A topographic map is a two-dimensional map that depicts three-dimensional terrain, while the height of the earth's surface is indicated using contour lines. As with any other map, the distance between two points on a topographic map is measured along a straight line connecting them, as if a bird were flying between these points. This is done in the first place, and only then is the surface topography and other terrain features that may affect the overall length of the route taken into account. Learn how to measure distance along a straight line.
§13. Map distance
To determine the distance between points of terrain (objects, objects) from the map, using the numerical scale, you need to measure the distance between these points in centimeters on the map and multiply the resulting number by the scale value.
Fig. 20. Measuring distances on the map with a compass meter
For example, on a map with a scale of 1: 50,000 (a scale value of 500 m), the distance between two landmarks is 4.2 cm.
Therefore, the desired distance between these landmarks on the ground will be equal to 4.2 · 500 = 2100 m.
A small distance between two points in a straight line is easier to determine using a linear scale (see Fig. 20). To do this, a compass meter is sufficient, the solution of which is equal to the distance between the given points on the map, applied to a linear scale and take a count in meters or kilometers. In fig. 20 the measured distance is 1250 m.
Large distances between points in straight lines are usually measured using a long ruler or compass gauge. In the first case, a numerical scale is used to determine the distance on the map using a ruler. In the second case, the solution ("step") of the compass meter is set so that it corresponds to an integer number of kilometers, and an integer number of "steps" is set aside on the segment measured by the map. The distance that does not fit into the integer number of "steps" of the compass gauge is determined using a linear scale and added to the obtained number of kilometers.
In this way, distances are measured along winding lines. In this case, the "step" of the compass meter should be taken 0.5 or 1 cm, depending on the length and degree of tortuosity of the measured line.
Fig. 21. Measuring distances along winding lines
To determine the length of the route on the map, a special device called a curvimeter is used. It is convenient for measuring winding and long lines. The device has a wheel, which is connected by a gear system to the arrow. When measuring a distance with a curvimeter, you need to set its arrow to zero division, and then roll the wheel along the route so that the scale readings increase. The resulting readout in centimeters is multiplied by the scale value and the distance on the ground is obtained.
The accuracy of determining distances on the map depends on the scale of the map, the nature of the measured lines (straight, winding), the selected method of measuring the terrain, and other factors.
You can most accurately determine the distance on the map in a straight line. When measuring distances using a compass meter or ruler with millimeter divisions, the average value of the measurement error in the flat areas of the terrain usually does not exceed 0.5–1 mm on the map scale, which is for a map of scale 1: 25 000–12.5–25 m , scale 1: 50,000 - 25-50 m, scale 1: 100,000 - 50-100 m. In mountainous areas with a large slope steepness, errors will be greater. This is due to the fact that when shooting the terrain on the map, it is not the length of the lines on the Earth’s surface that is plotted, but the length of the projections of these lines onto the plane.
With a slope slope of 20 ° and a distance of 2120 m on the terrain, its projection onto a plane (distance on the map) is 2000 m, i.e., 120 m less. It is estimated that at an inclination angle (slope steepness) of 20 °, the result of measuring the distance on the map should be increased by 6% (add 100 m per 100 m), at an inclination angle of 30 ° - by 15%, and at an angle of 40 ° - by 23 %
When determining the route length on the map, it should be noted that the distances along the roads, measured on the map with a compass or curvimeter, are shorter than the actual distances. This is explained not only by the presence of descents and ascents on the roads, but also by some generalization of the meanders of the roads on the maps. Therefore, the result of measuring the route length obtained on the map should be multiplied by the coefficient indicated in the table taking into account the nature of the terrain and the scale of the map. 3.
Scale of maps and their use
When creating topographic maps, the linear dimensions of all terrain objects projected onto a level surface are reduced by a certain number of times. The extent of this reduction is called the map scale. The scale of the map can be expressed in numerical form (numerical scale) or in graphic (linear, transverse scale), in the form of a graph.
Distances on a map are measured using usually a numerical or linear scale. More accurate measurements are made using the transverse scale.
On a linear scale, the segments are digitized, corresponding to distances on the terrain in meters or kilometers. This facilitates the process of measuring distances, since no calculations are required.
Determining distances and areas from a map. Measuring distances.
When using the numerical scale, the distance measured on the map in centimeters is multiplied by the denominator of the numerical scale in meters.
For example, the distance from the point of the GHS mark. 174.3 (apt. 3909) to a fork in the road (apt. 4314) on the map is 13.96 cm, on the ground it will be: 13.96 x 500 = 6980 m. (Map scale 1: 50 000 U-34-85 -BUT).
If the distance measured on the ground should be postponed on the map, then it should be divided by the denominator of the numerical scale. For example, the distance measured on the ground is 1550 m. On a map of scale 1: 50,000 it will be 3.1 cm.
Measurements on a linear scale are performed using a compass meter. A solution of the compass connects two contour points on the map, between which you need to determine the distance, then apply to a linear scale and get the distance on the ground. Curved sections are determined in parts or using a curvimeter.
Definition of areas.
It is useful to remember the following ratio of 2 x 2 mm., Are appropriate for the scale:
1: 25,000 - 0.25 ha = 0.0025 km2
1: 50,000 - 1 ha = 0,01 km2
1: 100 000 - 4 ha = 0.04 km2
1: 200 000 - 16 ha = 0, 16 km2
The determination of the areas of individual plots is carried out with the alienation of land for the Ministry of Defense.
The accuracy of determining distances on the map. Correction in the length of the route.
The accuracy of measuring lines, areas on a topographic map. You can buy truck tractors and trucks at the best prices on the website auto-holland.ru. All trucks passed pre-sale training and inspection control (instrumental, computer and visual).
The accuracy of measuring lines and areas, first of all, depends on the scale of the map. The larger the scale of the map, the more accurately the line lengths and areas are determined by it. Moreover, the accuracy depends not only on the accuracy of measurements, but also on the error of the card itself, inevitably during its compilation and printing. Errors can reach 0, 5 for lowland areas, and up to 0, 7 mm in mountains. The source of measurement errors is also the deformation of the map and the measurements themselves.
Absolutely with the same error, flat rectangular coordinates are determined from topographic maps of the above scales.
Correction to the distance for the slope of the line.
For example, the distance between two points, measured on a map, on a terrain with an inclination angle of 12 degrees is 9270 m. The actual distance between these points will be 9270 x 1.02 = 9455 m. Thus, when measuring distances on a map, you must enter corrections for the slope lines (relief).
Straight-line distances of great length in one six-degree zone can be calculated by the formula:
This method of determining the distance is mainly used in preparing artillery fire and when launching missiles at ground targets.