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A short class with Sarah and her students. The other ways are under More.
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Today we are discussing the essential observations before we compute the coordinates of traverse stations. Can anyone tell me what kind of measurements we need?
We need the magnetic bearing of at least one traverse line.
Exactly, that is important for calculating the direction. We also need the length of at least one line. Can anyone else list another observation?
Elevation of one traverse station?
Correct! Elevation helps us account for vertical differences which is essential. Now, can someone summarize the rest of the necessary observations?
We also need the included angles between traverse lines, vertical angles, and real-world coordinates of one station.
Great job! These observations help ensure the accuracy of our coordinates. Remember this acronym: MEVIR—Magnetic, Elevation, Vertical angles, Included angles, Real-world!
That's a useful way to remember everything!
Exactly. Now, let’s take a quick recap—what do we need to observe before proceeding with the computations?
Magnetic bearing, length, elevation, included angles, vertical angles, real-world coordinates!
Now that we've gathered our observations, let’s discuss how to calculate latitude and departure. Who can define what latitude is in this context?
Latitude refers to the northward measurement from the y-axis?
Precisely! And how about departure?
Departure is the eastward measurement?
Right again! Now, can anyone tell me the formulas to calculate these?
Latitude is calculated as Length multiplied by the cosine of the reduced bearing, and departure is Length multiplied by the sine of the reduced bearing.
Wonderful! Let's reinforce this with a mnemonic: LCRD—Length, Cosine for Latitude, and Sine for Departure. Can you think of a scenario where these calculations might differ?
If we’re working with lines going in different directions, right?
Yes! Now let’s summarize what we've learned today regarding latitude and departure calculations.
Let’s dive into the adjustments needed for traverse computations. Why do we need to make these adjustments?
To ensure our measurements are accurate?
Exactly! Errors can arise in our linear and angular observations. What are some specific adjustments we might make?
Adjustments of angular errors and bearings?
Yes! It's crucial that the sum of angles equals the expected sum. Can someone tell me how we might handle bearing adjustments?
We check the difference between the fore and back bearings?
Precisely right! Adjustments can be made if their difference is not 180 degrees. What should we remember about the sum of latitudes and departures in a closed traverse?
They should equal zero?
Well done! Always ensure you verify these principles to achieve accurate computations. Let's recap our discussion on adjustments.
If a traverse line measures 100 meters with a reduced bearing of 45 degrees, the latitude would be 100 * cos(45°) = 70.71 meters, and the departure would be 100 * sin(45°) = 70.71 meters.
In a closed traverse, if the calculated sum of interior angles yields an angle total differing from the expected sum, adjustments must be made to correct this discrepancy.
For bearings you must find, a magnetic line combined; add lengths, to know your way, latitude will save the day!
In a land of measurements, the clever surveyors laid out a vast plan. They started their journey at the magnetic north, checking their lengths by the sun's warm hearth. As they ventured forth, they took notes—‘Latitude here, departure there,’ they would boast. But oh, errors lurked in angles, they knew; thus, adjusting and correcting, their map grew!
MEVIR helps you recall: Magnetic, Elevation, Vertical angles, Included, Real-world.
LCRD for Latitude and Departure: Length, Cosine, and Sine, Remember and always be fine!
Term
What do we need to establish before computing coordinates?
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Term
How do you calculate latitude?
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The direction or path along which something moves or along which it lies, measured in relation to magnetic north.
The northward projection of a line measured from the y-axis in traverse calculations.
The eastward projection of a line measured from the y-axis in traverse calculations.
A series of connected lines for surveying purposes that capture the geographical layout of a terrain.
This section discusses the process of computing the coordinates of traverse stations after completing field observations.
In this section, the methodology for calculating the coordinates of traverse stations is detailed, including the necessary field observations and the techniques used to end up with accurate latitude and departure values. The adjustments for errors encountered in traverse computations are also explained.
This section outlines the method for computing the coordinates of traverse stations essential for mapping areas in surveying. To ensure accurate calculations, several key observations must be made in the field:
Once data from the field is collected, the coordinates can be plotted on a plan relative to the x-axis and y-axis. For any line whose length and bearing are known, its projections (latitude and departure) can be calculated. Latitude is defined as the northward projection, while departure extends eastward, and they are calculated as follows:
The reduced bearing dictates the sign of both latitude and departure, essential for accuracy in geometric computations. Lastly, the traversal adjustments are discussed; ensuring that errors in both linear and angular measurements are corrected and that the computed coordinates accurately reflect the desired locations.