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Aircraft Avionics

Robert G. Loewy Georgia Institute of Technology

I. Definitions of Avionics Components (Glossary) II. Aircraft Avionics Systems, General III. Traditional Avionics, MEP IV. Avionics Applications Influencing Aircraft Design; VMS V. Impact Of “Smart Materials” VI. Summary

I. DEFINITIONS OF AVIONICS Power Source Most avionics system components require COMPONENTS (GLOSSARY) power sources independent of pilot/crew; i.e., avionics systems are “active” systems. Power sources may be Actuator An element of a control system that will move electrical (e.g., batteries, generators, fuel-cells) or me- another element, by providing a force, pressure or mo- chanical (e.g., hydraulic pumps and reservoirs, pneu- ment (force acting through a lever arm) in response to matics, etc.) a command signal. Processor A system component which may analyze (i.e., Effector A control system element that will provide the extract useful information from), combine or store sig- desired change in an aircrafts’ behavior; e.g., aerody- nals or may model aircraft behavior for comparative namic control surface such as a “rudder,” to change purposes. Such operations may be analog or digital; heading, or a “speed brake” to reduce flight speed. when the latter, processors have much in common with Linkage A control system component that carries use- computers, but usually having special, i.e., more lim- ful signals, forces or moments from one location to ited functions, rather than being general-purpose. another location. These useful signals can be analog Sensors A device that responds to some physical quan- electromagnetic or optical or digital, i.e., quantitative, tity such as pressure or temperature (or conceivably a and such transport can be within the aircraft or from chemical quantity such as acidity) by converting it to a and to points external to the aircraft. Only when forces useful signal. and moments are transmitted are linkages mechanical. Software The capability of digital processors and the When digital signals are transmitted the linkages are complexity of their functions, defined above, are such often called “data buses.” Data buses are the conduits that the (usually) specialized codes that command their through which outputs are sent or inputs are received operations are considered a separate avionics “com- by a digital system or subsystem in order to perform ponent.” In written form such computer or processor its function. codes may require tens of thousands or millions of

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lines of instructions and their development may in- ages (fly-by-optics, FBO) are used less often than elec- volve equal or greater expense than the “hardware” trical linkages (fly by wire, FBW) and in FBW systems elements of avionics systems whose components are there is no need for electro optical transducers. Where defined elsewhere in this glossary. fiber optics linkages are used it is usually because of their Transducer A device that takes a useful signal in one superior capabilities for carrying large quantities of infor- form, say electrical, and converts it to another useful mation (high bandwidth) and insensitivity to ElectroMag- form, perhaps optical. (Note that “sensors” and “actu- netic Interference (EMI), including that associated with ators” are, in a more general sense “transducers,” but lightning. common usage restricts the meaning of the term as de- Once aircraft were recognized as vehicles with realiz- fined here.) able potential for transportation, the need for a number of Transponder A component which, on receiving an Elec- kinds of electronics-based equipment became apparent, troMagnetic (EM) signal, often coded, will respond by based on the importance of increasing aircraft utility and sending a similar signal, usually after a known, con- safety. These functions, roughly in the chronological or- trolled delay time. der in which the related avionics equipments were first adapted for use on aircraft in service use, are as follows:

II. AIRCRAFT AVIONICS 1. Communication SYSTEMS, GENERAL a. Ground to air b. Air to ground The term “avionics” results from combining “aviation” c. Air to air with “electronics,” in recognition of the growing use and 2. All weather, blind flying importance of the application of devices making use of 3. Navigation electronics in aircraft design, development and operation. 4. Limited visibility landing Aircraft avionics systems, however, make use of compo- 5. Bad weather avoidance nents which may not all be electronic, and an understand- 6. Flight path stability augmentation ing of their functions usually requires consideration of 7. Improved flight handling qualities the whole system. Figure 1 illustrates a hypothetical sys- 8. Flight data recording tem for control of an aircraft about its pitch axis (i.e., 9. Collision avoidance pointing the “nose” of the aircraft up or down), which 10. Formation flying (military) would “boost” the pilot’s force output in moving an aero- 11. Target acquisition (military) dynamic control surface by a variable and appropriate 12. Secure identification (military) amount, depending on the aircraft’s flight speed. In this 13. Crew/passengers comfort improvement case “the pilot’s longitudinal sidearm controller motion 14. Structural load alleviation is converted into an electrical signal by a motion1 sensor 15. Terrain avoidance (Loewy, 2000). That electrical signal is converted to an 16. Noise reduction optical signal by an electro-optical transducer. Fiber optic a. Internal linkages carry the optical signal to a processor. After be- b. External ing transduced back into an electric signal, it is amplified 17. Suppressing servo-aeroelastic instabilities or attenuated there according to a second signal originat- 18. Performance improvement ing from an airspeed sensor ( this may be simple gain changes), so that the aircraft’s pitch response will be the It will be noted that this list is long, some items involve same at all airspeeds (assuming this is a desirable char- further breakdown (Items 1 and 16), and since such adapta- acteristic). The signal from the processor then regulates a tions continue apace, any attempt at completeness is likely valve on a hydraulic actuator, which drives the aircraft’s to soon be thwarted by new developments. For example, elevator, i.e., pitch attitude control surface. Several com- in-flight entertainment systems for commercial airliners ments may be pertinent for this illustrative example. The are not listed, but they could be considered avionics sys- electromechanical input valve on the hydraulic actuator tems. Their use is already commonplace and the services might be considered a transducer, but for our purposes they provide are growing by leaps and bounds. it is viewed as part of the actuator. Such an assembly is As implied by the order of functions in the list, often called an integrated servoactuator. Fiber optic link- the application of electronic devices to aircraft can be thought of as beginning with radios for communications 1 For illustrative purposes: side-arm controllers usually have force, (Items 1(a) and (b)), between aircraft crew members— rather than motion sensors. pilots, copilots,navigators, flight engineers, etc.—and P1: FHK Encyclopedia of Physical Science and Technology EN001H-913 May 8, 2001 14:54

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FIGURE 1 Schematic of avionics components in a Fly-By-Optics (FBO) flight control system for the pitch axis. (From Loewy, R. G. (2000). “Avionics: A ‘New’ senior partner in aeronautics.” AIAA J. 37(11), 1337–1354.)

ground crew members; among dispersed crew members With the advent of devices (so-called “control actua- of large aircraft—although this is more likely to use tele- tors”) capable of moving aircraft control effectors (e.g., phone rather than wireless technology—e.g., from the aerodynamic surfaces) reliably and as quickly or more cockpit of military aircraft such as bombers, on the one quickly than a human pilot, avionics systems could be hand, to the tail gunner via an “intercom,” for example, on used, not only to help the pilot and crew perform their the other; and (Item 1(c)) between flight crews of different missions but also to fly the aircraft safely. These automatic aircraft. systems are often referred to as Vehicle Management Sys- Later, what can be considered radio technology, i.e., tems (VMS). To emphasize the highly integrated nature transmitters and receivers of wireless EM signals, was ap- of VMS into the aircraft for which they are part of the plied to navigation (i.e., helping the pilot know where to control system—on an equal, flight-safety footing along go) and landing aides (i.e., helping the pilot to land safely, with airframe structure, aerodynamic shape and propul- particularly under reduced visibility conditions). In mili- sion systems—it is useful to think of VMS avionics as tary applications of aircraft, such “assistance” by avionics part of the host vehicle. As might be expected, then, for the pilot and/or other crew members was extended VMS avionics are not “added on” but are usually con- to acquiring and identifying targets; pointing, firing or sidered during the design or developmental stages of the launching weapons; countering—i.e., thwarting through introduction into service of a new or substantially modi- so-called “electronic countermeasures”—similar systems fied flight vehicle. used by the enemy; and identifying himself/herself as In a “gray area” between MEP and VMS are what, at friendly to members of the same forces. The last is known their introduction as early as 1917, were called “auto- as IFF, for “Identification, Friend or Foe.” All such func- matic pilots” or “autopilots.” These systems began by us- tions can be performed more or less automatically to such ing roll attitude sensors, heading sensors (e.g., magnetic an extent that, taken together, such systems are often re- compass), altitude sensors (e.g., barometric altimeters), ferred to as “the pilot’s associate.” These kinds of avionics airspeed sensors (e.g., “pitot-static” pressure tubes), etc to systems are also referred to in the military as the “Mis- automatically adjust (i.e., “hold” constant) wings in a level sion Equipment Package” (MEP). It is useful to think of position, aircraft direction, flight altitude and speed, re- all avionics systems which assist pilots and crew in per- spectively, by sending appropriate corrective commands, forming their “mission,” even if it is a civilian transport for example, to rudder and ailerons (yaw and bank ef- moving passengers or cargo from one place to another, fectors) and longitudinal control stick and engine throttle as MEP. Emphasizing the “added-on” nature of MEP, the (speed and climb/rate of descent effectors). Such avionics aircraft in which it is installed is often referred to as the systems were initially thought of as relieving pilot fatigue “host vehicle.” on long flights (particularly in an era of low cruising P1: FHK Encyclopedia of Physical Science and Technology EN001H-913 May 8, 2001 14:54

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speeds). With increasing avionics component capabili- tively. The architectures of such systems should then be ties, as discussed in Section IV, autopilots have devel- such as to include at least triple redundancy and a con- oped into the much more sophisticated, Automatic Flight tinuous comparison of performance among them in “real” Control Systems (AFCS). Perhaps the most important of time, so that a failure can be identified, in what is often the enabling new capabilities is the greater responsiveness called “voting,” and an automatic shut off of the system to commands on the part of actuators, i.e., their higher which has failed—or has even been subject to degraded “bandwidth” or high frequency capabilities. Among the performance—will take place. AFCS functions making use of these newer capabilities are included Items 4, 6, 7, and 13 through 18. The last of these could include such measures as automatic pump- III. TRADITIONAL AVIONICS, MEP ing of fuel from one tank to another to keep the aircraft’s center of gravity in its most favorable position on long A. Communication and Navigation flights. Systems in General Although avionics systems in the MEP category can, in Radio technology is based, fundamentally, on the fact that many instances be “added on” well after the fundamental an alternating electrical current (ac) in a wire will radi- aircraft design is completed, those responsible for their in- ate EM energy into space. If the relationship between the tegration into the host aircraft still must provide (a) space length of the wire and the frequency of the ac, f , is such within the airframe, (b) stress-free mounting points which that the wire length is half a wavelength, λ, almost all limit the shock and vibration transmitted to this equip- the power not turned into heat in the wire will be radi- ment, and (c) an environment of limited maximum temper- ated. This behavior of half wavelength wires is the basis atures and EMI and acoustic fields. Such must, of course, of EM “transmitting antenna” design. A half wavelength also be provided for VMS avionics. Further, when trans- wire which intercepts the EM radiation will also convert mitting/receiving antennae (the internal/external linkages) its energy into ac current most efficiently and is the basis are involved, their locations should minimize interference for “receiving antenna” design. Note that the relationship with the signals to be sent or received and “cross talk” between frequency and wavelength is given by to/from other EM sources. This is particularly challeng- ing for aircraft designed to have low radar cross sections, c (in distance per second) f (inH ) = , so-called “stealth” configurations. z λ Another way to categorize avionics systems in broad where c is the velocity of propagation of EM radiation, terms is to note that there are those for which the con- which is that of light in a vacuum (about 300 × 106 m/s). sequences of failures are such that a pilot can correct or Sending and receiving antennae can be based (1) on the compensate for them with reasonable effort, or those for ground (terrestrial), (2) in aircraft or (3) in spacecraft. In which it is not reasonable to expect a pilot to do so. For our general, the larger the antenna in terms of wavelengths of purposes, in this consideration, it does not matter whether the radiation transmitted, the narrower will be the pattern the failure is of the type in which the system simply stops of radiation. This can lead to some large airborne antennae working or if it causes the system to drive to a full authority (see Fig. 2, for example). Some antennae are designed to position unbidden—a so-called “hard-over” failure. be omni-directional or nondirectional, i.e., they transmit Systems for communication, navigation, or bad weather EM radiation in a spherical pattern. In such a case the ratio avoidance may well be important for safety of flight and of received to transmitted energy is equal to hence be duplicated or provided in multiple installations of higher redundancy; but the consequences of their fail- Receiver Antenna Area, ure can reasonably be expected to be compensated for 4πR2 by a pilot if means exist to identify their improper oper- where R is the distance, or range, between transmitting ation. As a consequence, the duplicated systems do not and receiving antennas. usually have to operate simultaneously, but can be left in Although specific portions of the frequency spectrum a “stand-by” mode until needed. Other systems, having (i.e., all the values of f to be used) must be allocated to to have frequency response characteristics well beyond prevent different systems from interfering with each other, what a pilot can do simply to operate effectively, include for many years and by general agreement, radio transmis- those for maintaining proper aircraft attitude in all weather sion frequencies have been designated in the following flying, performing limited visibility landings, augmenting “bands” (Skolnik, 1962) (Table I). flight path stability, and suppressing aeroelastic instabili- There is a marked tendency to use higher and higher ties. The consequences of such systems failing, therefore, frequencies, and some of the categories in Table II have will unfold much too quickly for a pilot to respond effec- also been widely used for about 50 years, but with some P1: FHK Encyclopedia of Physical Science and Technology EN001H-913 May 8, 2001 14:54

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FIGURE 2 Early warning E-2C aircraft. (From Skolnik, M. I. (1962). “Introduction to Radar Systems,” McGraw Hill, New York.)

different applications overseas (Reference Data for Engi- tion of the electrical characteristics of the earth (which neers (1985) (Table II). influence “ground waves,” those propagating along the Many factors affect the transmission of EM radiation. Earth’s surface), atmospheric noise (such as caused by Some are a function of radiation frequency, others a func- lightning), ionospheric properties (which influence “sky waves,” those reflected by characteristics of the Earth’s TABLE I Designated Frequency Bands for EM Radiation atmosphere). The influence of the Earth is, as might be expected, important for transmissions from ground sta- Name Abbreviation Frequency Wavelength tions, and is sometimes referred to as causing “site sen- Very low VLF 3 to 30 kHz 100 to 10 km sitivity.” Very high frequencies (i.e., above 30 MHz) are frequency mostly line-of-sight waves, and above 3 GHz, atmospheric Low frequency LF 30 to 200 kHz 10 to 1 km and precipitation scattering and absorption become Medium MF 300 to 3000 kHz 1 km to 100 m significant. frequency High frequency HF 3 to 30 MHz 100 to 10 m Very high VHF 30 to 300 MHz 10 to 1 m B. Terrestrial Based Navigation Systems frequency Ultrahigh UHF 300 to 3000 MHz 1 m to 10 cm The term “avionics” usually implies equipment carried frequency and/or functions carried out aboard aircraft. To understand Superhigh SHF 3 to 30 GHz 10 to 1 cm some of their complexities, however, it is useful to know frequency something of the ground-based systems with which the air- Extremely high EHF 30 to 300 GHz 10 to 1 mm borne avionics components interact. There are, in general, frequency two kinds of ground-based navigation systems; so-called P1: FHK Encyclopedia of Physical Science and Technology EN001H-913 May 8, 2001 14:54

