Difference between revisions of "Effect of station angle on location errors"

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  | isbn    = ISBN 9781560801153
 
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== Problem ==
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== Problem 7.2 ==
 
If the error in Shoran time measurements is <math>\pm 0.1 \mu s</math>, what is the the size of the parallelogram of error in Figure 7.2a when (a) <math>\theta=30^{\circ}</math> and (b) <math>\theta=150^{\circ}</math>? Take the velocity of radio waves as <math>3\times 10^{5}</math> km/s.
 
If the error in Shoran time measurements is <math>\pm 0.1 \mu s</math>, what is the the size of the parallelogram of error in Figure 7.2a when (a) <math>\theta=30^{\circ}</math> and (b) <math>\theta=150^{\circ}</math>? Take the velocity of radio waves as <math>3\times 10^{5}</math> km/s.
  

Latest revision as of 15:36, 8 November 2019

Problem 7.2

If the error in Shoran time measurements is , what is the the size of the parallelogram of error in Figure 7.2a when (a) and (b) ? Take the velocity of radio waves as km/s.

Background

Shoran is a radio-navigation device which measures the 2-way traveltime between the point of observation and a fixed station. Using two fixed stations, the point of observation can be located by swinging arcs centered at the two stations; for large distances the arcs become nearly straight lines.

The traveltimes are subject to error , so the ranges are , , 2. Swinging the four arcs corresponding to these time values, we get a parallelogram of error such as that in Figure 7.2a; the location lies somewhere inside this parallelogram.

Solution

In Figure 7.2a, the error in range

Figure 7.2a  Parallelogram of error for traveltime uncertainty of

.

The long diagonal m.

The short diagonal m.

To get the figure for we merely reverse the arrow on or ; therefore the error values are the same as for .

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