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Interactive Audio Lesson
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Introduction to Bearings
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Today, we'll explore how bearings help us in surveying. Can anyone tell me what a bearing is?
Is it the direction of a line from a point?
Exactly! Bearings help us define the direction of survey lines with respect to the meridian. We have two types: True meridian and Magnetic meridian. Can anyone explain the difference?
The true meridian is based on the north-south poles, while the magnetic meridian uses a compass to find magnetic north.
Correct! So, when we talk about bearings, we are often dealing with these two principles. Now, let's discuss how we compute angles using bearings.
How do we actually find the angles between two lines?
Great question! If we know the bearings of those lines, we can compute the included angle. Let's explore the conditions for this.
Included Angles Computation
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To compute the included angle between two lines, we draw a sketch of their bearings. Does anyone remember how to compute the included angle based on their positions?
We take the difference of the angles if they are on the same side of the meridian.
That's right! If both lines are on the same side of the meridian, the included angle is simply the difference of their reduced bearings. Now, what happens if they're in different quadrants?
Then we subtract the sum of the reduced bearings from 180 degrees.
Yes! And if the lines are in adjacent quadrants?
We add the reduced bearings in that case.
Exactly! Finally, if the lines are not on the same side and not opposite, we use the whole circle bearings.
Examples of Angle Computation
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Let's work on an example together. If we have two lines with WCB of 75° and 150°, how would we compute the included angle?
Since both are on the same side of the meridian, we just need to subtract them?
Correct! So what do we get?
The included angle would be 150° - 75° = 75°.
Great! Now let's try one where the bearings are in different quadrants. If we have WCB of 210° and 330°, what should we do?
We would subtract the sum of the bearings from 180°.
Exactly! Let’s calculate.
Common Errors and Local Attraction
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What are some errors we might encounter when determining bearings?
Local attraction can affect the magnetic readings, right?
Correct. Local attraction can distort the compass reading and affect our bearing computations. How can we verify if local attraction is affecting our readings?
We can check if the fore bearing and back bearing differ by 180°.
Right! That's a great way to ensure our measurements are accurate. Remember to always check your bearings against local conditions!
Introduction & Overview
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Quick Overview
Standard
The computation of included angles from the bearings of lines in a closed traverse is essential in surveying, allowing for the calculation of angles based on given bearings and their relationships determined by their relative positions.
Detailed
In surveying, bearings of lines can directly help compute the included horizontal angles in a closed traverse. Specifically, if the bearing of one line and the included angles between various lines are known, the bearings of other lines can be calculated using the relationship: Bearing of a line = given bearing + included horizontal angle. The section describes different scenarios for included angle computation based on the positioning of the lines relative to the meridian and provides examples to illustrate how to determine angles through graphical representation of bearings.
Audio Book
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Overview of Included Angles
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In a closed traverse, bearings of lines may be calculated if bearing of one of the line and the included horizontal angles between various lines are known, using the relationship:
Bearing of a line = given bearing + included horizontal angle (1.5)
Detailed Explanation
This chunk introduces the concept of included angles in a closed traverse. Here, a closed traverse refers to a path where the starting and ending points are the same, forming a closed shape (like a polygon). The bearings of different lines (the directions of the lines with respect to a reference direction) play a critical role in navigating this closed path. The key formula provided allows surveyors to calculate the bearing of any line by knowing one bearing and the angles included between that line and other lines. Essentially, if you know where one line is pointing, you can find the direction of another line relative to that one using their included angles.
Examples & Analogies
Imagine you're at a park with multiple pathways. If you know the direction of one path (like going north) and you have measured an angle towards another path (like turning 30 degrees to the east), you can clearly understand and define the direction of that second path. This way, knowing one path's direction allows you to calculate the others around it.
Finding Included Angles
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If at any point, bearings of any two lines are known, the included angle between these two lines can easily be found by drawing a sketch, and then taking the difference of angles.
