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Aircraft navigation is the science about the means and tools of controlling aircrafts while flying from one point on earth’s surface to another according to the trajectory selected in time and space. 

1.1. General information on aircraft control and navigation

Aircraft navigation involves the set of actions of determining aircraft’s position in space and the flight according to selected track at the specified height using the least amount of fuel, and safe and timely arrival to the destination. The majority of these complex actions are automatically or semi-automatically performed by flight control systems. During the flight, pilots need to perform may other actions: constantly monitor the air space and avoid collision with other aircrafts, observe storm clouds and make decisions on how to fly them around, notify flight control services about the times of flying over intermediary waypoints and borders of flight control regions, communicate data on weather conditions, inform about any changes in the aircraft navigation plan, and communicate other data.
Arrival to the destination is only possible after determining the initial position of the aircraft (visually and following the reading of devices). Afterwards, flight direction is determined, distance to the specified location, speed, and fuel reserve, and estimated time of arrival to the destination are calculated.
During the flight, pilots perform two main operations: aircraft control and navigation. Aircraft control involves maintaining the position of the aircraft in the air, or changing the position by managing flight speed and aerodynamic control surfaces. When the aircraft is well-managed, pilot can easily maintain it’s position in space, or to change it. Then, the pilot is able to determine the position of the aircraft, select flight direction and height, and contact flight control services through radio communication. This is called aircraft navigation.
Aircraft control and navigation may be carried out either manually when the pilot himself perform navigation calculations and controls aerodynamic surfaces with the help of ropes, or automatic when navigation calculations and control of aerodynamic surfaces are performed by automatic control equipment.

1.2. Aircraft management and control parameters

The initial question that arises when talking about aviation is how the aircraft wings or helicopter blades maintain the heavy loads in the air. The answer lays in the basic laws of air flow going around these aircraft aerodynamic surfaces. These laws are common both for planes, helicopters or other similar aircrafts, therefore we only speak about planes in this section.
According to Bernoulli’s principle, when gas (or fluid) flow moves around a body, e.g. a wing, the pressure on its surface shall be less at the points where flow speed is higher. A wing or any other aerodynamic surface is directed so that the higher speed of flow is at the top (Figure 1a). The higher pressure from the bottom lifts the surface up thus creating aerodynamic force R (Figure 1b). .

Figure 1. Lift force

Explications to picture:

Slėgis iš viršaus – Pressure from above

Slėgis iš apačios – Pressure from the bottom
Keliamoji jėga – Lift force
Aerodinaminė jėga – Aerodynamic force
Atakos kampas – Angle of attack
Oro srautas – Air flow
Styga – Chord line

The amounts of lower and higher pressures depend on the speed of flight, air density, wing shape, smoothness of the surface, and wing orientation of the air flow (angle of attack). The difference between these pressures is called coefficient of lifting capacity C or coefficient of the angle of attack.
When increasing the angle between the surface and the air flow to a critical value, the speed of air flow over the surface increases, and further encloses the upper side of the surface thus increasing aerodynamic force.
The angle between the air flow and the surface, e.g. chord line of wing chord line, is called angle of attack or angle of incidence α.
A change in the angle of attack causes the changes in the size, location, and direction of aerodynamic force; it is not perpendicular to the air flow or to the chord line. When the angles of attack α are small the aerodynamic force R is easier to be distributed to vertical and horizontal components: the actual wing lift force Y that is perpendicular to the air flow, and the wing opposition force P which coincides with the air flow.
When flying straight at the same height at a constant speed, the lift force is equal to the force of gravity of the aircraft. Air resists to the movement of wing and the entire aircraft, and therefore engine’s traction force needs to compensate the resistance P. When the plane is going up or down, or when the direction or speed of plane is changed the balance of all these four aerodynamic forces changes. The pilot needs to observe these aerodynamic forces either visually or based on the readings. For example, when the speed of flight reduces, the reduced lift force cannot compensate gravity force, and the plane starts sinking. When the ground is too close the pilot may not be able to increase the speed on time (lift force), and a crash may follow. When the angle of attack is small the lift force may be less than the force of gravity, and the plane might start to sink. When the angle of attack is increased to a critical level (approx. 20°), air flow starts detaching from the surface, the pressure at the top of the surfaces increases, and the lift force starts reducing rapidly. Increasing the engine thrust results in increased flight speed, and air resistance increases proportionally to the square of speed which in turn may result in overloads to aircraft body. Resistance starts to increase when the angle of attack is approaching the critical value.
The size of aerodynamic forces depends not only on the speed of flight but also on the density of air (flight height). Since the lift force and resistance increase following the increase of the angle of attack, there is only one angle of attack when the ratio of lift force and resistance force is the highest.
From taking off until landing, the plane is flying following the trajectory (moves in three-dimensional space) changing the height, direction and speed of flight. The trajectory of the plane is controlled by pilots or flight control systems. This is carried out with help of control surfaces. While flying under the selected trajectory, two ways of controlling the plane are possible. When the plane is not in the required point of trajectory, or when it’s position in space does not satisfy the requirements, the position of aircraft aerodynamic control surfaces is changed. When the plane starts flying at the selected direction at the required speed, the positions of control surfaces remain unchanged or are adjusted slightly.
A plane moving in air is affected by aerodynamic forces. The magnitude of these forces depends on weather conditions, such as density, viscosity, humidity, and compressibility. Air density obstructs movement. Therefore, managing a plane close to earth and high in the sky where air thinned out differs.
Every part of plane or other aircraft is subject to the gravity of earth; the resultant force of all the particles is concentrated in the aircraft mass centre MC (Fig. 2). Every point in the surface of aerodynamic plane is under pressure of air flow; the resultant force of the forces is concentrated in the centre of lift force. Similarly, the centres of thrust and drag forces are generated. When the centres of these forces and the centre of mass do not match, the momenta M that twist the plane in space occur. The momenta are easy to analyze from the perspectives of plane’s longitudinal axis X, transverse axis Y, and vertical axis Z.

