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. (Continue, begining at No.20 )

1.5. Total and static pressure systems devices

Static and total pressure systems

During the flight, pilots need to know the altitude of the aircraft, the speed and direction of flight, take-off or landing rate, and what is the deviation from the selected flight altitude. During the flight, aircraft is surrounded by nothing but air. It gives the necessary information for many devices. In practice, only three parameters of the surrounding air are used, i.e. air pressure, temperature, and air resistance when flying. Air intake and supply systems are called static and total pressure systems.
Every material body is pressed by surrounding air. The amount of air pressure is determined by atmospheric properties. They change consistently depending on the height; however, they are not exactly the same at different places on Earth or at the same place but different time. Close to the Earth, there is more air and its density is higher; therefore, the higher above the ground the body is the air is less dense resulting in less pressure on the body. Changes in temperature result in changes in the density of air, therefore, air pressure depends on the temperature also. Near the surface of the Earth, when the altitude increases by one kilometre, pressure reduces more than in the case when the altitude changes from 9 to 10 kilometres. In aviation, air pressure is measured by millimetres of mercury, hectopascals or millibars, in USA – in inches of mercury.
The pressure of air surrounding the body is called static pressure PS. Despite there are places on Earth where the altitude is below sea level (e.g. Caspian Sea coast), it is agreed that zero level is the sea level and the static pressure is highest at this level. At the height of approx. 5.5 km, the pressure reduces by half. As air pressure slightly depends on its temperature, therefore at the same height but different air temperature, static pressure slightly differ. Knowing the air pressure (static pressure) alone allows determining the altitude of aircraft in flight. While following a certain route knowing the exact absolute height is not essential. More important is to prevent the aircrafts coming two close when the routes are intersecting; therefore, while measuring the altitude, the errors occurring due to outside air temperature is not compensated as the error is equal to all the aircrafts at the same altitude and at the same place.
Studies have shown that with increased altitude static pressure changes (decreases) consistently. Air is moving constantly, its temperature and density depends on the time of the day and time of year, geographical latitude, altitude above the Earth’s surface, and other factors. In order to facilitate altitude measurement, reduce the structural differences between the various types of altimeters, improve aircraft control and navigation the International Standard Atmosphere (ISA) is used demonstrating the dependence of air pressure on the altitude. It is agreed, that the temperature of standard atmosphere at sea level is T0 = +15 °C (288.15 °K), air pressure P0 = 101 325 Pa or 1 013.25 hectopascals (760 mm Hg, or 29.92 in (?) Hg, or 1 013.25 milibars), and air density ρ = 1.225 kg/m3. Average decrease in air temperature while rising up to 11 000 m in standard atmosphere is measured by temperature gradient τ = 0.0065 ºC/m (or 6.5 ºC/km), which shows the difference in air temperature given change of altitude by one metre (or one kilometre). When the altitude changes by 1 000 feet, air temperature changes by 1.98 ºC. From 11 km to 33 km, air temperature is 217 ºK. When rising still up, air pressure reduces by 1 hPa (1 mb) every 10 m (every 30 feet). If the actual air temperature overboard is not equal to the standard temperature, this will result in different air density, which leads to methodological height and speed measurement errors.
When flying in a hot air balloon, measuring of static pressure is very simple. It is more complicated in other aircrafts as there is air turbulence occurring that cause errors of measuring static pressure. This highly depends on the size and shape of aircraft, flight speed, and other factors. In such aircrafts, the static air pressure is taken by round shaped static pressure receivers. The holes must be necessarily located at the places where air swirls are the least. They cannot be even slightly angled against the air flow to avoid additional air getting in due to air resistance. Then the pressure gets through a hose to aircraft’s total/static pressure system devices: air speed indicators (ASI), vertical speed indicators (VSI), altimeters (ALT), and others. In larger aircrafts, static pressure receivers (holes) are most often located further from the front of the aircraft on the flat part of fuselage symmetrically on the both sides of the aircraft. Symmetrical arrangement reduces errors when aircraft is making turns. When making turns, the receiver on the external side gets more air, and the pressure is slightly higher. Inner side of an aircraft gets into some kind of “shadow” of air flow, and the air pressure of air that gets into this receiver is lower. After connecting the holes on the both sides by hoses, the average air pressure is more uniform. Through hoses, pressure is transmitted to cabin devices and other equipment measuring altitudes and speeds (Figure 10). The number of such devices (users of static pressure) is high; therefore, the number of static pressure receivers, i.e. holes on the sides of aircraft and the connecting hoses, is also high. Together they are called aircraft’s static pressure system.

