# Measurement of distances and determination of areas by topographic map, numerical, linear and transverse scale.

To measure distances using a topographic map, use a numerical, linear or transverse scale. Distances between points on a topographic map are usually measured by a compass gauge or curvimeter..

## Topographic map numerical scale.

This is the scale of the map expressed by a fraction, the numerator of which is one, and the denominator is a number that shows the degree of reduction on the map of the terrain lines. The smaller the scale denominator, the larger the map scale. The signature of the numerical scale on the maps is usually accompanied by an indication of the magnitude of the scale – the distance on the ground (in meters or kilometers) corresponding to one centimeter of the map.

For example 1:50 000 – in 1 centimeter 500 meters. The scale in meters corresponds to the denominator of the numerical scale without the last two zeros. When determining the distance using a numerical scale, the line on the map is measured linear, the result in centimeters is multiplied by the scale value.

## Linear scale topographic map..

Linear scale is a graphic expression of a numerical scale. It is a straight line divided into certain parts, which are accompanied by signatures, meaning distances on the ground.

## Transverse scale topographic map.

Transverse scale – a graph (usually on a metal plate) for measuring and plotting distances on a map with extreme graphic accuracy (0.1 mm). The standard (normal) transverse scale has large divisions equal to 2 cm, and small divisions (left on the graph) equal to 2 mm. In addition, on the graph there are segments between the vertical and inclined lines, equal in the first horizontal line of 0.2 mm, in the second – 0.4 mm, in the third – 0.6 mm, etc.. Using the standard transverse scale, you can measure and plot distances on a map of any (metric) scale. The transverse distance reference consists of the sum of the reference based on the graph and the distance reference between the vertical and inclined lines. In the figure above, the distance between points A and B (with a map scale of 1: 100,000) is 5500 meters (4 km + 1400 m + 100 m).

## Distance measurement on a map with a compass meter.

When measuring distance in a straight line, the compass needles are set at the end points, then, without changing the compass solution, the distance is measured on a linear or transverse scale. In the case when the compass solution exceeds the length of the linear or transverse scale, the integer number of kilometers is determined by the square coordinate grid, and the remainder is determined in the usual scale order.

## Measuring distances on a map by way of building up a compass solution. ## Measuring distances on the map with a compass step. It is convenient to measure broken lines by successively building up the compass solution in straight sections. Measurement of distances and lengths of curved lines is carried out by sequential deposition of the compass step. The magnitude of the compass step depends on the degree of tortuosity of the line, but, as a rule, should not exceed 1 cm. To exclude a systematic error, the compass step length, determined by scale or ruler, should be checked by measuring the line of a kilometer net 6–8 cm long.

The length of the curved line measured on the map is always slightly less than its actual length, since it is not the curve line that is measured, but the chords of individual sections of this curve. Therefore, a correction must be introduced into the results of measurements on the map — the coefficients of increasing distances.

## Measuring distances on the map with a curvimeter.

By rotating the wheel, the arrow of the curvimeter is set to zero division, and then the wheel is rolled along the measured line with uniform pressure from left to right or from bottom to top. The resulting readout in centimeters is multiplied by the scale value of this map.

## Determination of distances by the rectangular coordinates of points.

The determination of the distances to the rectangular coordinates of points within one map zone can be done according to the formula where D is the line length, x1, y1 are the coordinates of the starting point of the line, x2, y2 are the coordinates of the end point of the line.

## Determination of areas by squares of the kilometer grid of the map.

The area of ​​the plot is determined by counting whole squares and their shares, estimated by eye. Each square of the kilometer grid corresponds to: on maps of a scale of 1:25 000 and 1:50 000 – 1 km2, on maps of a scale of 1: 100 000 – 4 km2, on maps of a scale of 1: 200 000 – 16 km2.

Based on the book Methods of Autonomous Human Survival in Nature.
Edited by L. A. Mikhailov.