Additional information, curiosities and glossary of terms

Date: 04/12/2022 Author: Antonio H.

GPS (Global Positioning System), It is a system that allows to locate an object that is on Earth with high precision. To do this, the receiving device locates at least four satellites from the satellite network placed in orbit, from which it receives signals that indicate the identification and the time of the internal clock of each satellite. With this information the distance to the satellite is calculated. Knowing the distance to these satellites and by the "trilateration" method, the GPS device can determine the position on the Earth's surface.

With three satellites, the device is capable of determining the latitude and longitude of its position, that is, its position in two dimensions. By adding a fourth satellite, it will also be able to calculate the altitude, obtaining the position in three dimensions. The signals emitted by each satellite form a sphere with the satellite in the center, the point of intersection of all the spheres is what determines the position where the GPS receiver device is located.

Satelites GPS

Satelites 2D


As a curiosity, the satellites transmit on three different frequencies of the radio frequency L band (1000 – 2000 MHz) of the electromagnetic spectrum.


Global Positioning Systems There are currently four major global positioning systems:


GPS: The best known and currently used is GPS, which is a system owned by the United States Department of Defense and consists of three parts: orbiting satellites, base stations, and receivers. Its coverage extends to the whole world. Its real name is NAVSTAR (Navigation Satellite Timing and Ranging).

GLONASS (GLobalnaya NAvigatsionnaya Sputnikovaya System): It is Russia's state-owned positioning system and also has worldwide coverage.

Galileo: Galileo has been developed by the EU as an alternative to GPS and GLONASS.

BeiDou: It is the system created by China and has worldwide coverage although it offers greater precision in Asia and the Pacific. BeiDou means Big Dipper in Chinese.

There are also other systems, although their coverage is only regional, such as the NavIC system in India or the QZSS system in Japan.

Waypoint (reference point) It is a specific position of a point on Earth defined by geographic coordinates. It is identified by a name and usually incorporates an icon or graphic symbol and other additional information such as a comment, date, altitude.

Geographic coordinates Spherical angular coordinate reference system to represent locations on earth. At least three values will be needed to represent a location: one for the horizontal position, one for the vertical position, and a third indicating the distance to ground level, which is identified as sea level. The values of horizontal and vertical position are usually given in sexagesimal degrees, since these are angles whose center is the Earth.

The terrestrial sphere is divided with imaginary lines called meridians and parallels. Meridians are lines that run from the North Pole to the South Pole. The prime meridian, zero meridian or Greenwich meridian is the imaginary line that joins the north and south poles passing through the town of Greenwich in England, the rest of the meridians take this as a reference. To the east the meridians are taking positive values up to 180º while to the west the values taken are negative.


The latitude of a point on the earth's surface is the angle between the plane passing through the equator and the line passing through the point and the center of the earth. All points with the same latitude form imaginary circles that are "parallel" to each other and parallel to the equator, which is the larger of the "parallels."

The longitude of a point on the earth's surface is the angle between the plane passing through the Greenwich meridian and the plane of the meridian passing through the point. All points with the same length form semicircles that pass through the poles similar to the segments of an orange.

Latitud y longitud


Notation systems: sexagesimal degrees and decimal degrees, The sexagesimal system is used to express measurements of time and angles using three groups of values: degrees, minutes, and seconds. It is based on the number 60 and is the system traditionally used in paper maps.

Time: 1 h 60 min 60s
Degrees: 1º 60’ 60”

In the case of geographic coordinates, for latitude it is usually indicated, in addition, the hemisphere to which they belong, north (N) or south (S) and for longitude, if they are to the east (E) or to the west (W). (W in English).

For example: 39°49'51.8"N 3°46'49.2"W

Northern Hemisphere: Latitudes between 0° and 90°
Southern Hemisphere: Latitudes between 0° and -90°
East of Greenwich Meridian: Longitudes between 0° and 180°
West of Greenwich Meridian: Longitudes between 0° and -180°

In computer applications, the decimal system is usually used, in which minutes and seconds are transformed into a decimal number.