2 pav. Lėktuvo ašys ir šių ašių atžvilgiu veikiantys momentai
Fig. 2. Plane’s axes and momenta operating with respect to these axes

Explications to picture:
Vertikalioji (pokrypio) ašis Z – Vertical (yaw) axis Z
Išilginė (posvyrio) ašis Z – Longitudinal (roll) axis Z
Skersinė (polinkio) ašis Y – Transverse (pitch) axis Y

During the flight, the plane not only moves in a three-dimensional space but also changes orientation of the axes with respect to the Earth. The angle between the longitudinal and horizontal axes of an aircraft is called pitch (Fig. 3). The angle is positive when the longitudinal axis is directed upwards from the horizontal plane, and negative when it is directed downwards. The pitch shows the position of an aircraft with respect to the horizon rather than the direction of movement. The angle of attack and the pitch are not equal since the flow of air not always move horizontally, and the chord line (the line connecting the most remote front and rear wing points) is not parallel to the longitudinal axis of the aircraft.
The angle between the transverse axis of the aircraft and the horizon is called roll. It is positive when the right wing is lower. Roll occurs when aircraft angle turns around its longitudinal axis.
Plane’s rotation angle around the vertical axis is called yaw. The plane’s position in space is managed by changing speed vector (speed and direction of flight).
Yaw defines the extent of aircraft’s turning around the vertical axis. The heading of an aircraft is the angle between the selected line on the horizontal plane, e.g. the meridian, and the longitudinal axis of the aircraft.
Yaw, roll, pitch, and angle of attack are the main parameters of controlling the plane. They are measured with the help of attitude indicators, gyro verticals, and inertial systems.

Figure 3. Pitch and the angle of attack

Explications to picture:

Sparno styga – Chord line of the wing
Išilginė ašis – Longitudinal axis
Atakos kampas  – Angle of attack
Oro srautas –  Air flow
Polinkis – Pitch

Controlling a plane and a helicopter is similar in many aspects, however control devices are different, therefore we will not speak about helicopters.
Planes are controlled with the help of aerodynamic planes. When aerodynamic forces impact the plane, the aircraft is subject to respective momenta; it changes its position in space and moves in the required direction. When there is no need to change plane’s position, control planes are positioned so they are not subject to aerodynamic forces.
The balance of forces and momenta is required to maintain the constant speed of a plane at the same height. When an aircraft maintains the position or restores the position after a random disturbance, it is called a statically stable aircraft. High static stability of a plane is not a good feature as higher momenta (higher surface control forces) are required to change its position in space.
Plane’s stability is important with respect to all the three axes, however the critical significance in maintaining the aircraft’s stability lays in longitudinal stability, i.e. stability with respect to transverse axis (pitch stability). The left and right sides of the plane are almost symmetrical, therefore the centre of mass and the centre of lift force are not very distant from the longitudinal axis; no significant roll momenta are present and they do not alter significantly upon changes in the flight speed and density of air. The situation with longitudinal stability is different. The place of centres of mass in an empty and loaded aircraft differs, and the position of the centre of lift force depends on the flight speed, air density, angle of attack, etc. Centre of masses may be before the centre of lift force (heavier front) and behind it (heavier rear). This results in occurrence of larger pitch momentum. At the rear of the majority of aircrafts, the horizontal surface (stabilizer) is smaller than wing surface, which improves longitudinal stability through offsetting the momentum of pitch.
A modern plane has many aerodynamic control surfaces. They may be divided into primary and secondary. In all the planes, there are three main primary control surfaces: ailerons, rudders, elevators (Fig. 4). They operate as extensions of wings, keel, and stabilizer; and in neutral position, does not affect the aircraft stability. Primary surfaces perform the main aircraft control functions by changing its position in space with respect to the centre of mass.

