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Wave Propagation

Antenna Theory Parameters

Special Antennas

✖Reflection Height refers to the effective altitude at which an electromagnetic wave is reflected or refracted by the ionosphere during long-distance radio propagation.ⓘ Reflection Height [h_ref]			+10% -10%
✖Maximum Usable frequency is the highest radio frequency that can be used for transmission between two points via reflection from the ionosphere.ⓘ Maximum Usable Frequency [F_muf]			+10% -10%
✖Critical frequency is the highest magnitude of frequency above which the waves penetrate the ionosphere and below which the waves are reflected back from the ionosphere.ⓘ Critical Frequency [f_c]			+10% -10%

✖Skip distance is defined as the distance b/w transmitting antenna and a point where that wave is first received after reflection from ionosphere.ⓘ Skip Distance [P_d]

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Formula

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Skip Distance

Formula

`"P"_{"d"} = 2*"h"_{"ref"}*sqrt(("F"_{"muf"}/"f"_{"c"})^2-1)`

Example

`"21714.28m"=2*"1170m"*sqrt(("420Hz"/"45Hz")^2-1)`

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Skip Distance Solution

STEP 0: Pre-Calculation Summary

Formula Used

Skip Distance = 2*Reflection Height*sqrt((Maximum Usable Frequency/Critical Frequency)^2-1)
P_d = 2*h_ref*sqrt((F_muf/f_c)^2-1)
This formula uses 1 Functions, 4 Variables

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Skip Distance - (Measured in Meter) - Skip distance is defined as the distance b/w transmitting antenna and a point where that wave is first received after reflection from ionosphere.
Reflection Height - (Measured in Meter) - Reflection Height refers to the effective altitude at which an electromagnetic wave is reflected or refracted by the ionosphere during long-distance radio propagation.
Maximum Usable Frequency - (Measured in Hertz) - Maximum Usable frequency is the highest radio frequency that can be used for transmission between two points via reflection from the ionosphere.
Critical Frequency - (Measured in Hertz) - Critical frequency is the highest magnitude of frequency above which the waves penetrate the ionosphere and below which the waves are reflected back from the ionosphere.

STEP 1: Convert Input(s) to Base Unit

Reflection Height: 1170 Meter --> 1170 Meter No Conversion Required
Maximum Usable Frequency: 420 Hertz --> 420 Hertz No Conversion Required
Critical Frequency: 45 Hertz --> 45 Hertz No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

P_d = 2*h_ref*sqrt((F_muf/f_c)^2-1) --> 2*1170*sqrt((420/45)^2-1)

Evaluating ... ...

P_d = 21714.2810150371

STEP 3: Convert Result to Output's Unit

21714.2810150371 Meter --> No Conversion Required

FINAL ANSWER

21714.2810150371 ≈ 21714.28 Meter <-- Skip Distance

(Calculation completed in 00.004 seconds)

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< 16 Wave Propagation Calculators

Field Strength of Space Wave

Go Field Strength = (4*pi*Electric Field*Height of Receiving Antenna*Height of Transmitting Antenna)/(Wavelength*Antenna Distance^2)

Skin Depth or Depth of Penetration

Go Skin Depth = 1/Conductivity of Antenna*sqrt(pi*Relative Permeability*[Permeability-vacuum]*Frequency of Conductor Loop)

Phase Difference between Radio Waves

Go Phase Difference = 4*pi*Height of Receiving Antenna*Height of Transmitting Antenna/(Antenna Distance*Wavelength)

Height of Layer

Go Ionospheric Layer Height = Skip Distance/(2*sqrt((Maximum Usable Frequency^2/Critical Frequency^2)-1))

Maximum Usable Frequency

Go Maximum Usable Frequency = Critical Frequency*sqrt(1+(Skip Distance/(2*Ionospheric Layer Height))^2)

Propagation Distance

Go Skip Distance = 2*Ionospheric Layer Height*sqrt((Maximum Usable Frequency^2/Critical Frequency^2)-1)

Line of Sight

Go Line of Sight = 3577*(sqrt(Height of Receiving Antenna)+sqrt(Height of Transmitting Antenna))

