How to Use a Prism Slope Correction

Prisms can find the error caused by measuring road and hill slopes by hand.

Road workers and foresters use many methods for finding the slope of a road or hill. Problems arise due to variations on the road or hill. In general, measured slopes often end up being longer than intended. In order to compensate for this distance, road workers and foresters must use a method for correcting the slope. In order to do this, they must compute the slope, slope angle and zenith angle. Although there are many ways to calculate these dimensions, using an electronic distance meter (EDM) in combination with a prism is one of the simplest and most accurate.

Things You'll Need

• Electronic distance meter
• Prism
• Measuring tape
• Pencil and paper
• Scientific or graphing calculator

Instructions

1. Set up the prism on the top or bottom of the hill you wish to measure; most prism slope correction sets use a prism mounted on top of a large pole.

2. 

   Set the prism on one end of the hill and the EDM at the other.

   Set up the EDM on the hill or in the valley opposite the prism; the EDM will be at the top and the prism will be at the bottom, or vice versa. Make sure these two devices line up with one another in a straight line angled top to bottom.

3. Measure the distance between the prism and the eye of the EDM with a measuring tape; this will be the hypotenuse.

4. Turn on the EDM and record the calculated angle. The EDM computes the angle formed between an imaginary vertical line through its center and a straight line going from the eye of the EDM to the prism -- this is the zenith angle.

5. Use the zenith angle to calculate the angle of the hill. Calculate the hill angle by subtracting the zenith angle from 90 degrees; this works because the angles are complementary. A negative resultant angle indicates a down slope and a positive angle indicates an up slope.

6. Calculate the horizontal length of the hill from the eye of the EDM to the prism with the equation: Horizontal Length = hypotenuse * cosine of hill angle.

7. Calculate the vertical height of the hill from the eye of the EDM to the top of the prism with the equation: Height = hypotenuse * sine of hill angle.

8. Measure the height of the prism pole from the bottom of the pole to the center of the prism, and subtract the resultant height from the calculated hill height; this will be the hill height, starting at a point on the hill lining up with the eye of the EDM to the top of the hill.

9. Calculate the slope of the hill by dividing the hill height by the hypotenuse. Alternatively, if you do not need the height and length for other computations, you can calculate the slope with the equation: Slope = tangent of hill angle.

10. Calculate the slope correction with the equation: Slope Correction = hypotenuse * (1 - cosine of zenith angle). The actual slope of the hill or road will be within a range of the calculated slope plus or minus the slope correction.

Tips & Warnings

• Be extremely careful when measuring slope correction on roads. It is best to wait for times when traffic is at a minimum.

References

• University of Wisconsin-Madison: Forest Biometry Lecture Number 11: Variable Plot Cruising I
• Vermessungs-Suchmaschine: Slope Correction
• Georgia State University: Prisms
• Integrated Publishing: Correcting for Slope
• Clark University: Right Triangles