Figure 4. Light aircraft control surfaces

Explications to picture:
Pokrypio keitimas  – Yaw change
Kilis – Keel
Krypties vairas – Rudder
Aukščio vairas – Elevator
Stabilizatorius – Stabilizer

Eleronas  – Aileron
Skersinė ašis – Transverse axis
Išilginė ašis – Longitudinal axis
Posvyrio keitimas – Roll change
Polinkio keitimas – Pitch change
Eleronas – Aileron

Angular positions of aircraft are changed with the help of ailerons, rudders, and elevators (stabilizer). All these control surfaces perform two main functions – control planes and stabilizes their position. Aircraft flight path is controlled through controlling these surfaces. Then the surfaces move slower however at higher interval. When stabilizing the position of the aircraft in the trajectory, control surfaces move more quickly however at smaller interval.
Ailerons are fitted along the rear edge of wings, closer to the ends of wings. Ailerons are used to alter aircraft flight heading: when turning the steering wheel in the cabin (steering wheel, helm), the roll and ailerons coherently rotate to different directions. The lift force of the wing with its aileron rotated upwards reduces, and the one of the other wing increases. As a result of these two forces, the plane rotates around its longitudinal axis (i.e. making a roll). The total lift force of an aircraft is no longer vertical – the emerged horizontal component alters the yaw (heading). Ailerons are operated manually with the help of ropes that connects ailerons with the steering wheel in the cabin. If required, the shear force of a steering wheel is increased with the help of drive train (hydraulic or electromechanical amplifiers). When the flight path is automatically controlled, the drive trains of ailerons are controlled by automatic pilots or other automatic control systems.
Rudder and keel are used to maintain the stability of aircraft yaw (heading). By operating the rudder, aircraft yaw is maintained or slightly changed. It is operated with the help of pedals or automatically, by turning the rudder to the left or right. The emerging aerodynamic force turns the rear of the aircraft either to the left or to the right, and the “nose” of the aircraft starts turning. When there is a need to change the yaw more (change the heading) ailerons are used. Rudder is also used for compensating slippage when the plane is making a turn; operation of ailerons and the rudder is then aligned. Rudder is operated manually with the help of ropes that connects the rudder and the pedals in the cabin; if necessary, shear strength of pedals is reinforced by power train. When the trajectory of fight is managed automatically, power train of the rudder is operated by autopilot or other automatic control systems. Irregularities of air flow, engine thrust imbalance, and other factors cause aircraft turbulence in the interval of several degrees, therefore, rudder operation scheme in larger aircraft contain automatic turbulence inhibitors.
An elevator is used to change aircraft pitch by pulling a joystick towards you or pushing it away. In this way, a required aircraft height and speed are maintained (speed is reduced by increasing the pitch). The elevator is used to alter flight height while taking off and landing. When pulling the joystick towards oneself, elevator’s rear edge rises. Air flow starts pressing the elevator down, which reduces the lift force of aircraft “tail”. Since the lift force of wings does not change, when the “tail” of an aircraft becomes heavier, aircraft starts rotating around its transverse axis, and the pitch increases (aircraft’s nose rises up). When pushing the helm against, the elevator is pushed downwards, the lift force of the wheel plane increases, the “tail” of the plane rises, and the pitch reduces. Elevator is operated same as other primary control surfaces.
The secondary aerodynamic control surfaces (Fig. 5) involve slats, flaps, stabilizers, air and ground fairings, and trimmers. In the first place, their purpose is to help controlling the aircraft with the primary surfaces; they improve aircraft stability or operability at certain moments of flight.

Fig. 5. Large aircraft control surfaces

Explications to picture:

Užparniai – Flaps
Krypties vairo sekcijos – Rudder sections
Aukščio vairai – Elevators
Vidinis eleronas – Inner aileron
Spoileriai – Spoilers
Išorinis eleronas – External aileron
Priešsparniai – Slats

