Vertical Distances and Angles (clinometer)

In previous classes we used the Brunton Pocket Transit for measuring horiztontal angles, and as a hand level. It has, however, one more very important usage--as a clinometer, or device for measuring vertical angles. For example, if a field worker needed to calculate the height of a tree or a cliff, or the depth of a canyon (a vertical distance), she or he could do so without having to climb the object or feature, thereby risking life and limb. The procedure is actually quite simple, and is carried out in stages.

1. The field worker measures the horizontal distance from the object or feature to some point where the top (or bottom) is visible.[example]

2. Standing on this point, the field worker measures the vertical angle of the top (or the bottom) of the feature or object using a clinometer.

3. Given that the object or feature stands at a 90 degree angle to the earth's surface, the field worker now knows the length of one side, and two adjacent angles, of a triangle. Using a little trigonometry: Height = horizontal distance times the tangent of the vertical angle plus the eye height of the field worker. Depth = horizontal distance times the tangent of the vertical angle minus the eye height of the field worker.[example]

If it is easier to measure a "slope distance" (one measured along the gradient) than a horizontal distance, the equation needs only to be modified slightly--Vertical distance = slope distance times the sine of the vertical angle, plus or minus the eye height of the field worker. A table of natural sines for each degree, from 1 to 45, is on the cover of the Brunton compass for ready reference.

In those cases where a fieldworker needs to calculate the height or depth of an object on top of, or below, a feature (For example, a tree on the top of a hill), two vertical angles need to be factored in--one to the top, and one to the bottom of the object. The difference between these two vertical angles is the height (or depth) of the object.[example]

Using the clinometer.

1. Open the cover of the Brunton so that the sighting arm is fully extended parallel with the face of the instrument.

2. Turn the peep sight or sighting tip at a right angle to the sighting arm.

3. Position the mirror at approximately a 45 degree angle to the instrument's face.

4. Hold the compass in a vertical plane, with the sighting arm pointed toward your eye, but approximately one foot away so that the point being sighted and the axial line in the sighting window can be focused clearly.

5. Look through the window of the lid and find the point to be sighted, then tilt the compass until the point of the sighting arm, the axial line of the window, and the point sighted coincide.[example]

6. Move, actually rotate, the clinometer by the lever on the back of the compass body until the tube bubble, as observed in the mirror, is centered.

7. Check to make sure the sights are still aligned, then bring the compass down and read and record the angle.

8. Repeat the entire procedure as a check.

Direct slope readings.

In some cases, such as when one needs to know the slope of a surface, he or she can determine the gradient directly by placing the clinometer on the ground. Once in place, the clinometer lever is rotated until the tube bubble is centered. The compass is then picked-up and the angle read and recorded.

Obviously, the accuracy of this method is specific to only one point on the surface. Several readings, in various places should, therefore, be taken and averaged. For soft surfaces, such as sandy slopes, fieldworkers can improve the accuracy of direct clinometer readings by placing the Brunton on the field notebook after it is placed on the surface.

Suggested Additional Readings

Job 7

Created by William E. Doolittle. Last revised 1 October 2004, wed