A map is a bird’s-eye view of the whole or a part of the earth drawn on a plane with special marks, reduced to the desired scale using mathematical methods. The information to be drawn on the map is natural forms such as generally seas, lakes, streams, mountains, hills, caves, or artificial facilities such as roads, dams, irrigation canals, fences, walls, and buildings. Apart from these, the geographical coordinate network is usually shown on maps. Special marks, lines, colors, and shapes indicate natural and artificial details.A map is a representation of a bird’s-eye view of the whole or a part of the earth drawn on a plane with special marks, reduced to the desired scale using mathematical methods. The information to be drawn on the map is natural forms such as generally sea, lake, stream, mountain, hill, cave, or manmade facilities such as road, dam, irrigation canal, fence, wall, and building. Apart from these, the geographical coordinate network is usually shown on maps. Natural and man-made details are indicated by special marks, lines, colors and shapes.
MAP PROJECTIONS
GENERAL PRINCIPLES
In simple terms, the map is the depiction of various information in the area it covers on a plan plane with certain standards.
The shape of the earth is generally accepted as a rotational ellipsoid (the shape formed by rotating any ellipse about one of its axes) or, more simply, a sphere. Whether the world is considered a rotating ellipsoid or a spherical map, the information on this curved surface is transferred onto the map, which is a plane. Information on such curved surfaces is transferred to map planes by using mathematical and geometrical rules. This process is called MAP PROJECTION.
In map projection, the surface information may not be transferred directly to the plane. Instead of a plane, other geometric surfaces such as cones, which can transform into a plane when cut along their main lines or cylinders can also be used. The plane or other auxiliary surfaces that can be transformed into a plane used in map projection are called PROJECTION SURFACE. Map projections created by mathematical rules are used for the construction of large-scale maps. For some very small-scale geographical maps or atlas maps, there are projection types developed using the rules of projection geometry. This type of projection is called PROJECTION. There is always a length, area, and shape relationship between the information on the world and the information subject to map making. When this information is transferred to a projection surface, the relations do not remain as they were on the original surface; some changes occur. The changes and distortions occurring in projection are called DEFORMATION. It is possible to calculate the deformation in different projection types. Firstly in map production, the meridians and parallels that make up the geographical coordinate network are displayed on the projection surface. Then, the information about the surface of the earth is transferred to the projection surface. Only one of the relationships between the information of the earth’s surface in terms of length, area, and shape is desired not to change when transferred to the projection surface, and mathematical relations are established accordingly. Deformation (distortions) are categorized into three groups length, area, and angle.
If the lengths in certain directions on the earth’s surface do not change on the projection surface and remain the same, this projection is called Length Preserving Projection. Likewise, if the area does not change, it is called Area Preserving Projection, if the shapes are similar, it is called Conform or Angle Preserving Projection.
Map projections have only one of these three properties. There is no map projection exhibiting all three features.

CLASSIFICATION OF MAP PROJECTIONS
The basis of map projections is to transfer the details of the earth’s surface on a plane with minimum errors in the most appropriate way according to the intended use of the maps to be made. Map projections are classified as follows:
- BY DESIGN:
- True projections
- False projections
- BY PROJECTION SURFACE TYPE:
- Projections onto a plane
- Projections onto a cone
- Projections onto a cylinder
- BY AXIS STATUS:
- Polar (Normal-Azimuthal) projections
- Equatorial (Transversal) projections
- Inclined axis projections
- BY THE FAITHFUL FEATURE:
- Angle accurate projections (Conform – Angle Preserving)
- Field accurate projections (Equivalent – Area Preserving)
- Length accurate projections (Equidistance – Length Preserving)
MERCATOR PROJECTION
This projection is an angle accurate projection system made onto a cylinder oriented in the north-south direction and tangential to the equator. When the cylinder is unfolded on the plane, the meridians are parallel and equidistant, and parallel circles are seen as parallel lines whose intervals increase as you go from the equator to the poles. In the projection, the angles between the meridian and parallel circles are 90° and equal to their original on earth i.e. the angles are preserved. In the projection system, there is no absolute scale to the projection, since the spacing of the parallel circles widens towards the poles and the meridians are projected parallel to each other. The scale is arranged differently along the meridian and parallel circles. Since the distance between the parallels will reach infinity as you go towards the poles, the poles cannot be shown in this projection system. Therefore, this projection system is used for the regions between the 80° north and 80° south parallels.
Since it is an angle-preserving projection, the Loxodromes (Loxodrome: The curve that connects two points on earth and forms the same angle with the meridians between these two points) are seen as straight in the projection. This system is the most suitable system for marine and aerial maps since aircraft and ship routes are easily drawn with straight lines.