Secondary surfaces also improve other aircraft’s characteristics, e.g. increasing wing lift force with the help of flaps and slats results in reduced take-off and landing speeds thus reducing the time the aircraft spends on the runway.
Air fairings are small aerodynamic surfaces on the top of wing. Lifting of them results in increased roll momentum that forces the wing downwards. Air fairings work together with ailerons, therefore ailerons may be smaller for they require less force.
Stabilizer is a horizontal aerodynamic surface at the rear of an aircraft. It improves longitudinal stability of an aircraft when fuel consumption changes the balance, loads of different weight are being carried, or upon significant change in aerodynamic forces during the flight. Light aircrafts are equipped with uncontrolled stabilizers with an elevator at the rear part, or are only equipped with an elevator. In the latter case, elevator also performs the function of a stabilizer. Stabilizer of larger aircrafts is operated (reset) automatically; it works together with the elevator: when tilting the elevator further from the neutral position, the stabilizer is being reset automatically until the elevator returns to the inswept position with respect to the stabilizer. Therefore, elevator may be smaller, operation requires less force, and it never gets to the edge position (there is always power reserve left).
Without a stabilizer, an elevator for a large aircraft would be large-sized and requiring powerful power trains. Operation of a stabilizer does not require powerful power trains. It is not being tilted like an elevator but is rather reset manually or automatically. The range of stabilizer movement is approximately 15–19 degrees.
Taking into account the position of the control surface, and the engine thrust, the moments of force for wing and tail surfaces are formed. They maintain the aircraft in the required position or adjust it by turning the aircraft around its longitudinal, transverse or vertical axes. Aircraft control system is the entirety of devices and appliances that stabilizes the position of the aircraft in space or adjusts it manually or automatically. Aircraft control involves maintenance or adjustment of pitch, roll, and yaw, wing lift force, and aircraft speed. While operating an aircraft, the fact the aircraft has six degrees of freedom of movement in space needs to be taken into account. It can move in the directions of three coordinate axes and rotate around them.
Controlling the power trains of aerodynamic surfaces by cables is rather complicated; the cables require good technical maintenance. There are aircrafts with electrical control of power trains (Fly by Wire). Trains are controlled by integrated cockpit sensor signals instead of cables.
The aircraft position in space is defined by the angles of pitch, roll, and yaw, and the position with respect to air flow – angle of attack and slip angle. When changing aircraft’s position in space and the engine thrust, the following components of navigation are adjusted: altitude, speed, heading, drift, etc. Position in space, and components of navigation are measured by avionics equipment and devices. Knowing the navigation and control components, the pilot controls the flight path himself, or the signals of avionics devices are used for automatic control. Larger aircrafts have many devices and equipment installed showing the information required for aircraft control and navigation. These devices include attitude indicator, gyro-verticals, altimeters, flight speed cameras, the angle of attack and overload gauges, slip gauges, indicators of flight control surfaces’ positions, etc. However, these devices are not enough, and their constant monitoring cause stress for the pilots. While operating an aircraft, there might be various unexpected situations, and the pilots need to respond to them adequately. Secondary aerodynamic surfaces improve aircraft’s characteristics, and aircraft control becomes more reliable, faster, and easier using automatic flight path and engine control devices.

