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A short class with Sarah and her students. The other ways are under More.
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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.
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.
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.
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!
A method of surveying where lines connect back to the starting point, enabling complete angle computations.
The process of calculating bearings based on known measurements and angles.
Distortion in measurements due to nearby magnetic interference.
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.
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°.
When bearings meet, the angle's neat, compute the lines that can’t retreat.
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!
SAME (Same Side: Angle's Magnitude Equal; Different: Add Degrees).
BICE (Bearings Include Calculated Angles).
Term
Included Angle
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Term
Bearing
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Term
WCB
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Term
RB
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The direction of a survey line with respect to a reference direction, typically measured in degrees.
The angle formed between two survey lines.
Bearing measured as an angle in a clockwise direction from a true north direction.
Bearing expressed as an angle relative to the north or south direction, limited to less than 90 degrees.
An error in magnetic compass readings due to nearby magnetic materials affecting the magnetic field.
This section explains how to compute the included angles between survey lines using bearings.
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.
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.