GAUSS-KRUGER PROJECTION
This projection is also known as Conform Transversal Cylindrical Projection. This projection is an angle-preserving projection system and is made on the cylinder parallel to the equator. The cylindrical zone is tangent to the earth along the middle meridian, and the cylindrical axis is perpendicular to the earth’s axis of rotation. There is no length deformation along the middle meridian at which the cylinder is tangent. Increasing deformations occur as the zone moves away from the middle meridian. To avoid deformation, one should not go too far from the tangential meridian.
For example, in cartography, points are projected up to 3° away at most. If the area to be mapped is large, the projection of the area can be done by using a larger number of cylinders.
UNIVERSAL TRANSVERSAL MERKATOR (UTM) PROJECTION
The UTM projection was developed based on the Gauss-Kruger projection. The main feature of this projection system is the correctness of the angles and the length of the zone central meridian. The middle meridian and the equator are accurately traced. In the UTM projection, starting from the 180° meridian, the world is divided into 60 zones with longitudinal intervals of 6°. The zones are numbered from 1 to 60 in ascending order to the east. Each zone represents a projection system. The cylinder is tangent to the earth along the middle meridian of the zone. Thus, 3° right and 3° left of a zone are in the same zone. The territory of Turkey is located in zones with middle meridians of 27°, 33°, 39°, and 45° and the numbers of these zones are 35, 36, 37, and 38. These zones are the basis for the production of maps with a scale of 1:25000 and smaller. Larger scale maps (e.g. 1:5000) zone widths are taken as 3°. Thus, the middle meridians of 27°, 30°, 33°, 36°, 39°, 42°, and 45° zones are used in large-scale map making for Turkey. In the UTM projection, the regions between the 84° north parallel and the 80° south parallel are projected into zones. The maps of the Polar Regions between the 84° north parallel and the North Pole and the 80° south parallel and the South Pole are made according to the Universal Polar Stereographic (UPS) projection system. In the UTM projection system, there is no deformation on the meridian where the cylinder is tangent (zone central meridian). The deformation rises as the zone moves away from the middle meridian. Starting from the zone central meridian and gradually increasing towards the end of the zone, the deformation was tried to be distributed appropriately in this projection system. For this purpose, it is assumed that there is no deformation approximately in the middle of the distance between the zone central meridian and the zone edges. Thus, the maximum deformations at the ends of the zone were minimized and deformation was artificially created on the zone-middle meridian, which could not deform. This situation arose from the need to reduce deformations that would affect the use of maps. In the UTM projection, x and y coordinate values are multiplied by the reduction factor of 0.9996, to prevent abnormal growth (extreme deformation) of the lengths. To avoid a negative x value to the left of the zone central meridian, 500000 meters is added to the x value reduced by the reduction factor. Since y values are positive in the Northern Hemisphere, no constant value is added. However, for the Southern Hemisphere, 10000000 meters are added to the value of y reduced. The coordinates obtained in this way are called RIGHT and UP values.
In Turkey, the General Command of Mapping is authorized to produce 1:25000, 1:50000, 1:100000, and 1:250000 scale topographic maps using the UTM projection.

UNIVERSAL POLAR STEREOGRAPHIC (UPS) PROJECTION
In this projection, if the northern region is to be studied, a part of the sphere should be projected onto a plane with the projection point at the South Pole, and the projection point should be at the North Pole if the study is to be carried out for the south region. Usually the projection plane is placed so that there is only one point of contact at the pole.
In projection, meridians are straight lines emanating from the poles, and parallels are projected as concentric circles with the pole as the center. In this projection, there is a large expansion in the outer periphery relative to the center. In projection the angles are correct.

This projection is widely used in the middle meridians and especially in making maps of countries and continents with little latitude differences but considerable longitude differences (e.g. India, Egypt, USA, and Canada).
Projection can be done in two ways:
- Single Standard Parallel Projection: The cone is placed on the sphere in such a way that the vertical of the apex of the cone passes through the pole. Thus, the cone is tangent to the sphere from a pole to a parallel, and this parallel is called the standard parallel. In this projection, only the length of the parallelepiped to which the cone is tangent is correct.
Single Standard Parallel Projection

1. Single Standard Parallel Projection: The cone is placed on the sphere in such a way that the vertical of the apex of the cone passes through the pole. Thus, the cone is tangent to the sphere from a pole to a parallel, and this parallel is called the standard parallel. In this projection, only the length of the parallelepiped to which the cone is tangent is correct.
Double Standard Parallel Projection

In projection, the length of these two standard parallels is accurate. While the length distortion increases from the northern standard to the pole. From the other standard parallel to the equator, the length deformation (distortion) on the parallels between two standard parallels is relatively small.
In Lambert Conformal Conic Projection, meridians are straight lines emanating from a single point, and parallels are concentric circles drawn at true distances. The parallels and meridians intersect perpendicularly, and the center of parallel circles is the intersection of the meridians. Our 1:500000 and smaller scale maps were made with this projection method.
Universal Transversal Mercator

DIRECTIONS
In everyday life, directions are roughly indicated in terms such as right, left, forward, backward, and straight. In the military, there is a need for a common term and usage agreement that is valid all over the world in specifying the directions. In this respect, four main directions are taken as a basis and used. These are north (N), south (S), east (E), and west (W).

STARTING DIRECTIONS
Grid North: It is the direction of the vertical grid lines on the map. Grid North is marked with the letters GN.