1.3. Aircraft navigation

The line the centre of mass of a moving aircraft follows is called flight trajectory. While on the way to the destination, an aircraft needs to move following the selected trajectory without unpermitted deviations in space and time. Pilots needs to know not only the position of an aircraft in space or with respect to air flow (control elements), but also its location (coordinates), flight height, direction and speed, aircraft position in relation to the ground points, and other data that are called navigation elements.
The most easily navigated are aircrafts that fly slow and low when there is high visibility, and it’s possible to orient oneself by observing the earth (visually). In such case, the simplest navigation devices – height, speed, and heading meters – are enough. It might seem that everything is very simple: checking the map, turning the aircraft in the right direction, and flying following the readings of the compass. However this is not the case in the reality. Side wind is carrying the aircraft to the side from the selected direction; magnetic compass is not very precise, therefore the pre-known visual landmarks, i.e. railroad, highway, river, lake, need to be observed. Some sections from one landmark to another might need to be covered changing the direction of flight thus extending the trajectory of the flight.
Visual flight is only permitted provided high visibility around the aircraft, and sufficient distance from the aircraft to the cloud base. Such height and visibility requirements are called Visual Flight Rules (VFR). When flying according to the visual flight rules, pilot receives lots of visual information; however the major devices are required.
When the altitude is higher, or meteorological conditions are worse, pilot shall observe Instrument flight rules (IFR) during the flight. While flying following the Instrument flight rules, the pilot relies only on navigation and control devices. The required information is obtained by measuring the air pressure around the aircraft, aircraft orientation in Earth’s magnetic field using gyro devices. The accuracy of determining the actual aircraft location has significantly improved after the introduction of radio navigation tools – radio compass Automatic Direction Finder (ADF), radio navigation receiver VOR (Very High Frequency Omni Directional Radio Range), Distance Measuring Equipment, GNSS (Global Navigation Satellite System), ILS (Instrument Landing System), etc.
Aircraft navigation tools may be divided into the following three groups – those measuring angles, distances, and speeds. According to the navigation tools used, aircraft navigation may be divided into the following main types: instrumental navigation, radio navigation, inertial navigation, navigation light, and automatic flight control.
Instrumental navigation has been known since the introduction of aircrafts. At those times, the simplest devices were pressure altimeters, magnetic compasses, airspeed gauges, and a clock. These devices were simple and reliable, however, the accuracy of determining aircraft location using these devices decreases with longer flight distances (times); magnetic compasses stops working in higher latitudes.
Modern aircrafts are equipped with far more accurate control and navigation devices, however, the older ones remain in use. Most often, they are used as backup ones.
Radio navigation tools are installed in all the aircrafts; and operation of the majority of them requires ground facilities. The accuracy and range of radio navigation tools depend on the radio frequency used, modulation, position of an aircraft in relation to ground facilities, and other radio-technical parameters. Radio navigation may be divided into four main groups – distant, close, satellite, and landing. Radio navigation tools operate reliably and accurately in low visibility conditions, during day and night, in continents and oceans. The main features of these tools useful for navigation include constant speed of radio waves, and propagation of these waves in the shortest path from the transmitter to the receiver.
Inertial navigation instruments operate autonomously measuring aircraft accelerations occurring due to the effect of non-gravitational forces – engine thrust and air resistance, lift force, and so on. These navigation tools are expensive but they operate at all altitudes regardless of weather conditions, and therefore they are used for large aircraft. After adjusting or resetting the exact coordinates of aircraft location immediately before the flight, inertial system can continue measuring the coordinates of the aircraft to determine its position in space, measure the speeds and the distances covered, however the accuracy worsen with increased flight time.
Navigation lights and other visual navigation tools are used in air ports. The tools involves various lights and signalling systems, coloured smoke, etc. They are intended to help pilots to orient upon taking off, landing, or rolling down the runways when other navigation systems no longer operative. The aircrafts themselves are equipped with navigation lights. These include navigation lights, external lights and flashes.
Automatic control of aircraft path in space and time requires using flight control systems. They receive control and navigation signals from the systems of total and static pressure, gyro devices, inertial, radio and satellite navigation systems. Navigation calculations, adjustment of the operation of all the system navigation tools, and controlling aircraft flight according to the selected programmes is performed automatically. Automatic control systems may be of various level of complexity – autopilot, command-based, automatic, and programmed control of flight trajectory. The most simple are autopilots that stabilize aircraft’s position in space. Automatic control systems not only stabilize aircraft’s position in space but also perform simple trajectory changing manoeuvres. Using computer-controlled trajectory control systems, pilot only observes the heading of flight. Command-based control systems automatically process all the information required for controlling the aircraft, and the pilot only needs to follow the instructions.
Larger aircrafts are equipped with at least several identical navigation tools. When one if defective the other can still be operated. The same navigation elements may be read by several different devices operating under different principles. When using them together, the defects of some of them may be compensated by others, and as a result, pilots get more precise navigation data.
The main purpose of navigation tools is to provide the pilots with accurate information about the coordinates of the location of an aircraft; they can measure the altitude, direction, and speed of flight.
Due to imperfections of navigation tools or other reasons, an aircraft deviates from the selected trajectory, therefore, it is usually said that an aircraft moves along its actual trajectory. Its projection on Earth’s surface is called TMG (Track Made Good) or Track Actually Flown. The mismatch between the actual and the selected trajectories (road lines) is measured by deviations in vertical and horizontal planes and in time. Beside the data on the trajectory, pilots are given the time when they have to arrive at the destination and the interim waypoints. The range and time of operation for the majority of navigation tools are limited; therefore timely use of other tools is important.

1.4. Navigation parameters

The coordinates of aircraft location, the direction and speed of flight are called parameters of navigation and control. The main parameters of navigation are the following:
– altitude (absolute, true, standard), flight level;
– aircraft speed (reading-based, calibrated, the actual, equivalent, Macho, vertical, and ground);
– aircraft heading (true, magnetic, conditional);
– the coordinates of aircraft location, radio beacon bearing (azimuth), track angle (selected and actual),
Distance covered, time (departure, arrival, or delay), aircraft’s position in relation to another object (or object’s position in relation to the aircraft), etc.
Manual or automatic operation of an aircraft maintaining it at the selected trajectory is only possible knowing all the necessary navigation and control parameters. They are measured by navigation and control tools.
Navigation parameters may be determined in the following two ways:
1. Given the initial position of an aircraft and constantly measuring the direction and speed of flight, the pilot himself or navigation tools automatically calculate the distance flown, and determine the actual location of the aircraft. Therefore, this navigation technique called dead reckoning (DR). The advantage of this navigation method is the autonomy of the used navigation tools; no ground-based navigation aids are required. Unfortunately, upon the loss of initial information or even temporary disruption of the process of identification of the actual data, the further navigation is usually not possible or with significant deviations errors. The most known navigation tools used by pilots to determine actual navigation parameters in relation to initial location include inertial systems INS, Doppler meters, magnetic and gyro navigation instruments, air data computers, and even the simple barometric devices. Using these tools, the accuracy of navigation deteriorates with increased flight time due to accumulation of navigation calculation errors.
2. At any moment of flight, the required navigation information is directly obtained by determining the actual aircraft location and measuring other navigation parameters. The devices used in this case include the ones using the systems of full and static pressure as well as radio navigation aids – GPS receivers, radio compasses ADF, navigation and landing system VOR / ILS, DME distance measuring equipment and others. No initial data are required, and no calculations are carried out with respect to the initial location, however, air pressure and temperature around the aircraft needs to be measured, or receive signals from ground facilities or satellites. The navigation accuracy does not depend on the flight time, though it reduced when the aircraft is far from ground navigation facilities.
Flight trajectory is planned by the pilots before the flight. They assess whether the navigation tools in available will ensure the necessary accuracy of the trajectory. During the flight, navigation and control parameters are being measured, and deviations from the selected trajectory in space and time are established. When these deviations exceed the pre-set limits, pilots or the automatic flight control system change the position of aircraft control surfaces and engine thrust until the deviations are reduced, and the aircrafts returns to the selected trajectory. On the route, the size of deviation from the selected trajectory in, e.g. nautical miles depends on the accuracy of navigation aids and pilot’s actions while controlling the aircraft (piloting technique).
Data on flight altitude, speed, direction of flight, aircraft climbout or descent rate is among the most useful for aircraft navigation. Without knowing this information, pilots cannot operate even the simplest aircraft. The devices that show these data are located at the best visible place – just in front of the pilots.
Flight altitude is the distance measured between the ground or any other supporting surface and the aircraft. Flight altitudes are measured by pressure altimeters, radio signals, inertial, satellite, and other devices. With respect to the support level, absolute, true, and standard flight altitudes are used in aircraft navigation (Figure 6).