Figure 10. Total and static pressure system

Pilnutinio slėgio kamera – Total pressure chamber
Pilnutinio slėgio vamzdelis – Total pressure hose
Lauko oras – Outside air
Drenažo skylutė – Drainage hole
Spiralės – Spirals
Šildymo jungiklis – Heating switch
Drenažo skylutė – Drainage hole
Atsarginis statinio slėgio imtuvas – Replacement static pressure receiver
Statinio slėgio imtuvai – Static pressure receivers
Statinio slėgio vamzdeliai – Static pressure hoses

Another aircraft system that supplies air to devices is called total pressure system. The faster body moves, the higher is air resistance. This feature is applied while measuring aircraft speed. Air resistance is proportional to the increment of static pressure PS which occurs when aircraft moves. Static pressure with this increment is called total pressure PP. The difference between the total and static pressures is called dynamic pressure  PD:

PD = PP – PS.

Knowing the speed of air flow V going around a material body and the density of air ρ, dynamic pressure may be calculated according to the following formula:

PD =  ρV2 ⁄ 2

The total pressure from the outside gets in through tube-shaped air receivers which are called total pressure receivers or Pitot tubes (Figure 10). The front end of the tube is open and directed against air flow while the rear end is closed. The tube is oriented in parallel to the air flow flowing around the aircraft. Then, air pressure forms in the tube in proportion to the aircraft speed. To avoid the effects of air swirls on measurements, these tubes are installed further from the surface of the aircraft.
Compressed air (total pressure) is further transmitted from receiver to aircraft devices. In a large aircraft, there is a large number of total pressure users, therefore a large aircraft is equipped with two, three or more receivers of air pressure. At the sides of some total pressure receivers, there are static pressure holes; such receivers are connected to the devices by separate static and total pressure hoses. All the total pressure receivers and the hoses connecting them to the devices are collectively called the total pressure system. During the flight, total pressure receivers can ice up quickly, therefore, they are heated with the help of electrical current by heating the spiral located inside. Heating is turned on before the flight even if the temperature is positive no later than 5 minutes before taking off, and turned off no later than 2 minutes after landing.
Air constantly gets to the static and total pressure systems. The moisture contained in the air condenses and might clog the tubes in the system or freeze, therefore, the systems are equipped with many water registrars where the accumulated water can be released.
Static and total pressure systems are required for aircraft navigation, therefore, there are main and secondary systems installed in aircrafts (main and secondary static and total pressure receivers and hoses). In case the receivers of the main system get iced-up or clogged, aircraft devices are disconnected from the main system and connected to the auxiliary system with a help of valves controlled by a handle in the cabin.

Measurement of flight altitude

Imagine there is a man standing in a room on the fifth floor of the house and holding a book above a table. What is the altitude of the book? Some will say that altitude is the distance from the book to the surface of the table. Others would measure the distance to the ground. Still others might measure the altitude from the ground that building is standing on. The altitude would be approximately 15 metres. There would unlikely be those who would measure the altitude from the sea level. The reader should now understand that the altitude of a book, a plane or any other object depend on the selected reference surface – table, floor, ground, or other.
Contrary to a car, an aircraft moves in a three-dimensional space. Altimeter is the main tool in vertical navigation; it ensures flight safety. Flight altitude is measured in feet according to the well-established tradition (1 foot is equal to 0.305 metres).
Light aircrafts are equipped with barometric altimeters. Larger planes and helicopters are equipped with both barometric and radio altimeters and also satellite and inertial navigation systems that can also measure altitude.

Barometric altimeters

Barometric altimeters (Figure 11) measure flight altitudes from the selected (reference) pressure level set by the pilots. These altimeters are only supplied static pressure of air surrounding the aircraft. Barometric altimeters measure aircraft flight altitude from -1 000 to +50 000 feet (from -300 m to 15 km or even more). They are among the oldest aviation devices. They are not large, and therefore, can be installed in the instrument panel in the cockpit.
The longer arrow in the scale shows the altitude in hundreds of feet, while the shorter one shows it in thousands of feet. There are altimeters that have a third arrow or an index showing tens of thousands of feet. Altitude may be shown by a digital drum rather than by arrows.
Changing the time and location of the aircraft in space results in changes in the static pressure of the surrounding air. Air pressure in different places of the Earth’s surface (or in the same place only different time may be different, therefore, barometric altimeters are equipped with not only altitude scale but also with a scale (or a drum) of reference pressure.