Magnetic North: It is the direction from any point on the Earth’s surface to the magnetic pole, or the direction in which the compass needle points when released, without being subject to any magnetic influence. Magnetic north is usually indicated by a half arrow.

True North: This is also called geographic north. It is the direction from any point on the Earth to the North Pole. The direction of all longitude circles (meridians) is true north. True north is generally marked with a star.

DECLINATION DIAGRAM
Declination diagrams on large-scale maps are used to orient the map with sufficient accuracy with the compass and to calculate the deviation angles.
This diagram shows the deviation angle values and grid approach value of the map to which it belongs.
Declination values are the values of the year written on the map. The deviation angles are corrected according to the current year. These values are given to the accuracy of one degree minute, one milliradian, or one grad minute.
Using the Declination Diagram:
1. If grid north is east of true north (if the current location is east of the zone central meridian of the map used):

The given are values for the year 1990. If this diagram is used in the year 2000: 2000 – 1990 = 10 years
The annual change is +1′.2
The 10-year change is 10*1′.2 = 12′. 12′ is added to the declination angle values.
Natural Declination Angle (b): 3° 20′ + 12′ = 3° 32′
Grid – Magnetic Declination Angle (c): 2° 02′ + 12′ = 2° 14′
2. If grid north is west of true north (if the current location is west of the zone central meridian of the map used):

The given are values for the year 1990. If this diagram is used in 2000: 2000 – 1990 = 10 years
The annual change is -1′.6
The 10-year change is 10*1′.6 = 16′ 16′ is subtracted from the declination angles
Grid-Magnetic Declination Angle (c): 5° 15′ -16′ = 4° 59′
Natural Declination Angle (b): 3° 27′-16′ = 3° 11′
ANGLE UNITS USED ON THE MAPIN MAPPING
- Degree: It is one of the most used angle units. Subunits of the degree are minutes and seconds. Each angle that covers the 360 equal parts of a circle’s circumference from the center is called a degree. Sixty equal divisions of a degree are each called a minute. Each of the 60 equal divisions of a minute is called a second.
1° = 60′, 1′ = 60″. (1° = 60′ = 3600″)
The degrees, minutes and seconds are written as follows:
43° 24′ 56″ (43 degrees, 24 minutes, 56 seconds).
A circle is 360° and a right angle is 90°.
2.Grad: Each of the 400 equal parts of the circumference of a circle is called a grad. Each of the 100 equal parts of a grad is called a grad minute. Each of the 100 equal parts of a grad minute is called a grad second.
Grad (g), minute (c), second (cc) signs. A circle is 400 grads; a right angle is 100 grads.
3.Milliradian: The angle that covers each of 6400 equal parts of a circle’s circumference from the center is called Milliradian. 100 milliradian is called 1 whole. A circle equals to 6400 milliradians, a right angle to 1600 milliradians.
PROTRACTOR
- Protractors can be of various shapes: full circle, semicircle, square or rectangular. All of these divide a circle into units of angle measurement and, whatever their shape, they have graduations on the outer edge and a center point on the inner side. The center point is the center of the protractor circle, and all the graduation lines pass through this point.

2. To find the grid direction angle from one point to another on the map:
a- A line is drawn connecting these two given points. The line should be long enough to cut the protractor graduations from the protractor center.
b- The hole in the center of the protractor is coincided with the intersection of the drawn line and one of the grid lines in the north-south extension.
c- Provided that the hole in the center of the protractor remains at the intersection point, the 0-3200 milliradian line of the protractor (the line passing over the hole in the center of the protractor) is overlapped with the grid line in the north-south extension.
d- The grid direction angle is read where the line connecting the two points intersects the protractor.

3. To draw a direction given the grid direction angle from a known point on the map:
a- The center point of the protractor is placed directly on the known point and the 0-3200 milliradian line becomes parallel to the grid line in the nearest north-south extension on the map.
b- Without disturbing the position of the protractor, the value of the given grid direction angle is determined from the appropriate graduation and marked on the map.
c- The first point and the newly marked point are connected with a line.
d- This line is the grid direction angle direction.
SCALE
IMPORTANCE OF SCALE
In map-making, it is not possible to draw the lengths measured in the field in real size on a piece of paper. Therefore, the bird’s eye view of all or part of the earth is drawn in a reduced size. This reduction is done to a certain extent to improve accuracy. The ratio mentioned here is the map scale. Scale plays an important role both in the production and use of maps. When making use of the map, first of all, its scale should be known. Map scale is an important factor affecting the content of the map. The larger the scale of the map, the richer, more accurate, complete, and close to nature its content will be. As it can be understood from here, the scale is a criterion that determines the content and accuracy of the map as well as its areas of use.
For example small-scale maps cannot show all the details seen on large-scale maps. However, some details that are considered important in terms of the scale and intended use of the map are included on the map. This occurs as a result of the generalization process made as the scale of the map decreases. Generally, as the scale of the map decreases, details that are important to the purpose of the map are shown larger in order to focus the user’s attention in this direction. For this reason, less important details are shown slightly offset or not shown at all. The extent of this shift and the selection of details (generalization) increase continuously with decreasing scale.
DEFINITION OF THE SCALE