Figure 6. Altitudes of aircraft flight

Explications to picture:

Standartinis aukštis – Standard altitude
Absoliutusis aukštis  – Absolute altitude
Pereinamasis aukštis – Transitional altitude
Žemė – Earth
Jūros lygis – Sea level
Standartinis lygis  – Standard level

Absolute Altitude is the height of the aircraft above the earth’s surface above which it flies. The true altitude is measured above the mean sea level. At low heights, absolute or true altitudes are measured to avoid high over-ground obstacles. The heights of these obstacles are specified in maps and navigation databases. While flying above the transitional height set by international agreements, the standard height is measured; there are no over-ground obstacles, and the only things to avoid are collisions with other aircrafts. Standard altitude or pressure altitude is measured above the perceived standard level where atmospheric pressure is equal to 1013 hPa (760 mm Hg). Above the standard support level, the air space is divided into 1000-feet wide flight levels.
Another group of navigation parameters is flight speeds. Wing lift force, efficiency of controlling aerodynamic control surfaces, and overloads resulting from air resistance depend on the aircraft movement speed in air and air density. Indicated air speed (IAS) is proportional to air resistance, and defines the lift force as well as the efficiency of controlling the aerodynamic control surfaces. This speed is measured even in the lightest aircrafts; however the distance covered cannot be calculated by knowing only this speed. In larger aircrafts, calibrated air speed (CAS) is calculated instead of air speed IAS; it is more accurate than IAS since air pressure measurement errors are taken into account. When flying at the speed higher than 400 km/val, air compressibility starts to increase, and combined with IAS (or CAS), equivalent air speed (EAS) may be calculated according to the compiled tables. Aircraft movement speed with respect to Earth is called ground speed (GS) that is used for calculating the distance covered. If there is no wind, the true air speed (TAS) in respect of the surrounding air is equal to the ground speed GS. The true air speed TAS is measured by correcting IAS by air density signal as air density depends on flight altitude and air temperature. When flying motor aircrafts, vertical movement of air masses is ignored, and the true air speed shall be the speed aircraft moves horizontally in respect of the surrounding air. If there is wind, and knowing TAS, the distance covered may be calculated quite accurately given wind direction and speed. Since IAS is proportional to air resistance, it cannot be used for judging the optimum ratio of lift force and air resistance which is important for fuel economy. After calculating the Mach speed M (ratio of speed of sound and the TAS) flight economy may be improved. When an aircraft is taking off, landing, or changing the flight altitude, altitude change rate or the vertical speed (VS) are calculated.
The speeds IAS, CAS, TAS and M are measured in respect of the surrounding air. Ground speed GS is measured in respect to the Earth using radio-technical or inertial methods as during the flight, aircraft is surrounded only by air. Vertical speed VS is measured in respect to the surrounding ait or by assessing the rate of change of the aircraft position in inertial space by inertial systems.
Heading is the direction to which the longitudinal axis of aircraft is directed. Heading is measured from the reference direction, e.g. the true or magnetic meridian of the aircraft location. If there is no wind, heading coincides with the velocity vector (track line or track). The direction (position) of track line at the Earth’s surface is defined by track angle in respect to the reference direction. In order for an aircraft to move in space following the selected tract under conditions of side wind, the aircraft needs to be slightly angled in the direction of wind taking into account its direction and speed. Then the longitudinal axis no longer coincides with the selected track line, and an angle called Drift Angle δ (Drift) is formed between the aircraft’s longitudinal axis and the actual track line. Drift angle is measured by inertial navigation systems and Doppler meters. If drift angle selected correctly, aircraft moves at the selected track line.
True heading (TH) is the angle on horizontal plane between the reference direction northwards from the aircraft (aircraft’s true meridian) and at the horizontal plane projection of the longitudinal axis (Figure 7). Geographical or true north is well visible on the map, however its location or direction is difficult to determine by the devices in the aircraft. Maps indicate the coordinates (latitude and longitude) of waypoints and other locations, and the true headings. True heading is calculated by inertial systems INS and satellite navigation tools GPS. Inertial systems are complex, expensive, and therefore installed only in large aircrafts.