Detailed Explanation
In this chunk, the method to find the included angle between two lines based on their bearings is described. When surveyors know the bearings (angles) of two lines, they can visualize these lines on a sketch. By measuring the angles and subtracting one from the other, they find the included angle, which is the angle formed between the two lines. This is a practical skill in surveying, as it helps in determining precise angles needed for construction and mapping.
Examples & Analogies
Think of a game of darts. If you know the angle at which you're standing (let's say 30 degrees) and the angle at which the dartboard is set (say 90 degrees), you can easily find out how to adjust your aim to hit the center by finding the included angle between where you're aiming and the dartboard. In surveying, this skill is crucial for aligning structures accurately.
Different Scenarios for Angle Calculation
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If the lines are on the same side of the meridian and in the same quadrant (Figure 1.17a), the included angle ∠AOB = the difference of the reduced bearings of OA and OB. If the lines are on the same side of the meridian but in different quadrants (Figure 1.17b), the included angle ∠AOB = 180° – sum of the reduced bearings of OA and OB. If the lines are not on the same side of the meridian but they are in the adjacent quadrants (Figure 1.17c), the included angle ∠AOB = sum of the reduced bearings of OA and OB. If the lines are not on the same side of the meridian and also not in the opposite quadrants (Figure 1.17d), the included angle ∠AOB = 360° – difference of the whole circle bearings of OA and OB.
Detailed Explanation
This chunk discusses specific conditions under which the included angles are calculated based on their bearings. It breaks down various scenarios regarding the positioning of lines in relation to a reference meridian. For instance, if both lines lie in the same quadrant and on the same side of the meridian, simply subtracting their reduced bearings will yield the included angle. Conversely, if they are in different quadrants, more complex calculation rules apply. These different cases emphasize the importance of understanding the spatial relationships between lines to make accurate calculations.
Examples & Analogies
Imagine you’re driving in a city with quadrants divided by main roads (like a grid). If you’re at a corner (like a line on the meridian) and want to calculate the best way to turn onto another street (the included angle), knowing whether you’re turning into the same block or crossing into the next block (quadrant) impacts how sharply you need to turn. Similarly, in surveying, recognizing the alignment of lines relative to a reference direction ensures accurate routes are plotted.
Definitions & Key Concepts
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Key Concepts
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Closed Traverse: A method of surveying where lines connect back to the starting point, enabling complete angle computations.
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Bearing Computation: The process of calculating bearings based on known measurements and angles.
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Local Attraction Error: Distortion in measurements due to nearby magnetic interference.
Examples & Real-Life Applications
See how the concepts apply in real-world scenarios to understand their practical implications.
Examples
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If line OA has a WCB of 60° and line OB has a WCB of 120°, the included angle ∠AOB is 120° - 60° = 60° since both are in the same quadrant.
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If line OA has a WCB of 300° and line OB has a WCB of 60°, we subtract their sum from 180°, which yields the included angle ∠AOB = 180° - (300° + 60°) = 180° - 360° = -180°.
Memory Aids
Use mnemonics, acronyms, or visual cues to help remember key information more easily.
🎵 Rhymes Time
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When bearings meet, the angle's neat, compute the lines that can’t retreat.
📖 Fascinating Stories
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Imagine two friends (lines) walking from the same point—one takes a left and the other a right, their included angle measured from eastern sight!
🧠 Other Memory Gems
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SAME (Same Side: Angle's Magnitude Equal; Different: Add Degrees).
🎯 Super Acronyms
BICE (Bearings Include Calculated Angles).
Flash Cards
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Glossary of Terms
Review the Definitions for terms.
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Term: Bearing
Definition:
The direction of a survey line with respect to a reference direction, typically measured in degrees.
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Term: Included Angle
Definition:
The angle formed between two survey lines.
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Term: Whole Circle Bearing (WCB)
Definition:
Bearing measured as an angle in a clockwise direction from a true north direction.
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Term: Reduced Bearing (RB)
Definition:
Bearing expressed as an angle relative to the north or south direction, limited to less than 90 degrees.
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Term: Local Attraction
Definition:
An error in magnetic compass readings due to nearby magnetic materials affecting the magnetic field.