Scale is the ratio of the length between two selected points on the map to the horizontal length between the same two points on the earth (in the same unit of measure).
The ratio to be established between the measured length and the length to be drawn to be able to draw a length that we will measure on the land by reducing it to the desired ratio on paper is called scale.
NUMERICAL MAP SCALE
Map scale is defined as a numerical map scale, as it is often expressed as a fraction. Mathematically expressed as:
Map Scale = Map Length / Land Length = ML/LL
The land length should always be taken as the horizontal length. For example, if we want to determine the scale of the map since a horizontal length of 1 km in the field is 4 cm on the map
Map Scale = 4 cm/1 Km = 4 cm/100000 cm = 1/25000.
As can be seen from the above process, another important issue in determining the scale is that the numerator and denominator of the fraction must be in the same unit. As can be seen clearly, the map scale is unitless and the numerator is always denoted by the number 1.
If we express the scale formula as
M = 1/m = ML/LL
it means unit length on the map (1) and unit length on the land (m), here
M = Map Scale
m = Scale Number
According to the numerical example above, one unit of length on the map corresponds to 25000 units of length on the land. If 1 cm is taken as a unit, 1 cm on the map becomes 25000 cm on the land; if 1 m is taken as a unit, it means that 1 m on the map corresponds to 25000 m on the land.
Whether the map scale is large or small is determined from the fraction that gives the numerical map scale. As a general rule, the larger the number of scales, the smaller the scale of the map.
For example 1/10000 is greater than 1/20000
If the scale of the map is known, the horizontal length corresponding to each measured length on this map can be easily determined;
ML / LL = 1 / m LL = m*ML
For example, what is the LL if the ML=4 cm on a 1/50000 scale map? LL=m * ML=50000 * 4=200000 cm =2 Km.
Or vice versa is also valid. For example, the length of a horizontal length of 1000 m in the field on a 1 / 25000 scaled map
ML=LL / m=1000 / 25000=0.04=4 cm.
The map scale is defined only in terms of the ratio of the lengths, not the areas. For example: if a 1/25000 scale map is reduced to a 1/50000 scale; although the lengths are reduced by 1/2, the areas are reduced by 1/4. In other words, the length of 4 cm corresponding to 1 km on the 1/25000 scale map is 2 cm on the 1/50000 scale map, whereas the 1/25000 scale map covers only 1/4 of the 1/50000 scale map.
LINEAR SCALE (GRAPHIC SCALE)
Calculation is required to convert the lengths measured on the map to the land length with the help of a numerical scale. In order not to deal with these calculations, there is usually a linear scale outside the bottom inscription of the maps next to the numerical scale value on each map. A linear scale is a ruler printed on a map from which lengths on the map can be measured as actual land lengths. The ruler has a starting point (0). From this point to the right, sections are marked according to the length units (km, land mile, nautical mile, yard) to be used in the length measurement, taking into account the map scale. This part is called the Principal Scale. The tenths of the major scale are shown from the zero point to the left. This part is also called the additional scale and serves to measure lengths more accurately (directly to decimal points).
For example: To draw a linear scale in meters length measurement on a 1:25000 scale map, first draw two parallel lines 12 cm long and 1.5 mm apart. It is first divided into 4 cm sections (m=25000, ML=4 cm LL=ML*m=100000 cm=1000 m). In the next 4 cm section from the left end, zero (0) and 1000 m, and 2000 m numbers are written to the right. The part to the left of the zero starting point is divided into ten equal parts. Since each section in this section is 4 mm, it corresponds to 100 m. Here, numbers are written to increase by 100 to the left of zero, or 500 is written only between zero and 1000. Small pieces between them are found by counting if necessary. There are multiple linear scales in various units of length (meter, mile, yard, etc.) used on most maps.

USING THE LINEAR SCALE
Linear scale is generally used in two situations:
- To find the natural equivalent of any length measured on the map as horizontal length in the field:
a) The length of a line between two points on the map:
a.1. It is determined with a compass as follows. The left foot of the compass is placed on the zero point of the linear scale on the map. If the right foot lands on one of the full graduations on the principal scale, the digit read in this graduation becomes the desired length. If the right foot does not fall on the full graduation, as is often the case, the right foot of the compass is shifted to the left so that it comes to the first full graduation on the principal scale. Corresponding to this shifted length, the graduation hit by the left foot of the compass on the additional scale is measured from zero to the left. The desired distance is found by adding the length read on the additional scale to the length corresponding to the full graduation on the principal scale.
a.2. The same process can be performed with a straight-edged piece of paper instead of a compass. For this purpose, paper is placed between two points to be measured. The points are marked with lines on the paper with a pencil. Then, these lines are applied to the linear scale on the map, as explained above to find the land length.