Figure 11. Barometric altimeter and its scheme

Aukščio skalė – Altitude scale
100 ft rodyklė – 100 ft arrow
Anerodinė kapsulė – Aneroid capsule
Statinio slėgio imtuvas – Static pressure receiver
Atraminio slėgio nustatymo rankenėlė – Reference pressure switch
1000 ft rodyklė – 1000 ft arrow
Atraminio slėgio langelis – Reference pressure
10000 ft rodyklė – 10000 ft arrow

At the front of the device, there is reference pressure adjustment knob. By rotating this knob, pilot sets the level of reference pressure on the reference pressure scale or drum to be used for measuring the altitude (Figure 12). When the static pressure that gets into the device is equal to the reference pressure, the altimeter shows zero. In higher altitudes, barometric altimeter shows altitude that does not change while aircraft flies above uneven earth surface. Before and during the flight, pilots can change one reference pressure by another. This is performed in order for all the aircrafts to use the same reference level for flight altitude at certain stages of flight. This is required not for the aircrafts to fly at the same altitude but rather to ensure safe interval of vertical distance between aircrafts flying at different altitudes. There are strict rules set for setting reference pressure for altimeters. Air traffic controllers inform the pilots what reference pressure should be set with respect to specific section of the flight.

Figure 12. Reference pressure scale marked in inches of mercury

The design of classic barometric altimeter is very similar to the one of indoor barometer. Static pressure PS that corresponds to the aircraft’s altitude is passed through receiver’s hose to hermetic housing of altimeter and deforms the aneroid capsule inside (Figure 11). All the air is removed from the capsule, and when on earth, it is strongly pressed by air. When going up, static pressure reduces, the capsule expands and passes the movement via crankshafts to the major axis that rotates the arrows. The diameter of the capsule is 5 centimetres. The displacement of the moving centre is only a half of a centimetre, therefore, it is difficult to manufacture a device that would show the altitude at the accuracy of ten feet. Using two or three capsules connected in sequence, the displacement X is larger and the device is more accurate. Linear dependency between the rotation angle of arrows and the altitude measured is obtained using capsules with logarithmic characteristics of pressure that is obtained by respective profiling of the walls of the capsule.
Altimeters (barometric and radio) in aircraft can show different altitudes. This depends on the surface level that is taken as a reference level for measurements. Devices measure the following altitudes:
1. Absolute altitude HA or the height of an aircraft from the terrain (field, hill, hollow). When aircraft flies above a hilly terrain HA changes accordingly. The most accurate measurements are made by radio altimeters. Pilots use absolute altitude in a broader sense when it is measured by barometric altimeter from some selected reference level, e.g. from the surface of the runway. For example, the altitude from sea level of Kaunas International Airport is 256 feet, while in case of Vilnius Airport it is 646 feet (197 m). If the altimeter is set the current reference runway surface pressure, the altimeter will show zero.
2. True altitude HT: considering the Earth as ellipsoid, the currently determined distances from the centre to any point of the surface of this ellipsoid. The least distance is to the sea level. If the surface of the Earth would be made of water, then the shape of the Earth would be the above-mentioned ellipsoid. Land is rising above the water. The distances from sea level to any point on land surface are very accurately measured with the help of geodesic measurements. The true height HT is the distance from sea level to a certain surface, and the aircraft. The altitudes of runways in airports and of other surfaces, or obstacles in air are specified in maps in true numbers. Since there is no sea under the land surface, its level is often called Mean Sea Level (MSL). Meteorologists notify the flight controllers, and they inform the pilots of the current air pressure at sea level at the current place for it depends on weather conditions and can slightly change in the course of several hours. After setting this reference pressure in the altimeter of standing or flying plane, it will show the altitude above the sea level. For example, the altimeter of an aircraft located near sea coast will show zero altitude, and the altimeter of the one standing on Kaunas Airport runway will show 256 feet. By deducting the altitude of airport runway from the true altitude (shown on the altimeter) we will know the absolute flight altitude with respect to the aircraft. Measuring the true flight altitude when landing, the aircraft touches the runway at the point when the altimeter shows the altitude above the sea level. This would be 256 feet if landing in Kaunas, and 646 feet if landing in Vilnius.
3. Standard altitude HS or Pressure Altitude. Standard altitude HS is measured above the level where at the temperature of +15 °C there is air pressure of 1013.25 hectopascals (760 mm Hg or 29.92 inches Hg). Air pressure and temperature at the actual sea level changes and is not always equal to standard pressure, therefore, zero standard level may be lower and higher that the actual sea level. In practice, it is a rare case that with air pressure of 1013.25 hectopascals there with be standard temperature of +15 °C, therefore, the more air temperature differs from the standard temperature, the more changes air density and the altitude measurement errors increase.
When taking off, at the transition altitude (in Lithuania, it is equal to 1500 m or 5000 feet) the pilots change the true and absolute reference level of barometric altimeter into the standard one, and aircrafts are directed at what flight level they should fly. When landing and crossing the upper limit of the transition height, the true and the absolute reference levels are set again. The transition level of flight is the lowest possible flight level above the transition altitude.
After setting the reference standard pressure, the pilot does not need to adjust the reference level every time while flowing to/from zones with different weather conditions. Flight altitude is no longer dependant on the specific air pressure and temperature in the airfield. However, the reference pressure level will be the same for all the aircrafts so as to ensure safe vertical distance between them when flying at different altitudes (flight level FL).
Barometric altimeter can always measure the standard altitude above the reference level as it is calibrated for this altitude in the factory. A pilot only needs to calibrate the altimeter by setting the standard reference pressure of 1013.2 hPa (760 mm Hg or 29.92 inches Hg) on the scale or on the drum. There is no need to ask the flight controller what air pressure is in a certain place.
After setting all the arrows to zero mark, the altimeter shows current air pressure on the pressure scale.
4. Density Altitude. When manufacturing barometric altimeters, it is difficult to install in them temperature correction mechanism, therefore, the height is measured not taking the temperature into account, i.e. the altitude is most accurate given the standard air conditions. The more air conditions differ from the standard ones, the larger are altimeter errors. When flying above transition height, the errors may be not taken into account as with changing air conditions all flight levels shift up or down proportionally, and the vertical distance between aircrafts flying at the adjacent flight levels remains almost unchanged.
When flying low or on the ground, air conditions need to be taken into account. The density of warm weather is lower, and the same pressure is higher above the ground. When air temperature decreases, air gets compacted. The density of air is directly proportionate to the pressure and inversely proportional to the temperature. However, certain air density is only obtained given the specific combination of air pressure and temperature. This means that basically, aerodynamic characteristics of an aircraft and engine mode depend not on the actual altitude above the sea level in metres or feet but rather on the density of air at that altitude, i.e. density altitude. Density altitude is the density set according to the air density with the correction for non-standard temperature. Density altitude is found according to the provided table, and calculated by using the formulas.
The left aircraft (Figure 13) flies under warm air conditions; therefore, its altimeter shows lower flight altitude than it really is. The actual altitude of this aircraft (distance above the ground) is higher than showed by the altimeter. When flying under conditions of standard temperature, at the altitude of 3000 metres, the same altitude of 3000 metres will be shown in the altimeter of the aircraft in the centre. The aircraft on the right flies under conditions of colder than standard air, therefore, the methodological error has the opposite sign. Colder air is denser and more compressed. When the actual altitude changes from 0 to 3 000 metres, pressure changes will be more significant in cold air, and aircraft’s altimeter will show higher altitude. While flying at low altitudes, the most dangerous is the case when air temperature is very low. The actual aircraft altitude is then lower than showed by the altimeter, and the risk of hitting high over-ground obstacles increases.