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TABLE II Letter Designation of High-Frequency EM Bearing, as provided by direction finders, and distance, Radiation as provided by a DME, from the same ground station, al- Letter Frequency Letter Frequency lows the calculation of position relative to that ground sta- designation range designation range tion. In geometric terms, by establishing range and bear- ing, ground “point sources” allow an aircraft to place itself L 0.39 to 1.55 GHz Xb 6.25 to 6.90 GHz on the space curve intersection of a sphere (from range in- a Ls 0.90 to 0.95 GHz K 10.90 to 36.00 GHz formation) and a semi-infinite vertical plane which has S 1.55 to 5.20 GHz Ku 15.35 to 17.25 GHz one edge at the fixed ground station (from bearing infor- C 3.90 to 6.20 GHz Ka 33.00 to 36.00 GHz mation). If barometrically determined altitude information X 5.20 to 10.90 GHz Q 36.00 to 46.00 GHz is added, the position of the aircraft will be known. a Includes Ke band, which is centered at 13.3 GHz. Another kind of ground-based point source is intended to provide aircraft occasional, positive and absolute loca- tion information, often known as a “fix.” These EM radia- “point sources” and those that establish an EM radiation tion transmitters are known as “marker beacons” and they grid in space. Among point source ground systems are om- send a narrow, fan-like pattern vertically at fixed points nidirectional (nondirectional) beacons, which allow air- along the nation’s airways, with the pattern’s maximum borne direction finders to establish a heading direction or width aligned with the center-line of the airway on which “bearing” to the known position of the beacon. Direction they are located. Receivers in the aircraft provide the pilot finders consist essentially of a rectangular loop antenna with information as to which beacon has been or is being wired so as to send the difference in signals in the op- traversed. posite, vertical sides of the loop to a “receiver.” This dif- The VHF (Very High Frequency) band listed in Table I ference is zero when the sides of the loop are the same is used for voice communications to, from, and among distance from the beacon, at which point the plane of the aircraft. By combining communications and navigation loop is perpendicular to the line joining the aircraft and functions in the VHF band, some avionics components the beacon. The antenna loop is, therefore, rotated about can be made to do double duty. The success of this scheme an axis parallel to and equidistant from the two vertical has resulted in what is known as VOR (for VHF Omni- sides sensing the beacon’s signals, and its orientation must directional Range) and its adoption as an international be noted when the “receiver” indicates a null reading. To standard. In this system, the ground station radiates two minimize the aerodynamic drag on an aircraft in which a signals: one is omni-directional radiation whose carrier direction-finding antenna is to be mounted, two fixed an- VHF frequency is modulated at 30 Hz; the second is a tenna loops can be mounted so that their planes are at 90◦ cardioid (heart-shaped) pattern in the horizontal plane that to each other and the phase of their signals are compared rotates at 30 rps. The airborne receiver experiences both electrically from one to the other to achieve the same effect transmitted waves as 30 Hz signals and the phase angle as mechanical rotation. Direction finding systems can, al- between them, as related to the rotation angle of the car- ternatively, have the beacon placed in the vehicle and the dioid pattern, determines the bearing of the VOR beacon rotating loop antenna and receiver at the ground station. The nearly constant speed of EM radiation has led to its use to measure distance. Although other means of radio ranging (i.e., means to measure distance) exist, perhaps the simplest in concept is known as DME, for Distance Measuring Equipment. This system is internationally stan- dardized. Its operation is depicted in Fig. 3 (from Kayton and Fried, 1997). A transmitter-receiver on board the air- craft, known as an “interrogator,” sends a pair of very short EM pulses (3.5 µs long and 12 µs apart), repeated from 5 to 150 times per second. A transponder at a fixed, known ground station, on receiving these pulses, retransmits them after a 50 µs delay. The avionics component on the aircraft automatically determines the difference between sending and receiving times (very short compared to the period of the highest repetitive rate) subtracts the transponder de- lay and shows the distance from the ground station on a FIGURE 3 DME operation. (From Kayton, M., and Fried, W. R. control panel display. (1997). “Avionics Navigation Systems,” Wiley, 2nd ed., New York.) P1: FHK Encyclopedia of Physical Science and Technology EN001H-913 May 8, 2001 14:54

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from the aircraft. There is also a Doppler version of VOR (see Section III.E) in which a 9960-Hz carrier frequency is frequency modulated by the (simulated) rotation of a large diameter (480 wavelengths or 44-ft-diameter) antenna2 so as to be varied by ±480 Hz at 30 Hz. The same airborne equipment can be used to sense phase, hence bearing to the Doppler VOR beacon, as with ordinary VOR, but with less site sensitivity and greater accuracy. Maximum bearing er- rors at 20-mile distance with standard VOR are about 3◦ and with Doppler VOR, about 0.5◦. The military uses “point source” ground stations which combine systems for determining both bearing and dis- FIGURE 4 Hyperbolic lines of constant TD for a typical master- tance measurement. These systems are known as Tacan secondary pair. (From Kayton, M., and Fried, W. R. (1997). (Tactical Air Navigation). The distance measuring func- “Avionics Navigation Systems,” 2nd ed., Wiley, New York.) tion, i.e., range determination, is accomplished using the same pulse and frequency configurations as stan- dard DME. The Tacan omni-bearing operation, however, sition in space, as shown in Fig. 5 (Kayton and Fried, (a) uses frequencies from 960 to 1215 MHz (almost 10× 1997). higher than VOR) so that smaller antennas can be used; Since LORAN-C is affected by sky waves and uses (b) employs a multi-lobe radiation principle which im- ground waves, sophisticated corrections must be made to proves bearing accuracy; and (c) enjoys equipment eco- achieve maximum accuracy, and the usual ranges, a func- nomics as a result of using the same radio frequencies for tion of transmitter power, are measured in hundreds of range and bearing determination. miles. Accuracy of about 1/2 km is achieved roughly 95% The so-called “hyperbolic” systems, such as Loran, of the time, when differential techniques (see, for example, Omega and Decca, provide an alternative means of po- Section III.C) are used, adding redundant station pairs. sition determination. These systems, rather than using In the Omega system (which has been shut down for sev- “point sources,” consist of groups of transmitting stations eral years), transmitters emitted continuous waves, rather thought of as forming “chains.” A chain consists of at than pulses, and hyperbolic lines of position were estab- least three stations, of which one is a master transmitter lished by phase differences in signals received from a mas- and the other two are secondary transmitters. Each sta- ter/secondary station pair. Because one phase difference tion in a chain transmits EM pulses which are grouped between two continuous wave signals defined a series of closely in time and repeated at a certain rate. The inter- hyperbolas, multiple frequencies were used to eliminate val between the repeated transmissions of these groups of the ambiguity of which hyperbola was the pertinent one. pulses is known as the Group Repetition Interval (GRI), and it identifies a particular chain. The number of pulses in a group, the interval between them, the envelope which defines pulse shape, as well as GRI, establish the transmit- ted signal format, and it identifies each station in a chain. Since the positions of the stations are known, as are the timing of signals transmitted from master and secondary stations, the difference of the Time Of their signals’ Ar- rival (TOA) at an aircraft informs the aircraft that it must be somewhere on a space curve, which happens to be a hyperbola, in a horizontal plane determined by baromet- ric altitude. A series of these TOA’s, then, establishes a series of hyperbolas, as shown in Fig. 4 (from Kayton and Fried, 1997). If follows that TOA’s from that master and another secondary station establishes a second series of hyperbola. The two specific TOA’s informs the aircraft as to which two hyperbolas it must be on; their intersec- tions (plus barometric altitude) establish the aircraft’s po- FIGURE 5 Hyperbolic lines of constant TD for a typical triad. (From Kayton, and Fried, W. R. (1997). “Avionics Navigation Sys- 2 Actually a ring of individual EM transmitting elements. tems,” 2nd ed., Wiley, New York.) P1: FHK Encyclopedia of Physical Science and Technology EN001H-913 May 8, 2001 14:54

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Five frequencies were used at each station; four common less.” Decentralized systems clearly require the airborne and one station-unique. The frequency bands being VLF components to be both receivers and transmitters. (seeTableI),thesesignalswerepropagatedwithlowatten- uation between the Earth’s surface and a particular layer C. Satellite-Based Navigation Systems of the ionosphere, to great ranges. In fact, only 8 transmit- ting stations worldwide constituted an Omega system with Relatively soon after the successful orbiting of man-made accuracy within about 4 nm, 95% of the time. When 30 satellites about the Earth, attempts began with the objec- such stations were employed, using differential techniques tive of replacing or supplementing terrestrial radio naviga- among redundant pairs, position errors were diminished tion systems through the use of earth satellites. The major to about 2 km, 95% of the time, within 1000 km of the advantages provided are those of (1) coverage, since the monitor station. lines of sight, with enough satellites in the proper orbits Decca is also a system based on phase differences, but can be made to reach all points on earth; and (2) very one that uses low frequency carrier waves between 70 and stable operation. Their transmission frequencies (L band 130 kHz. Two station pairs are typically 110 km apart and navigation signals from the satellites and S band telemetry the range of coverage is typically 320 km. downlink to and up-link from the ground station) are also With the advent of digital technology, both the accuracy such as to make them all-weather systems. Two major and flexibility of the earlier systems’ information process- satellite radio navigation systems are included in an in- ing have increased. Further, the components’, particularly ternationally recognized Global Navigation Satellite Sys- the airborne components’, size and weight have been re- tem (GNSS); they are the U.S. Department of Defense’s duced. Since many aircraft radio communication and nav- NAVSTAR Global Positioning System (GPS) and the igation systems have shared both the same parts of the Russian Federation’s Global Orbiting Navigation Satel- EM frequency spectrum and a common technology, both lite System (GLONASS). Both systems have three ele- ground-based and airborne components of terrestrial sys- ments: (1) a constellation of earth-orbiting satellites (each tems which provide digital communication and navigation has 24, as of this writing), (2) ground stations; and (3) functions have been developed as integrated systems. That receiver/processor units in the user aircraft. The satellites is, the same EM carrier waveforms are used to carry both transmit EM signals which the ground station uses to track functions. them and from which the user aircraft determines its posi- Two basic types of terrestrial integrated communi- tion relative to the satellites. Very accurate atomic clocks cation-navigation systems, centralized and decentralized, aboard the satellites are the heart of GPS. TOA process- are in widespread use by the military. Operation of the ing in the ground stations allow simultaneous ranging from former is dependent on a central site, from which all users multiple locations, and since the ground stations’ positions determine their positions on an absolute basis. Such an are known—also allows determination of the satellite’s lo- arrangement facilitates the control of many users, more cation, velocity, and predicted orbital positions. The satel- or less simultaneously, although users ordinarily receive lite’s orbital position information is sent from the ground information on their positions automatically on the basis stations to the satellites, which transmit it to the user air- of periodic “requests” from the ground-based central site craft’s receiver processor, together with timing signals. or node. Users in these “Position Location and Reporting The user aircraft’s processor uses TOA data to establish Systems” (PLRS) are “cooperating” users; i.e., they are its position relative to (at least three) of the GPS satellites equipped with Radio Sets” (RS) equipped with accurate which, combined with the transmitted data on their posi- “clocks” and send a signal, individually identifiable, to tions, allows the user aircraft’s position to be known. An three or more ground stations (MS’s for Master Stations). obvious advantage from the avionics viewpoint of GPS The MS’s also have very accurate “clocks” and compar- type navigation systems is that the equipment in the user isons of their timing signals are made with those of the aircraft can be “passive” to the extent that user aircraft RS. Knowing “clock” signal differences and signal TOA need not transmit EM signals. information at two MS’s, places the user (the RS) on the A variety of corrections are required in GPS or space curve intersection of two (imaginary) spheres. Alti- GLONASS to achieve the position accuracy desired; such tude information, based on barometer data, establishes the include those compensating for clock errors, the rotation position of the RS at one of two points on this space curve, of the earth, ionospheric and tropospheric refraction, etc. and TOA data from a third MS eliminates this uncertainty. “Differential” principles can be used to eliminate errors Operation of the second, decentralized type of system common both to the user and a reference ground station. is such that each user determines its own coordinates rel- In “Differential Global Positioning Systems” (DGPS), a ative to other users’ positions. Since it is independent of “reference ground station” receives the same navigation central sites, decentralized systems are often called “node- signals as the user aircraft, but since its position is known, P1: FHK Encyclopedia of Physical Science and Technology EN001H-913 May 8, 2001 14:54

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all the errors in its calculated position can be determined. worth their additional complexity. INS is widely used in These become error corrections when the reference ground the military and on large civil passenger aircraft. station transmits them to the user aircraft. Through the use As principal components of inertial systems, ac- of DGPS, position errors can be reduced to within 1 to celerometers and gyroscopes have been subject to intense 10 m, depending on the user’s distance from the reference development efforts to improve their accuracy and elimi- station. nate responsiveness to influences which contaminate their GPS receivers can be quite small; one military version outputs. Design of accelerometers for inertial navigation is known as the MAGR (for Miniature Airborne GPS Re- systems are most often based on one of three concepts. ceiver) and the entire component, except for its antenna, The first is that of a pendulum on “flexures”—beams with is contained inside another avionics assembly; e.g., an in- very low stiffness in one direction, but stiff in the other ertial navigation system (See Section III.D, below). The two, perpendicular directions—and electrically restrained antenna itself, in a U.S. Navy system, is contained in a to a zero deflection at zero or reference acceleration. This circular housing with a diameter of less than 125 mm, has provides for “rebalancing” to ensure that response to one a height (thickness) of about 40 mm, and weighs about 2 n acceleration will not change the direction of sensing for (mass of about 0.1 kg). the next. The second makes use of very small, microma- chined silicon masses mounted on springs that are “soft” in one direction, stiff in the other two, also electrostatically D. Inertial Navigation Systems nulled; and the third employs vibrating beams whose stiff- The basis of inertial navigation is “dead reckoning” (see ness is so low in the direction of vibration that tensile force Section III.E, below), using accelerometers mounted on variations along the beam length cause changes in the fre- the aircraft to measure accelerations and integrating their quency of vibration, thus indicating acceleration along the signal outputs over time, first to obtain velocities and then beam length. a second time to determine position. Inertial Navigation Many types of gyroscopes are used in aircraft applica- Systems (INS) are self-contained, requiring no cooperat- tions for either indicating or providing signals in automatic ing ground stations or satellites sending EM signals to systems which provide control of aircraft attitude angle or the user aircraft; thus, they are not subject to interfer- angular rates. The earlier forms used a spinning wheel ences by an enemy or the weather. Since the processing of mounted in a gimbal (so as to be free to rotate about an the fundamental sensor output is an integration over time, axis perpendicular to its spin axis) and “floated” at neutral however, errors grow with time, and, if the orientation of buoyancy. Angular motion of the gimbal axis in a plane the accelerometers is not accurately known, aircraft at- containing the spin axis would then cause precession about titude changes—as a result of atmospheric disturbances the gimbal axis, which would indicate the gimbal axis’ or deliberate maneuvers—will contaminate acceleration angular rate. If this response were to be available again signals with changing gravity components. Corrections for later motions, this precession angle would have to be for these effects are accomplished in so-called “strap- “reset,” and such would be done by magnetic torquers, down” inertial systems in which gyroscopes are added to according to a “rebalance algorithm.” These and other sense angular motions. These “strap-down” inertial sys- gyroscopes were developed further, including such re- tems have become practical with the advent of Ring Laser finements as two perpendicular gimbals, electrostatic sus- Gyros (RLG’s) and Fiber Optic Gyros (FOG’s). These pension, etc. The less expensive, less maintenance prone devices correct for changes in acceleration direction elec- versions with drift rates of about 0.1 deg/h are still useful, trically, so that the linear, horizontal velocity and posi- for example, in tactical missiles, but are too inaccurate for tion predictions are as they should be for the purposes of long-range navigation. navigation. Although modern optical angular motion sensors are When inertial systems are activated, they must be still called “gyroscopes,” they function on other than New- “aligned,” to set the aircraft’s initial position and velocity tonian mechanical, i.e., “inertial,” principles. Because of properly and to orient its axes relative to the Earth; this pro- their accuracy, dynamic range, linearity, maintenance-free cess is known as “gyrocompassing.” The Earth’s rotation, nature, and reliability, RLG’s and FOG’s are now used in of course, imposes a centripedal acceleration whose mag- INS’s for almost all commercial and military aircraft. One nitude and direction (with respect to the “vertical,” i.e., the of two optical principles are used in these devices, but in local normal to the earth’s mean surface) varies with geo- either application, two laser beams propagate in what is graphical position. This and other such small errors grow essentially the same closed, planar path; one clockwise, sufficiently with time as to make “hybrid” systems, such the other counterclockwise. If the device containing the as those which “update” inertial systems periodically us- paths rotates about an axis perpendicular to the plane of ing GPS data, for example, in a process known as “aiding” those paths, the Sagnac Effect (1967), which results from P1: FHK Encyclopedia of Physical Science and Technology EN001H-913 May 8, 2001 14:54