b) If the length to be measured on the map is not straight, but a road, stream or any curve:
b.1. A compass is opened at a small enough aperture not to skip the corners of the curve, and the number of times it is applied with the compass to cross the curve is counted. By multiplying this number with the compass span value and applying the found length to the linear scale, the land length is found; or by initially applying the compass span value to the linear scale, the distance is found and multiplied by the number of applications of the compass to obtain the land length. However, since the curves are taken into account in this process, such measurements are inaccurate as the mistakes made in this process are multiplied by the number of applications. For this reason, it is more accurate to use variable compass apertures to make applications suitable for the curve instead of keeping the compass aperture constant. However, one should be very careful here. One should either apply each compass span to the linear scale and add them up, or draw each measured length on a piece of paper, transfer it to the line, add it up and apply the total compass length to the linear scale to find the length of the land.
b.2. The same process can also be performed with a straight-edged piece of paper. The paper is placed over the starting point of the curve to be measured and this point is marked on the paper. Then, by turning the paper along the curve, the parts that are close to the line are overlapped on the edge of the paper, and the overlapping parts are collected on the paper one after the other. Thus, the length of the curve to be measured is written flat on the paper. Then, this length on the paper is applied to the linear scale as above and the land length of the curve is found.

- To map a natural horizontal length measured in the field:
a) If the horizontal or reduced horizontal length measured in the field is close to one of the full graduation in the principal scale section of the linear scale, the right foot of the compass is applied to that section. The left foot is extended to whichever of the sections on the additional scale to the left of the zero. In this way, the length measured in the field is found as the aperture of the compass legs by using the linear scale. This length obtained can be carried on the map with the help of compass feet.
b) The same process can be performed by using a straight-edged paper instead of a compass.
SLOPE
DEFINITION OF SLOPE
The angle formed by the line between two points with the horizon plane (horizontal plane) is called the slope of that line. The slope of any line on the land is found by dividing the elevation difference (vertical length) between the points at the two ends of the line by the horizontal length between the same points.
This is equal to the tangent of the angle of inclination in the figure. The planning and successful implementation of any operation will be possible by selecting the appropriate tools and equipment for the terrain and slope conditions. In other words, it is very important to know the limitations of the terrain and slope conditions in the examination and evaluation of our own possibilities and capabilities and the enemy’s capabilities. This examination and evaluation will be made primarily on the map.
Elevation curves are used for any information that needs to be known or found about the slope.
Slopes are generally classified as steep, moderate and gentle slopes. The slope has a great effect on pedestrian walking speed, motorized and live transportation vehicle speeds and climbing possibilities.




SLOPE CALCULATION
CALCULATING OF SLOPE BETWEEN TWO POINTS ON THE MAP IN PERCENTAGE
- The horizontal length between two points whose slope is to be calculated is measured on the map and converted to the land length according to the map scale.
Land Length (LL) = Number of scales (m)*Map Length (ML) = Horizontal Length (HL)
- The heights of both points are found with the help of contour lines and the height difference between the two is calculated.
Vertical Length (VL) = Elevation of Point B (HB)*Elevation of Point A (HA)
- The ratio of the height difference (vertical length) to the horizontal length gives the slope.
Since the result will be a fraction, it can be converted to a percentage with a simple proportion.
EXAMPLE: Let the horizontal length between points A and B on the map be 3000 m, the height of point A is 550 m, and the height of point B is 700 m. Accordingly, the height difference (VL=HB-HA) between points A and B becomes 150 m. In this case, the slope from A to B is
SLOPE = VL/HL=150/3000=0.05=5/100=5%.
When using a fraction or percentage to describe the slope, a plus or minus sign should be given with the slope each time to indicate that the slope is increasing or decreasing.
In the above example the slope would be +5% from A to B and -5% from B to A.
EXPRESSION OF SLOPE BETWEEN TWO POINTS ON THE MAP IN ANGLE UNITS
Since the ratio of the height difference to the map distance is the slope, to find out how many degrees correspond to the ratio obtained as 0.05 or 5% when this ratio decreases per the example above
- If there is a table of natural values of trigonometric functions, the number 0.05 is sought from its tangent column and the value of 2° 52′ at the level of this number is defined as the inclination angle.
- If there is a logarithm table of trigonometric functions, first the logarithm of 0.05 is found as 8.69897 from the logarithm ruler of numbers. Angle value at the level of 8.69897 from the tangent column in the angles section of the logarithm is 2°52′.
- If there is a pocket calculator with trigonometric functions, write the number 0.05 and get the ARCTAN directly to calculate the angle as 2° 52′.
- If none of the above are present, in order to convert the percent slope to angle value, the results are obtained by multiplying the result by the constant number of 57.3 if it is required in degrees, the constant number of 1000 if desired in milliradian, and the constant number of 63.6 if desired in grads. This method gives near-accurate results at angles up to 20 degrees.
EXAMPLE: Formula of slope in degrees
VL/HL= 360/2n=VL/HL*57.3
0.05*57.3 = 2° 865’
To find the fraction of degrees in minutes:
If 1°=60′,
0° 865’=x
x=60*0.865=51′.9=52′
As a result, the slope is 2° 52′ in degrees.
EXAMPLE: The formula for slope in milliradians
VL/HL=6400/2n*1000
0.05*1000=50 milliradian
EXAMPLE: Formula of slope in grads
VL/HL=400/2n=VL/HL*63.6
0.05*63.6=3 grads 18 minutes are obtained.
CROSS-SECTION
DEFINITION OF CROSS-SECTION
Information about the general structure of the terrain can be obtained by looking at the situation of the contour lines on the map. However, in cases where accuracy is demanded, it is necessary to extract cross-sections of the directions to be examined. The best way to describe the terrain along a given direction is by cross-section.
A cross-section is a scaled surface line on a map along a direction, between two points, or along a non-linear line. In other words, it is the scaled display of the fluctuation (rise or fall) occurring along the cross-section line on the land surface with a continuous line.
The surface curve expressing the cross-section of the land is the intersection of the vertical plane containing the cross-section direction or the beginning and end points of the cross-section and the center of the Earth with the surface of the Earth. In non-linear cross-sections, it is the intersection of the corrugated surface with the earth, which includes the traced section line and the center of the Earth. Land profiles are required in the surveys of numerous engineering projects. For example, in road construction projects, in the design of energy transmission lines, and in the design of irrigation and drainage channels, it is necessary to know the land profiles.