Skip Distance

Go Skip Distance = 2*Reflection Height*sqrt((Maximum Usable Frequency/Critical Frequency)^2-1)

Refractive Index of Ionosphere

Go Refractive Index = sqrt(1-((81*Electron Density)/Operating Frequency^2))

Maximum Usable Frequency in F-region

Go Maximum Usable Frequency = Critical Frequency/cos(Angle of Incidence)

Normal of Reflecting Plane

Go Normal of Reflecting Plane = Wavelength/cos(Theta)

Wavelength of Plane

Go Wavelength = Normal of Reflecting Plane*cos(Theta)

Parallel of Reflecting Plane

Go Parallel of Reflecting = Wavelength/sin(Theta)

Electron Density

Go Electron Density = ((1-Refractive Index^2)*Operating Frequency^2)/81

Critical Frequency of Ionosphere

Go Critical Frequency of Ionosphere = 9*sqrt(Electron Density)

Antenna Beamwidth

Go Antenna Beamwidth = (70*Wavelength)/Antenna Diameter

Skip Distance Formula

Skip Distance = 2*Reflection Height*sqrt((Maximum Usable Frequency/Critical Frequency)^2-1)
P_d = 2*h_ref*sqrt((F_muf/f_c)^2-1)

How is Skip distance generated?

Radio waves from a particular transmitting antenna do not all get refracted by a particular layer of the ionosphere; some are absorbed, some refracted while a portion escapes to the next layer. At this higher layer, there is a possibility of this radio wave being bent downwards to earth again. This bending happens because each layer of the ionosphere has a refractive index that varies from that of the others.Because of the differing heights of refraction, or apparent reflection, the radio waves hit the earth surface at different points hence generating the skip distance.

When is the value of skip distance reaches its peak?

Skip distance is greatest during the night when the ionosphere is the highest because it differs from suns presence or absence.

How to Calculate Skip Distance?

Skip Distance calculator uses Skip Distance = 2*Reflection Height*sqrt((Maximum Usable Frequency/Critical Frequency)^2-1) to calculate the Skip Distance, The Skip Distance is defined as the minimum distance between the earth’s surface and the radio signal’s transmission point. Skip Distance is denoted by P_d symbol.

How to calculate Skip Distance using this online calculator? To use this online calculator for Skip Distance, enter Reflection Height (h_ref), Maximum Usable Frequency (F_muf) & Critical Frequency (f_c) and hit the calculate button. Here is how the Skip Distance calculation can be explained with given input values -> 21714.28 = 2*1170*sqrt((420/45)^2-1).

FAQ

What is Skip Distance?

The Skip Distance is defined as the minimum distance between the earth’s surface and the radio signal’s transmission point and is represented as P_d = 2*h_ref*sqrt((F_muf/f_c)^2-1) or Skip Distance = 2*Reflection Height*sqrt((Maximum Usable Frequency/Critical Frequency)^2-1). Reflection Height refers to the effective altitude at which an electromagnetic wave is reflected or refracted by the ionosphere during long-distance radio propagation, Maximum Usable frequency is the highest radio frequency that can be used for transmission between two points via reflection from the ionosphere & Critical frequency is the highest magnitude of frequency above which the waves penetrate the ionosphere and below which the waves are reflected back from the ionosphere.

How to calculate Skip Distance?

The Skip Distance is defined as the minimum distance between the earth’s surface and the radio signal’s transmission point is calculated using Skip Distance = 2*Reflection Height*sqrt((Maximum Usable Frequency/Critical Frequency)^2-1). To calculate Skip Distance, you need Reflection Height (h_ref), Maximum Usable Frequency (F_muf) & Critical Frequency (f_c). With our tool, you need to enter the respective value for Reflection Height, Maximum Usable Frequency & Critical Frequency and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Skip Distance?

In this formula, Skip Distance uses Reflection Height, Maximum Usable Frequency & Critical Frequency. We can use 1 other way(s) to calculate the same, which is/are as follows -

Skip Distance = 2*Ionospheric Layer Height*sqrt((Maximum Usable Frequency^2/Critical Frequency^2)-1)

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