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Interactive Audio Lesson
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Understanding the Purpose of Adjustment
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Today we are going to talk about the adjustments needed in a closed traverse. Can anyone tell me why we need to adjust our measurements during surveys?
I think it’s because there might be some errors in the measurements?
Exactly! In a closed traverse, the measurements might not close perfectly due to various errors. We need to find and correct these errors.
What kind of errors are we talking about?
Good question! We will discuss three main types: angular errors, bearing errors, and closing errors.
Why is correcting these errors so important?
Correcting these errors helps us produce accurate maps and survey data, which are crucial for engineering and construction projects. Remember, *accuracy is key*!
To remember the types of errors, think of the acronym **ABC**: A for angular errors, B for bearings, and C for closing errors. Let’s proceed to discuss each type in detail.
Adjustment of Angular Errors
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Let’s dive into angular errors first. The sum of the angles in a closed traverse should equal a specific formula based on the number of sides. Can anyone recall what that formula is?
(2n - 4) x 90 degrees, right?
Exactly! That’s the right formula. If the measured angles don't equal this formula, we have an angular error.
How do we distribute these errors?
We can distribute the errors equally or based on the magnitude of each angle. Which do you think is more accurate?
Distributing based on the magnitude should be more accurate since larger angles might have greater errors.
Exactly! It’s a more precise method. Now, let’s summarize: Key point 1 is the formula for angles, Key point 2 is the method of distribution. Remember these for your practice.
Adjustment of Bearings
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Now, let’s look at bearings. When we measure a traverse, we sometimes use bearings instead of angles. What can you tell me about the relationship between fore and back bearings?
They should differ by 180 degrees, correct?
That's correct! If they don't, there's a bearing error. So what should we do with this error?
Adjust them to ensure they differ by 180 degrees?
Exactly! It’s essential for accuracy. Here’s a memory aid: think of **F-B** for Fore-Back bearings which should maintain that 180-degree difference. Let’s progress to closing errors next.
Closing errors! What are those?
Closing errors occur when the sum of latitudes and departures do not equal zero. It's crucial for fit in our plotted map. Remember L and D for Latitudes and Departures.
Are there specific rules for adjusting these?
Yes, we can use Bowditch or Transit rules for computations. Remember these are essential to balance and ensure accuracy!
Applying Adjustment Techniques
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Let’s imagine you’ve completed a closed traverse. What would your first step be regarding the adjustments discussed?
I’d check the angles to see if they sum up correctly according to the formula.
Correct! Next, if they don’t sum correctly, you would adjust those angles. What comes after that?
I’d check the bearings next.
Exactly! You’d want to ensure that fore and back bearings differ by 180 degrees. After that?
Check for closing errors using latitudes and departures?
Yes! Finally, apply your preferred adjustment method, either Bowditch or Transit rule. Remember this sequence: Angles → Bearings → Closing Errors.
In summary, today we covered the importance of adjustments in a closed traverse, addressing angular and bearing errors, and how to handle closing errors effectively.
Introduction & Overview
Read a summary of the section's main ideas. Choose from Basic, Medium, or Detailed.
Quick Overview
Standard
In the adjustment of a closed traverse, errors in measurements may result in a closure discrepancy, which requires correction through methods such as adjusting angular errors, bearings, and closing errors. The adjustment ensures accurate coordinates for plotting traverse stations.
Detailed
Adjustment of a Closed Traverse
In the context of surveying, a closed traverse consists of multiple connected line segments that return to the starting point. However, due to inherent errors in observations—both linear (distances) and angular (angles)—the plotted coordinates may not form a perfect closure. This discrepancy, known as the closing error, necessitates adjustment for accurate computational purposes. The adjustment involves:
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Adjusting Angular Errors: The sum of the measured interior angles should equal
\[(2n - 4) * 90°\] where n is the number of sides in the traverse. Observational errors must be quantified and evenly distributed among angles or adjusted according to their magnitudes. - Adjusting Bearings: When bearings are measured instead of angles, the closing error can be determined by comparing the fore and back bearings of a traverse line, which should differ by 180°. Corrections are made accordingly to ensure consistency across all bearings.