CROSS-SECTION SCALE
There are two different scale concepts in the cross-sectioning process. The first is the horizontal scale and the other is the vertical scale. While no problem arises because the horizontal scale is the same as the map scale along the cross-section, if the heights are tried to be shown at the same scale, the height differences cannot be reflected on the section line in a way that is easily visible.
As the scale of the map gets smaller, the fluctuation in the cross-section line, indicating the height differences, becomes more and more imperceptible.
In order to eliminate the mentioned inconvenience, the scale of the heights is kept larger than the map scale (i.e. the horizontal scale) as the scales of the maps get smaller. In other words, there is an exaggeration in the representation of heights. The smaller the horizontal scale, the higher the exaggeration rate.
The vertical scale is the scale found by multiplying the horizontal scale with the amount of exaggeration determined to better express the heights. The vertical scale is always greater than the horizontal scale, and the amount is equal to the proportion of the exaggeration. In reality, there is no rule in exaggerating the elevations in cross section, unlike the horizontal scale. The purpose of cross-sectioning is to determine the vertical scale.

CROSS-SECTION TERMS AND DESCRIPTIONS
- Topographical Peak:The highest of part a hill
- Military Summit: A fixed line or point from the highest part of the front slope of any hill or ridge towards the skirt of that hill or ridge from which surveillance is most practicable. The military peak is always below the topographic peak.
- Cross-Section Scale: Two separate scales are used while cross-sectioning. These are horizontal scale and vertical scale.
- Horizontal Scale: It is the ratio of the distance measured along the cross-section direction to the actual land length on the section. If the measurement is taken without changing the map while making a cross-section, the horizontal scale is the same as the map scale.
- Vertical Scale: The cross-section line represents both the horizontal distances on the map and the elevation and descent of the land. However, as the map scale of the height differences on the surface decreases, the vertical scale is mathematically found by multiplying the exaggeration ratio by the horizontal scale (Vertical Scale=Horizontal Scale*Exaggeration Ratio)
- Defilade: It is the natural and artificial heights between two points determined on the land or on the map that may interfere with the visibility and the effects of weapons (firing).
- Mutual Visibility: The ability of two points to see each other
- Invisible Zone: It is the whole zone hidden from sight by the defilade.
- Height of Line of Sight: The depth of the invisible zone, the maximum height of the invisible zone, or the height of a particular point in the invisible zone.

AREAS OF USE OF CROSS-SECTION
- Marking visible and invisible areas
- In the planning of road and railway construction
- In the planning of oil pipeline construction
- In the planning of soil splitting and filling works
- In the investigation of the real conditions of a piece of land
- In measuring the slope of a piece of land (vertical scale=horizontal scale)
- In measuring the movement distance
- In the design of energy transmission lines
- In the design of irrigation and drainage canals

TAKING CROSS-SECTIONS FROM THE MAP
THINGS TO KNOW FIRST IN TAKING CROSS-SECTIONS
The scale of the map, the number of meters every one of the equidistant contours, the determination, and restriction of the direction in which the cross-section will be made, and whether or not exaggeration will be made in the representation of the heights, that is, the vertical scale is determined.
-Scale of the map
-How many meters the equivalent height curves cross
-Determination and delimitation of the direction to be sectioned
-Whether there will be exaggeration in the representation of heights, that is, the vertical scale should be determined
The parallel lines to be drawn on the paper to be used for cross-sectioning show the consecutive contour lines on the map. In other words, these parallel lines are the same lines that correspond to the isotropic curves that express heights from sea level.
Determining the spacing of parallel lines is the most important point of cross-sectioning. This interval is the vertical scale equivalent of the height differences between the contour lines.
EXAMPLE:
Map scale: 1:25000
Height exaggeration rate: 2.5-fold Spacing between contour lines: 10 m
Vertical Scale=Horizontal Scale*Exaggeration
= 1: 25000*2.5
= 1: 10000
Parallel Line Spacing (mm) =Vertical Scale*10 m*1000
= 1: 10000*10*1000
= 1 mm
ORDER TO FOLLOW