39°49'51.8"N 3°46'49.2"W = 39.831045, -3.780322

For the manual conversion of sexagesimal degrees to decimal degrees, the sum of:

Degrees + minutes divided by 60 + seconds divided by 3600:


39°49'51.8"N = 39 + (49/60) + (51.8/3600) = 39.8310
3°46'49.2"W = 3 + (46/60) + (49.2/3600) = 3.7803

To carry out the conversion there are multiple applications and calculators on the internet

Unevenness and slopes The unevenness, by definition, is the difference in height between two or more points. The zero level point will be the point where we start the route, regardless of the height of that point at sea level.

The accumulated unevenness will be positive if the final height is greater than that of the starting point (we have accumulated meters ascending) and negative if the final height is less than that of the starting point (we have accumulated meters descending). If the starting point and the end point coincide, the accumulated difference in level will be zero.

Strictly, to calculate the cumulative difference in elevation of a route, we will add the positive difference and the negative difference. For example, on a circular route that climbs a 500-meter pass and has the same start and finish point, the positive difference in altitude will be 500 meters and the negative difference of another 500 meters, so the accumulated difference in level will be 1000 meters. On any route with the same starting point and arrival point, the positive accumulated difference will be equal to the negative accumulated difference.

As usually the routes are not usually just going up or down, but there are concatenated ascent sections and descent sections, the positive cumulative difference will be the sum of all the height gains and the negative one of all the height losses. Therefore, it will not coincide with the height gained or total altitude gain, which is the difference between the highest elevation and the lowest elevation of the route.

Example: We start from point A with an altitude of 500 meters above sea level and end at point F with an altitude of 600 meters above sea level, passing through intermediate points B, C, D and E.



We add all the altitude gains in the ascending sections:
A-B: 600-500 = 100
B-C: 1000-600 = 400
D-E: 1300-700 = 600
Positive cumulative drop: 1,100 meters

We add all the altitude losses in the descending sections:
C-D: 700-1000 = -300
E-F: 600-1300= -700

Negative cumulative elevation gain: -300 – 700 = -1,000 meters

Total cumulative drop: 1,100-1,000 = 100 meters.

In cycling when talking about "accumulated unevenness" reference is usually made to the positive unevenness, since it gives a better idea of the difficulty of the route.

To determine the difficulty of a route, as important as knowing the unevenness is knowing the slopes of the different ramps. The slope is the relationship between the distance climbed vertically and the horizontal distance traveled to ascend it. A quick and simple formula to calculate the average slope of a section would be the following as long as the vertical distance and the horizontal distance to the point of ascent are known:

Slope (%) = Vertical distance x 100 /Horizontal distance


According to known data: distance travelled, elevation angle, vertical distance, etc. There are other methods in which trigonometric calculations are applied.





Altitude, Height and Elevation It is common to use the terms altitude and height interchangeably to refer to a location. Next we will recall the definition of these terms.

Height is the vertical distance of a body from the earth's surface (the ground or the sea).
Altitude is the vertical distance of a body from sea level, regardless of whether the object is on the earth's surface or above it (plane, drone, ...)
Elevation is the vertical distance to sea level of a point that is on and in contact with the Earth's surface.

In the following graph, we see that the green point is located at a certain altitude and at a certain height, while the yellow point on the ground surface is at a certain altitude, but its height is zero since it is touching the ground. The land on which it is located is at a certain elevation.


In certain cases the values may coincide, although we will be referring to different concepts. For example, for the yellow dot the elevation matches the altitude and if the body were flying over the sea, its altitude would match its height.




Basic notions about map interpretation: contour lines Isolines are used to represent the distribution of a variable (temperature, atmospheric pressure...) on a surface. The isolines are lines that join points with the same value on the surface, the value can be the one that is chosen, temperature (isotherms), pressure (isobars), precipitation (isohyets).
The isolines that join points of equal altitude of the terrain are known as "contour lines" and allow the representation of the terrain surface in two dimensions.