Figure 13. Methodological errors in altimeters‘ temperature measurements

Skrydžio aukštis lygus tikrajam – Flight altitude higher than the actual one

Oras šiltesnis nei standartinėje atmosferoje – Air is warmer than in standard atmosphere
Oras šaltesnis nei standartinėje atmosferoje – Air is colder than in standard atmosphere

Air density must be estimated while taking off and while landing. Due to changes in air density on the same runway, the aircraft’s engine thrust, wing lift force and other aerodynamic parameters change, e.g. at very high temperatures, the taxi time of aircraft significantly increases.
Simple altimeters show the altitude with arrows, the accuracy of measurements is approx. ±10 metres close to the ground, and approx. ±30 metres in high altitudes. In larger aircrafts, altimeters not only show flight altitude but also replace measurement results by electrical signals and transmit them to automated aircraft control systems, radio transponders, engine thrust control devices, flight data registrars, and other systems. The main axis of such altimeters drives the rotor of contactless sinusoidal-cosinusoidal transformer via gear pairs. The signal of height is obtained in the windings. In other altimeters, capsule deformation rotates the arrows and pushes the slide potentiometer further. Afterwards, other systems measure the resistance that corresponds to the height.
Radio altimeters that measure the absolute altitude above the ground are only installed in the larger aircrafts and the majority of helicopters. While taking off and landing, pilots use both barometric and radio altimeters. Radio altimeter is more accurate (close to earth’s surface, error is approximately ±0.5 m or even less). Radio altimeters of passenger aircrafts measure distances of up to 800 metres above the surface of the Earth. Larger aircrafts may be installed several radio altimeters. These devices are among the major devices that send the signals to aircraft’s flight management system FMS, ground proximity warning system GPWS, overload and other measurement systems. Military aircrafts use pulse radio altimeters that are capable of measuring high altitudes.

