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Velocity factor is used in communications, computing, electrical, engineering, networking, and applied sciences to define and manage systems that guide and pass through light and electromagnetic waves. Velocity factor helps us to understand how light and electromagnetic waves change speed when passing through a given medium like air, free space (vacuum), metallic conductors, and water. This understanding in turn helps us to make adjustments to systems in order to shorten communications time and to preserve the integrity of those systems so that they will continue to function as intended for as long as they are needed.
Velocity factor is the reciprocal of a refractive index applicable to a given medium. For example, one commonly used velocity factor for the medium of air (an atmospheric) is 0.999707085823853610892, the mathematical reciprocal of refractive index value 1.000293.
Velocity factor [ n-1 ] and refractive index [ n ] are ratios relating to speed of light and electromagnetic waves moving through specified media. As ratios, they have no dimension or unit values. However, the velocity factor ratio can be simplified to decimal form and then it can be read as time. The ratio of velocity factor , which has no unit values, easily converts to velocity of propagation by factoring in the speed of light.
Relative refractive index [ n ] is a ratio that compares velocity through one given medium (v1) to velocity through another (v2). The formula for relative refractive index [ n ] in its basic form is v1 / v2. This characterizes the two mathematically inverse perspectives of the ratios absolute refractive index and velocity factor, which compare the same two velocities from opposite points of view using v1 / v2 and v2 / v1. So, which comes first? Which is (v1) and which is (v2)?
Absolute refractive index [ n ] is a ratio that compares velocity through the medium of free space (vacuum) (c0 or v0) to velocity through a given medium (vm). The formula for absolute refractive index [ n ] in its basic form is c / vm.
Velocity factor [ n-1 ] is a ratio that compares velocity through a given medium (vm) to velocity through the medium of free space (vacuum) (c0 or v0). The formula for velocity factor [ n-1 ] in its basic form is vm / c.
From this perspective, either c0 or v0 will take the place of c in the formula to represent velocity through the medium of free space (vacuum), while the vm in the formula stands to represent velocity through a different medium or through another instance of the same medium of free space from a different observation time. Because velocity and wavelength are directly related by numeric value and set apart by different unit labels, then the numeric value for wavelength directly represents velocity within the earth's atmosphere while also representing distance, or wavelength. This relationship holds true where the velocity constant c is reached and cannot be exceeded, such as in later observation times in the medium of free space (vacuum). When c0 is reached at λ0, velocity can become confusing to follow. At this point, velocity factor [ n-1 ] steps in to represent velocity in free space (vacuum) by marking the time for velocity between points on a scale of seconds, while wavelength λ marks the distance traveled.
Frequency [ f ] is the ratio of absolute refractive index modified to define dimension and unit values. It compares velocity through a given medium (vm) to wavelength in the medium of free space (vacuum) (λ0). Frequency is commonly expressed as cycles per second with the unit Hertz (Hz). It does not change with a given medium having a discrete (single instance, single value) absolute refractive index. The formula for frequency [ f ] in its basic form is vm / λ0 Hz.
Absolute refractive index and velocity factor are defined as one (1.0) or as unity or as 100% at the constant velocity value for the speed of light and electromagnetic waves in free space (vacuum) (c0 or v0) at wavelength λ0 valued at 299,792,458.0 meters. Frequency f0 is likewise defined here as 1.0 Hz. Every medium other than free space (vacuum) will have an absolute refractive index greater than one. Within the earth's atmosphere, values for absolute refractive index are typically greater than unity, but in the medium of free space beyond earth, they are often at or less than unity. This is because one instance of constant velocity (c0) through the medium of free space is compared to itself at different observation times. As a result, these comparisons yield discrete frequencies, refractive indices, times, velocity factors, and wavelengths while the velocity constant goes unchanged. This is treated in similar fashion to relative refractive index.