USES OF THE CROSS-SECTION
POINT TO POINT
It is the simplest sectioning process to understand whether two opposite points see each other.
Two points to be cross-sectioned are connected with a line on the map and the desired cross-section is drawn on this line. In cases where mutual visibility is desired, there is no need to make cross-sections across the entire line. Only the high points detected along the section line are passed onto the drawing. A straight line connects the two points in the section. If none of the cross-sectional heights exceed this line, it is understood that there is visibility between the two points in the field.
POINT TO LINE
They are the sections taken to determine the visible and invisible parts of a land part, such as a position or an access road that cuts the front lines. The current location (observation post or any other place) is marked on the map and a line is drawn at each end of the section to be cut. The highest points within the angle formed between these lines are selected, cross-sectional lines are drawn from each of them to the location, and cross-sectioning is applied from point to point. The hidden parts of the road in the target area should be specified in order to show the true boundaries of the invisible areas.
POINT TO REGION
It is a cross-section taken to determine the length and width of dead spots or areas that can be protected from enemy fire within the firing range. Various sections showing all the high and low points sufficiently reveal the topographic situation of the region. The right and left borders of each scanned region are transferred to the corresponding cross-section lines on the map. Thus, the width and length of the invisible regions appear. These parts are also traced on the map for easy reading. When the status of a wider region is desired to be determined, more cross-sections are taken on both sides and the regions are extended to where they are needed.
LINE TO ZONE
In cases where it is necessary to determine the visible and non-visible areas from the observation posts along a line, or to determine the best way of placing the weapons along a line to take the area under fire, it is necessary to take cross-sections from the line to the area. For this, cross-sections are taken from various points (from point to region) along the ridge. For each, the non-visible regions are marked and placed on the map with an overlay. In this way, dead spots and areas that are not visible or that weapons cannot see and shoot are revealed.
DETERMINATION OF THE HEIGHT OF LINE OF SIGHT
The ability of a defilade to provide vertical cover against enemy fire and surveillance can also be easily determined by taking a cross-section. It is used to determine whether our troops advancing along a valley that cuts the enemy front will be fired upon or seen by the enemy if the locations of enemy weapons or lookout points are known.
QUICK CROSS-SECTION
A cross-section study to quickly reveal whether a location will be visible when viewed from a point (peak) is called a quick cross-section.
On a map for quick cross-sectioning:
- Connect the point where you are standing with the point you are looking at.
- On this line, the defilades that will obstruct the view are marked.
- Find the altitude of the standing point, the point being looked at and the defilade points.
- The perpendiculars are subtracted from the standing point and the defilade.
Height of the Vertical Line from the Standing Point =
Altitude of the Standing Point – Altitude of the Viewing Point/10*2
Height of the Vertical Line from the Defilade =
Altitude of the Defilade – Altitude of the Viewing Point/10*2
- The parts bordering both verticals are joined and extended towards the point of view.
- The point of view is non-visible if it is below this line, if it is above it, it is visible. If it is right on the line, it appears tangent.
If you do not have time, the altitude of the location, the altitude of the target, and the altitude of the terrain in between is determined on the map. On a blank sheet of paper, a vertical line is drawn from the current location (e.g. 950 m, 9.5 cm perpendicular) according to the altitude. The distance of the defilade is taken from the map and a perpendicular line is drawn from the defilade. Similarly, the distance to the target is transferred to the paper. Then, a perpendicular line is drawn from the target. The ends of these perpendiculars from the current location and the target are connected by a line. If the perpendicular from the defilade falls below this line, there is visibility; if it cuts, there is no view.

FINDING THE QUICK CROSS-SECTION THROUGH CALCULATION
The quick cross-section can also be found by calculating the height and distance ratios. For this, the similarity in right triangles formed by heights and distances is used.
Altitude of observed location – Target altitude = h defilade altitude – Target altitude = h’
Observation post target distance = l
Defilade to target distance = l’
The height h’ in the figure represents the difference in altitude of the target. The similarity in the triangles indicates that the observation post and the target are tangentially facing each other.
Considering the EB / DA = BC / AC = EC / DC ratio
1. The target appears tangential when h’ / h = l’ / l.
2. The target appears well when h’ / h < l’ / l. 3. When h’ / h > l’ / l, the target does not appear at all.