Aircraft’s speed measurement

These devices measure aircraft’s speed with respect to the surrounding air or with respect to the ground. Based on the principle of operation, they may be divided into manometric, radio-technical and inertial.
Manometric devices use data on air pressure and air resistance to the aircraft that is proportional to the difference of total and static pressures. As air resistance depends on the density of air, air resistance is high while flying close to the ground, and significantly lower when flying high and maintaining the same speed with respect to the ground. Therefore, there are several methods of speed measurements: using total and static pressures, outside air temperature and information about air compressibility with respect to speed of the aircraft. Accuracy of measurements increases if errors caused by imperfect arrangement of total and static pressure receivers on the surface of the aircraft are taken into account. The following speeds are measured using the manometric method: IAS (Indicated Air Speed), CAS (Calibrated air speed), EAS (Equivalent air speed), TAS (True Air Speed), Mach M (Mach Speed), and the VS (Vertical Speed).
IAS, which is often called indicated speed, is proportional to air flow resistance. It determines the size of aerodynamic forces that impact on the aircraft, and as a result, it determines the operability of the airplane. This parameter defines the size of wing lift force and overloads that affect the aircraft. Pilots need to accurately identify the indicated speed at all stages of the flight from taking off until landing.
Indicated air speed is measured by ASI (Air speed indicator). You can find this device in all the aircrafts. The static pressure PS is supplied to the sealed housing of air speed indicator (Figure 14). Inside the housing, there is a diaphragm (manometric capsule) supplied with total pressure PP. When aircraft is not moving, these two pressures are equal, and the diaphragm remains in the initial position. The higher is the airspeed, the higher total pressure gets to the diaphragm thus expanding it. Expanding diaphragm rotates the arrow of the device. Variations in flight altitude and speed result in changes in total and static pressures; however, the difference (dynamic pressure) is always equal to air resistance with respect to the aircraft.

Figure 14. Air speed indicator speed

Sektorius – Sector
Svirtelė – Lever
Pilnutinio slėgio antvamzdis – Total pressure sleeve
Statinio slėgio antvamzdis – Static pressure sleeve
Diafragma – Diaphragm
Ašelė su dantratėliu – Axis with pinion

Diaphragm together with arrow can rotate the rotor of sinusoidal-cosinusoidal transformer or the slide of potentiometer. Electrical signal of indicated speed is sent to automated trajectory control and other systems. When air temperature and pressure match the standard levels, indicated speed close to the ground is approximately equal to the ground speed of the aircraft. While flying high at the same speed, air resistance and IAS reduces. Close to the ground, where air density is high, even a slight angling of control surface results in changes in aircraft position. At higher height, control surfaces need more angling in order for the aircraft to make the required manoeuvre, or the indicated air speed must be significantly higher.
When indicated speed is reducing, the aircraft losses its manageability and might start falling. At high speeds, overloads occur due to air resistance. Air speed indicator may have a coloured scale showing permissible and dangerously high speeds (Figure 15).

Figure 15. Air Speed Indicator (ASI)

Raudona greičio padala, kurio niekada negalima viršyti – Red speed limit that can never be exceeded
Geltona pavojingų greičių skalė – Yellow scale of dangerous speeds
Didžiausias kreiserinis greitis – Maximum cruising speed
Didžiausias greitis kada galima išleisti užsparnius – The maximum speed at which the flaps may be released
Žalia galimų greičių skalė – Green scale of permitted speeds
Smukos greitis su neišleistais užsparniais ir važiuokle – Speed of falling with unreleased flops and the undercarriage
Balta galimų greičių skalė su išleistais užsparniais – White scale of permitted speeds with released flops
Smukos greitis su išleistais užsparniais ir važiuokle – Speed of falling with released flops and and the undercarriage

