubic quantity, or boundary, this such as a cubic foot, cubic yard, cubic centimetre, and etc. It is habitual to express a volume in cubic terms, this in three mutually perpendicular co-ordinates, wrongly called “dimensions.” It is also habitual to express electric relations in the same manner, a corner of a cube, such as Psi, Phi, and Q. This now is three dimensional, a 3D relation, since Psi, Phi, and Q are dimensions. The cubic relation itself has no substansive dimensions, it is only the metrical dimension of space expressed by a group of three mutually perpendicular co-ordinates. This is important.
It is given here that a one centimetre cube is the elemental unit of the dimension of space, a volume of one cubic cm. This is about the size of a common sugar cube, but instead of sugar, this cube is filled with electric induction. It is a cube of electricity. What exists outside the boundaries of this cube is for now unknown, it is excluded by the boundaries. For most of the examples that follow, all space is filled with 10-C transformer oil, the dielectric. All boundaries enclosing, or dividing, this space are sheet copper, the metallic. Here given is the metallic-dielectric geometry, such as a power transformer, or a static condenser, two fundamental apparatus in electrical work.
In the case of the 200 mile long A.C. power line the basic element of space is the span. This is first order space. Here it is given as per 600 feet, this now a unit value. It now equals one, one span. This unit value is known as a differential element, it is indivisible, the smallest “line on the ruler.” It relates to the Newton-Leibnitz concept of the infinitesimal.
It is considered that cubic, or third order space, is the most general expression of space, a metrical dimension. Since the ordinary transformers and condensers utilized in power engineering are of considerable volume, it is then allowable to consider one cubic cm. as a differential element, that is, an infinitesimal quantity if space. Taking the, one cubic cm. of space, as a unit value, gives the differential element of the metrical dimension of space. It is hereby about the size of a sugar cube, but filled with 10-C oil. Hence the VOLUME is given as ONE cubic cm., the AREA as ONE square cm., the DISTANCE as ONE cm., the SPAN as ONE per cm., the DENSITY as ONE per square cm., and the CONCENTRATION as ONE per cubic cm., all faces, corners, spacings, and etc. of this unit cube are ONE. Hence our differential, indivisible, element of the metrical dimension of space. All orders, or powers, of this space equals one, one squared is one, one cubed is one, and etc. All are one.
This may just as well have been a cubic yard, or a cubic nanometre. The consideration of “unit value” is to reduce the size to the point to which there is no distinguishable variation of the substansive dimension with respect to the unit of the metrical dimension of space. It is then a space scalar condition, no variation in space. For example, consider the 200 mile long A.C. power line. It has a propagation velocity very near that of light. For a frequency of 60 cycles per second, this gives the wavelength as 2880 miles in length. The total distance of this line is 200 miles, this a significant fraction of a quarter wave or an impedance to admittance transformation. However the per 600 feet of a span is an infinitesimal fraction of the quarter wave distance. Hence the distance between towers, the spans, serve as the differential element. It is then 600 feet is of unit value, indivisible. There are no intervening towers.
No perceptible variation of the series E.M.F., E in Volts, or the shunt displacement, I in Amperes, exist along this 600 foot span of A.C. power line. Hereby it is said the E.M.F. per span, or the displacement per span. In the general case it is given as Volts per span and Amperes per span. These dimensional relations represent the voltage gradient and current gradient along the length of line. Dimensionally it is;
1) Volts per cm.
2) Ampere per cm.
It should be noted that this pair of gradients exist in space quadrature to the previous given gradients, the dielectric gradient, d, and the magnetic gradient, m. This is a fundamental relation in electro-magnetic induction and its propagation.
It can be seen that each span has a back E.M.F. in series with the power flow, and a displacement, or charging, current in shunt with the power flow. These are a consequence of the electric field of induction in a time rate of variation, the 60 cycle, or 377 radians per second. These are transmission impairments and give rise to a delay in propagation which progressively compounds down the line, from span to span. These differential elements, or spans, must be summed up, or INTEGRATED, in order to determine the total E.M.F., total displacement, and the total delay in propagation. This is not so easy of a task. Now for higher orders of space the situation is that order more difficult.
In the application of the metrical dimension of space to the substantial dimensions of electricity, the concept of magnetic inductance, and electro-static capacity, are utilized. Steinmetz, in his “Impulses, Waves, and Discharges”, established the inductance and the capacitance as the “Energy Storage” coefficients of the electric field of induction. It must be noted that here the term ELECTRIC FIELD is NOT the “electro-static” field, it is the union of the dielectric and magnetic fields of induction. Erase the “electric field” wording of the one wing parrot. These two distinct dimensional relations, the INDUCTANCE and the CAPACITANCE serve to define the ability of bounded to contain the electric field of induction, this field representing STORED ENERGY.
What follows here is the development of the properties related to the dielectric and magnetic fields and the interaction of these with the bounding metallic-dielectric geometry. Considerations involving energy will be arrived at later on. In this view inductance and capacitance now represent GEOMETRIC CO-EFFICIENTS, expressing the relation of the BOUNDING GEOMETRY with the fields of induction which it bounds. In essence inductance and capacitance are of a scalar form. Here enters the concepts of what is known as “radionics.” The inductance and capacitance each exist in distinction to the electricity itself. The inductance and capacitance ultimately serve as geometric expressions. This is important. Hereby they can be expressed as completely metrical dimensional relations, that is, having no substansive dimension.
We have of yet actually given the dimensional relations which make up inductance and capacitance. Further considerations involving the electric field have yet to be understood. Break, more to follow…
DE N6KPH
thats okay we tolerate bothers with an attitude but only for so long hope he works with the open source community soon
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