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the fact that light waves are unmoved by motion along the transmitter power requirements are small; and they work light path of the medium in which they’re transmitted— very well for low vehicle velocities. makes the light’s path in the direction of device rotation As to the principle on which Doppler radars are based, appear to be longer and the light’s path in the opposite consider that wave motion emanating from a source mov- direction appear to be shorter. The RLG makes use of a ing with respect to the receiver is sensed as having a “resonator” principle, the FOG can use that principle or changed frequency; the magnitude of the change depend- interferometry. ing on the relative velocity, higher if the source and re- Because the front part of a laser light beam is coherent ceiver are moving closer, lower if they are moving farther (i.e., all components are in phase) the interference be- apart. This so-called “Doppler effect” is experienced al- tween two beams propagating in opposite directions in an most every day acoustically, for example, if a fast-moving optical resonator forces a standing wave within the opti- auto or train passes with its horn or whistle blowing. In cal cavity. When this type of RLG’s housing rotates about a directly analogous way, the frequency of a radar signal the circular path’s centerline, then, the nodes and/or antin- return shifts if the transmitter and reflecting surface have odes of the standing wave, which are fixed in space, can be relative velocity along the line of EM transmission. This “counted” and interpreted as angles in the azimuthal direc- provides a means, using reflection returns, to determine tion around the circular path. The light sensor of an FOG the speed of an aircraft relative to the ground or water using the interferometry principle experiences phase dif- over which it is flying. Doppler radars, mounted on an ferences where the two, counter-rotating laser light beams aircraft, use microwave frequencies in an internationally emitted simultaneously are recombined, since one’s path authorized band, between 13.25 and 13.4 GHz. This pro- is longer and the other’s shorter, depending on the sense vides narrow beams of EM radiation, which can be pointed and magnitude of the angular rotation of the device about at the ground at relatively steep angles. The last has the the path’s centerline. The positions of the lines of inter- additional benefit of reducing the probability of detection ference can then be interpreted as a measure of rotation in military applications. angle. Most optical gyros used in INS’s, as of this writ- For Doppler navigation, at least three radar beams are ing, are of the interferometer type; employing light paths needed to determine three components of velocity relative of between 10 to 40 cm in length; weighing between 5 to the earth’s surface, and three aircraft attitude measure- and 20 n (mass between 0.5–2.0 Kg) per axis; and having ments in three perpendicular planes are needed to resolve root-mean-square accuracies of about 0.05◦. the Doppler radar measurements into components in an The typical INS, using these components, then (Kayton earth-related, geodetic coordinate system, as needed for and Fried, 1997), requires about 8000–16,000 cc in vol- dead reckoning navigation (Fig. 6). If the three Doppler ume, 30–150 W of power, weighs approximately 85–130 n radar beams are arranged as shown in Fig. 7, and a differ- (mass between 9–14 Kg) and has a velocity accuracy ence taken of the returns from signals A and B, the Doppler of about 0.75 m/s (rms) and navigational accuracy of shifts of the lateral components will cancel, whereas the 1.5 km/h. These modern airborne systems are relatively longitudinal components, being of opposite sign, will be expensive ($50,000 to $120,000). added. This arrangement, known as a “Janus” system (after the Roman God who could see both backward and forward), increases system accuracy. For the usual beam E. Doppler Radar and Dead angles to the horizontal of about 70◦, a Janus system will Reckoning Systems “Dead reckoning” is an old maritime term used to describe navigating (itself a maritime term) by using known initial position, the vehicle’s velocity vector (speed and direc- tion), and how long that velocity has been maintained, to determine the vehicle’s new position. If velocity is mea- sured, say, relative to the surface of a body of water, it is clear that positions determined by dead reckoning will be in error by the existence of currents in that water. For ships whose speed is not great relative to currents, this is important; for fast flying aircraft it is much less so. Use of Doppler radars to measure relative speed in modern dead reckoning systems, however, has some significant advantages; for example, like INS, they are self contained, FIGURE 6 Resolution of aircraft velocity into navigable needing no terrestrial or satellite cooperative station; their components. 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the possibility of mid-air collisions, controlled flight into terrain, or collisions on airport taxiways or runways, ve- hicle borne avionics equipment plays important roles in these functions. Installation of airborne, mid-air collision systems provides protection against such calamities in- dependent of ground control and in addition to the na- tion’s Air Traffic Control (ATC) system. The Traffic Alert and Collision Avoidance System (TCAS) uses a scanning radar transmitter in one aircraft to trigger the response of a transponder in any aircraft so equipped within its range. In the version of TCAS most used, TCAS II, the distance between two aircraft and their altitude separation are cal- culated, based on the transponder signal returns, and the FIGURE 7 Lamda arrangement of three Doppler radar beams. crew is alerted about 40 sec before the closest Point of Approach (CPA) is to be reached, if the separation is pre- have an error in horizontal velocity of only about 0.015% dicted to be small. This alert is known as a “traffic advi- per degree of error in the aircraft’s pitch attitude. Without sory” and displays the range, bearing and altitude of the the Janus arrangement the same metric would be about 5%. aircraft posing collision danger. If the danger continues, about 25 sec before CPA, a “Resolution Advisory” (RA) F. Instrument Landing Systems appears showing the climb or descent maneuver recom- What is known as the Instrument Landing System (ILS) mended to increase the miss distance. Since both TCAS- consists of (1) “localizer” transmitters, located at the cen- equipped aircraft must be properly advised as to how to terline of and off the ends of runways, which provide lat- change their flight paths, TCAS II has an air-to-air data eral guidance to aircraft approaching to land; (2) “glide link communicating between the two aircraft, to coordi- slope” transmitters located beside runways near the end nate RA’s. A version known as TCAS I does all of this of the runway over which the aircraft first passes in landing except displaying RA’s. All air carrier aircraft operating (the “threshold”), which provide vertical guidance; and (3) in U.S. airspace with 10 to 30 passenger seats must have marker beacons reporting progress along the glide-path to TCAS I, all with more than 30 seats must have TCAS II. the pilot of the landing aircraft. As air travel departure and arrivals increase and, with All three, localizer, glide slope, and marker beacon them, airport congestion, the danger of collision between transmitters, radiate continuous wave EM energy at ra- aircraft on the ground also increases. Ground-based sys- dio frequencies. Their radiation patterns in space and in tems to aid the regulation of ground movement of aircraft specific frequency channels provide signals to an aircraft include surface movement radars and taxiway lights mod- receiver indicating deviations from the desired height as ulated to indicate specific taxi routes. These don’t, at this a function of range from the end of, and lateral displace- writing, require avionics equipment on the aircraft. There ment from the centerline of, a particular runway. The re- are, however, aircraft systems that use transponders to al- ceiver, then, displays information to the pilot that only is low ground-based “interrogators,” located with taxiway “nulled” when the aircraft is “on course” to landing, and lights, to derive identification and location information these information signals grow with the level of deviation and relay it to tower controllers. to either side or above/below the proper course. In “auto Commercial, in fact all civil, aviation must keep a safe land” systems, such deviation signals are “hard-wired” to altitude above terrain in all flight modes other than take- the AFCS (see Section IV). In the ILS airborne equipment, off and landing. Military aircraft, however, must often a Morse-Code identification signal is received audibly in approach the ground for weapon delivery, precise recon- the cockpit on the localizer band, and a voice transmission naissance, or—for extended flight times—to avoid detec- from the airport’s control tower may also be provided. Sig- tion or defensive weapons. Those with the last of these nal standards for ILS are established internationally, and requirements are usually equipped with “terrain follow- about 1500 ILS’s are operational at airports throughout ing” equipment. These are automatic systems having For- the world. ward Looking radars and Infra-Red (FLIR) sensors and radar altimeters (see Section III.I, below). The first two of these measure the range and angle from the horizontal G. Collision Avoidance Systems of the terrain before the aircraft. Flight path control com- Although ground control of aircraft flight plans and flight mands, based on a computed terrain profile in a vertical paths in real time have as a prime objective eliminating plane, based on the forward-looking radar returns with P1: FHK Encyclopedia of Physical Science and Technology EN001H-913 May 8, 2001 14:54

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pilot monitoring, directly control the pitch attitude, hence lowable for safe operations are exceeded for wind speeds “angle of attack” and lift of the aircraft, so as to main- or turbulence; 5 m/s, for example, is often considered such tain a desired height above the terrain. The radar altime- a limit for turbulence. The atmospheric phenomena asso- ter checks the altitude prediction, and the FLIR provides ciated with thunderstorms and “microbursts” and known back-up data to ensure that the radar commands flight over as “wind shear” is susceptible to detection using Doppler such obstructions as power lines. In civil aviation, Con- processing avionics. This extremely dangerous condition trolled Flight Into Terrain (CFIT) has become a safety is associated with a column of air with high downward issue of increasing concern, particularly in mountainous vertical velocity flows which, on contact with the ground regions and under conditions of reduced visibility. Appro- must flow horizontally (i.e., radially) outward in all di- priate avionics therefore, may soon be appearing on all air- rections. An unsuspecting aircraft flying directly toward craft above a certain size in terrain avoidance applications. the vertical column, near the ground (as in a landing ap- proach), is flying into a head wind until it passes the center of the column, at which time it is abruptly subject to a tail- H. Weather Radar Systems wind. The associated loss of lift may not be restored before Airborne weather radar systems make use of the reflectiv- disastrous contact with the ground. Weather radar to sense ity of clouds, precipitation, dust particles at low altitudes these potentially calamitous conditions are installed at a and ice crystals at high altitude. Their intent is to deter- few airports. Plans are underway to install weather radars mine the position of air having the kinds of motion that can specifically capable of detecting wind shears on all com- make flight dangerous or uncomfortable. The magnitude mercial aircraft with detection range capability sufficient of reflections, compared with stored models, allows pre- to allow this atmospheric phenomenon to be evaded. cipitation rates and whether it is rain, snow or hail, to be determined. Positions are determined by the elevation and I. Radar Altimeters scanning (heading) angles of return signals and range by “gating,” i.e., “enabling” the receiver only at the specific For certain specialized functions, down-looking radars are times when a signal reflected from that range would be re- used to measure “tape-line” altitude; i.e., distance above ceived. Further, the wind speeds and turbulence intensities the ground immediately below the aircraft. Low flying mil- are measured by Doppler effects, usually by processing the itary aircraft may use radar altimeters for correlating ter- return timing of pairs of pulses. rain contours with stored map-matching navigation infor- Weather radars and multiple use radars with weather mation. In civil aircraft operation, radar altimeters can be defining functions are usually mounted in the nose of used to assist automatic landing systems. Although other the aircraft (see Fig. 8, from Kayton and Fried (1997)) techniques have been used, in one currently used radar al- carrier wavelengths in either C or X band are used, and the timeter, a continuous wave is generated whose frequency weather displays usually show weather formations within is modulated with a period much longer than the time re- about 100 km ahead of the aircraft. Warnings can be given quired for the ground-reflected signal to return to the air- to the pilot if stored levels regarded as the maximum al- craft. Comparison of generated frequency with returned

FIGURE 8 Avionics placement on multi-purpose transport (From Kayton, M., and Fried, W. R. (1997). “Avionics Navigation Systems,” 2nd ed., Wiley, New York.) P1: FHK Encyclopedia of Physical Science and Technology EN001H-913 May 8, 2001 14:54

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frequency for the known modulation schedule, then, is tail download (with positive static margin) so that the tail’s a measure of elapsed time, hence the distance above the drag, i.e., “trim drag,” will be less. The cumulative effect terrain. Antennae beam width, for this function, must be of these beneficial design changes, resulting from allow- wide enough to provide a return from a flat earth when the ing an avionics SAS to compensate for RSS, is to reduce aircraft pitches and rolls over the normal range. Radar al- the fuel required for the same range-payload combination timeters have the 4.2 to 4.4 GHz frequency band assigned and a higher net thrust-to-weight ratio. The latter is par- to them, allowing use of two small, microstrip antenna’s, ticularly important for fighter aircraft because it improves one to transmit, one to receive, producing beam widths of maneuverability. between 40 and 50◦. If the separation between this pair is If the unaugmented flying qualities of an aircraft are at least about 0.8 m, the transmitted/received signals’ mu- sufficiently poor to constitute a risk to flight safety, how- tual interference will be reduced enough that, even after ever, the reliability of the SAS must be extremely high, the loss of signal intensity experienced in ground reflec- e.g., approaching that of primary structure. Further, pro- tion, useable information will still remain in the received visions must be made to assure the kind of controllabil- signal. Radar altimeters are usually only used for tape-line ity that avoids hazardous aircraft attitudes and/or angular altitudes of less than 1500 m; current continuous wave ver- rates even in the unlikely event of “hard-over,” i.e., abrupt, sions require less than1Wofpowerandhaveaccuracies full control travel, system failures. In the case of the F-16, of about 0.5 m below 30 m and about 2% above 30 m. this resulted in a quadruply redundant SAS. Implications for the aircraft’s design went beyond the fundamental per- formance and maneuverability characteristics mentioned IV. AVIONICS APPLICATIONS before. As stated in (Droste and Walker (1990), “Since INFLUENCING AIRCRAFT the pilot would not be able to control the aircraft in the DESIGN; VMS pitch axis without the electrical system, there was no jus- tification to retain a mechanical pitch system. The pilots’ A. Flight Path Stability; AFCS command could now be electrically combined with the Means to provide equilibrium, stability, and control for stability system with no penalty. Removal of mechanical aircraft are obviously essential. Yet devices and arrange- connection between pilot and the control surfaces was the ments of aerodynamic surfaces to carry out these func- logical result.” That is, making the SAS highly reliable and tions are usually detrimental to such aircraft performance fail-safe allowed the use of an FBW flight control system as how far the aircraft can carry a given payload, its max- with no mechanical control system to back-up the elec- imum speed, etc . Tail surfaces, for example, add weight trical system. FBW control systems also facilitate means and aerodynamic drag, and having the aircraft CG forward to enhance the way an aircraft responds to a pilot’s com- of the wing’s center of lift as required for positive natural, mand. These aircraft avionics systems are referred to as i.e., unaugmented, stability in pitch, requires a download Control Augmentation Systems (CAS). on the tail for equilibrium. The present-day capabilities It should be clear that avionics systems capable of SAS of avionics, with actuators capable of high-frequency re- and CAS functions can also perform “autopilot” functions sponse to control inputs, allow designers to deliberately as mentioned in Section II, above. When all these functions take advantage of the often superior range-payload, high- are integrated into one system, it is commonly referred to speed, and high-maneuverability performance of config- as an Automatic Flight Control System (AFCS). urations whose unaugmented flying qualities are grossly unsatisfactory, by incorporating an avionics-based Stabil- B. Load Alleviation ity Augmentation System (SAS) to compensate for un- stable flight path characteristics. Figure 9 (from Loewy Another example of avionics systems usage is in maneu- (2000)) illustrates one of the advantages of Reduced Static ver load-limiting. The prototype of the F-16, the YF-16, Stability (RSS) in pitch that was exploited in the basic de- was designed for a limit normal load factor (n) of 9 times sign of the F-16 Falcon jet fighter. By integrating so-called gravity, or “9g”, throughout most of its flight envelope, RSS into the basic aircraft design, equilibrium of pitching but as low as 6.5g in some critical areas. To prevent pilots increments was achieved with the horizontal tail generat- from exceeding these limits, pilot commands were atten- ing lift rather than download, so that the lift that the wing uated by avionics-based controls as a function of Mach must produce to carry the weight of the aircraft is reduced. number (forward speed divided by the speed of sound), This means a smaller wing with less structural weight and altitude, and Angle Of Attack (AOA). This system also drag can be incorporated into the overall design. Further, limited AOA in an absolute sense, i.e., independent of for equal offsets of the wing’s lift from the aircraft CG, ei- Mach number and altitude. The associated automatic AOA ther fore or aft, the tail lift (with RSS) can be less than the (or n)—limiting schedule is shown in Fig. 10 (from Loewy P1: FHK Encyclopedia of Physical Science and Technology EN001H-913 May 8, 2001 14:54

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FIGURE 9 Relaxed static stability. (From Loewy, R. G. (2000). “Avionics: A ‘New’ senior partner in aeronautics.” AIAA J. 37(11), 1337–1354.)