ASI indicated speed up to 200 nodes is measured at the accuracy of ±(2–8) percent. When measuring higher speeds, the accuracy is ±(1–4) percent.
Calibrated air speed CAS is measured the same as indicated air speed additionally taking into the account the static pressure measurement errors of a specific aircraft depending on the location of static pressure receivers on the aircraft surface and the characteristics of air flow around the aircraft (e.g. angle of attack). Errors are larger with lower speeds (while taking off and landing) and large angles of attack. When such errors are absent, the values of indicated and calibrated air speeds are equal. CAS is used instead of IAS as the difference is really small (few nodes). At speeds higher than 200 nodes, air compressibility and equivalent air speed EAS are taken into account. Due to air compressibility, pressure in the Pitot tube increases, and CAS (or IAS) is shown increased. The higher is the calibrated air speed, the larger is the difference between CAS and EAS.
The true air speed TAS is the speed of the aircraft relative to the surrounding air. In formulas, TAS is often marked by letter V. If there is no wind, it is quite the same as aircraft’s speed relative to the ground (ground speed). The true speed of a flying air balloon is always equal to zero as it is not equipped with any power engine and moves at the same speed and to the same direction as the surrounding air. Given the true speed it is possible to calculate the distance covered. In older aircrafts, it was the only way to find out the distance covered given the duration of speed. While measuring the true speed, not only the air resistance but also its density is taken into account.
Firstly, true speed indicators compensate reduction of air resistance with increasing altitude. However, this is not enough as the value of true speed needs to be as accurate as possible. Corrections need to be made in relation to temperature changes, occurrence of the effect of air compressibility, increased aircraft’s speed, increase in total and static pressure measurement, and given the turbulence at the places where receivers are attached on aircraft surface. True speed needs to be measured as accurately as possible. Then it is possible to calculate the ground speed and the distance covered more accurately. The difference between the true and the ground speed is larger when the aircraft flies against wind or downwind.
In modern aircrafts, true speed indicators are used as auxiliary one since more accuracy is obtained by measuring the ground speed by radio or inertial navigation aids.
Inside true speed indicator, there are manometric diaphragm and barometric capsule installed (Figure 16). The static pressure PS is supplied to the sealed housing of air speed indicator. Through another tube, total pressure PP is supplied to diaphragm. The arrow of true speed indicator is rotated by diaphragm together with the capsule. With increased altitude, manometric diaphragm expands less (XM reduces) due to reducing air resistance. Barometric capsule expands due to reduction of static pressure (XB increases), therefore, turning of arrow shows the true speed rather than the indicated speed, i. e. the total of diaphragm and capsule movement.

Figure 16. Scheme of true speed indicator

In mechanical TAS indicators that are not that complicated, only static pressure (altitude) variation is taken into account as the signal of outside temperature XT is hard to be transmitted to the cabin mechanically. The dependency of standard air temperature on height is known; therefore temperature-caused errors may be reduced by barometric capsule. The accuracy of TAS indicators is approximately ±8 nodes at lower altitudes, and approx. ± 5 percent at higher altitudes.
More accurate electrical true speed indicators compensate for outside air temperature. Diaphragm and capsule rotates the slide of potentiometer rather than the arrow. The true speed is reflected by the voltage of the potentiometer slide, or the resistance between the slide and the end of potentiometer. It is easy to transmit electrical signal to the chain of potentiometer from outdoor thermometer, and to correct the measurements.
While moving in the air, aircraft is subject to air resistance, which results in heating up. Outside air temperature indicator also heats up, and as a result, the total air temperature TAT measured is higher than the actual static air temperature SAT. Friction-induced temperature increase needs to be compensated or calculated, or otherwise TAS or other measurements will be inaccurate. The size of compensation is set with the help of temperature indicator.
At the zero level of standard atmosphere, the values of true and calibrated speeds are equal: when HST = 0, then CAS = TAS. Since CAS is similar to IAS, the term IAS is more often used in literature indicating that IAS = TAS when HST = 0.
Smaller aircrafts may be equipped with only a single meter of indicated air speed. Operation of an aircraft requires IAS, while navigation requires TAS. IAS does not allow accurate setting of the angle for compensating drift; also, ground speed calculation error can be very large, and the estimated time of arrival ETA can be very inaccurate. However, even using TAS, navigational calculations are not accurate enough, and larger aircrafts are equipped with radio or inertial navigation systems measuring the ground speed GS.
The speed IAS (CAS) is proportional to air resistance. This parameter allows determining the size of lift force and the controllability of the aircraft (how the aircraft reacts to the movements of aerodynamic surfaces), however, it does not say anything about the characteristic of air flow around the aircraft. At the altitudes of 1 km and 10 km, and given equal indicated speeds, the ratios of lift and resistance forces will not be the same, the centres of lift force will not coincide, and the air flows around aerodynamic surfaces are distributed unevenly. Characteristics of sound propagation in air, and the features of moving aircraft at that place are the same and equally dependent on the current parameters in space, therefore, in case of an aircraft flying at high altitude, it would be expedient to measure Mach speed instead of IAS. Based on Mach speed, the most economical flight mode (a car uses less fuel when its speed is approx. 90 km/hour.). The speed of sound in air depends on the temperature; therefore, the speed of sound is different at different altitudes. Mach speed M is the ratio of aircraft’s true speed and the speed of sound in air G: M = TASV / G. The scheme of Mach speed gauge is almost the same as that of TAS indicator only without compensation for temperature as the size of sound speed G depends in the temperature.
Aircraft altitude changes (altitude change rate) are measured by barometric vertical speed indicators VSI or inertial systems. VSI is often called vertical speed indicator (Figure 17).

