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Sum of Departures Formula:
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Sum of Departures is the algebraic sum of departures where departure of a line is its projection onto a line at right angles of the reference meridian. It is an important concept in traverse surveying calculations.
The calculator uses the formula:
Where:
Explanation: This formula calculates the sum of departures based on the closing error and sum of latitudes in a traverse survey, using the Pythagorean theorem relationship between these values.
Details: Accurate calculation of sum of departures is crucial for error analysis and adjustment in traverse surveying. It helps in determining the accuracy of the survey measurements and in distributing errors appropriately.
Tips: Enter closing error and sum of latitudes in meters. Both values must be valid numerical values, and the closing error must be greater than the absolute value of sum of latitudes for a real solution.
Q1: What is closing error in surveying?
A: Closing error is the error formed during traverse surveying when the final point doesn't coincide with the starting point, indicating measurement inaccuracies.
Q2: What are latitudes in traverse surveying?
A: Latitude of a line is its projection onto the reference meridian (north-south line), representing the north-south component of the line.
Q3: What happens if the sum of latitudes squared is greater than closing error squared?
A: The result would be an imaginary number, indicating inconsistent input data or measurement errors that need to be rechecked.
Q4: How is this formula derived?
A: The formula is derived from the Pythagorean theorem, where the closing error represents the hypotenuse, and the sum of latitudes and sum of departures represent the other two sides of a right triangle.
Q5: What units should be used for input values?
A: Consistent units should be used (typically meters in surveying), and all measurements should be in the same unit system for accurate results.