(2000)). The production version of the F-16 was designed mance, assuming that proper account is taken of the struc- with a 9g limit normal load factor throughout the oper- tural, i.e., weight consequences, attendant on the bending ational envelope, eliminating the need for this particu- and shear loading associated with such a spanwise distri- lar avionics system, but roll rate (angular velocity about bution of lift. The second physical law is often expressed the aircraft’s longitudinal axis) limiting was retained with in so-called “Goodman Diagram” form: (McClintock and variable limits as a function of AOA as a means of en- Argon (1966), for example), which shows that the lower suring good handling qualities at the extreme maneuver the steady stresses in a material, the higher are the allow- attitudes at which strong dynamic coupling between an- able alternating stresses for which the material will have gular motion about two inertial axes exists. indefinite life; the so-called endurance limit. Because a A second example of a load alleviation avionics system major source of alternating stresses on airplane wings is is provided by the arrangement used to extend the wing “gusts” (i.e., atmospheric turbulence) in cruise flight, an structure’s fatigue life as an interim measure during the automatic system was installed on the C-5A during its development of the Lockheed C-5A military transport air- development phase that sensed the onset of turbulence plane. The operational concept on which this automatic (using, as sensors, accelerometers or wing bending strain system was based followed from two physical laws, one gauges) and called for both ailerons, i.e., those on port aerodynamic, the other in mechanics of materials. First, and starboard wings, to retrim slightly upward when gust a wing will have minimum drag induced by lift (induced loads exceeded some level. This reduced the lift on the drag) if the spanwise lift distribution approaches an ellipti- outboard wing sections. To preserve total lift, of course, cal distribution. This will maximize range-payload perfor- the aircraft pitch attitude would be increased, but the total P1: FHK Encyclopedia of Physical Science and Technology EN001H-913 May 8, 2001 14:54

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FIGURE 10 Original YF-16 AOAG Limiter Concept. (From Loewy, R. G. (2000). “Avionics: A ‘New’ senior partner in aeronautics.” AIAA J. 37(11), 1337–1354.)

effect would be a spanwise lift distribution deviating from hence loads caused by turbulence, to levels of acceptable the approximately elliptical by having less load outboard, alternating stresses. If it failed with the ailerons in the more inboard. This load distribution reduces steady wing up position, the pilot could take some range-preserving root bending moments and associated steady stresses be- actions which might, for example, adversely affect flight cause of bending, relative to that produced by elliptical time, but preserve flight safety. In either case, however, distributions. appropriate pilot action would depend on having displays With this avionics system operative, the aircraft would that reveal the existence and nature of the failure in this have optimum cruise efficiency in smooth air, i.e., turbu- system. Redundancy in this kind of automatic control sys- lence below some predetermined level, and lower aero- tem and a requirement for full or partial authority opera- dynamic efficiency when cruising in turbulent air. In tur- tion after a single failure, however, would not be necessary bulence, however, its wing root structural material would characteristics. enjoy a more favorable position on the Goodman Diagram, Load limiting as described in the F-16 example clearly so as to improve the wing structure’s fatigue life. If such a requires VMS response as quick or quicker than a pilot system were found to be advantageous for an operational can command. Thus, as a consequence of the level of re- aircraft in the part of preliminary design concerned with liability needed, all possible failures in systems compo- wing structural weight, its designers could rely on lower nents must be accounted for in design stages and adverse combinations of steady and alternating stresses than would consequences minimized. This requires that multiple sen- have existed if the more nearly elliptic spanwise lift distri- sors and processors be provided for redundancy. It is not bution had been carried under all atmospheric conditions. unusual for large commercial jet transports to have five Note that no quick-acting automatic actuation would be full authority digital processors to control pitch, roll, and required for this spanwise lift distribution modification in yaw; and to have each such computer divided into two rough air. However, because flight path control effectors physically separated channels. The first one, the control (ailerons) are involved, only limited authority would be channel, is permanently monitored by the second one, the given the actuators. Thus, if the system failed so as not to monitor channel. In the case of disagreement between con- operate, the pilot could compensate by reducing airspeed, trol and monitor, the computer affected by the failure is P1: FHK Encyclopedia of Physical Science and Technology EN001H-913 May 8, 2001 14:54

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iting and gust alleviation for comfort purposes using many of the same system components. Figure 12 (from Loewy (2000)) is a control diagram for processors in a system to provide the last of these three functions. In that fig- ure the words “Fuselage Acceleration” indicate the per- tinent sensor, and the words “Control Surface” indicate the aerodynamic effector (ailerons or elevators, or both). As an indication of the kind of improvement possible us- ing such systems, Fig. 13 (from Loewy (2000)) shows the magnitude of Gust Load Alleviation (GLA) achieved on tests. Here wing bending moment is a direct indicator of FIGURE 11 Gust frequency spectrum. (From Loewy, R. G. dynamic lift variations caused by continuous turbulence, (2000). “Avionics: A ‘New’ senior partner in aeronautics.” AIAA J. which will result in passenger/crew vertical accelerations 37(11), 1337–1354.) as measured by wing accelerometers and bending strain gauges and using the wing’s ailerons as corrective control effectors. turned off automatically, while the computer with the next highest priority takes control. In addition, to prevent com- mon mode failures, designers of such systems will often D. Suppressing Servo-Aeroelastic Instabilities accept the cost penalties associated with dissimilarity to Structural problems of a dynamic and/or aeroelastic nature provide two types of computers. are usually thought of as falling into either self-excited or forced vibratory classes. In aircraft, forced structural dy- C. Crew/Passenger Comfort Improvement namic response of airframe components has many sources of excitation. Some of these are (1) gusts, i.e., atmospheric In addition to the emphasis on safety associated with the turbulence, as mentioned in Sections IV.B and C; (2) air- responsibility of carrying passengers, competition among craft wake induced turbulence (examples include tail buf- airlines to win the business of these passengers motivates fet as caused by both boundary-layer separation and by commercial transport airplane designers to make flight trailing vortices from rotor/propellers where such exist; as comfortable as possible for their customers despite (3) engine and rotor/propeller vibratory hub forces and atmospheric turbulence. As seen in Fig. 11 (from Loewy moments; (4) rotor/propeller blade tip passage in close (2000)) there are significant frequency components in at- proximity to a fuselage; (5) transmission of gear box vi- mospheric turbulence which place systems designed to brations at tooth contact frequencies; and (6) rapid fire ameliorate those effects above 2 Hz; and this frequency is weapon recoil and/or muzzle pressures in military aircraft. beyond a human pilot’s control input capabilities. The phenomenon known as “flutter” of wings and tail It is possible to take advantage of avionics systems’ surfaces, the latter usually coupled with aft fuselage mo- high frequency capabilities, to carry out AFCS, load lim- tion, and both sometimes coupled with control surface

FIGURE 12 Turbulence damping: Principle of one lane (from Loewy, R. G. (2000). “Avionics: A ‘New’ senior partner in aeronautics.” AIAA J. 37(11), 1337–1354.) P1: FHK Encyclopedia of Physical Science and Technology EN001H-913 May 8, 2001 14:54

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in and improving coupling between the structural modes active in the aeroelastic instability.

V. IMPACT OF “SMART MATERIALS”

Smart materials are thought of as those which produce electric voltages when strained (the “direct” piezoelec- tric effect, for example), and/or become strained when subjected to electric or magnetic fields or temperature changes. Examples of the latter behavior include piezo- electric materials (the “converse” piezoelectric effect), FIGURE 13 Power spectral densities of bending moment due to magnetostrictive materials, and “shape memory” alloys continuous turbulence with GLA System On & Off. (From Loewy, (which change states, and thereby dimensions or shapes, R. G. (2000). “Avionics: A ‘New’ senior partner in aeronautics.” AIAA J. 37(11), 1337–1354.) depending on temperature), respectively. The strain sens- ing characteristic gives piezoelectrics potential for use as sensors, the strain-inducing behavior of the last three, po- tential as actuators. Among the unique properties of such deflections, is in the self-excited, i.e., aeroelastic stability materials for use in avionics systems are included the pos- class. So are the whirl-flutter and coupled rotor-wing phe- sibility of distributing them throughout a structure, rather nomena which can be thought of as including “mechanical than concentrated at specific points as are such sensors as instabilities,” such as helicopter so-called “ground reso- accelerometers or strain gages, or as actuators are, which nance” (a misnomer), as a subcase. Pilot-Induced or Pilot- drive the rotation of a control surface, for example. In Assisted Oscillations (PIO or PAO) can also be a special some applications, very high frequency response is avail- category of these phenomena. able, as well. Where distributed sensing has advantages, The design of systems to suppress aeroelastic or smart materials are considered for embedding as “just an- aeromechanical instabilities must consider such systems other fiber” in advanced filamentary composite materials, as SAS, active, if such exist, because of their possible and embedding may be considered for distributed actua- effect on the unaugmented aircraft’s structural dynamic tion too, but usually at a surface of the structure. and/or aeroelastic behavior. When a stable aeroelastic Using smart materials and structures techniques also mode is destabilized by a flight path control system such as holds promise for more spatially continuous variations of SAS, this is often called “spillover.” Aeroelastic stability shapes and other properties, with the elimination of dis- (and flight path stability, for that matter) must, therefore, continuities in slope angles at the surface—often impor- be assured with all systems functioning in all possible tant from aerodynamic considerations. modes of operation, including partial failures. Active mod- Piezoelectric materials are particularly promising for ification of structural and/or aeroelastic phenomena by avionics functions requiring high frequency sensing means of avionics systems may, in any event, be thought and/or actuation. For example, techniques are being devel- of as acting by virtue of either reducing the (usually aero- oped which could be integrated into turbine engine con- dynamic) forcing functions, generating directly opposing trols, to allow turbo-machinery performance increases and forces, or by introducing stiffness changes and/or addi- reductions of chemical and/or particulate elements in their tional damping into the motions crucial to the instability. exhaust harmful to the environment. Turbine engine per- The U.S. Air Force investigated the use of avionics to formance generally improves the closer their operations reduce airframe structural design criteria to ensure aeroe- are taken to compressor stall. Yet stall in service opera- lastic, i.e., flutter, stability more than 20 years ago. In tion is unacceptable. Feedback control has been shown that research, a modified B-52 jet bomber aircraft was to be capable of extending the effective stable flow range flown 18 km/h faster than its flutter speed. The Flutter of axial compressors and rejecting persistent disturbances Mode Control (FMC) system employed in that program which, otherwise, would cause the system to incur rotating had vertical accelerometers in pairs at four locations on stall. the wing, which produced signals which, processed by As regards achieving more efficient and “cleaner” com- shaping filters, drove outboard ailerons in one indepen- bustion, a key consideration is in avoiding combustion dent loop, sensors to surfaces, and outboard flaperons, in instabilities. Such instabilities can involve large ampli- a second. The system was predicted to increase flutter tude acoustic oscillations sufficient to cause mechanical placard speed by more than 30% by increasing damping or thermal damage, and passive approaches to avoiding P1: FHK Encyclopedia of Physical Science and Technology EN001H-913 May 8, 2001 14:54

336 Aircraft Avionics

them have generally not been satisfactory. On the other finding the enemy and/or neutralizing the enemy may be hand, tests using active control systems have been shown the fundamental reason the mission is undertaken in the to be promising. A pressure sensor at an upstream loca- first place. These broad functional categories can be listed tion in the combustor where all axial acoustic modes are as follows: expected to be significant, can provide a signal processed so as to modulate the flow of a secondary gaseous fuel 1. Changing behavior of uncommanded airframes stream into the combustor, with gain and phase changing a. Flight path stability augmentations (SAS) with stability characteristics in real time. The secondary b. Aeroelastic instability suppression (FMC) fuel injector actuator requires a modulation rate variable c. Load reduction from 0 to 1500 Hz and the processor must rely on an “ob- 2. Changing behavior of uncommanded engines server” to “identify the amplitudes, frequencies and phases a. Compressor stall avoidance of several combustor modes in real time” (Loewy, 2000). b. Emission amelioration At this writing, it appears that a fuel injector suitable for c. Noise reduction such an automatic combustion instability controller, using d. Improving combustion efficiency smart materials, could be integrated within existing engine 3. Acting as pilot’s associate fuel-feed systems. Both the above applications of avion- a. Threat avoidance maneuvers ics components and techniques, and presumably others, to b. Target tracking/weapon pointing the design and operation of “intelligent turbine engines” c. Formation flying/station keeping seem highly likely, at some point in the future. d. Automated landings Although no applications of “smart materials” in avion- 4. Providing mission enabling pilot information ics systems of any kind have appeared in aircraft presently a. Communication in service use, they continue to have considerable promise: b. Navigation for example, to reduce structural vibration resulting from c. Collision/terrain avoidance tail buffet; to increase the aircraft speed at which panels d. Target/threat location exposed to the airstream will flutter; to change the twist— and thereby improve the performance of rotor blades; and SEE ALSO THE FOLLOWING ARTICLES to produce lifting surfaces (wings and tails) particularly those constructed with “tailored”filamentary composite AIRCRAFT INSTRUMENTS • AIRCRAFT PERFORMANCE materials, which will have superior aeroelastic stability AND DESIGN • AIRCRAFT SPEED AND ALTITUDE • AIR- characteristics. PLANES,LIGHT • FLIGHT (AERODYNAMICS)

VI. SUMMARY BIBLIOGRAPHY It is useful, particularly in view of the integration of avion- ics components into more than one functional system, to Droste, C. S., and Walker, J. E., (1990). “A Case Study on the F-16 think of these systems as being of the kind that (1) change Fly-by-Wire Flight Control System,” AIAA, Inc., Reston, VA. the behavior of the uncommanded airframe, (2) change the Kayton, M., and Fried, W. R. (1997). “Avionics Navigation Systems,” behavior of the uncommanded engines, (3) modify the pi- 2nd ed., Wiley, New York. Loewy, R. G. (2000). “Avionics: A “New” senior partner in aeronautics,” lot’s command signals, (4) provide mission-related com- AIAA J. 37(11), 1337–1354. mand signals; and (5) provide mission-enabling informa- McClintock, F. A., and Argon, A. S., (1966). “Mechanical Behavior of tion to the pilot. The last of these is a function that allows Materials,” Addison-Wesley, Reading, MA. the pilot to fly where he/she wants to go and to use the “Reference Data for Engineers: Radio, Electronics, Computer and Com- routes he/she chooses to get there—in the case of gen- munications” (1985). 7th ed., Sams, Howard W. & Co., Indianapolis, IN. eral aviation, commercial and military transport aircraft. “Sagnac Effect,” Review of Modern Physics (April 1967). Vol. 39, No. 2. In the case of combat aircraft, equipment providing this Skolnik, M. I. (1962). “Introduction to Radar Systems,” McGraw Hill, function can be considered part of the “payload,” because New York. P1: GHA/FPW Revised Pages P2: FPP Qu: 00, 00, 00, 00 Encyclopedia of Physical Science and Technology EN001-906 May 25, 2001 21:9

Aircraft Aerodynamic Boundary Layers

Jean Cousteix ONERA and SUPAERO

I. Introduction II. Body in Motion in a Fluid III. Stresses and Heat Fluxes in a Fluid IV. Laminar and Turbulent Flows V. High Reynolds Number Flows VI. An Example of Boundary Layers: Falkner-Skan Solutions VII. Laminar-Turbulent Transition VIII. Turbulent Boundary Layers IX. Drag Reduction X. Concluding Remarks

GLOSSARY Navier-Stokes equations Equations governing fluid flow. Reynolds number Dimensionless number which gives Boundary layer Thin layer of viscous, possibly turbu- the magnitude of the ratio of inertial forces to viscous lent, flow near a wall where the velocity exhibits very forces in a flow. fast variations normal to the wall. Boundary layers de- Skin friction or wall shear stress Stress at the wall due to velop at high Reynolds numbers. viscosity. The corresponding force applied to the body Diffusion of momentum (or heat) Transport of momen- is parallel to the wall. tum (or heat) by viscosity (or thermal conductivity). Stress tensor Second-order tensor defined at any point Dissipation Transformation of kinetic energy into heat in a flow and determining a force applied to a surface due to the deformation work of viscous stresses. element bounding a volume of fluid. The dimension of Drag Component of aerodynamic forces aligned with the stress tensor components is a force per unit surface. relative velocity between the body and the free stream. Viscosity Property of a fluid by which momentum dif- Inviscid flow Approximation in which viscous effects are fuses in a flow. Viscosity smooths inhomogeneities of negligible. momentum.

