Estimation of height is a useful skill for Scouts, and is often tested in competitions.
Each one of the below methods needs to result in a height measurement in meters, and the input into some of these methods needs to be distances and heights in meters or centimetres. Scouts are hardly likely to carry around a ruler or tape measure, so each scout should know some of the physical dimensions of their own body to attain this, such as:
- The width of the thumb in mm.
- The span of the outstretched hand in cm.
- The length of the forearm in cm.
- The length of ones pace in cm.
- Ones height in m.
The knowledge of these measurements above is an important prerequisite to most these height estimation methods below. Without them, accurate height determination is not easily attainable.
This is a great method of height estimation when the ground is level and the object for which you need to determine the height is fairly upright and perpendicular to the ground.
- From the object measure a distance of 9 units along the ground. The units can be anything, paces, stave lengths, meters or even the height of one of your scouts.
- Place an upright stave in the ground at the 9 unit distance.
- Mark a point in the ground, 1 further unit back, using the same unit that you used to measure the 9 units from the object.
- At the point that you have just marked on the ground, place your eye as close as possible to the ground and look up at the top of the object.
- Ask a fellow scout to put a finger on the stave and move it up or down on the stave until your eye, the finger and the top of the object are in line.
- Once they are in line measure the distance to the ground from the scout’s finger, Height A in the diagram above.
- The height of the object is 10 times what you have measured in Height A.
Note: You may have to adjust the size of the unit you choose, to obtain an easy determination of the object height.
This method is best used when the sun is low in the sky and casting fairly long shadows. Needless to say it, cannot be used around noon.
- Measure the height of the stave, call it Sh.
- Measure the length of the staves shadow, call it Ss.
- Measure the length of the object (tree) shadow, call it Os.
- The height of the tree then is Os divided by Ss multiplied by Sh.
This method is most probably the easiest and quickest method, but also the least accurate. Perhaps you can figure out why?
- Look for a straight stick the same length as your straightened arm.
- Hold the stick up in a perpendicular position at the end of your extended arm as per the diagram.
- While holding this pose, step backwards away from the object whose height needs to be determined until you eye, the top of the stick and the top of the object are in line.
- The height of the object is then determined by your distance from the tree.
Proportional stick method
This method is a quick and fairly accurate method of determining the height of an object, but using proportional measurements of an object of known height.
- Place a scout of a known height near the object of which you need to determine the height.
- With a small stick in hand and your arm steady walk some distance backwards from the scout, until the top of the stick is in line with the top of the scouts head, and the bottom of the stick, where you are holding it, is in line with the feet of the scout. At this point, stop moving backwards. Take note of the distance from your hand to the top of the stick, and let’s call that distance X.
- Keeping your arm steady move the stick up incrementally by X, until the top of the stick is in line with the top of the object of unknown height. Count the number of times you have to move the stick up.
- The height of the object, the tree in the case of the diagram, is the height of the scout multiplied by the number of times you had to move the stick up.
Note: You may have to adjust the size of the stick in your hand and you distance from the tree, so that final stick alignment with the height of the object is an exact multiple. A stave or anything else of a known length, can be substituted for the scout.
This method is a quick and fairly accurate method of determining the height of an object. Best used when the object of which height you need to determine is some distance away.
- Holding a stick upright on an extended arm, as in the diagram, align your eye, the bottom of the stick and the bottom of the object, as well as your eye, the top stick and the top of the object. You may need to adjust the length of the stick and your distance to the object to accomplish this.
- Once you have done this, turn your arm through 90°, maintaining the alignment between your eye, the bottom of the stick and the bottom of the object.
- Then ask one of your scout colleagues, to stand at a right angle relative to your position with the object, and distance him or herself from the tree, such that there is alignment between your eye, the top of the now horizontal stick and his or her position.
- The distance between the scout and the object is now equal to the height of the object, x in the diagram above.
Note: What one is reproducing here is the length of the object, tree in this case, if it had been felled and is now laying on the ground.
This method will give you the relative height from your current altitude and is useful for more distant and very high objects. To use this method you need to know the horizontal or map distance to the object. This one can usually get from a map. For example on a 1:50 000 map, 2cm on the map equals 1 horizontal kilometre on the ground. This method requires the use of a calculator or a mobile phone, the latter of which most scouts nowadays carry.
- This method requires a scout to adapt a compass to function as a clinometer as in the diagram above.
- After achieving the alignment as indicated in the diagram, as close to the ground as practical, read off the angle where the string crossed the compass dial.
- Subtract 90° from the angle, and find the trigonometric tangent of the resultant angle and multiply it by the actual horizontal distance to the object. i.e TAN( Read angle - 90° ) X horizontal distance to the object.
- The answer will be the height of the object relative to your own height/altitude.