Figure 7. Magnetic and true headings

Explications to picture:

Žemės geografinis polius – Earth’s geographical pole
Žemės magnetinis polius – Earth’s magnetic pole
Išilginė ašis  – Longitudinal axis

Older aircrafts were not equipped with navigation aids that directly calculated the true heading. Now these aids are only absent in small aircrafts. Therefore, in navigation, magnetic heading MK is often used besides the true heading. It is measured in the same way as the true one, only it is measured in relation with the geographical rather than magnetic meridian MD. Magnetic meridian is a line connecting the northern and the southern Earth’s magnetic poles. The location of Earth’s magnetic pole does not coincide with the location of the geographical pole. The axis of Earth’s magnetic field is angled to the Earth’s axis of rotation by 11.5°. The northern magnetic pole of the Earth is located in the north-eastern Canada, about 1600 km from the North Pole. The location slightly changes every year. Therefore, in a general case, the magnetic meridian of some point on the Earth’s surface does not coincide with the geographical one. The angle ΔM between them has several names: variation, magnetic deviation, magnetic declination. Then TK = MK ± ΔM. When the northern end of magnetic meridian is point eastwards (to the right) from the true one, magnetic deviation is positive and marked with the letter E. Western deviation (negative) is marked with letter W. Every point on the Earth’s surface has its own magnetic deviation. In small and medium latitudes, magnetic deviation amounts to few degrees. Magnetic deviation in Vilnius and the majority of other Lithuanian cities is currently almost +5°, and only on the seaside, e.g. in Palanga, it is +4°.
Given magnetic deviation, magnetic heading (or other headings) may be recalculated into the true heading.
Aircraft’s magnetic heading is calculated by devices that are sensitive to Earth’s magnetic field, e.g. Ordinary magnetic compass or flux valve. When performing calculations, magnetic heading is measured by radio navigation aids and inertial systems. When an aircraft maintain its magnetic heading, its position line is loxodrome – a curve that passes through all the magnetic meridians at the same angle.
When measuring the heading with magnetic compasses or flux valves, an error occurs resulting from side (non-Earth) magnetic field and other factors. Direction indicated by magnetic compass is called compass meridian KD. The angle between compass meridian and aircraft’s longitudinal axis is called compass heading (CH).
Deviation of compass heading from the magnetic heading (compass error) is called magnetic deviation ΔK. It increases when compass is close to magnetized parts of the aircraft or close to wires carrying high DC. This deviation can amount to several degrees. This value changes depending on the angle of the aircraft with respect to the magnetic field. The size of magnetic compass deviation for particular aircraft is difficult to measure; currently, magnetic compasses are considered to be secondary navigation aids, therefore their deviation is no longer measured, and the pilots are not aware of the size of this deviation.
During the flight, it is not important what meridian or other reference line will be used for calculating aircraft’s heading. Another reference line called ‘relative meridian’, e.g. centre line of the runway, may be selected and used for calculating the heading. Given the angle between the relative and magnetic meridians, the same navigation tools may be used during the flight. When flying along the orthodrome (the shortest distance between two waypoints); the very orthodrome may be selected as the relative meridian. If the angle between the magnetic meridian MH and orthodrome is φ, then the orthodromic heading is OH = MH ± φ.
Location of an aircraft is also a navigation parameter. There are several most popular ways of determining aircraft location. Aircraft location may be calculated given the heading, speed and time of flight. There are navigation aids, e.g. inertial and satellite navigation systems that directly measure aircraft’s location. Aircraft location may be determined given the distances to the several waypoints on the Earth surface with known coordinates. Under the same principle operates the distance measuring equipment DME, and the hyperbolic radio navigation system “Loran-C”. GPS satellite navigation instruments determine aircraft’s location by measuring the distances to several Earth satellites the coordinates of which are well-known at the moment of measuring. If the coordinates of several waypoints on the Earth surface are known, aircraft location may be determined knowing the directions to these waypoints. Directions are measured by radio compasses ADF and VOR receivers. Aircraft location may be found given a point on Earth’s surface, and the distance to it. Under the same principle operates radio navigation systems VOR/DME and TACAN. Knowing the direction of flight, aircraft location is determined by calculating the distance covered from the starting point; for this purpose, inertial and Doppler systems are used.
Knowing only one of the navigation parameter, aircraft location cannot be identified. There might be cases when during the flight navigation parameter remains the same for an extended period of time. For example, when going northwards using a touristic compass the compass will show the direction up till the magnetic pole, i.e. the distance covered is the position line with constant compass readings. When flying at equal distance form a certain point at Earth’s surface, e.g. in case of DME transponder located in Kaunas Airport, aircraft position line will be a circle. Using a magnetic compass a pilot can follow the same heading all the time, i.e. this navigation parameter (heading) does not change in this case. In aircraft navigation, position line refers to geometric location of points where aircraft navigation parameter does not change. Knowing only one position line, aircraft location cannot be determined. Aircraft location shall be at the intersection of two position lines.
During the flight, aircraft coordinates may be determined following the over-ground radio beacons on the earth surface which exact locations are known. Aircraft navigation aids measure the bearings of over-ground radio beacons, and the distances to them (Figure 8). It is most convenient to fly towards the beacon or from it. Location coordinates of the aircraft may be calculated by measuring bearings of several radio beacons and distances to them,. Automated control systems perform this automatically.

