A clinometer, also called a tiltmeter, is an instrument that measures the vertical inclination, that is, the angle between a plane or the observer and a tall object. A simple, "fixed angle" clinometer provides the ability to move much forward and backward during measurements. A "clinometer made with a protractor" allows you to stay still and represents a handcrafted version of the instruments used very often in astronomy, topographic surveys, engineering and forest sciences.
Steps
Method 1 of 4: Making a Simple Clinometer
Step 1. Fold a square sheet of paper (20x20cm) to form a triangle
Bring the bottom right corner over the left side of the paper by aligning the edges perfectly to create a triangle. If you are using a regular rectangular sheet of paper, chances are there will be a large portion of it left over over the triangle. Cut or tear this strip. Eventually you will have one isosceles right triangle with an angle of 90 ° and two of 45 °.
Thick cardstock will make the tool more durable, but you can use any sheet of paper. At the end you can also glue it or secure it to a firmer base with duct tape to make it more sturdy
Step 2. Secure a straw to the hypotenuse of the triangle with tape
Align it with the longest side of the triangle, the hypotenuse, so that it protrudes slightly from the triangle. Make sure the straw is not bent or squashed and that it is straight along the side of the triangle. You can secure it with glue or tape. You will need to look through the straw when using the clinometer.
Step 3. Make a small hole near the end of the straw
Choose the end that is aligned with the corner and not the end that extends beyond the edge of the paper. You can use an awl or a pointed ballpoint pen for this job.
Step 4. Tie the twine to the hole
Push it through the hole and then tie a knot to keep it from slipping. Use a piece of string that is long enough to have several inches dangling from the base of the clinometer.
Step 5. Tie a small weight to the end of the twine
You can use a metal washer, paper clip, or other similar object. The sinker should hang 5 cm or more from the bottom corner of the tool to allow the string to swing freely.
Method 2 of 4: Using a Simple Clinometer
Step 1. Look at the tip of the tall object through the straw
Hold the end of the straw protruding from the clinometer near the eye and point the instrument at the object you want to measure, such as a tree. You will most likely have to tilt the triangle to see the tip of what you are aiming for.
Step 2. Move back and forth until the string lines up with the triangle
You need to find a point where you can hold the triangle completely flat without losing sight of the tip of the tree through the straw, by doing so you can measure it. The triangle is level when the weight keeps the twine perfectly aligned with one of the legs.
- When this happens, it means that the angle of elevation between your eye and the tip of the object is 45 °.
- If you have to squat or stand on a raised platform in order to find an optimal position, then you must consider the height of your eye while you are in that particular posture, unlike what happens when you observe the object while remaining normally standing, as it will be. described in the last step.
Step 3. Measure the distance between your position and the base of the object using a measuring wheel
Just like the small one on the clinometer, the huge triangle formed by you, the tip and base of the tall object has two angles of 45 ° and one of 90 °. The two sides of an isosceles right triangle are always equal to each other. Measure the distance that separates the base of the object from the position you were in in the previous step. The value you detect is approximately the height of the object, but there is one more thing to do before finding the final answer.
If you don't have a tape measure, just walk towards the object as normal and count the number of steps. Later, when you have a meter available, measure the width of one of your steps and multiply the value by the number of steps you counted earlier. At this point you have found the total distance and therefore the height of the object
Step 4. Add the height of your line of sight
Since you held the clinometer at eye level, you actually measured the height of the object from this "altitude". Use a tape measure to find the height of your eyes from the ground and add the result to the value you calculated earlier. Now you know the actual height of the object!
For example, if the eye height is 1.5m and the distance between you and a tree is 14m, the total height of the tree is 15m
Method 3 of 4: Making a Clinometer with a Protractor
Step 1. Get a 180 ° protractor
This tool has the shape of a semicircle on the edge of which the amplitudes of the corners are indicated. You can buy it anywhere, at the stationery or at the supermarket among school supplies. It would be better to choose a model with a small hole in the center, along the flat base.