On cartographic maps we will find two or three types of contour lines represented, normally in brown.

Contours: thinner lines.
Master contour lines: thicker lines.
Auxiliary contour lines: dashed thinner lines

A number is displayed on master curves that represents the absolute value of altitude along that line. The numbers are oriented so that the top of the number indicates which way the altitude value increases.
If between two master lines, for example 900 and 950, we find four level curves, these will divide the space into 5 parts and we will interpret them as the intermediate values between 900 and 950, that is: 910, 920, 930 and 940.
If a master line does not have an indication with a number, probably due to lack of space in the visualization, we will interpret that it follows the same interval as for the rest of the master lines.

The summits or tops are the points of the terrain of maximum relative altitude and are also shown on the map. In the following example we can see that there are several summits (indicated by a dot and numbers in black) of 999, 984, 883, 887, 1051... meters.



The gradient or degree of variation of the altitude is always perpendicular to the contour. When the lines are very close to each other, they indicate that the altitude variation is very fast, which means that the altitude increases or decreases sharply.
The distance between contour lines will depend on the scale of the map and is usually between 50 and 100 meters for the main lines and between 10 and 20 meters for the intermediate (thinner) lines.

The scale of a map indicates the equivalence between the actual distance and the distance represented on the map. For example, a scale of 1:10,000 means that one meter on the map equals 10,000 meters in reality, or that one centimeter on the map equals 10,000 centimeters in reality. Larger scales will cover more of the terrain but the detail will be less.

If the map has a legend or documentation of the symbols used, it is convenient to review it as it will provide us with a lot of information about the units of measurement used, the colors, orientation, scale and elements represented.

In the map of the previous image we can see that there are some non-permanent streams or rivers marked with a broken blue line.



also an olive grove on the left bank, below (at a lower altitude) a leafy area and scrub areas.




Simbolos suelos


Magnetic declination The magnetic field generated by the Earth is not immutable, on the contrary, it constantly varies both in its position and in its intensity and, moreover, periodically (in cycles of thousands of years) it is reversed. Currently, he travels about 100 meters a day.
Since a compass will always indicate the magnetic north pole, it is convenient to know the relationship or difference between the north indicated by the compass and the true or geographic north. This concept is magnetic declination.
Magnetic declination (“variation” in aeronautical navigation) is the angle between true (geographic) north and magnetic north, that is, it is the difference angle between geographic north and the north that a compass will mark.

Declinacion magnética

The magnetic declination will depend on the position on earth from where it is measured, being zero at the point on earth where they are aligned.

The following figure shows the declination for three points A, B and C located in different positions on the earth's surface. For point C the declination is zero since it is aligned with the geographic north pole and the magnetic north pole.
Declination is considered positive if magnetic north is east of true north and negative if magnetic north is west of true north.


Angulos declinacion

In order to know the magnetic variation in any point of the planet, maps are made where the magnetic declination in each location is indicated by means of isolines that represent a specific angle, since they are isolines that represent angles, they are called isogonas. Once our position or the position of the route is known, the closest isogonic line to our position will be taken as a reference. The special isogonic line that joins points of variation “0º” is called agonal line (without angle). A compass located in a position corresponding to an agonal curve points exactly to true north, since its magnetic declination will be zero.

Simbolos suelos

Map developed by NOAA/NCEI and CIRES
Published December 2019

Navigation concepts. Course and heading We will call course (course) the trajectory to follow, it is the planned or desired route between two points A and B. It could be identified as the straight line that joins both points.
The true course (TC: True Course) would be the angle in degrees between the true or geographic north and the course. It is measured from the geographic (or magnetic) north in a clockwise direction.
Since the meridians on a map all point to true north, they can be used as 0 degree references to measure angles to true north.
Since the geographic north and the magnetic north pole do not coincide (see the article "Magnetic declination" in the "Additional information, curiosities and glossary of terms" section of this site) we will also define the magnetic course (MC: magnetic course) as the angle in degrees between magnetic north and the course. It is measured from magnetic north and also clockwise.
In this case, the meridians cannot be used as references of 0 degrees, instead we will use the compass.
In some environments, the Desired Track (DTK) refers to the true course and the magnetic course interchangeably, depending on the north used as reference (geographic or magnetic).