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PHYSICAL and theoretical aspects of boundary layer flow are presented, stressing important effects such as fric- tion drag and separation. Laminar-turbulent transition and turbulence effects are also described. These phenomena have a strong influence on the development of bound- ary layers but their understanding and modeling are still largely open questions. Finally, drag-reduction techniques by means of riblets and laminarization are presented.

FIGURE 1 Fluid entrainment by a flat plate moving parallel to itself. I. INTRODUCTION

The aerodynamic flow around the wing of a civil air- etc. A fluid particle is entrained at the local velocity of the craft in cruise conditions is characterized by a very large flow. Reynolds number on the order of several tens of millions. In an inviscid flow, excluding the possibility of modi- The Reynolds number can be interpreted as the order of fications of the molecules’ structure at high temperature magnitude of the ratio of inertial forces to viscous forces. due to chemical reactions, for example, the spatial or tem- At high Reynolds numbers, viscous effects are negligible. poral variations of the thermodynamic properties of the This assumption is valid almost everywhere in the flow ex- fluid are associated with velocity variations or with inho- cept close to the walls where viscosity is effective. Viscous mogeneities of the initial or boundary conditions. effects are also important in wakes and jets. In a real flow, other phenomena modify the flow prop- With appropriate hypotheses, the Navier-Stokes equa- erties. Fluids, like solids, are heat conductors. Thermal tions are drastically simplified and the boundary layer the- conductivity is a property of the fluid that tends to even ory makes flow analysis much easier. Viscosity is respon- out the temperature differences in the fluid. If a volume of sible for friction drag or separation, which are among the hot fluid is in contact with a volume of colder fluid, ther- most important characteristics of a wing. These remarks mal conductivity creates a heat flux which transfers heat explain the key role played by boundary layers in aerody- from the hot fluid to the cold fluid. Fluids have another namics. property—viscosity—which tends to smooth the momen- As a general rule, the boundary layer flow is not laminar tum differences in the fluid, which implies a smoothing all along its development on a wing. Laminar-turbulent of velocity differences. For example, a body with a flat transition and turbulence take place more or less early ac- surface moving parallel to its surface entrains the fluid in cording to the conditions of boundary layer development. its neighborhood (Fig. 1). Momentum diffuses in the fluid. These phenomena have a strong influence on the behavior Momentum diffusion is similar to the heat diffusion which of boundary layers. At the present time, the understand- would take place if fluid at rest were in contact with a hot- ing of these phenomena is not complete and no definitive ter (or colder) plate. As shown in Fig. 1, the fluid velocity model exists. is equal to the velocity of the body along the fluid-body in- Basic concepts of aerodynamics and fluid mechanics terface. In standard aerodynamics, the temperature of the are reviewed in the first sections of this paper. The rest of fluid and of the solid are also identical along the fluid-solid the presentation is devoted to a description of the physical interface. and theoretical aspects of the following topics: boundary layer concept, laminar-turbulent transition, turbulence ef- A. Forces in the Fluid fects, and drag reduction techniques. Let us consider a fluid volume V surrounded by fluid and limited by a surface (Fig. 2). Let dσ be an element of II. BODY IN MOTION IN A FLUID this surface. First, let us assume that the flow is inviscid. Along dσ the volume V is submitted to a force normal In standard aerodynamics, air is a fluid considered as a to dσ which is called the pressure force. The pressure continuum. The concept of fluid particle is defined as force points towards the inside of volume V . In a viscous a volume of fluid large enough to contain a great num- flow, the pressure force is also present but another force is ber of gas molecules and small enough to be character- exerted on volume V . This additional force due to viscosity ized by averaged quantities which are uniform over the is not generally normal to dσ . In a viscous flow, the fluid fluid particle. A fluid flow is characterized by thermody- in V can also exchange heat with the outer fluid through namic properties such as pressure, temperature, density, dσ . P1: GHA/FPW Revised Pages P2: FPP Encyclopedia of Physical Science and Technology EN001-906 May 7, 2001 12:39

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FIGURE 2 Local forces on the surface of a volume of fluid. The FIGURE 4 Aerodynamic forces on an airfoil. vector n is a unit vector normal to dσ and pointing outwards fromV.

III. STRESSES AND HEAT FLUXES B. Forces on the Body IN A FLUID Now, let us consider the surface of a solid in contact with a fluid (Fig. 3). In an inviscid flow, along a surface element A. Modeling of Stresses and Heat Fluxes σ d the fluid exerts a pressure force on the solid; this pres- Frequently, the flow is described by the Euler variables, σ sure force is normal to d . In a viscous flow, an additional i.e., by the velocity field at any point in space and at any σ force due to viscosity is tangential to d ; heat transfer can time. The description is completed by the density, pres- σ also occur between the fluid and the solid through d . sure, and temperature fields. In aerodynamics, it is often convenient to consider that The velocity gradient is a second-order tensor whose ∂ the fluid is moving around the body at rest. Indeed, it components in an orthonormal axis system are ui . The ∂x j is shown that if the motion is stationary (independent of velocity gradient is broken down into a symmetric ten- time), the flow around the body moving through the fluid is sor sij (sij = s ji) and a skew-symmetric tensor rij (rij = equivalent to the flow around the body at rest immersed in −r ji): a moving fluid. Only the relative motion of the body with ∂ respect to the fluid is significant. In particular, in a wind ui = sij + rij tunnel, the body is at rest and the fluid moves around it. ∂x j An airfoil is a two-dimensional body designed to pro- with duce a lift. The relative velocity of the fluid with respect ∂ ∂ ∂ ∂ to the airfoil measured far ahead of the airfoil is the free- = 1 ui + u j = 1 ui − u j sij ∂ ∂ and rij ∂ ∂ stream velocity V∞ (Fig. 4). The chord c of the airfoil 2 x j xi 2 x j xi is the distance between the leading edge and the trail- The rate of strain tensor sij defines the deformation of ing edge. The chord line connecting the leading edge and a small volume of fluid, whereas tensor r defines the α ij the trailing edge forms an angle —the angle of attack rotation of this volume. Indices i and j can take the values or the incidence—with the free-stream velocity. The total 1, 2, or 3; x1, x2, x3 are x, y, z, respectively; and the force exerted on the airfoil is obtained by integrating the corresponding velocity components are u, v, w. pressure forces and the viscous forces over the body’s sur- Let V be a control volume of fluid (Fig. 2). The force face. The aerodynamic forces are resolved into the lift L exerted on the control volume over its surface element dσ and the drag D acting perpendicular and parallel to V∞, is respectively.  =  +  df df pressure df viscosity where the pressure force and the viscous force are given by:  =− δ σ  df pressure p ijn j d ei (1)  = τ σ  df viscosity ijn j d ei (2) The Einstein notation is used in the above formula. The repetition of an index in a term implies a summa- τ τ FIGURE 3 Forces applied to a surface element of a body in rel- tion. For example, ijn j is equivalent to j=1,3 ijn j (i.e., ative motion in a fluid. τi1n1 + τi2n2 + τi3n3). P1: GHA/FPW Revised Pages P2: FPP Encyclopedia of Physical Science and Technology EN001-906 May 7, 2001 12:39

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The quantities p and τij are called stresses. They have For air, the Prandtl number is considered as a constant the dimension of a force per unit area. The stresses p and P = 0.725 for temperatures below 1500 K, and the spe- τ  = ij are defined at any point in space, whereas df pressure cific heat at constant pressure cp is also a constant, cp  −1 −1 and df viscosity depend on the surface element via the unit 1005 J kg K . normal n. Viscosity and thermal conductivity are thermodynamic In relations 1 and 2, p is the pressure, τij is the viscous properties of the fluid. Even when the fluid is at rest, stress tensor, δij is the second-order unit tensor (δij = 1 these properties are defined. The behavior of the flow if i = j, δij = 0 otherwise), n j are the components of the is influenced by the effects of viscosity and thermal unit vector orthogonal to dσ and pointing outwards from conductivity—nonzero viscous stresses and heat fluxes— volume V , and ei are the unit vectors of the reference which exist only when there is a nonzero rate of strain and orthonormal axis system. Formulas (1) and (2) express that temperature gradient. the pressure force is normal to dσ, whereas the viscous τ force can have a tangential component. It is shown that ij B. Navier-Stokes Equations is a symmetric tensor (i.e., τij = τ ji). The amount of heat received by the control volume V The motion of the flow is governed by the Navier-Stokes through dσ per unit time is equations. These equations comprise =−φ σ r dQ j n j d The continuity equation which expresses the φ conservation of mass. where j are the components of the heat flux vector. r As a good approximation, air is considered as a The momentum equation which expresses Newton’s  = γ Newtonian fluid, i.e., the viscous stress tensor is expressed second law, F m : the acceleration of a fluid particle is due to external forces applied to it. by a linear function of the rate of strain tensor: r The energy equation which expresses the first ∂u τ = µ + κ l δ principle of thermodynamics: the variation of the total ij 2 sij ∂ ij xl energy (internal energy plus kinetic energy) of a fluid where µ and κ are viscosity coefficients. This relationship particle is due to the heat exchanged with the assumes that rij does not create any viscous stress. surrounding medium and the work done by the For most practical purposes in standard aerodynamics, external forces. Stokes’ hypothesis, 2µ + 3κ = 0, is valid. Then, the vis- cous stress tensor is given as: These equations are completed by a state equation. For a ∂ perfect gas, the state equation is τ = µ − 2µ ul δ ij 2 sij ij p R 3 ∂xl = ρ M T Stokes’ hypothesis implies that an isotropic compression R R = or dilatation does not create any viscous stress. where is the universal constant of perfect gases, . −1 −1 M The dynamic viscosity coefficient µ can be obtained 8 3145 J mol K ; and is the molar mass of the gas. = R = . −1 −1 from the kinetic theory of gases or experimentally. For air, Forair,wehaveR M 287 1Jkg K . a good representation of µ is obtained from Sutherland’s The Navier-Stokes equations are formula: ∂ρ Continuity equation + div(ρu) = 0 (3) + / ∂t µ = µ T 1 S T0 0 Momentum equation T0 1 + S/T µ = . −5 = ∂u Where 0 1 711 10 Pl (the unit is 1 Poiseuille ρ + (grad u) · ρu = div[−pδ + τ] (4) −1 −1 ∂ 1kgm s ), T0 = 273 K, S = 110.4 K. Sometimes, the t ¯ ¯ ν ν = µ kinematic viscosity coefficient is used, ρ . Energy equation The Fourier law is used to express the heat flux vector: ∂hi ∂p ∂T ρ + ρu · gradhi = + div(τ · u − φ) (5) φ j =−λ ∂t ∂t ¯ ∂x j where u is the velocity vector, τ is the viscous stress tensor, λ where the thermal conductivity is related to the viscosity δ is the second order unit tensor¯ φ is the heat flux vector, div through the Prandtl number P: is¯ the divergence operator, grad is the gradient operator, µc · P = p and denotes the dot product. In the above equations, hi λ is the stagnation enthalpy: P1: GHA/FPW Revised Pages P2: FPP Encyclopedia of Physical Science and Technology EN001-906 May 7, 2001 12:39

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|u|2 layers merge or in a jet which is formed downstream of an h = h + i 2 engine. where h is the static enthalpy. For an ideal gas (the specific heats at constant pressure cp and at constant volume cv are constants), the static enthalpy is related to the temperature IV. LAMINAR AND TURBULENT FLOWS by h = cp T . ρ ∂u A. Properties of Turbulence A typical term representing the inertial forces is u ∂x Let L be a length scale of the flow: this means that u Most often, on an aircraft, the boundary layers, wakes, and has a significant variation of order V0 over a length L. jets are not laminar but turbulent. No precise definition of It is assumed that the order of u is V0 and that the order ∂ ρ V 2 a turbulent flow exists, but some important characteristic ρ ρ ρ u 0 0 of is 0. Then the order of u ∂x is L . A typical term properties are ∂ µ ∂u representing the viscous forces is ∂x ( ∂x ). The order µ0 V0 of magnitude of this term is 2 . Then the order of the ratio r L The characteristic Reynolds number of turbulent flows of the inertial forces to the viscous forces is the Reynolds is large compared to unity. number: r Turbulence is a very efficient mixer. Momentum ρ = 0V0 L transfer by viscosity or heat transfer by conductivity RL µ 0 are slow processes, whereas turbulent motions are On a transport aircraft, the Reynolds number is very much more efficient in exchanging momentum and large compared to unity. The Reynolds number based on heat between parts of the flow that contain different the free-stream conditions and on the average chord length amounts of momentum and heat. On the average, a is several tens of millions. Indeed, the very large Reynolds turbulent flow is more uniform than a laminar flow. r number is a very important characteristic of aerodynamic The velocity field is three dimensional and rotational. flows. From the above interpretation, this would mean that Statistically, the flow can be two dimensional or even the viscous forces are negligible compared with the iner- one dimensional, but the velocity fluctuations are tial forces. This means it would not be necessary to take the three dimensional. This property has an important viscous forces into account and the inviscid flow approx- consequence on the rotational characteristic of the imation could be applied. This hypothesis is valid almost flow because the dynamics of vorticity are very everywhere except in the vicinity of the walls where the different if the velocity field is two or three velocity vanishes and where the local Reynolds number dimensional. In a two-dimensional incompressible can be small. Near walls, the velocity exhibits very fast flow, vorticity develops under the influence of variations normal to the surface. The strongly sheared flow convection and diffusion due to viscosity. In a generates viscous forces which are of the same order as three-dimensional flow, vorticity can be created or the inertial forces. The near wall flow structure is called destroyed by the action of the rate of strain tensor sij. the boundary layer (Fig. 5). Viscous forces also play an In particular, stretching of the vorticity line increases important role in wakes which develop downstream of a vorticity; this process plays an important role in wing when the upper surface and lower surface boundary turbulence. r Turbulence is a dissipative phenomenon. The deformation work done by the viscous stresses transforms kinetic energy into heat. This process also exists in laminar flows but is more efficient in turbulent flows. r Turbulence is described by Navier-Stokes equations. A turbulent field comprises a large range of length scales. For example, if turbulence is created in a cubic room, the largest scales of turbulence can be the dimension of the room. If the characteristic Reynolds number of these large-scale motions is large compared to unity, these structures behave as if the flow were inviscid. Due to the stretching process, smaller scale FIGURE 5 Typical velocity variations in a boundary layer. The turbulent motions exist and energy is transferred to shear flow generates viscous forces parallel to the wall and an them. This process is repeated until the characteristic associated diffusion of momentum normal to the wall. Reynolds number of these motions is near unity. The P1: GHA/FPW Revised Pages P2: FPP Encyclopedia of Physical Science and Technology EN001-906 May 7, 2001 12:39

