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Today, we will learn about calculating reduced levels using angle of depression. We start by understanding how to set the instrument at the observation point P.
What do we need to set up the instrument at point P?
You need a stable base, a leveling staff, and a clear view of the point Q. Once everything is set up, we can measure the angle of depression.
How do we measure that angle?
Using a theodolite, you'll align the line of sight to the staff at Q and note the angle. In this example, it's measured at 5° 36′.
What do we do with that angle?
We use it to calculate the height difference using the tangent function. Remember the acronym SOHCAHTOA for sine, cosine, and tangent!
So tangent helps us find height changes?
Exactly! Let's move forward with our calculations.
Now that we have the angle of depression, let's calculate the difference in elevation.
What is the formula we are using here?
The formula is D * tan(α), where D is the distance from P to Q, and α is the angle of depression.
In this case, D is 3000 m?
Correct! And our angle α is 5° 36′. Let's calculate that now.
Why do we need to consider curvature and refraction?
These factors can affect our distance measurements, making our results less accurate. We apply a correction to account for them.
And what is the correction for curvature and refraction?
For the distance of 3000 m, the combined correction is about 0.606 m. We subtract this from our height calculation.
Now that we have the height adjusted from the angle of depression, we can find the R.L. of Q.
What is the formula for that?
We have the R.L. of the instrument axis, which is the B.M. elevation plus the staff reading minus the height difference.
So it becomes 436.050 + 2.865 - 293.547?
Exactly! This gives us the R.L. for the staff station Q.
And we get 143.368 m for the R.L. of Q. Is that correct?
Yes! Excellent work! Understanding these calculations is crucial for accuracy in surveying.
The measure of the angle formed between a horizontal line and the line of sight to a point below.
A fundamental trigonometric ratio used in calculating heights and distances.
An adjustment made to account for Earth curvature in measurement.
Angle down, look around, tangent helps you measure ground.
Imagine you're on a tower, looking down at a ship with a friend measuring the angle.
Remember: T for Tangent, H for Height, D for Distance. THD helps in calculation.
RLT - Reduced Level Tangent - to remember the components needed for calculations.
Term
Reduced Level (R.L.)
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Term
Angle of Depression
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Term
Tangent Function
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The height of a point relative to a reference level, typically mean sea level.
The angle formed between the horizontal line from an observer and the line of sight down to an object below.
In trigonometry, the ratio of the opposite side to the adjacent side of a right triangle.
Adjustments made to measurements to account for the curvature of the Earth.
Adjustments made to measurements to account for the bending of light rays in the atmosphere.
This section discusses the calculation of Reduced Levels (R.L.) using angle of depression and distance.
The example illustrates how to compute the R.L. of a staff station using known distances and angles of depression from an observation point. The methodology involves calculating the difference in elevation due to distance and angles, as well as adjustments for curvature and refraction.
In this example, an instrument is set up at point P with a known elevation of 436.050 meters. By measuring the angle of depression to a vane at a distance of 3000 meters, several calculations are made to find the Reduced Level (R.L.) of the staff station Q, which is positioned 2 meters above the base of the staff. The calculation involves using trigonometric functions (specifically tangent) to determine the vertical height difference due to the angle of depression. Additionally, corrections for curvature and refraction are applied to ensure accuracy. This section emphasizes the importance of understanding how different factors affect the measurement of distances and elevations in surveying practice.