Curso verdadero y magnético

We will call heading (Heading) the angle formed by the north (geographic or magnetic) and the longitudinal axis of the aircraft (in the case of an airplane it would be where its nose points). It will be called true heading (TH: True Heading) if the angle is taken with respect to geographic north and magnetic heading (MH: Magnetic Heading) if it is taken with respect to magnetic north.

The heading does not necessarily coincide with the course since the aircraft or ship can change its orientation to counteract a crosswind or water currents. In the case of airplanes it is usual that, to maintain a constant course, the aircraft turns its nose slightly towards the wind.

The angle formed between the desired course and the heading of the aircraft will be called the drift correction angle (WCA: Wind Correction Angle) since, by definition, drift is the deviation of a ship from the established heading, for effect of wind, sea or current. It's basically the difference between where the ship is pointing and where it's actually moving. This angle is usually calculated by the flight computer. If the wind comes from the left, the correction angle will be negative. If it comes from the right it will be positive.

Ángulo deriva


Map Types The maps can be classified according to different criteria, in our case we will classify them according to the content and the way of representation.

Raster Map: They consist of georeferenced images, that is, it is an image file to which coordinates are assigned so that it is displayed in the correct location when opened with an application. They can be built with standard image formats (jpg, bmp...) accompanied by a calibration file, although there are specific formats for digital cartography

Mapa raster


Maps of this type can take up a lot of space in memory, so they are usually available as mosaic maps in which the entire map is divided into smaller pieces (tiles) to handle only the parts of the map corresponding to the area to be viewed. use.

Vector maps: This type of map is composed of vector objects such as polylines, polygons or points that contain additional information such as color, labels, type of terrain. These elements and other information will be arranged in layers that will be displayed based on the display options setting or zoom level. These maps may contain information that allows an application to automatically calculate routes.

Mapa vectorial


DEM: Digital Elevation Model. They are maps that contain only information about terrain altitude. They will normally be used in combination with another map to render it in 3D and assign altitude to route points and waypoints. (See section "Information on data calculation methods" on this site)

Depending on the mode of representation of the terrain, we can distinguish between:

Topographic map: Raster or vector map that represents the terrain using contour lines, colors and graphic symbols to show information about the area such as geographical features, roads, trails, sources...

Orthophoto: These are raster maps consisting of aerial images of the terrain with orthogonal projection (perpendicular to the surface). To avoid distortions due to the point of view of the camera, the aerial photographs are rectified to adapt them to the shape of the terrain.

Mapa ortofoto

Roads: These are vector maps especially oriented to urban and interurban navigation. Useful elements for the motorist or road user are highlighted.

Mapa carreteras


Map Projections

A map is a two-dimensional representation of the earth, which has three dimensions, the transition from a three-dimensional representation to two dimensions is known as a projection.
In order for there to be a correspondence between the points on the curved surface of the earth and those on the flat surface of a map, a grid is used with x and y coordinates obtained from the longitude and latitude coordinates through different mathematical calculations. This causes that there is inevitably a deformation when making the projection, so it will be depending on what parameters we want to read (distances, surfaces or angles) that one or another of the available projection systems will be used, making a projection that correctly represents impossible. all three simultaneously.

Based on this we can distinguish three types of projection:

Equidistant projection: where distances are preserved
Equivalent projection: where surfaces are preserved
Conformal projection: where the shape or relationship of angles between points is preserved.