Figure 17. Vertical speed indicator and its scheme

Kapiliarinė skylutė  – Capillary perforation
Statinio slėgio imtuvas  – Static pressure receiver
Diafragma  – Diaphragm
Statinio slėgio žarnelė – Static pressure hose

Observing vertical speed indicator allows for easier horizontal flying or changing the altitude at desired speed. Inside the vertical speed indicator, there is a manometric diaphragm. Static pressure is supplied to the diaphragm directly, and though a tiny capillary perforation K to the inside of the housing. While flying at the same altitudes, the pressures in the diaphragm and inside the housing are the same and the diaphragm remains in the initial position. When the altitude changes, the pressure in the diaphragm starts changing – it expands or compresses and rotates the arrow. Diaphragm deforms because air does not get inside the device quickly enough, and the pressure inside cannot change quickly. The faster flight altitude changes (the higher is the vertical speed) the more deformed becomes the diaphragm due to the difference of pressures. Deformation of diaphragm is proportional to the vertical speed. When flight altitude stabilize, the pressures inside the diaphragm and around it become equal, and the device start showing zero vertical speed. The defect of vertical speed indicator lays in its feature to show vertical speed after the aircraft starts flying horizontally. This lasts until the pressures inside the device and the diaphragm becomes equal. It takes a few tenths of a second close to the ground, and several minutes at high altitudes.
Vertical speed indicators are very sensitive; they react even to minor changes in flight altitude. When When the weather is calm, VSI is much faster in showing the starting drift (vertical speed) compared to altimeters, therefore maintaining stable flight altitude at zero vertical level is easier observing the vertical speed indicator rather than the altimeter. There are vertical speed indicators of different sensitivity level, e.g., 2 m/s or 4 m/s.

Air data computers

The majority of devices, including altimeters, speed meters and radio transponder, a flight level system, engine devices, automatic control system, the terrain warning system, flight information and other registrars, require data on total and static pressure as well as the ambient air temperature. Supplying pressure by separate hoses to each of these devices requires large number of static and total pressure receivers thus making pressure supply systems complicated. Due to possible condensation of moisture, hoses need to be well-serviced. The length and amount of hoses may be reduced with the help of Air Data Computer (ADC). Air data computer is located in the aircraft’s technical compartment. Inside, there is a barometrical capsule and manometric diaphragm installed. ADC static and total pressures supplied through hoses from pressure receivers, and air temperature data from temperature meter are converted by TAT into analogue and digital electrical signals of altitude and speed. These signals are then transmitted by ADC wires into cabin devices and other aircraft devices.
Traditional total and static pressure systems use barometrical and manometric diaphragms. Currently known are dozens of physical phenomena that are suitable to measure altitude and speed, including deformations of piezo crystals and changes in coil inductance caused by air pressures, etc.

