Fundamentals of Surveying (FS) Practice Exam

The curvature of the earth error associated with leveling a shot of 1000 ft is most nearly?

1. 0.024 ft

2. 0.032 ft

3. 0.035 ft

4. 0.055 ft

The correct answer is: 0.024 ft

To determine the curvature of the Earth error associated with a leveling shot of 1000 feet, it's essential to understand how the Earth's curvature impacts leveling measurements. The Earth's radius is approximately 20,902,880 feet, and the formula for calculating the drop due to curvature over a certain distance can be approximated using the formula: \[ \text{Drop} (\text{ft}) = \frac{d^2}{2R} \] where \( d \) is the distance in feet, and \( R \) is the radius of the Earth in feet. For a distance \( d \) of 1000 feet, you can substitute the values into the formula. Using the approximate value of Earth's radius as 20,902,880 feet: \[ \text{Drop} = \frac{(1000)^2}{2 \times 20,902,880} \] Calculating this gives: \[ \text{Drop} \approx \frac{1000000}{41805760} \approx 0.0239 \text{ ft} \] This value rounds to about 0.024 feet, aligning with the first choice. Therefore, the curvature of the Earth error for a 1000-foot