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A short class with Sarah and her students. The other ways are under More.
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Welcome class! Today, we'll be discussing traverse computations. Can anyone tell me why obtaining precise measurements is crucial in surveying?
It's important so that the map created is accurate!
Exactly, Student_1! We need to accurately gather data like magnetic bearings and elevations.
What kind of measurements are needed for coordinates?
Good question, Student_2! We need observations on magnetic bearings, the length of traverse lines, elevations, included angles, vertical angles, and known coordinates for at least one point.
What does latitude and departure mean?
Great inquiry! Latitude is the northward projection of a traverse line, while departure represents the eastward projection. Remember: Latitude is positive when going north! Let's continue this dialogue next class as well.
Continuing from our last session, who remembers how we calculate latitude?
It's the length of the line multiplied by the cosine of its reduced bearing.
Correct, Student_4! And departure? What do we multiply?
The length multiplied by the sine of its reduced bearing!
Exactly! We can summarize these calculations using L for length and θ for the reduced bearing. Can anyone give me the formulas?
Latitude equals L times cos θ and departure equals L times sin θ!
Well done! This is fundamental for mapping the traverse accurately. Let's keep practicing these calculations.
Today, we cover error adjustments. Why do you think closing errors occur?
They happen because of inaccuracies in measurement!
Exactly right! Angular and closing errors must be adjusted before we take our computations further.
How do we distribute the errors?
Great question, Student_4! Errors can be distributed equally or based on the magnitude of the angles. Which method do you think is more accurate?
The one based on magnitude!
Precisely. Once errors are adjusted, we ensure the sums of latitudes and departures are zero. Remember this concept as it’s crucial, especially for closed traverses!
Let’s discuss Gale's Traverse Table—a valuable tool! Can someone summarize its purpose?
It helps organize our computations for traverses!
Right! The table streams together adjustments and coordinates to avoid confusion. What essential steps are included in the table?
Adjust the included angles, compute latitudes and departures, apply corrections, and find coordinates!
Perfect summary! This systematic approach ensures our computations are neat and clear. Let's practice filling out such tables together.
The calculations required to determine coordinates of traverse stations based on field observations.
Geographical components derived from bearings and measurements, essential for mapping.
Techniques employed to correct inaccuracies in a closed traverse to ensure sum of measurements equals zero.
If a traverse line is 100 m long with a reduced bearing of 30º, its latitude would be 100 * cos(30º) = 86.6 m, and its departure would be 100 * sin(30º) = 50 m.
For error adjustments, if total latitude errors sum to 5 m, and there are four sides to adjust, each side could receive a correction of 1.25 m using equal distribution.
When traversing lines so straight, for latitude calculate, times the length times cosine's fate!
Imagine a surveyor setting out a traverse, facing the sun in the North, then marching East, measuring carefully. Each step counts as they plot the map, ensuring angles close upon return to their start, correcting their path along the way.
For latitude, remember: 'Length times Cosine', for departure: 'Length times Sine'.
LA - Latitude is North (A) and Departure is East (D), together they 'Lead A' correct traverse.
Term
What is Latitude?
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What is Departure?
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What is a Closing Error?
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What is Gale’s Traverse Table?
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A method of surveying where a series of connected lines are measured.
The northward projection of a traverse line.
The eastward projection of a traverse line.
The difference between the starting and ending points of a traverse due to measurement inaccuracies.
A tabular method for organizing and calculating traverse coordinates and adjustments.
Traverse computations involve calculating the coordinates of traverse stations using field observations, critical for detailed mapping.
This section outlines the process of computing coordinates for traverse stations by gathering various measurements, such as bearing and elevation, and then applying these to determine latitudes and departures. Adjustments are also discussed to ensure accuracy in closed traverses.
In traverse computations, after completing field observations, the next step is determining the coordinates of traverse stations, essential for creating accurate maps. Key observations necessary for coordinates include magnetic bearings, lengths of traverse lines, elevations, included angles, and vertical angles.
Coordinates are computed through latitude and departure, derived from the length of the line and its reduced bearing. Here, latitude represents northward projections and departure eastward projections. Each line's reduced bearing influences the sign of latitudes and departures, ensuring directionality in calculations. Following calculations, adjustments are made for closed traverses to eliminate errors due to imprecision in angular and linear observations. This includes distributions of angles and bearings, closing error adjustments, and ensuring the algebraic sum of latitudes and departures equals zero. Methods like Bowditch Rule and Transit Rule assist in correcting errors. Gale’s Traverse Table offers a systematic way to apply these computations and adjustments, enhancing overall accuracy.