Determining the height of objects by angular magnitude, by the shadow of the object, determining the steepness of slopes by sight, by comparing the height with the laying, using a plumb line and an officer’s ruler.

In field and field conditions it is sometimes very important and useful to possess the simplest applied methods for determining the height of objects. For example, a tree, tower, pillar or any other similar object on the ground. 

Determining the height of objects by angular magnitude, by the shadow of the object, determining the steepness of slopes by sighting, comparing the height with the laying, using a plumb line and an officer’s ruler.

To determine the height of objects by an angular value, first measure the distance to the object in meters and its angular value in thousandths. The height of the item is obtained by the formula: h = remote control / 1000. Where h is the height of the item in meters, D is the distance to the item in meters, Y is the angular value of the item in thousandths.

An example of determining the height of objects on the ground by the angular value.

The distance to the tower is 100 meters, and its angular magnitude from the base to the top is 2-20. The height of the tower will be equal to: h = 100 x 220/1000 = 22 meters.

Determining the height of objects by their shadow.

A milestone (pole, spade, etc.) is installed in an upright position at the object, the height of which is known. Then measure the length of the shadow from the milestone and from the subject. The height of the item is calculated by the formula: h = d1h1 / d. Where h is the height of the object in meters, d1 is the length of the shadow from the milestone in meters, h1 is the height of the milestone in meters, d is the length of the shadow from the object in meters.

An example of determining the height of objects on the ground by their shadow.

The length of the shadow from the tree is 42 meters, and from a pole with a height of 2 meters – 3 meters. The height of the tree will be equal to: h = 42 x 2/3 = 28 meters.

Determination of slope steepness by horizontal sighting and measuring steps.

Located at the bottom of the ramp at point A, a ruler is installed horizontally at eye level, sighted along it, and point B is noticed on the ramp. Then, in a couple of steps, measure the distance AB and determine the slope of the ramp using the formula: a = 60 / n. Where a is the slope of the ramp in degrees , n is the number of pairs of steps. This method is applicable with a steep slope of up to 20-25 degrees. Accuracy of determination of 2-3 degrees.

Determining the height of objects by angular magnitude, by the shadow of the object, determining the steepness of slopes by sight, by comparing the height with the laying, using a plumb line and an officer’s ruler.

Determination of the slope slope by comparing the height of the slope with its laying.

They stand on the side of the ramp and holding the edge of the folder and the vertical pencil horizontally in front of them at the eye level, determine by eye or by measuring a number showing how many times the extended part of the pencil MN is shorter than the edge of the OM folder. Then 60 is divided by the resulting number and as a result, the slope of the ramp is determined in degrees.

For greater accuracy in determining the ratio of the height of the slope and its laying, it is recommended to measure the length of the edges of the folder, and use a ruler with divisions instead of a pencil. The method is applicable when the slope of the ramp is not more than 25-30 degrees. The average error in determining the slope slope is 3-4 degrees.

An example of determining the slope slope by comparing the height of the slope with its laying.

The height of the extended part of the pencil is 10 cm, the length of the edge of the folder is 30 cm. The ratio of laying and height of the slope is 3 (30:10). The slope of the ramp will be 20 degrees (60: 3).

Determination of the slope slope using a plumb line and officer line.

Prepare a plumb line (a thread with a small weight) and apply it to the officer’s line, holding the thread with the finger at the center of the protractor. The ruler is set at eye level so that its edge is directed along the slope line. In this position, the rulers determine the angle between the stroke of 90 degrees and the thread on the scale of the protractor. This angle is equal to the slope of the ramp. The average error of measuring the slope of the ramp in this way is 2-3 degrees.

Based on materials from the Handbook of Military Topography.
A. M. Govorukhin, A. M. Kuprin, A. N. Kovalenko, M. V. Gamezo.

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