# Estimation of Heights, Lengths, Weights

## Estimation of Height and Widths

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.

An average man's measure:

Nail joint of forefinger, or breadth of thumb : 1 inch

Span of thumb and forefinger: 8 inches

Span of thumb and little finger : 9 inches

Wrist to elbow (this also gives you the length of your foot) : 10 inches

Elbow to tip of forefinger (called "cubit") : 17 inches

Middle of kneecap to ground : 18 inches

Extended arms, from finger-tip to finger-tip, is called a "fathom" and nearly equals your height.

Pulse beats about 75 times a minute. Each beat is a little quicker than a second.

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 quite a useful skill for a Scout during pioneering projects, camping or going on an adventure trip. After learning all these skills, he will be able to estimate the height of a tree, building or even a specific distance. It is also one of the tests conducted at the King Scouts' Standardization.

### Heights

#### Measuring Heights - 1-in-10 method

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.

#### Measuring Heights - Stick method

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.

#### Measuring Heights - Pencil Method or Proportional Method

Have a friend whose height you know stand beside a tree, or tie a ribbon around the tree at your own height. Step back and hold a pencil or a stick at arm's length in front of you. With one eye closed, sight over the stick so that the top of it appears to touch the ribbon or your friend's head. Place your thumbnail on the stick where it seems to touch the base of the tree. Now move the stick up to see how many times this measurement goes into the height of the tree. Multiply that number by the height of your friend or the ribbon, and you will know the height of the tree. You can also use this method to measure buildings, waterfalls, and walls.

#### Measuring Heights - Tree-felling method

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.

Diagram

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 themself from the tree, such that there is alignment between your eye, the top of the now horizontal stick and their 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.

#### Measuring Heights - Shadow Method

The method can be used only if the sun is able to cast a shadow. First is we measure the shadow cast by the tree (from the base of the tree to the shadow of it's top), we label this length as AB. We then measure the shadow cast by someone or an object of known height, we label this as CD.

We merely solve the unknown height by use of proportions, by equating:

#### Measuring Heights - Inch-to-Foot Method

From the foot of the object you are to measure pace eleven (11) units, we label it distance AB. A unit can be any number of paces, so if we say our unit is five paces then 11 units is equivalent to 55 paces. Place something to mark the point B. From B take one more unit forward, this is distance BC. From location C lie down on the ground such that your eyes are close to the ground as possible. Sight the tree with the marker on B in your line of sight. Note where your line of sight cuts the marker to the tip of the tree. That spot is labelled as D. The distance of BD in inches is the estimated height of tree in feet.

#### Measuring Heights - TAN Method

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.

### Widths

#### Measuring Widths - Napoleon Method

Stand on one shore of a stream. Bow your head, chin against your chest. Hold your hand to your forehead in a salute. Move your hand down until the front edge of it seems to touch the opposite shore. Without changing the position of your hand, make a quarter turn. Notice the point at which the edge of your hand seems to touch the near shore. Pace off the distance to that point, and you will know the width of the river. Napoleon might have used the brim of this hat instead of his hand. If you are wearing a cap with a visor, so can you.

#### Measuring Widths - Stride or Step Method

Select an object on the opposite side of the river, such as a tree and we mark it as A. Mark the point directly in front of the object on the opposite side of the river, mark it as point B. Take at least 50 paces to point C, so as to form line BC. Note that line BC should be perpendicular to line AB. Mark point C with a stick or another person. Again, pace another distance to point D. The distance CD is half the distance of BC. From point D, pace another distance to point E. Line DE is parallel to line AB. Point E is marked on a location wherein you can see point C forming a straight line with point A. Meaning when you look at the stick on point C. it somewhat blocks your line of sight to point A. The distance AB is twice the distance DE. AB = DE x 2. We can alter the method a bit. Instead of having distance CD half the distance between BC, we can make it equal to each other. Do the same method to find point E. Using this alternative, AB=DE. This is more accurate.

#### Measuring Widths - Compass Method

Locate an object on the other side of a river. Stand on your side and point the direction-of-travel arrow towards the object. Align the magnetic needle to 45O indicator of the compass housing. Pace the line BC while pointing the direction-of-travel arrow towards the object all the time. Point C is marked when the compass is oriented (magnetic needle is directly above the orienteering arrow). The distance BC is a rough estimate of distance AC. You have just formed a 45-45-90 triangle, which has two of its sides equal to each other.

### Weights

The first step to weigh the package is to determine the referenced weight in grams or in kilogrammes as measure unit that you have in your house. If possible these objects should already have the weigh written on it. For example, a 1 kg pack of sugar.

This will help you to compare the object to the package in order to determine the weight. Try to have several references to have as many references as possible.

You can make a scale. This is a basic lever-word problem.

In order to solve it by this means, however, you will need to use some tools. The accuracy of your answer depends on the accuracy of these tools.

You must have an object whose weight you know.

You must have an accurate ruler.

A straight stiff beam to use as a balance beam.

A fulcrum that allows the beam to balance freely.

Here's a sketch of the set-up

Here's how you solve the problem using a known weight for reference:

Multiply known weight by the distance from the fulcrum (d1)

Divide that amount by the distance from the fulcrum to the unknown weight (d2).

Thus,

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