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A level was set up at a point A and distance to the staff station B was 100 m, the net combined correction due to curvature and refraction as applied to the staff reading is
- a)0.00673 m
- b)0.000673 m
- c)-0.000673 m
- d)-0.00673 m
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
A level was set up at a point A and distance to the staff station B wa...
Correction due to curvature:
d = Horizontal distance between two points in kM, R = Radius of curvature of earth in km = 6370 km
After submitting values of d and R in km we will get Cc in m
Correction due to curvature will be always negative
∴ Cc = -0.0785 d2, d is substituted in km
Corrections due to refraction:
Correction for refraction is always positive
∴ CR = 0.01122 d2, d is substituted in km
Combined correction:
C = Cc + CR
C = -0.0785 d2 + 0.01122 d2
C = -0.06735 d2
d = 100 m = 0.1 km
C = – 0.0673 d2
where d is in km, C is in m
C = - 0.0673 × 0.12 = - 0.000673 m
d = Horizontal distance between two points in kM, R = Radius of curvature of earth in km = 6370 km
After submitting values of d and R in km we will get Cc in m
Correction due to curvature will be always negative
∴ Cc = -0.0785 d2, d is substituted in km
Corrections due to refraction:
Correction for refraction is always positive
∴ CR = 0.01122 d2, d is substituted in km
Combined correction:
C = Cc + CR
C = -0.0785 d2 + 0.01122 d2
C = -0.06735 d2
d = 100 m = 0.1 km
C = – 0.0673 d2
where d is in km, C is in m
C = - 0.0673 × 0.12 = - 0.000673 m
Most Upvoted Answer
A level was set up at a point A and distance to the staff station B wa...
The given problem is related to the combined correction due to curvature and refraction in leveling. In leveling, the curvature correction accounts for the curvature of the Earth's surface, while the refraction correction takes into consideration the bending of light rays as they pass through the atmosphere.
Given data:
Distance from point A to staff station B = 100 m
To calculate the combined correction, we need to consider the formula:
Combined correction = curvature correction + refraction correction
1. Curvature Correction:
The curvature correction is given by the formula:
Curvature correction = (Distance^2) / (2 * Radius of curvature)
Here, the distance is 100 m, and the radius of curvature is the radius of the Earth. Assuming the Earth to be a perfect sphere, the radius of curvature can be taken as 6371000 m.
Curvature correction = (100^2) / (2 * 6371000) = 0.007879 m
2. Refraction Correction:
The refraction correction is given by the formula:
Refraction correction = (K * Distance) / (Radius of curvature)
Here, K is the refraction constant, which depends on the atmospheric conditions. For normal atmospheric conditions, the value of K is 0.13.
Refraction correction = (0.13 * 100) / 6371000 = 0.00000204 m
3. Combined Correction:
Now, we can calculate the combined correction by adding the curvature correction and refraction correction:
Combined correction = 0.007879 + 0.00000204 = 0.007881 m
The result is rounded to the nearest millimeter, so the combined correction is approximately 0.0079 m.
Since the question asks for the net combined correction, we need to consider the sign. The combined correction is positive, indicating that the staff reading needs to be increased by this amount.
However, the correct answer is option 'C', which states -0.000673 m. This suggests that there might be an error in the given options or the calculations provided. It is recommended to double-check the given options or re-calculate the combined correction to obtain the correct answer.
Given data:
Distance from point A to staff station B = 100 m
To calculate the combined correction, we need to consider the formula:
Combined correction = curvature correction + refraction correction
1. Curvature Correction:
The curvature correction is given by the formula:
Curvature correction = (Distance^2) / (2 * Radius of curvature)
Here, the distance is 100 m, and the radius of curvature is the radius of the Earth. Assuming the Earth to be a perfect sphere, the radius of curvature can be taken as 6371000 m.
Curvature correction = (100^2) / (2 * 6371000) = 0.007879 m
2. Refraction Correction:
The refraction correction is given by the formula:
Refraction correction = (K * Distance) / (Radius of curvature)
Here, K is the refraction constant, which depends on the atmospheric conditions. For normal atmospheric conditions, the value of K is 0.13.
Refraction correction = (0.13 * 100) / 6371000 = 0.00000204 m
3. Combined Correction:
Now, we can calculate the combined correction by adding the curvature correction and refraction correction:
Combined correction = 0.007879 + 0.00000204 = 0.007881 m
The result is rounded to the nearest millimeter, so the combined correction is approximately 0.0079 m.
Since the question asks for the net combined correction, we need to consider the sign. The combined correction is positive, indicating that the staff reading needs to be increased by this amount.
However, the correct answer is option 'C', which states -0.000673 m. This suggests that there might be an error in the given options or the calculations provided. It is recommended to double-check the given options or re-calculate the combined correction to obtain the correct answer.
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A level was set up at a point A and distance to the staff station B was 100 m, the net combined correction due to curvature and refraction as applied to the staff reading isa)0.00673 mb)0.000673 mc)-0.000673 md)-0.00673 mCorrect answer is option 'C'. Can you explain this answer?
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