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B. Averaged Navier-Stokes Equations The fluctuations of the flow characteristics are described by the Navier-Stokes equations, but their range of length and time scales is very large. The storage space and CPU time required to resolve this spectrum of fluctu- ations in practical situations are not available and will not be available in the foreseeable future. For research purposes, in simple flow configurations, direct numerical simulations consisting of solving the three-dimensional, unsteady Navier-Stokes equations are a very valuable tool. Other techniques consist of calculating the largest struc- FIGURE 6 Time variation of the velocity in a point of a turbulent boundary layer. The signal looks random. tures in the flow and modeling their interaction with the smaller structures. Large eddy simulations are a field of intense research. For practical applications, the averaged Navier-Stokes viscosity is efficient in transforming all the kinetic equations are used. The flow characteristics are broken energy into heat and no smaller motions exist. These down into an average component and a fluctuating com- dissipative scales are called the Kolmogorov scales. ponent. In an incompressible flow, the average is defined For realistic cases, these scales are very different from as a statistical or ensemble average. For example, the av- the molecular scales and the turbulent field can be erage longitudinal component of velocity is considered as a continuum. r Turbulence is a nonlinear phenomenon due to the N = 1 nonlinearity of the Navier-Stokes equations. This u lim ui N→∞ N property makes the problem very difficult. i=1 r Turbulent flows are not predictible. Even if it were where ui are samples taken in different repetitions of the possible to solve the Navier-Stokes equations same flow (the same experiment is repeated many times). perfectly (using numerical methods), the least error Theoretically, the number of samples is infinite. In an ex- would contaminate the flow after a finite time. In a periment, this number is large but not infinite. In the same given point of space, it is impossible to know the way, the pressure is broken down into average and fluctu- variation of the velocity after this time. ating components. In a compressible flow, the best way to r Turbulence has a random character. At first sight, the define an average is not a trivial matter. Very often, mass- variation of the velocity as a function of time in a weighted or Favre averaging is used. The average velocity given point of space looks random (Fig. 6); however, u˜ is turbulence consists of coherent structures (Fig. 7). The ρ = u correlation of the velocities in two points of space is u˜ ρ nonzero when the separation distance is not too large. • The coherent structures have finite dimensions in where denotes a statistical average. Statistical averages space and time. are used for the density and pressure. The advantage of this breakdown is that the continuity equation has the standard form and it is possible to work on closed systems as is done usually. To obtain the equations for the average flow, the Navier- Stokes equations are averaged, taking into account the breakdown of the flow. For the sake of simplicity, it is sufficient here to give the equations for incompressible flows: div(u) = 0 (6) ∂u ρ + (grad u) · ρu = div[−pδ + τ + R] (7) ∂t ¯ ¯ ¯ In these equations, all the quantities are averaged quan- FIGURE 7 Visualization showing coherent structures in a turbu- tities but the sign • has been omitted when there is no lent boundary layer flow. [Courtesy of M. Stanislas.] confusion. P1: GHA/FPW Revised Pages P2: FPP Encyclopedia of Physical Science and Technology EN001-906 May 7, 2001 12:39

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The above equations—the Reynolds equations or aver- aged Navier-Stokes equations—show that turbulence af- fects the average flow only through the tensor R which is the Reynolds stress tensor. In an orthonormal axis¯ system, the components of this tensor are =−ρ Rij ui u j FIGURE 8 Boundary layer coordinate system. The Reynolds stress tensor components come from nonzero velocity correlations. This tensor is symmetric ber for the boundary layer is based on an appropriate length = since ui u j u j ui . The Reynolds stresses are grouped scale—its thickness—which is very small compared with with the viscous stresses and appear as apparent turbu- a characteristic length of the body. The boundary layer lent stresses. In fact, these terms occur when the nonlinear hypothesis also requires the boundary layer thickness to convection term of the momentum equation is averaged: be small compared to the wall curvature radius. According to the boundary layer hypothesis, the main ui u j = ui u j + u u i j viscous forces are parallel to the wall and diffusion oc-

The term ui u j has been put in the right-hand side of the curs essentially in a direction normal to the wall (Fig. 5). averaged momentum equation to express the equivalence Another important consequence of the boundary layer hy- between momentum and force. pothesis is that the static pressure variations across the The turbulent kinetic energy per unit mass is boundary layer are negligible. 2 2 2 The boundary layer theory can also be applied to a tur- u u u + v + w k = i i = bulent flow. Below, the boundary layer equations are writ- 2 2 ten for a turbulent flow but, for the sake of simplicity, they The Reynolds stresses represent the influence of tur- are given for a two-dimensional steady flow (the mean flow bulence on the average flow. There is no obvious way of is two dimensional and steady). The x-coordinate follows

relating ui u j to the mean flow properties, and Eqs. (6) the contour of the body and the y-coordinate is normal to and (7) are not closed. The Reynolds stresses are addi- it (Fig. 8). The compressible flow equations are tional unknowns which must be modeled in order to solve ∂ρu ∂ρv the Reynolds equations. The turbulence modeling prob- Continuity equation + = 0 (8) ∂x ∂y lem is a major difficulty which has not yet been solved to describe all turbulent flows with a unique model. For x-Momentum equation certain classes of flows, turbulence models are able to give reasonable results. ∂u ∂u ∂p ∂ ∂u ρu + ρv =− + µ − ρ u v (9) ∂x ∂y ∂x ∂y ∂y V. HIGH REYNOLDS NUMBER FLOWS ∂ = p y-Momentum equation 0 ∂ (10) A. Boundary Layer Hypotheses y Viscous forces are negligible compared with inertial forces Energy equation when the Reynolds number is large. For the flow around ∂h ∂h ∂ ∂u an airfoil, this conclusion is nearly correct except that it ρ i + ρv i = µ − ρ v

u ∂ ∂ ∂ u ∂ u leads to important contradictions with physics. If viscous x y y y effects were negligible everywhere in the flow, an airfoil at ∂T low speed would have no drag. Common experience tells + λ − ρ v

∂ h (11) us that this result is wrong. A second drawback would be y that the continuity of velocity or temperature along the These equations are completed by the state equation: interface between a solid and a fluid would be violated. R p = Prandtl introduced the idea that, in a laminar flow, vis- ρ M T cosity should affect the flow even if the Reynolds number µ∂u is very large. The viscous effects are confined in a thin Inthe x-momentumEquation(9),theviscousstress ∂y layer near the wall—the boundary layer—where the vis- is associated with an apparent turbulent stress −ρ u v . cous forces are of the same order as the inertial forces. Equation (9) expresses that the acceleration represented This hypothesis is not at variance with the meaning of the by the left-hand side is due to the pressure forces and Reynolds number. Simply, the significant Reynolds num- to viscous and turbulent stresses (Fig. 9). In the energy P1: GHA/FPW Revised Pages P2: FPP Encyclopedia of Physical Science and Technology EN001-906 May 7, 2001 12:39

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flow. In this way, the boundary conditions for the inviscid flow in the region y>δ are the same in both flows; this ensures that the flows are identical. In the region y<δan equivalent (fictitious) inviscid flow is defined as a contin- uation of the inviscid flow, and the characteristics of this fictitious flow are invariant along a normal to the wall. In order to have the same mass flow in the real flow and in the fictitious flow, the latter is limited to a region δ1 < y <δ. The equality of mass flow gives: δ δ δ FIGURE 9 Streamwise forces in a boundary layer. The stress τ is ρudy= ρeue dy = ρeue dy − ρeueδ1 ∂u µ 0 δ1 0 the sum of a viscous stress ∂y and an apparent turbulent stress

−ρ u v . from which the definition of the displacement thickness δ is Equation (11) the heat flux −λ ∂T is associated with an 1 ∂y δ apparent turbulent heat flux ρ v h . The contribution ρu δ1 = 1 − dy of viscosity and thermal conductivity is to diffuse mo- 0 ρeue mentum and energy in the y-direction. By extension, the As the mass flow is the same in the real flow and in the effect of turbulent terms is called turbulent diffusion. The fictitious flow, the displacement surface y = δ is a stream above equations are written assuming that the ensemble 1 surface for the equivalent inviscid flow. The displacement averages are identical to mass-weighted averages. thickness thus represents the distance by which the body should be displaced in order to represent the boundary B. Boundary Layer Characteristics layer effects in the equivalent inviscid flow. Another way to represent the boundary layer effects in The boundary layer is associated with important charac- an equivalent inviscid flow is to define a blowing velocity teristics such as the skin-friction coefficient and the dis- at the wall (Fig. 11): placement thickness. The skin-friction coefficient is a di- δ mensionless quantity defined from the wall shear stress: d(ue 1) vb = τ dx = w c f Then the equivalent inviscid flow is defined from the wall 1 ρ u2 2 e e to infinity, but at the wall the boundary condition is now a whereρe and ue are the values of the density and of the blowing velocity, vb. longitudinal velocity at the edge of the boundary layer. The momentum thicknessθ and the shape factor H are The wall shear stress is also defined: ∂ δ u ρu u δ1 ∂w = µ θ = − = ∂ 1 dy; H y y =0 0 ρeue ue θ The displacementthickness is introduced when compar- The momentum thickness is the thickness which is added ing the real flow and an equivalent inviscid flow (Fig. 10). to the displacement thickness in order to have the same Along the boundary layer edge y =δ, the flow character- flux of momentum in the real flow and in the fictitious istics are the same in the real flow and in the equivalent flow.

FIGURE 10 Displacement thickness. FIGURE 11 Blowing velocity. P1: GHA/FPW Revised Pages P2: FPP Encyclopedia of Physical Science and Technology EN001-906 May 7, 2001 12:39

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C. Equivalence with Navier-Stokes Equations At high Reynolds numbers, the Navier-Stokes equations are equivalent to a system consisting of the inviscid flow equations and the boundary layer equations, the two sys- tems being coupled by the displacement thickness or the blowing velocity. From the standard boundary layer the- ory, the flow around an airfoil can be calculated according to the following sequence (Fig. 12):

1. An inviscid flow calculation is performed around the FIGURE 13 Boundary layer calculation domain. physical airfoil. In this calculation, the surface of the airfoil is assumed to be impermeable. 2. A boundary layer calculation is performed using as an direction along the streamlines, and they also propagate input the pressure obtained in the first step at the wall along normals to the wall. If the problem is restricted to in- of the airfoil. compressible, two-dimensional, steady flows, the bound- 3. A new inviscid flow calculation is performed. During ary conditions are this step, the boundary layer effects are accounted for. r If the displacement thickness concept is used, the At an initial station x = x0, the velocity profile is δ prescribed u = u(x , y). body is displaced by a distance equal to 1 (Fig. 12). r 0 If the blowing velocity concept is used, the boundary At the wall, no slip conditions are prescribed: u = 0, v v = 0. condition at the wall is the value of b determined r from the boundary layer calculation. At the boundary layer edge, the velocity is equal to the inviscid velocity u = ue. The external velocity ue is This method works as long as the boundary layer has not related to the pressure by the Bernoulli equation: separated. When separation occurs, the concept of bound- ary layer can still be used but the sequence described above dp due =−ρeue can no longer be used and the solution is more compli- dx dx cated. According to their mathematical nature, the boundary layer equations are solved step by step in the downstream direction using marching methods from station x = x0 D. Solution of Boundary Layer Equations (Fig. 13). In practice, the initial station x = x0 is the stag- The boundary layer equations are solved by numerical nation point of the airfoil where local solutions are known methods. According to the standard theory, the pressure (Section VI). is known (from the solution of inviscid equations as men- tioned above). The boundary layer equations form a sys- tem of parabolic equations. The mathematical nature of VI. AN EXAMPLE OF BOUNDARY LAYERS: this system is similar to the heat equation. Without re- FALKNER-SKAN SOLUTIONS versed flow, perturbations propagate in the downstream Particular solutions of boundary layer equations exist when the external velocity is m ue = kx where k and m are constants. Such a flow would be ob- tained at the wall of a wedge in an inviscid flow (Fig. 14). The opening angle of the wedge is βπ with:

β = 2m m + 1 The variables ξ and η are introduced: y m + 1 u x ξ = x; η = e FIGURE 12 Viscous-inviscid interaction. x 2 ν P1: GHA/FPW Revised Pages P2: FPP Encyclopedia of Physical Science and Technology EN001-906 May 7, 2001 12:39

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FIGURE 14 Inviscid flow on a wedge.

It can be shown that the solution to the boundary layer equations is such that: u = f (η) ue and the momentum boundary layer equation is f + ff + β(1 − f 2) = 0 = η ζ ζ, = df , = d2 f with f 0 f ( ) d f dη f dη2 . The bound- ary conditions are f = 0 and f = 0 when η = 0, f = 1 when η →∞ FIGURE 15 Falkner-Skan self-similar solutions. The boundary layer equation is now an ordinary differ- ential equation instead of a partial differential equation as were the original equations. The Falkner-Skan solutions the pressure gradient is positive. In addition, the corre- are self-similar. The solution at a station x2 can be deduced sponding velocity profile has an inflexion point. This is from the solution at any another station x1. The transfor- a condition of instability of the velocity profile when a mation rule is simply through the use of the variable η: the small perturbation is introduced in the boundary layer. Ex- velocity profile u expressed as a function of the physical perimental results show that, in a two-dimensional flow, ue variable y at a given station is obtained from the veloc- laminar-turbulent transition occurs earlier when the pres- ity profile at another station by an affinity transformation sure gradient is positive. on the distance to the wall. This property transforms the When β −0.19884, the slope of the velocity profile partial differential equations into an ordinary differential at the wall is zero (i.e., the skin friction is zero). In a

equation for f . two-dimensional flow, this is characteristic of the onset of The numerical solution of the Falkner-Skan equation is separation. Let x be the extent of a boundary layer ele- shown in Fig. 15. Each velocity profile corresponds to a ment limited by two planes perpendicular to the wall. The given value of β (i.e., a given value of the wedge angle). pressure force exerted on this element per unit of width When β>0, the flow is accelerated (i.e., the external ve- −ρδ dp is dx x. When the pressure gradient is positive, the locity increases in the downstream direction); when β<0, pressure force is negative (i.e., is opposite to the flow di- the flow is decelerated. The case β = 0, studied by Blasius, rection). If the average kinetic energy contained in the corresponds to the flow over a flat plate. According to the boundary layer is not large enough to sustain this oppos- boundary layer jargon, a flat plate is an (infinitely) thin ing force, the flow does not follow the wall any longer and body whose surface is parallel to the free-stream velocity. separation occurs (Fig. 16). Then, the pressure gradient in the flow on a flat plate is zero. When m = 1, ue = kx, the flow corresponds locally to the flow in the vicinity of the stagnation point on an air- foil. Then, the solution for m = 1 can be taken as an initial condition at the stagnation point for boundary layer cal- culations. The pressure gradient has a great influence on the shape of the velocity profile and on the thickening of the bound- FIGURE 16 Boundary layer separation in a two-dimensional ary layer. The results show that thickening is faster when laminar flow. P1: GHA/FPW Revised Pages P2: FPP Encyclopedia of Physical Science and Technology EN001-906 May 7, 2001 12:39

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On an airfoil, separation can occur when the angle of The solution for the stream function ψ has the normal attack increases. On the rear part of the upper surface, mode form: −α α −ω the intensity of the positive pressure gradient increases ψ = φ(Y )e i X ei( r X T ) with the angle of attack. Separation is generally not de- sirable for several reasons. When separation occurs on Here, all the quantities are normalized by a reference the rear part of an airfoil, the separated flow is like a length related to the boundary layer thickness and a ref- dead water zone where the pressure is more or less con- erence velocity V0. The quantitity i is the pure imaginary 2 =− stant. The pressure distribution on the airfoil is very dif- number such that i 1. A perturbation is characterized α ω ferent from the distribution calculated in an inviscid flow by its wave number r , its pulsation , and its ampli- α α > and the airfoil performance is degraded. When the an- fication coefficient i . When i 0, the perturbation is α < gle of attack increases, the lift decreases and the drag damped; when i 0, the perturbation is amplified; when α = increases because of these pressure changes. The airfoil i 0, the wave is neutral. enters a stall regime. In addition, the flow is likely to be- The linearized Navier-Stokes equations give the Orr- come unstable, which is not at all desirable for a transport Sommerfeld equation for the stream function: aircraft. ∂4φ ∂2φ − 2α2 + α4φ ∂Y 4 ∂Y 2 ∂2φ ∂2U VII. LAMINAR-TURBULENT TRANSITION − iR (αU − ω) − α2φ − α φ = 0 ∂Y 2 ∂Y 2 The change from laminar to turbulent regime—the where α = αr + iαi , U is the velocity profile of the basic so-called laminar-turbulent transition—often originates flow, and R characterizes its Reynolds number: from an instability phenomenon (Fig. 17). In a two- V dimensional flow, the boundary layer is laminar near the = 0 R ν leading edge. Downstream, traveling waves occur natu- rally, and the flow is unsteady. At first, the waves are two The boundary conditions of the Orr-Sommerfeld equation dimensional and the corresponding wave vector is parallel express that the velocity perturbations are zero at the wall to the general direction of the flow. Downstream, complex and vanish at infinity. phenomena occur before the flow becomes turbulent. In the Orr-Sommerfeld equation, the input is the profile The theoretical analysis of the first step of transition U(Y ) and its Reynolds number. A nontrivial solution is is performed using stability theories. The results of these obtained for certain combinations of α and ω, which are theories are relatively well confirmed by experiments. The eigenvalues of the Orr-Sommerfeld equations. Then, for α ω simplest theory consists of studying the variation of small given values of r and , a nonzero solution is found for α perturbations. The Navier-Stokes equations are linearized certain values of i . Therefore, it is possible to say whether about a basic state—for example, the Blasius boundary a perturbation with a given frequency and wave number is layer or any other laminar boundary layer. The longitudi- stable or unstable. nal variations of the basic flow are neglected, and the solu- The results of this linear theory are used to define tran- tions to the linearized Navier-Stokes equations are sought sition criteria. These criteria are based on the calculation as normal modes. In a two-dimensional incompressible of the amplification rate of the most unstable waves. A flow, the continuity equation for the perturbations uˆ and vˆ transition criterion says that transition occurs when the of the velocity components is satisfied if a stream function amplification rate reaches an empirical critical threshold. ψ is introduced: The solutions of the Orr-Sommerfeld equation show ∂ψ ∂ψ that the Reynolds number plays an essential role in the sta- = v =− bility of a laminar boundary layer and therefore in transi- uˆ ∂ ; ˆ ∂ Y X tion. However, the Reynolds number is a parameter among others. A positive pressure gradient, wall roughnesses, free-stream turbulence, and noise tend to promote tran- sition at a lower Reynolds number. Flow compressibility and wall temperature level are also important parameters. In a three-dimensional flow on a swept wing (Fig. 18), the secondary flow occuring in the boundary layer can trigger transition when the flow is accelerated, even in the vicinity of the leading edge where a two-dimensional flow FIGURE 17 Transition process on a flat plate. would remain laminar. In addition, the turbulent boundary P1: GHA/FPW Revised Pages P2: FPP Encyclopedia of Physical Science and Technology EN001-906 May 7, 2001 12:39

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Second, the amount of kinetic energy contained in a boundary layer is larger when the flow is turbulent. Sep- aration occurs when the kinetic energy contained in the boundary layer is not sufficient to overcome the pressure force opposing the motion. A turbulent boundary layer is therefore able to sustain a stronger positive pressure gra- dient than a laminar boundary layer without separating.