To improve the result of the projections, geometric surfaces can be used that will later be lowered in the plane. Let's see some of the most common:

Cylindrical projection. It is obtained by placing a tangent cylinder to the terrestrial sphere at Ecuador. The Mercator projection is the best known cylindrical projection. The meridians and parallels will be perpendicular in the projection, the distance between the parallels will increase as the latitude increases. This will produce a larger deformation the further away the north or south position is from the Equator. The Equator will be the only line where the scale will be preserved. The territories and countries located further north will appear larger than life and the poles are not represented as they would be at infinity. Although this system causes the areas near the poles to be greatly distorted, it is useful for navigation since it is a type of "conformal" projection, that is, it preserves the angular relationship between points.

Proyección cilíndrica

The Transverse Mercator projection is a variant of the Mercator projection where the meridians are expanded to the east or west of the Greenwich meridian. The meridians are represented by curved lines parallel to each other and convex towards the equator. In this case, the distortions are greater the further away the position is from the Greenwich meridian and this will be the only line where the scale will be preserved.

Proyección transversa

The Universal Transverse Mercator Projection (U.T.M.) is another projection system, based on the transverse projection, which divides the globe into 60 sectors or zones along the Equator (each sector covers 6 degrees of longitude). Each zone has a central meridian and the intersection of this central meridian with the Equator is established as the "x" and "y" origin of the zone.


Proyección transversa de Mercator UTM

Conical projection: Meridians and parallels are projected onto a conical surface tangent to the vertex of the cone on the axis formed by the poles. The meridians will become straight lines starting from the pole and the parallels will become concentric circles centered on the poles.

Proyección cónica


Clouds can give us valuable information, we are going to review the different types of clouds that we can find on our outings.

Proyección cónica

High clouds (above 6,000 meters)

Cirrus clouds: White, somewhat transparent, do not have interior shadows or cast a shadow on the ground. They form long, thin filaments, sometimes aligned like tufts of hair. They are formed mostly by ice crystals and usually produce halos with the sun or moon. With few and fine cirrus clouds, the weather will be stable, but it will probably tend to get worse if they begin to acquire volume and density.

Cirrocumulus: Similar to cirrus clouds but more dense, forming an almost continuous layer with rounded shapes. They also do not have interior shadows and are completely white. They usually anticipate the arrival of a cold front. They can also form halos.

Cirrostratus: Appears as a white and transparent layer like a veil that covers part of the sky without a clear structure. They usually present elongated striations of a certain width. They form halos. They usually appear before a large increase in cloudiness and worsening weather.

Medium clouds (between 2,000 and 6,000 meters)

Alto cumulus: They are white and bluish gray. With inner shadows. They are made up of water and ice. They are denser and more compact and have a varied appearance, lenticular, globular, stratiform. They do not produce precipitation, but anticipate the arrival of bad weather due to storms.

AltoStratos: Forms a translucent gray or bluish sheet with dense clouds mixed with finer areas. They allow the passage of the sun that will appear as a luminous disk. They are usually a harbinger of fine rain and a drop in temperature.

Nimbostratus: Dark gray in color with more or less opaque areas. They block the sun completely. They give precipitation with a high probability of light or moderate character, both rain and snow.

Low clouds (between 0 and 2,000 meters)

Stratocumulus: White with gray areas of different intensities. Large size and notable vertical development. These types of clouds do not usually cause precipitation.

Strata: Gray in color and poorly defined, it looks like fog since they are low above the ground and can cause a light drizzle.

Cumulonimbus: They are clouds of great vertical development, being able to cover from the lowest level to the highest. They are dense and their upper part sometimes extends into a large plume, the lower part being dark in colour. It usually produces showers and electrical storms. It is made up of large water droplets and ice crystals on top.

Cumulus: Large, flattened base and large bumps at the top. White color with abundant leftovers. They tend to be typical in stable and sunny weather and do not present a risk of precipitation although they can grow to form cumulonimbus clouds when there are strong updrafts and high humidity.




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