s = seconds. Period T, or time, measured in seconds and in parts of a second, is an important perspective of velocity factor that highlights how long it takes for an electrical signal, radio communication, or specified wavelength to propagate, or travel, from a starting point to an end point. This is why velocity factor is also called velocity of propagation. For example, with a velocity factor of 1.0, it takes 1.0 s for a wavelength to form across the distance of 299,792,458.0 m, or 299,792.458 km. This example of velocity of propagation just described a fundamental characteristic of the speed of light. In the vacuum of free space beyond earth, the sun shines across the distance of the astronomical unit (au), defined as 149,597,870,700.0 m or as 149,597,870.7 km, to get near to our planet. The velocity factor for this distance is 499.004783836156411913, also known as "light-time for [the astronomical] unit distance." It is defined by the formula au / c. This means that it takes more than 499 s of time or 8.31 minutes or 8 minutes and 19 seconds for sunlight and electromagnetic waves to travel the au in the medium of free space (vacuum).
c0 = the speed of light and electromagnetic waves in free space (vacuum). This particular velocity is a constant valued at 299,792,458 meters per second (m/s or m*s-1). As mentioned earlier, c0 can also be expressed as c or v0 when representing the medium of free space (vacuum) as part of a formula for relative refractive index.
c0 translates to 29.9792458 centimeters per nanosecond (cm/ns or cm*ns-1) and to Tc0 = 3.3356409519815204957557671447492 nanoseconds per meter (ns/m or ns*m-1), and to Tc0 = 1.0167033621639674471063578257196 nanoseconds per foot, giving rise to the term "light foot," shortened from the longer description "light-time for the foot unit distance."
There is a linear mathematical relationship between wavelength and velocity factor that is based on constant velocity (c0 or v0) at the speed of light and electromagnetic waves in free space (vacuum). This means that less time is required for the formation of shorter wavelengths and that more time is required for the formation of longer wavelengths.
As wavelength (λ) decreases, absolute refractive index (n) and frequency (f) increase. As wavelength (λ) decreases, velocity factor and period time in seconds (s) for propagation also decrease in lockstep with it.
As wavelength (λ) increases, absolute refractive index (n) and frequency (f) decrease. As wavelength (λ) increases, velocity factor and period time in seconds (s) for propagation also increase in lockstep with it.
By extension, less travel time is needed for light and electromagnetic waves to propagate across shorter distances and more travel time is required for longer ones. Thus, we come to understand that sunlight travels between 490 and 507 seconds (s) (8 minutes 10 seconds to 8 minutes 27 seconds) to reach Earth along the range of the astronomical unit (au) of distance at 149,597,870.7 kilometers (km), while no less than 2.00138457118891229745 milliseconds (ms) are required for a fiber optic cable measuring only 600 kilometers (km) in length to carry light through it from end to end. These examples illustrate that in the medium of free space beyond earth, typically observed values for velocity factor are at or greater than unity, and that within the earth's atmosphere, such values are often observed to be less than unity.
The ratio of velocity factor, like its alternate expression velocity of propagation, is one of several related perspectives on current flow and the movement of light and electromagnetic waves. The same reciprocal mathematical relationship exists between velocity factor and frequency as does between velocity factor and refractive index.
Velocity factor can be expressed in decimal form to render a simple count of seconds and portions of seconds in time for propagation to travel from start to end along a specified distance or wavelength associated with one medium. A linear mathematical relationship between time, velocity factor, and wavelength demonstrates that shorter wavelengths need less time to form than longer ones. We use these mathematics to compute travel time for propagation of light and electromagnetic waves across any distance, regardless of wave formation, between any two known points.
Absolute refractive index, frequency, and velocity factor converge at unity for free space (vacuum) where frequency f0 equals 1.0 cycle per second (Hz), wavelength λ0 equals 299,792,458.0 meters (m), and velocity constant c0 equals 299,792,458.0 meters per second (m*s-1). Near to earth, we commonly see values for velocity factor at less than unity, but in the medium of free space beyond earth, they are often at or greater than unity.
Frequency, medium, refractive index, time, velocity factor, and wavelength all contribute to our knowledge and understanding of how systems function at the nuts and bolts level to effectively and safely exchange current flow between facilities and the Earth. Successful tweaking of such systems to strengthen the GCP Model is what The Integrated Systems Bonding Project seeks to achieve.