B. Turbulent Boundary Layer Structure A turbulent boundary layer is composed of two layers FIGURE 18 Mechanisms of laminar-turbulent transition in a (Fig. 20): three-dimensional boundary layer on a swept wing. r Near the wall, the viscous stress is larger than or is of layer on the fuselage can perturb the boundary layer de- the same order as the apparent turbulent stress. This veloping on the leading edge of a swept wing. The leading inner region is studied by introducing the wall variables y+ = y uτ and u+ = u . The viscous length edge boundary layer is then turbulent and the wing bound- ν uτ ν τw scale is based on the friction velocity uτ = ary layer is contaminated. uτ ρ where τw is the wall shear stress. r Away from the wall, the turbulent shear stress is much VIII. TURBULENT BOUNDARY LAYERS larger than the viscous stress. This outer layer is fully turbulent and is characterized by the velocity scale uτ and the length scale δ, the thickness of the boundary A. Effect of Turbulence layer. An important effect of turbulence is to mix the flow very efficiently. As a result, the inhomogeneities in the flow are Experiments and theoretical considerations based on smoothed. Compared with a laminar boundary layer, the the theory of matched asymptotic expansions show that velocity profile in a turbulent flow is fuller in the core of the velocity profile in the inner region follows a universal the flow. At the wall, in a laminar or turbulent flow, the law u += f (y +) called the law of the wall (Fig. 21). This velocity is zero. Then, the velocity profiles resemble those law is universal in the sense that it does not depend on the of Fig. 19. conditions under which the boundary layer develops—for Two conclusions can be drawn from this observation. example, the value of the Reynolds number or the pressure First, the slope of the velocity profile at the wall is much gradient. In particular, in the part of the inner layer that is steeper in a turbulent flow than in a laminar flow. The far enough from the wall (y+ > 50), it is established that turbulent skin fiction is much higher: the velocity profile has a logarithmic form:

τw turbulent  τw laminar

FIGURE 20 Shear stresses in a flat plate turbulent boundary layer. The boundary layer has a two-layer structure. The inner FIGURE 19 Typical velocity profiles in a laminar and a turbulent layer thickness is exaggerated in this figure. The inner layer and boundary layer. the outer layer overlap to give a logarithmic velocity law. P1: GHA/FPW Revised Pages P2: FPP Encyclopedia of Physical Science and Technology EN001-906 May 7, 2001 12:39

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tures. This flux is governed by inviscid mechanisms, and the amount of dissipation is imposed by the characteristics of the large structures. The dissipation rate is evaluated as:

3 = u l l This result is equivalent to saying that the time scale u of u2 large structures is equal to the time scale required to dissipate an amount u2 of turbulent kinetic energy. The ratio of dissipative to energetic scales is FIGURE 21 Law of the wall in semi-logarithmic coordinates. The η − / v − / τ − / +< + + = 3 4 = 1 4 = 1 2 logarithmic law is valid for y yL where yL depends on the con- Rl ; Rl ; Rl ditions in which the boundary layer develops: Reynolds number l u θ and pressure gradient. where Rl is a turbulence Reynolds number: vl R = 1 l ν u += ln y ++ C (12) χ As the Reynolds number is much larger than unity, there whereχ is the von Kar´ man´ constant. Experimentally, the is a large gap between the small and large scales. The values ofχ and C areχ= 0.41 and C = 5. All the tur- behavior of small-scale structures is nearly independent bulence models should reproduce this result in order to of the behavior of large-scale structures. model the boundary layer correctly. D. Turbulence Models C. Simplified Representation of Turbulence In a boundary layer, the origin of turbulence is the shear ∂u Turbulence models use a description of turbulence based ∂y . As a general rule, it is assumed that if two phenomena on the concept of scales (velocity, length, time). Two are in efficient interaction, their time scales are of the same classes of structures play an important role: the large (en- order. Therefore, if shear is the only source of turbulence, ergetic) structures characterized by scales u,l, and θ and its time scale is of the same order as the turbulence time the small (dissipative) structures characterized by v,η, scale: and τ. The order of magnitude of u is the square root of u ∂u the turbulent kinetic energy; the order of l in a boundary = l ∂y layer is the distance to the wall y for the inner layer and l isδ for the outer layer; the time scale is θ= . Experiments show that the velocity fluctuations u and u The dissipation rate is used to estimate the order of the v are well correlated. The order of − u v is thus u2. The smallscales.Bydefinition,thedissipationrate represents Prandtl mixing length model states: the amount of turbulent kinetic energy transformed into ∂u 2 heat per unit time. The dissipation rate is the deformation − v = 2 u l ∂ work performed by the fluctuations of viscous stresses. y For a unit mass, the definition is where the mixing length l represents a turbulence length = 2ν s s scale. Near the wall, the length scale of large structures ij ij is the distance to the wall l ∼ y. If it is assumed that

where sij is the rate of strain fluctuation. −ρ u v τw (Fig. 20), the logarithmic law is obtained. From this definition, the time scale τ is such that Precisely, with l = χy, the logarithmic law (12) is exactly =ν τ2 . Since the dissipative structures efficiently trans- reproduced. Very close to the wall, the model must take formkineticenergyintoheat,theircharacteristicReynolds into account the effects of the wall on the turbulence struc- v η number ν is on the order of unity. The dissipative or ture and modifications are needed. In the outer layer, the Kolmogorov scales are then evaluated as: length scale is proportional to the boundary layer thick- = . δ ν3/4 ν 1/2 ness. Good results are obtained with l 0 085 . v = (ν)1/4; η= ; τ= The mixing length model was specially developed for 1/4 wall boundary layers. For wakes or jets, the expression of An approximate value of is the flux of energy trans- the mixing length must be modified. More general models ferred from the large structures to the dissipative struc- use transport equations for turbulence characteristics—for P1: GHA/FPW Revised Pages P2: FPP Encyclopedia of Physical Science and Technology EN001-906 May 7, 2001 12:39

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example, the turbulent kinetic energy k and its dissipa- tion rate . These equations are deduced from the Navier- Stokes equations written for the velocity fluctuations. The exact equations are not directly a turbulence model be- cause several terms are unknown correlations between velocity fluctuations or between velocity fluctuations and pressure fluctuations. These unknown terms require mod- eling. The k − model is a popular model. FIGURE 23 Riblet surfaces. = u3 u = From the inviscid estimate l and the relation l ∂u ∂y , the shear stress is expressed as: and form drag. Friction drag is due to the boundary layer and is obtained by integrating the wall shear stress over 2 ∂ k u the surface of the aircraft. Induced drag is associated with − u v =Cµ ∂y the finite dimension of the wings and is due to lift. The pressure is lower on the upper surface of the wings than where Cµ is a constant. This expression is the basis of the on the lower surface in order to produce lift. A flow turns k − model. around the tip of the wings from the lower surface to the up- The k- and -model equations for a two-dimensional per surface and generates vortices trailing a long distance incompressible shear layer are behind the aircraft. These vortices modify the effective ∂k ∂k ∂u ∂ k2 ∂k angle of attack of the wings and turn back the lift vector, u + v =− u v − + C (13) ∂x ∂y ∂y ∂y k ∂y leading to a drag component. Form drag results from the integration of pressure on the body (excluding induced ∂ ∂ ∂u drag). u + v = −C u v − C ∂x ∂y k 1 ∂y 2 In all cases, friction drag accounts for a large share of the total drag of the aircraft and many endeavors have been ∂ k2 ∂ devoted to reducing this drag. + C (14) ∂y ∂y where the constants are determined from experimental re- A. Riblets sults. In particular, the properties of the logarithmic layer Riblet surfaces are made of grooves aligned with the flow are used. (Fig. 23). The role of these surfaces is to reduce the friction The above model is valid for the outer layer of the drag of a turbulent boundary layer. boundary layer. Near the wall, the model is modified to Experiments in wind tunnels have shown that riblets are take into account the wall effects on turbulence. efficient in reducing the wall shear stress when the riblet dimensions are adapted to the boundary layer character- istics. The optimal dimensions are expressed in terms of IX. DRAG REDUCTION wall units. For triangular shapes with h = s, a friction drag reduction of 8% is obtained when h+ = s+ is in the range The drag breakdown on various aircraft (business jets of of 10–15. In terms of physical dimensions, these figures the Falcon type, civil transport aircraft of the Airbus type, give a size on the order of a few hundredths of a millimeter. supersonic aircraft such as the Concorde) shows three Riblets are efficient in subsonic, transonic, and supersonic main sources of drag (Fig. 22): friction drag, induced drag, flows (Fig. 24). It should be noted that the wetted area (the

FIGURE 22 Drag breakdown on different types of aircraft. P1: GHA/FPW Revised Pages P2: FPP Encyclopedia of Physical Science and Technology EN001-906 May 7, 2001 12:39

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B. Laminarity An even more efficient means of reducing friction drag is to laminarize the boundary layer, as skin friction is much lower in a laminar flow than in a turbulent flow. It is more relevant to laminarize the upper surface be- cause the turbulent skin friction is higher than on the lower surface. Laminarization is commonly used for sailplanes. The airfoil shape is designed to generate a negative pres- sure gradient over a large area of the wing surface. On a sailplane, the wing has no sweep and the flow on the wings is nearly two dimensional. A negative pressure gra- dient has the property of stabilizing the laminar regime. A typical pressure distribution on the upper surface of FIGURE 24 Efficiency of riblets. a wing as shown in Fig. 25a is conducive to the lam- inar regime in two-dimensional flow over a significant extent. area in contact with fluid) is much larger for riblet surfaces In a three-dimensional flow, transition can occur due than for smooth surfaces. Thus, a smooth surface does not to the instability of the boundary layer streamwise flow produce the lowest friction. or of the crossflow (Fig. 18). The streamwise instability The underlying mechanisms are not completely under- occurs under the same conditions as in a two-dimensional stood, but it is almost certain that riblets interact with the boundary layer. A negative pressure gradient increases the near-wall turbulent structures which are responsible for transition Reynolds number, whereas a positive pressure turbulence production. The optimal size of riblets is con- gradient reduces it. However, crossflow instability can de- sistent with this explanation. velop in the presence of an accelerated flow, whereas the Flight tests have confirmed the results obtained in wind streamwise flow is stable. tunnels. An A320 research aircraft was covered with ri- Wing shaping is more complicated for preserving nat- blets over 75% of its wetted area. Fuel consumption was ural laminarity in a three-dimensional flow. For moderate measured with and without riblets. For cruise conditions, sweep angles (less than 20◦), a typical pressure distribu- a reduction of 1.6% of the total drag of the aircraft was tion is shown in Fig. 25b for the upper surface of a wing. recorded. This result is consistent with laboratory results Such a pressure distribution results from a compromise de- on the friction drag reduction and with the fact that friction signed to minimize streamwise and crossflow instabilities. drag accounts for about 45% of the total drag of the air- Near the leading edge, the flow is strongly accelerated; in craft and only 75% of the aircraft surface was covered with this way, the streamwise instability is eliminated and the riblets. In any case, such a drag reduction is significant for crossflow instability is delayed. Downstream, a milder ac- an aircraft. celeration minimizes the risk of streamwise instability and

FIGURE 25 Pressure distribution producing laminar boundary layers (a) in a two-dimensional flow, and (b) on a swept wing. P1: GHA/FPW Revised Pages P2: FPP Encyclopedia of Physical Science and Technology EN001-906 May 7, 2001 12:39

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the crossflow development is limited because the pressure ticular, the two wings of a Falcon 900 were equipped with gradient is moderate. wall suction and this demonstrator was conceived in an For higher Reynolds numbers or for higher sweep an- operational framework (suction system, anti-icing system gles, wing shaping is not sufficient to maintain a laminar providing protection against insect pollution). An A320 regime. Another technique consists of applying boundary laboratory aircraft was also tested in flight with a laminar layer suction at the wall. In practice, suction is performed fin equipped with wall suction. Laminarity on a vertical through perforated walls. Very tiny holes are drilled by fin is relatively simple because a fin has no high lift de- means of laser techniques, for example; the holes are a vice and integration of the suction system is easier. A fin few hundredths of a millimeter in size and are spaced also has the advantage of being symmetrical. However, a few tenths of a millimeter apart. Wall suction has the the high angle of sweep is a real challenge for laminar- property of decreasing the boundary layer thickness and ity. Flight tests were very successful, as laminarity was modifying the shape of the velocity profile, which is more obtained over 60% of the chord. stable. Wall suction reduces the intensity of the cross- flow which is very favorable to maintaining the laminar regime. X. CONCLUDING REMARKS Leading edge contamination is a third mechanism that can prevent the boundary layer from being lami- The boundary layer concept was invented at the begin- nar (Fig. 18). Leading edge contamination is character- ning of the twentieth century (i.e., about hundred years ized by a Reynolds number R¯ which increases when the ago). At that time, this very inspired approximation of sweep angle φ increases, when the free-stream veloc- Navier-Stokes equations appeared as a breakthrough in ity V∞ increases, and when the leading edge radius r0 aerodynamics and opened the doors to new knowledge. increases. For a swept circular cylinder, this Reynolds It has been said that the boundary layer was the key to number is aerodynamics. Since then, intensive efforts have been devoted to this 1/2 V∞r0 sin φ tan φ field and the progress made is really impressive. For exam- R¯ = ν 2 ple, the problem of attached laminar boundary layers can be considered as solved. The question of boundary layer From experiments, the boundary layer is laminar when separation is now well understood and, although this prob- R¯ < 250; however, for a civil transport aircraft, R¯ is above lem has not been completely solved, practical solutions this critical value, at least near the wing root. exist. Two approaches can be employed to delay leading edge In addition, numerical solvers of averaged Navier- contamination. One possible approach is to use a so-called Stokes equations are becoming a routine tool in research Gaster bump—a device proposed by Gaster—which is a laboratories and in aircraft companies. At least in princi- small bump placed on the wing leading edge at a cer- ple, these solutions are able to describe the complete flow tain distance from the fuselage, well outside the fuselage field around an aircraft. The question, then, is whether boundary layer. The bump diverts the flow coming from the boundary layer concept is still valuable or is old- the fuselage and creates a stagnation point from which fashioned. Undoubtedly, the answer is that the bound- a fresh boundary layer develops. This device can delay ary layer remains an invaluable model. At least two rea- the onset of leading edge contamination up to values of sons can be given. First, understanding the behavior of the R¯ around 350 or 400. A much more efficient way of de- flow around a wing, for example, requires understanding laying leading edge contamination is to use suction in the the boundary layer. The correct interpretation of numer- wing leading edge region. With relatively moderate suc- ical or experimental results often requires a good grasp tion rates, leading edge contamination has been delayed of viscosity effects. Second, many questions are still un- up to R¯ = 700, but this value is certainly not the maximum solved. Among them, laminar-turbulent transition and the value that can be reached with wall suction. turbulent regime are two of the most difficult problems in Flight tests have confirmed the possibility of laminarity physics. Boundary layers, wakes, and jets are obviously on a civil transport aircraft or on a business jet. For exam- places where turbulence plays an essential role. The un- ple, experiments were performed on a Boeing 757 which derstanding of turbulence development is far from being flew with wall suction on the wing. The boundary layer complete and its modeling is not at all satisfactory. Clearly, was laminar up to the shock wave (i.e., about 60% of the work is needed in this field and wall boundary layers are chord). In Europe, much effort has been devoted to the an appropriate model for these studies. study of laminarity, and flight tests were performed on a Another challenging topic is drag reduction. Bound- Fokker 100 to analyze natural transitions. In France, flight ary layers have an important contribution to drag. As tests were performed on different Falcon aircraft. In par- mentioned in a previous section, different techniques are P1: GHA/FPW Revised Pages P2: FPP Encyclopedia of Physical Science and Technology EN001-906 May 7, 2001 12:39