1.6.  Aircraft heading calculations by magnetic devices

Aircraft heading is the angle between the selected reference direction on the horizontal plane and the longitudinal axis projection aircraft on this plane. In aviation, the following three reference directions are usually selected for heading calculations: northern direction of the geographical or magnetic meridian, and the “northern” direction of the orthodrome. The headings are respectively called the true heading, magnetic heading, and the orthodromic heading. In certain cases, heading is calculated using other reference directions; such heading will then be called relative heading. When heading is calculated relative to the main axis of gyroscope used in the aircraft, such heading will be called gyroscopic heading.
Devices sensitive to magnetic heading in aircrafts include magnetic compasses and flux valves. These devices select only one direction from all the directions, i.e. the direction to Earth’s magnetic pole. Magnetic meridian in this case shall be the reference direction. Direction of the true meridian in the aircraft is determined by inertial systems. Orthodromic heading is measured by gyroscopes and radio navigation aids.
Aircraft’s magnetic compasses are equipped with heading scale instead of an arrow. To reduce the vibration of the scale, it is contained in a liquid. Such magnetic compasses are of simple construction, reliable and small, however they have some weaknesses due to which they cannot measure accurately the heading of modern aircrafts. The most significant weaknesses include the following:
– compass is sensitive to external (non-Earth) magnetic fields;
– closer to magnetic poles, horizontal component of Earth’s magnetic field reduces and can no longer rotate the scale; therefore, compasses cannot be used in latitudes over 70° degrees;
– compass cannot be used as a sensor for heading signal as it cannot transmit electrical signal of scale position remotely;
– friction and the liquid obstruct the scale rotation; when the aircraft is turning , the liquid pulls the scale, and the scale hanging on the needle starts vibrating. Compass is only suitable for usage when the position of an aircraft is stable;
– compass errors increase when the aircraft makes pitches, yaws, and rolls, especially at greater accelerations and when the position of the aircraft is not horizontal.
Due to the mentioned weaknesses and low accuracy level, magnetic compasses in larger aircrafts are used as backup devices in case other heading measurement devices are faulty. For determining magnetic heading, more accurate flux valves are used.
Similarly as simple compasses, flux valves are devices sensitive to Earth’s magnetic field. Electrical signal of the valve is not stable and cannot be sent to the indicator in the cabin. The best is to use the signal of flux valve for adjusting the gyroscope; the signal of gyroscope then matches the magnetic heading and remains constant while the aircraft performs manoeuvres in space.
A simple flux valve is composed of two parallel cores made of “soft” magnetic material, e.g. permalloy. Even in a weak magnetic field, permalloy becomes magnetized to the level of saturation, and gets completely demagnetized after removing the field. One core has one side of the coil winded around, and the other core has the other side of the coil winded the opposite direction (Figure 18). Such coil L1 is called a primary coil. The cores and the coil are manufactured very accurately.

Figure 18. Scheme of flux valve

When supplying variable electrical current UF, into the primary coil, the cores become magnetized subject to high current. The coils are winded around the cores in opposite directions, and therefore the cores acquire opposite magnetic fields. The magnetic fields Φ1 of the both cores compensate one another, and the total magnetic field of the cores will be equal to zero. When such sensor receives an external, e.g. Earth’s magnetic fields H, magnetic fields of the same direction Φ2 are generated. The fields Φ1 and Φ2 are summed resulting in increased magnetic field at one core, and reduced magnetic field at another one. The total magnetic field of both cores will not be equal to zero. The size of total magnetic field depends on the orientation of cores and external magnetic field α. When the cores are rotated at the horizontal plane, the size of the total magnetic field becomes proportional to the angle between the lines of external field and the axes of the cores. If a coil L2 which is called signal coil is winded over the cores with the primary coils, a current proportional to the total magnetic field inside it will be generated. This type of sensor is installed in the aircraft that is accurately oriented to the magnetic north so as the total field is equal to zero. When the aircraft is rotated, the current proportional to the angle of rotation, i.e. aircraft heading, is generated in the signal coil L2 of the sensor. Such sensor operates as magnetic compass. It is more accurate than magnetic compass, and the current can be transmitted remotely, however the rest weaknesses characteristic to compasses remain. Such sensor does not react to the direction of rotation as cos(±α) = cosα.
The characteristic of inductive sensor are better when using three pairs of cores arranged in a triangle instead of two pairs. In aircrafts, inductive sensors are installed in the places where the external magnetic fields generated by aircraft’s structure cause less distortion to Earth’s magnetic field, e.g. under the wing or near the tail. In order to increase the accuracy of the sensor, and ensure the cores remain horizontal in case of aircraft roll and pitch, it is fitted on gimballed platform and immersed into a special liquid. Magnetic inductive sensors are not used as independent heading-setting devices. Most often they are used as sensors for more complex inductive compasses (Figure 19) or heading systems.

Figure 19. Inductive compass

Selsinas – Selsyn
Variklis – Engine
Kurso skalė – Heading scale

The cores of inductive sensor arranged in a triangle are crossed by Earth’s magnetic field H. The coils of the cores are connected to selsyn, and the currents in the selsyn windings generate selsyn’s magnetic field oriented the same as the field H. Inside the selsyn, there is a signal coil SR with the current proportional to the orientation of the coil in the inner selsyn’s field, i.e. field H. The amplifier S enhances the flow and transmits it to the electric motor control winding VVA. The engine rotates the heading scale and the coil SR until the current reduces to zero. The scale rotates and stops at the index showing the magnetic heading. Upon rotation of the aircraft, the orientation of inductive sensor in the field H changes, and current is again generated in the signal coil SR; the engine rotates the scale to another position, and other heading is showed.
Manoeuvres of aircraft change the signals of inductive sensor, which prevents from changing the heading accurately. The heading needs to be adjusted after aircraft’s position becomes stable.

To be continued