- Adjusting Closing Errors: The sum of all latitudes and departures from the measured coordinates should equal zero. If not, adjustments must be made to ensure this balance, using rules like Bowditch or Transit to calculate corrections. The overall goal is to minimize errors, providing accurate coordinates for plotting and further analysis in surveying.
Audio Book
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Introduction to Adjustments
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Due to errors present in the observations, the coordinates of a closed traverse stations when plotted may not close itself, but will have a small difference. The errors in the linear and angular observations therefore are to be adjusted before using them for computational purpose. It is also called Balancing a Traverse. These errors include:
(a) Adjustment of angular errors
(b) Adjustment of bearings.
(c) Adjustment of closing error of traverse
Detailed Explanation
In a closed traverse, when you collect data from various measurement points, inaccuracies or errors can emerge due to various factors. As a result, the final plotted coordinates may not coincide as expected. This discrepancy is termed the 'closing error'. To correct these errors before proceeding with calculations, adjustments are made in three main areas: angular errors (related to the angles measured), bearings (the directional readings), and closing errors (the overall difference in coordinates). Balancing a traverse ensures that the data is accurate for further analysis.
Examples & Analogies
Imagine you're following a map to navigate through a city but misread some directions along the way. When you arrive at the final destination, you realize that you're a block away from where you intended to be. Adjusting your path based on the initial mistakes is like balancing a traverse; you're correcting your route to ensure you end up where you need to go.
Adjustment of Angular Errors
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(a) Adjustment of angular error
In a closed traverse, the sum of all interior angles should be equal to (2n–4) x 900, and that of the exterior angles should equal (2n + 4) x 900, where ‘n’ is the number of sides in a closed traverse. The difference between this sum and the sum of the measured angles in a closed traverse is called the angular error of closure. The angular error of closure should not exceed the least count of theodolite (x) used, i.e., x √n. If it exceeds, observations are to be repeated. These permissible errors are shown in Table 1.6.
Detailed Explanation
Every closed traverse has a specific expectation for the sum of its interior angles, calculated using the number of sides (n) in the traverse. If the sum of the measured angles deviates from this expected total, this difference is known as the angular error of closure. To ensure accuracy, this error must stay within certain limits; if it falls outside, it's necessary to repeat the observations. The permissible error thresholds can vary depending on the precision requirement of the survey.
Examples & Analogies
Think of building a model with blocks. If you measure the space wrong for your corners, the structure won't fit together properly. Just as you must double-check measurements before committing, surveyors confirm that their angles align with the expected values to ensure their 'building' (the traverse) fits perfectly.
Adjustment of Bearings
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(b) Adjustment of bearings
Many times, bearings of a traverse are measured, instead of angles. In such cases, the closing error in bearings may be determined by comparing the fore bearing of a line and back bearing of that line of a closed traverse, as they should differ by 1800. The difference is the error which has to be adjusted in the bearings. Alternatively, we compare the known bearing of the traverse line with the measured bearing, and difference, if found, is adjusted in the bearings.
Detailed Explanation
When working with bearings instead of direct angle measurements in a closed traverse, surveyors must ensure that the fore bearing (the direction to the line) and the back bearing (the direction from the line) of the same traverse line are accurate; they should ideally differ by 180 degrees. If there's a discrepancy, it's considered a closing error that needs adjustment. By verifying and correcting these bearings, surveyors help ensure that all calculated directions are consistent and reliable.
Examples & Analogies
Imagine you're at a beach with friends, and you agree to meet at a certain spot by following a marker. If one person walks the wrong way (say, they aim for the marker but aren’t looking closely), they might end up far from the group instead. Correcting their route by checking the path against the known marker is like adjusting the bearings to ensure everything aligns.
