Difference between revisions of "Radiolocation errors because of velocity variations"

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  | isbn    = ISBN 9781560801153
 
  | isbn    = ISBN 9781560801153
 
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== Problem ==
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== Problem 7.1 ==
 
Ground conductivity affects radio-wave velocity because of currents induced in the earth. Range calculations assuming that travel is over normal seawater thus may be in error if this is not true. What errors are involved for travelpaths over the terrains in Table 7.1a?
 
Ground conductivity affects radio-wave velocity because of currents induced in the earth. Range calculations assuming that travel is over normal seawater thus may be in error if this is not true. What errors are involved for travelpaths over the terrains in Table 7.1a?
  

Latest revision as of 15:36, 8 November 2019

Problem 7.1

Ground conductivity affects radio-wave velocity because of currents induced in the earth. Range calculations assuming that travel is over normal seawater thus may be in error if this is not true. What errors are involved for travelpaths over the terrains in Table 7.1a?

Table 7.1a. Radio-wave velocities over various terrains.
Terrain Velocity (km/s)
Seawater 299 670
Freshwater 299 250
Farmland 299 400
Dry sand 299 900
Mountains 298 800

Background

Radio-navigation methods are used to determine distances in marine surveys and the velocity is generally assumed to be that over saltwater.

Solution

Let Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle V_{S}} be velocity over normal seawater and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle V_{T}} velocity over other terrains. If we use Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle V_{S}} to calculate ranges, the error in range calculations will be Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \Delta x=t\left(V_{S} -V_{T} \right)} and the relative error is Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \Delta x/x=1000\left(1-V_{T} /V_{S} \right)} m/km. When Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle V_{T} <V_{S}} , the error will be positive, meaning that the calculated range is too great. The results are shown in Table 7.1b.

Table 7.1b. Location errors for various terrains.
Terrain Velocity (km/s) Error (m/km)
Seawater 299 670 0.0
Freshwater 299 250 1.4
Farmland 299 400 0.9
Dry sand 299 900 –0.8
Mountains 298 800 2.9

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