Figure 8. Heading angles and bearings

Explication to picture:
Išilginė ašis
– Longitudinal axis

Relative bearing (RB) of a radio beacon is the angle between aircraft’s longitudinal axis and the direction pointing to this radio beacon.
The bearing of radio beacon in respect of the aircraft refers to the angle on the horizontal plane between the northern direction of the meridian and the direction to the over-ground radio beacon. Bearing may be measured both from magnetic MN, and geographic TN meridians. Then it is called respectively magnetic (MB or QDM) and the true (TB) radio beacon bearing. When drawing the lines of directions from aircraft to beacon (or from beacon to aircraft) on maps, the bearing of radio beacon QDM is most often recalculated into the true aircraft bearing in respect of the beacon QTE or the magnetic aircraft’s bearing with respect to the beacon QDR (they differ by 180°) by measuring them from the respective beacons’ meridians MN or TN. Aircraft’s bearing in respect of radio beacon (QDR or QTE) refers to the angle on horizontal plane between the northern direction of the respective beacon’s meridian and the direction to the aircraft.
In aircrafts, the bearings of over-ground radio beacons are measured by navigation receivers VOR, and relative bearings are calculated by radio compasses ADF in degrees from 0 to 360. Knowing bearings or relative bearings of at least two over-ground beacons allows determining aircraft’s location. Air traffic control services in larger airports use direction finders that determine the direction of an aircraft (bearing) by receiving the signals of the radio station. The value of bearing is communicated to the pilots.
Aircraft location may be determined by not only measuring the angles between the longitudinal axis and direction to radio beacons or by measuring angles between beacon’s meridian and direction towards the aircraft but also by measuring the distances D to several radio beacons, or differences of these distances. Then these measurement data are processed and used for determining aircraft’s position lines.
Aircraft ground speed, distances, and differences of distances to the beacons and angles are measured by navigation aids. Based on the purpose, these aids may be divided into the following groups: those measuring angles (aircraft radio compasses, bearing calculators and over-ground radio direction finders), distances (range finders with over-ground transponders), differences of distances (navigation systems “Loran-C”), ground speed (Doppler speedometers).
Receivers of radio navigation devices that measure distances to over-ground beacons receives the signals of these radio beacons and based on them determined the direction (angle) to these beacons. Radio beacon is a radio transmitter with its exact location known. Aircraft position line using radio navigation aids that measure angles is a straight line passing through the beacon and aircraft location.
Using distance-measuring radio navigation aids, aircraft position line is a circle with equal distances in the centre of which is over-ground radio beacon. The radius of the circle is equal to the distance between the beacon and the aircraft. Currently in use are aircraft navigation aids that measure distances to satellites rather to over-ground beacons. They are called satellite navigation aids GPS. Using satellite-based navigation aids, aircraft location is a position sphere rather than a position line with a satellite in the centre. Radius of the sphere is equal to the measured distance.
When using navigation aids that measure differences of distances, position lines on horizontal plane look like hyperboles with over-ground radio transmitters in the points A and B. Distance D between the tarp stations is called a base. In the point V (aircraft location point) equal difference of distances is determined with respect to the stations DA – DB (Figure 9).

Figure 9. Position lines when measuring the differences of the distances

Time is also a navigation parameter. Most commonly used is international time UTC. Departure or arrival of aircrafts may be specified in the local time. During the flight, important is the ground time intended to fly from one waypoint to another.

(To see continue in next No)