Adjustment of Closing Error
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(c) Adjustment of closing error
For all the sides of traverse, latitude and departure are computed using the adjusted RB of lines, and proper sign is used as per the quadrant of traverse line. Ideally, the sum of all latitudes and sum of all departures must be zero in a closed traverse. But due to errors in the field measurements (e.g., bearings, distances, etc., the sum of all latitudes and sum of all departures, individually, may not come out to be zero).
Detailed Explanation
In a closed traverse, after adjusting for angular and bearing errors, it's essential to analyze the latitude (north-south distances) and departure (east-west distances) calculations for each side. Ideally, when summed up, these adjustments should balance out to zero which indicates complete closure. However, practical errors can cause these sums to differ, leading to a closing error. Identifying this discrepancy is crucial for ensuring the overall accuracy of the traverse.
Examples & Analogies
Consider a relay race where each runner has to finish at the same line. If one runner takes a longer route, the final team's distance will be off. It’s essential to adjust the timing or speed of the last runner to ensure they all finish at the goal line together, similar to adjusting latitudes and departures to ensure all sides of a traverse meet accurately.
Correction Methods
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The latitudes and departures are now adjusted by applying the correction to them in such a way that the algebraic sum of the latitudes and departures should be equal to zero. Any one of the two rules (Bowditch Rules and Transit Rules) may be used for finding the corrections to balance the survey:
(1) Bowditch Rule: It is also known as the Compass rule. It is used to adjust the traverse when the angular and linear measurements are equally precise.
(2) Transit Rule: The Transit rule is used to adjust the traverse when the angular measurements are more precise than the linear measurements.
Detailed Explanation
To effectively balance the traverse, corrections are applied to ensure that both the latitude and departure sums equal zero. Two common methods are employed for this process: the Bowditch Rule, which is suitable when all measurements are equally precise, and the Transit Rule, which is advantageous when angular measurements are more reliable than linear ones. These rules help in distributing the error corrections efficiently across the traverse.
Examples & Analogies
Think about editing a group essay. If one person’s contribution is off-topic, you might need to adjust their content to ensure coherence. Using a uniform editing approach (like the Bowditch Rule) keeps it simple while selectively correcting more precise contributions (like the Transit Rule) makes for a clearer, refined final product.
Definitions & Key Concepts
Learn essential terms and foundational ideas that form the basis of the topic.
Key Concepts
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Adjustment: The process of correcting measurement errors in surveying.
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Closure: Ensuring that the traverse returns to its starting point.
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Latitude & Departure: Coordinates that help identify the position of survey points.
Examples & Real-Life Applications
See how the concepts apply in real-world scenarios to understand their practical implications.
Examples
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If a closed traverse consists of four sides and the sum of measured angles is 360°, it indicates correct angular closure.
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Using a Bowditch rule to adjust latitudes in a traverse where total latitude error is -0.5m over perimeter of 100m.
Memory Aids
Use mnemonics, acronyms, or visual cues to help remember key information more easily.
🎵 Rhymes Time
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In a closed traverse, don’t feel dispersed; if angles mislead, adjustments you need!
📖 Fascinating Stories
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Imagine a traveler following paths that connect back to the beginning, only to find they’re slightly off; they must review their steps, ensuring every angle matches the expected path.
🧠 Other Memory Gems
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To remember types of adjustments, think ABC: A for angular errors, B for bearings, C for closing errors.
🎯 Super Acronyms
Use **LDC** to remember
- Latitude
- Departure
- and Closing error—key concepts in surveying adjustments.
Flash Cards
Review key concepts with flashcards.
Glossary of Terms
Review the Definitions for terms.
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Term: Closing Error
Definition:
The discrepancy that occurs when the end point of a traverse does not meet the starting point due to measurement errors.
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Term: Angular Error
Definition:
The difference between the measured angles and the theoretical angles that should be present in a closed traverse.
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Term: Bearing
Definition:
The direction of a line segment with respect to north, often expressed in degrees.
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Term: Latitude
Definition:
The north-south component of a coordinate in a traverse, indicating the distance moved north or south.
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Term: Departure
Definition:
The east-west component of a coordinate in a traverse, indicating the distance moved east or west.