ROUGH LOCATION DETERMINATION AND MOVING TO THE DESTINATION
ROUGH LOCATION DETERMINATION
The method of determining the location of the destination point by determining the direction of travel and distance from a certain point is called rough location determination. In other words, it is an application to find the location of a point in the field with polar coordinates. To go from a selected point A to point B:
- Mark the location of the starting point A and the destination point B on the map.
- Connect these two points with a straight line.
- By measuring the length of this line, the terrain (map) distance is calculated.
- The grid direction angle from A to B is measured on the map.
- The measured Grid Direction Angle (GDA) is converted to Magnetic Direction Angle (MDA).
- The calculated magnetic direction angle is connected to the compass and the direction to be traveled is determined.
- When the calculated distance from A to the determined direction is traveled, B is reached. The land distance calculated by measuring from the map is the horizontal distance. You should keep in mind that the land distance will be longer depending on the roughness and the slope of the land.

Mark the starting point A and the destination point B on the map.

Connect these two points with a straight line.

By measuring the length of this line, the terrain (map) distance is calculated.

The grid direction angle from A to B is measured on the map.

The measured Grid Direction Angle (GDA) is converted to Magnetic Direction Angle (MDA).

The calculated magnetic direction angle is connected to the compass and the direction to be traveled is determined.
TRAVERSE
ROUGH LOCATION DETERMINATION AND MOVING TO THE DESTINATION (TRAVERSE)
It is preferable to take the shortest route to the destination along a straight line from a certain starting point. The terrain and the risk of being seen by the enemy often do not make it possible to reach the target in a straight line. For this reason, from the starting point to the target, a path consisting of interconnected broken lines is followed. This type of navigation consists of establishing a rough position using polar coordinates, then using this point as a starting point and proceeding in the same way to a second point towards the destination.
The points where the direction changes until reaching the destination are called control points. These points must be carefully recognized and selected in order to maintain the direction and go towards the target.

CASES FOR ROUGH LOCATION DETERMINATION AND MOVING TO THE DESTINATION
- If the map of the region is outdated
- If the scale of the region map is small
- In regions where there is very little land detail (desert, vast plains, etc.)
- Advancing in densely wooded areas
- When there is a land disturbance (cliff, etc.) that will prevent the passage in the walking direction
- During night walks
ORDER OF WORK IN ROUGH LOCATION DETERMINATION AND MOVING TO THE DESTINATION
- The starting and destination points are marked on the map.
- Control points on the route are marked on the map.
- From the starting point to the destination, all points including control points are connected by a straight line following each other. The distances between the points and the direction angles from one point to the other are measured.
- The direction angles and the values of the distances are written on a scale. This is called a walking chart.
- In the walking chart, the direction angle to the next point is written next to each control point in MDA.
- Moving to the starting point, the MDA to the first control point is connected to the compass.
- A clear guiding point is selected in the determined direction and the movement is started towards it. (Easily recognizable single trees or buildings during the day, objects projected on the horizon, etc., at night the North Star can be used as a guide.)
- The distance from the guiding point to the control point without losing eye contact is checked from the vehicle’s kilometer clock. If on foot, the distance is found by stepping.
- When it is decided that the control point has been reached, it should be ensured that the point marked on the map is reached by making a thorough land survey. (Otherwise, as a result of chain errors, it is possible to go to a very different place instead of the destination)
- To go from the first checkpoint to the second, the operations in (6), (7), and (8) are repeated.
- Upon reaching the destination point, a detailed map and land survey are performed to check whether the current location is the destination. If possible, the traverse should be connected to at least one known point on the route. This is achieved by passing over a well-known point to be selected while traveling.
CONSIDERATIONS FOR ROUGH LOCATION DETERMINATION AND MOVING TO THE DESTINATION
- On foot:
a- An approximate step length is considered to be 75 cm. However, it is of great benefit for each person to know their own stride length. For this purpose, a measured length should be stepped and the average step length should be calculated. In the field, a correction should be made to the stride lengths according to the following conditions.
- Slopes: Steps get lengthen on descents, and shorten when on ascends.
- Winds: Frontal winds shorten the stride length, while the wind blowing from behind increases the stride length.
- Type of Soil: Sandy, gravelly, muddy and similar grounds shorten the step length.
- Precipitation: Snow, rain and ice shorten the stride length.
- Clothing: Clothing that is too heavy shortens the stride length, type of footwear affects stepping and therefore the stride length.
- Mental and physical condition affects stride length. Fatigue shortens stride length.
b- During angle measurement with a compass, the compass should be kept away from metal objects such as steel helmets and rifles.
- On Motorized Land Travels:
The rough location determination by motor and the operations to be performed on motorized land travel are the same as those performed on foot land travel. However, two important points should not be forgotten:
a- Direction measurements with a compass should be made away from the vehicle (approximately 20 m) and the compass should never be used inside the vehicle.
b- Distance measurements are made with the distance indicator available in the vehicle. For this reason, the lengths are written on the walking chart in terms of the unit (km, miles) in which the distance indicator is used.
3. Rough Location Determination and Moving to the Destination in Cases of No Map:
Reaching the target with rough location determination can also be applied in cases where there is no map in hand.
Procedures to be carried out are similar to those to be carried out when a map is available. However, since there is no map at hand, the sketch showing all points from the starting point to the destination is drawn on a plain paper instead of a map. Starting from the first point, direction angles and distances to other points are written. The north direction is marked on the sketch.