If you don't want to buy a protractor, you can search online and find printable templates. Print it out, carefully cut it out along the edges, and glue it to a sturdy base such as cardstock or postcard
Step 2. Attach a straw to the straight base
Lay it on or near the straight edge of the protractor, so that it is parallel to it, and hold it in place with tape. Check that the straw goes through the colon 0º which are at opposite ends of the straight edge.
If you don't have a straw, roll a sheet of paper into a tight cylinder and use it instead
Step 3. Tie some string through the hole in the center of the protractor diameter
Most of these tools have a small hole on the flat edge, between the two 0 ° marks, and vertically aligned with the 90 ° notch along the curved edge. If the protractor in your possession does not have the hole or it is in another place, glue the string or tape it in the center of the diameter. Make sure the string hangs freely several inches below the tool.
If you are using a paper protractor, you can drill the hole with an awl or a fine-tipped pen. Do not try to do the same with a plastic protractor, as the material is quite weak and would shatter
Step 4. Attach a small weight to the free end of the twine
Tie a paper clip, metal washer, or other twine-like object. When you hold the clinometer in your hand, the wire will dangle over the circular edge of the meter and the weight will hold it taut past the notch that indicates an angle, such as 60 °. In this way you can know the inclination in which you are holding the instrument and use this data to find the height of distant objects, according to the method described in the next section.
Method 4 of 4: Using a Clinometer Made with a Protractor
Step 1. Observe the tip of the object of your interest through the straw
Grab the tool so that the curved part is facing down and tilt it until you can see the end of the tall object (such as a building) through the straw or paper tube. This method allows you to calculate the angle between you and the tip of the object or its height.
Step 2. Measure the angle using the protractor
Hold it steady until the hanging wire stops. Calculate the angle between the midpoint of the protractor (90 °) and the one crossed by the twine by subtracting it. For example, if the wire intersects the edge of the protractor at 60 °, the elevation angle between you and the tip of the object is 90–60 = 30 °. If the wire were positioned at the 150 ° notch, then the elevation angle would be 150-90 = 60 °.
- The elevation angle is always less than 90 °, since this amplitude indicates a direction perpendicular to the ground.
- The solution is always a positive value (greater than 0 °). If you subtract a larger number from a smaller one and get a negative value, just remove the "minus" sign and you will get the correct answer. For example, if you calculate 60-90 = -30º, the elevation angle is actually + 30º.
Step 3. Calculate the tangent to this angle
The "tangent" of an angle is defined as the ratio between the cathetus opposite the angle under examination and the adjacent one. In this case the right triangle is formed by three elements: yourself, the base of the object and its upper end. The side opposite the corner under consideration is the height of the object, while the adjacent side is the distance that separates you from the base.
- At this point you can use a graphing or scientific calculator, an online calculator or a table with the various tangents for each angle and thus obtain the value you are interested in.
- To proceed with a calculator, press the TAN key and type in the angle value you found. If you get a solution less than 0 or greater than 1, then change the angle setting from radians to degrees and try again.
Step 4. Measure the distance that separates you from the object
If you want to know its height, you need to know how far it is from you. Use a tape measure or count the number of steps you need to take to reach the base. Then measure the width of one of your steps, when you have a meter available. Distance is equal to the length of one step multiplied by the number of steps you took previously.
Some protractors have a ruler on the flat edge of the semicircle
Step 5. Use the values you found to calculate the height of the object
Remember that the tangent of the angle in question is equal to (height of the object) / (distance between you and the base of the object). Multiply the value of the tangent by the distance you measured and you will have the height of the object!
- For example, if the elevation angle is 35 ° and the distance that separates you from the object is 45 units, then its height is 45 x tan (35 °) or 31.5 units.
- Add the height referred to the eye level to the value found, since the clinometer was used at a higher level of the ground.
Advice
It is much easier to use a clinometer created with the protractor with the help of another person. One will look at the object through the straw and the other will look at the position of the string
Warnings
- In general, the handcrafted clinometer is not used for precision work, such as topographic surveys. In this case it is necessary to rely on an electronic tool.
- If the ground at the base of the object you are looking at is at a different level than yours, then you may be getting inaccurate data. Try to measure or estimate the difference between the heights and subtract or add it to the results.