Aircraft Aerodynamic Boundary Layers 317

available to reduce skin-friction drag significantly. Active TATIONAL AERODYNAMICS • FLIGHT (AERODYNAMICS) control of turbulence is another way that is under study • FLOW VISUALIZATION • FLUID DYNAMICS at the present time and for which new ideas are emerging continuously. The principle of active control is to detect the development of turbulence from the measurement of BIBLIOGRAPHY some characteristic feature—wall pressure or wall shear stress, for example—and to apply a perturbation to the Cebeci, T., and Cousteix, J. (1999). “Modeling and Computation of flow in order to cancel this development. Up to now, these Boundary-Layer Flows,” Springer-Verlag, Berlin/New York, and studies have been performed in the laboratory, either ex- Horizons Publishing, Long Beach, CA. Drazin, P. G., and Reid, W. H. (1981). “Hydrodynamic Stability,” Cam- perimentally or numerically. In other fields, active control bridge University Press, Cambridge, U.K. techniques are used in real life. For example, noise re- Lesieur, M. (1990). “Turbulence in Fluids,” Kluwer Academic, duction is already achieved by using such techniques. It Dordrecht/Norwell, MA. is reasonable to expect that turbulence manipulation will Piquet, J. (1999). “Turbulent Flows: Models and Physics,” Springer- become a reality. Verlag, Berlin/New York. Sagaut, P. (1998). “Introduction a` la simulation des grandes echelles´ pour les ecoulements´ de fluide incompressible,” Springer-Verlag, SEE ALSO THE FOLLOWING ARTICLES Berlin/New York. Schlichting, H. (1968). “Boundary-Layer Theory,” McGraw-Hill, New York. AIRCRAFT PERFORMANCE AND DESIGN • AIRCRAFT Tennekes, H., and Lumley, J. L., (1972). “A First Course in Turbulence,” SPEED AND ALTITUDE • AIRPLANES,LIGHT • COMPU- MIT Press, Cambridge, MA. P1: FYD Final Pages Qu: 00, 00, 00, 00 Encyclopedia of Physical Science and Technology EN001F-916 May 31, 2001 11:7

Aircraft Instruments

W. B. Ribbens University of Michigan

I. Introduction XII. GPS Accuracy Augmentation II. Aircraft Communication Systems XIII. GPS Integrity and Availability III. Navigation XIV. Receiver Autonomous Integrity Monitoring IV. Distance Measuring Equipment (RAIM) V. LORAN XV. Inertial Navigation VI. Automatic Direction Finding XVI. Instrument Landing System (ILS) VII. Long-Range Navigation XVII. Additional Precision Approach Systems VIII. Navigational Coordinate Systems XVIII. Air Data System IX. Satellite-Based Navigation System XIX. Attitude and Heading References X. The GPS System Structure XX. Autopilot—Flight Management Systems XI. WAAS (FMS) XXI. Glass Cockpit

GLOSSARY trolling attitude having the feature of variable aircraft stability. Aircraft instrumentation Electronic apparatus neces- Full authority digital engine control (FADEC) Elec- sary for voice/digital communication, navigation, at- tronic engine control system for regulating engine per- titude measurement, flight path control, and system formance within a safe operating envelope with com- monitoring. mand inputs from the flight crew. Air data system Instrumentation for accurately calcu- Glass cockpit Solid state display system capable of al- lating critical flight variables (e.g., airspeed, altitude) phanumeric data or pictorial display to the flight crew from onboard measurements. eliminating the need for any electromechanical display. Altitude and heading instrumentation Electronic Inertial navigation system (INS) Electronic posi- equipment for measuring and displaying to the flight tion/velocity vector determination derived from mea- crew the aircraft orientation relative to Earth coordi- surements of acceleration along and about aircraft axes. nates and its velocity vector components. Instrument landing system Instrumentation for pre- Flight management system Electronic system for auto- cisely and accurately measuring and displaying to the matically controlling aircraft flight path along segments flight crew the aircraft flight path during the landing of its route from departure to destination. phase of flight used under severely adverse weather Fly by wire All electronic flight control system for con- conditions.

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338 Aircraft Instruments

Radio navigation Aircraft location/position determina- 6. Various engine performance and operating safety tion based upon signals from ground-located transmit- parameters, including ters. a. Oil pressure and temperature Satellite navigation Position/location and velocity vec- b. Angular speed of critical rotating parts (e.g., tor determination derived from signals transmitted crankshaft) from a constellation of satellites (global positioning c. Airflow monitoring gauge (e.g., manifold pressure) system, GPS). Transceiver Two-way radio voice communication be- For operations under IFR under FAR part 91, additional tween flight crew and controlling authority. equipment beyond that required for VFR operation in- cludes the following: I. INTRODUCTION 1. Radio equipment suitable for navigation using Aircraft instrumentation provides the flight crew with the navigational facilities to be used during the flight as capability to perform many functions, including commu- well as two-way voice and/or data communications nication, navigation, monitoring the status of onboard sys- between the aircraft and the controlling agency tems, diagnosing problems or system failures that occur in 2. Aircraft attitude indicating equipment for displaying flight, measuring/monitoring aircraft attitude, monitoring pitch, roll, and yaw weather, and monitoring the position of other aircraft (i.e., 3. Slip/skid indicating equipment those that pose a potential collision hazard). The actual in- 4. The altimeter which is adjustable for local strumentation required depends upon the aircraft category atmospheric pressure and the type of flying involved. 5. Precision clock (HH = hours, MM = minutes, SS = The least capability required of instruments is for light, seconds) single-engine, general aviation aircraft licensed by the 6. Aircraft heading and turn rate indicating equipment Federal Aviation Administration (FAA) under Federal Air Regulations (FAR) part 23 for day visual flight rules (VFR) It should be noted that in traditional light (general avia- operations. Instrumentation progresses from this category tion) aircraft, some of this equipment was electronic (i.e., and type of flying to greater and greater complexity, reach- avionics) and some was mechanical. ing the greatest requirement for transport category aircraft The avionics suite installed on any given airplane is a (licensed by the FAA under FAR part 25) and flying under function of the aircraft category (i.e., general aviation or instrument flight rules (IFR). The appropriate FARs for transport etc.) and upon its intended operations (e.g., part the first category are under FAR part 61. For noncommer- 91 or 135 or 121). Presented below is a listing of avion- cial instrument flying FAR part 91 specifies requirements. ics equipment that is a superset of the possible choices Commercial operations other than regularly scheduled air- for avionics equipment. The listing below is based upon line operation (including air taxi and air cargo operations) functionality of the equipment. are conducted under FAR part 135 rules. For airline oper- ations, the rules are given in FAR part 121. Each aircraft category and flight operation has instrumentation require- 1. Communications ments such that the higher category requirements tend to a. Ground-based voice—air traffic control (ATC) be a superset of requirements for lower requirements. It is b. Ground-based data link (ATC future) perhaps instructive to begin with the simplest aircraft in- c. Satellite based strumentation and progress through the various categories 2. Navigation and flight operations to the most complex. a. Radio land based The minimum instrumentation required for day VFR b. Satellite flying in light aircraft includes the following: c. Inertial platform 3. Landing aids 1. Airspeed indicator a. Land based 2. Altimeter b. Satellite based 3. Magnetic direction finder (compass) 4. Attitude indicating 4. Fuel gauge indicating quantity of fuel in each tank 5. Air data system 5. Landing gear position indicating device for 6. Flight control retractable landing gear aircraft 7. Flight safety P1: FYD Revised Pages Encyclopedia of Physical Science and Technology EN001F-916 May 10, 2001 10:30

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II. AIRCRAFT COMMUNICATION surveillance radar data that can be used to maintain safe SYSTEMS aircraft separation. Instructions are given to the crew to fly specific trajectories via assigned heading, airspeed, and Aircraft communication systems function for the sole pur- altitude. pose of providing a communication link between each in- At some appropriate point in the airspace, the crew will dividual airplane and the appropriate ATC authority. The be instructed to contact the next controlling authority on appropriate control authority is a function of the phase of a specified carrier frequency. For flights conducted above the flight and the nature of the flight (i.e., VFR or IFR) but a certain altitude (e.g., 8000 ft), the controlling authority is independent of the aircraft category, that is, to say all will be one of the ATC centers. The ATC centers are at civil aircraft have similar (in function) radio communica- widely spaced locations, e.g., Cleveland, Chicago, Min- tion equipment from the smallest general aviation aircraft neapolis, etc. This process of “hand-off” from one control through the largest part 121 transport aircraft. Military air- authority to the next continues until the aircraft reaches its craft have additional radio equipment beyond that which destination, where it will sequentially maintain two-way is required for flying in civilian airspace. However, this radio communication with approach control, tower, and equipment differs only in certain detailed aspects (e.g., ground control authorities. carrier frequency band) from its civilian counterpart. The communication radios in civilian aircraft are essen- There are several levels of control authority with which tially conventional transceivers that operate in the VHF the flight crew must establish two-way radio communica- portion of the spectrum. The carrier frequency fc is in the tion. At the larger airports serving air carriers, communi- band cations typically begin with communication with “clear- . ≤ ≤ . ance delivery.” For IFR operations, the crew will have 118 000 fc 136 975 MHz previously filed a flight plan with the ATC system. (Note: in 25 kHz increments offering 760 separate channels. Each this can be filed verbally via telephone to a government controlling authority is assigned a specific carrier fre- agency known as a flight service station (FSS) for pri- quency along with the portion of airspace that it must con- vate general aviation or via a computer link for an air trol. Normally, dual aircraft communication transceivers carrier.) are fitted to the aircraft for redundancy. The clearance delivery authority can verify the details In modern aircraft communication systems, the tuning of the flight plan and its acceptance by ATC. Any changes for both transmitter and receiver is crystal controlled. A that might be required (e.g., due to a radio navigation facil- digital frequency synthesizer generates signals at each car- ity being temporarily out of service) can be made during rier frequency within the VHF aircraft radio band (on all the exchange with a branch of ATC known as clearance 760 channels). Figure 1 is a simplified block diagram of a delivery. At the end of the communication with clearance typical aircraft communication transceiver. delivery, the flight plan has been finalized and accepted by The aircraft communication transceiver functions to- both ATC and the flight crew. gether with a separate electronic module called an “audio The next level of authority contacted by the crew is the panel.” This device routes the microphone input from the so-called ground control which controls aircraft ground crew microphones to the particular transmitter being used movement. The flight crew will maintain two-way ra- and routes audio output from the particular receiver in use dio communication via a specific carrier frequency (e.g., to the crew headphones/loudspeaker. 121.7 MHz) with ground control until the aircraft has tax- The transmitter is a conventional amplitude-modulated ied to the active runway. (AM) system in which the amplified audio signal from At this point the crew is instructed to contact the control the crew microphones varies the carrier amplitude. Let the tower on its assigned carrier frequency. The control tower carrier frequency selected by the pilot be fc. The output personnel have the authority to regulate aircraft movement of the digital frequency synthesizer is e fs(t): on the ground and in the air in the vicinity of the airport (typically within a 5-mile radius of the airport). This au- e fs(t) = E fs sin(2π fct). thority issues clearance to taxi onto the runway and then, when it is safe, to take off. Two-way radio communication For each sinusoidal component in the voice (audio) signal with the control tower is maintained by the crew until they at a frequency, fm , the signal from the modulator, eAM,is are specifically instructed to contact departure control on given by a specific carrier frequency. eAM(t) = EAM[1 + m sin(2π fm t + φ)] sin(2π fct), The departure control authority regulates aircraft move- ment in predetermined specific airspace in the vicinity of where m (the modulation index) is proportional to the the airport. Departure control personnel have access to amplitude of the audio signal and m < 1. P1: FYD Revised Pages Encyclopedia of Physical Science and Technology EN001F-916 May 10, 2001 10:30

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Amplifier (the crew repeats ATC instructions to confirm that the eAM To antenna Input signal Modulator R-F message was received and acknowledged). In an attempt from audio (AM) amplifier to reduce the workload burden and to improve system effi- panel ciency, experiments are being conducted in which certain fC instructions are relayed to the flight crew through a dig- Carrier frequency Digital frequency ital data link. It is anticipated that the digital data link selector synthesizer f – f C IF will provide a supplement to the voice link rather than a R-F replacement for it. amplifier f f From C IF tuner and IF detector antenna amplifier and LPF Mixer III. NAVIGATION Amplifier AGC Except for relatively low altitude (e.g., h ≤ 8000 ft above ground level) and/or local area flying, all aircraft require To audio navigation aids. In principle, under VFR conditions, point panel to point navigation can be accomplished with acceptable Microphone Output to accuracy to locate the airport of intended landing by means ( input ( Audio transmitter of a suitable map, a magnetic compass, and a clock. In Pilot Headphone panel Input from practice, and particularly under IFR conditions, greater or receiver accuracy and precision in navigation are required than ( speakers ( that available from the above. Microphone Headphone Electronic navigation aids, coupled with attitude ( input ( or measuring equipment, have provided sufficient precision ( speakers ( and accuracy to conduct poor weather operations since the Copilot early 1930s. However, significant progress in the perfor- FIGURE 1 Communication transceiver block diagram. mance of such navigation aids has evolved in the interven- ing years. It is beyond the scope of this article to provide a history of that evolution. Rather, a survey of the technol- The receiver portion of this system is a conventional su- ogy as of the late 20th century and the early 21st century perheterodyne receiver. The input signal from the aircraft is provided specifically with reference to IFR flight antenna is proportional to the transmitter signal (eAM(t)). conditions. This signal is amplified and sent to the mixer. The mixer The electronic navigation aids utilized in any flight de- is a two-input electronic circuit that is functionally equiv- pend upon the phase of the flight and the actual weather alent to an analog multiplier or similar nonlinear func- conditions. The greatest precision and accuracy are re- tion of its two inputs. The other input to the mixer is a quired during the final phase of landing an aircraft in − sinusoid at frequency fc fIf, where fIf is an interme- the lowest visibility weather conditions. The technology diate frequency (IF). The output of the mixer includes exists to provide navigation with sufficient accuracy so components at the sum and difference of its inputs (i.e., that when coupled to a flight control system the aircraft ± − fc ( fc fIf)), both of which have the same modulation can complete an automatic landing under zero-zero con- as the input signal from the antenna. ditions (i.e., ceiling of zero and zero visibility) using what The intermediate frequency amplifier is a narrow band is known as a category IIIc landing system. However, to filter/amplifier tuned to fIf such that its output is propor- understand this system, it is helpful to review navigation tional to aids of lower precision and accuracy. The navigation on a point to point flight is conducted [1 + m sin(2π fm t + φ)] sin(2π fIft). via preplanned routes known as airways. These airways This signal is an AM signal at a fixed frequency ( fIf). consist of segments of essentially locally straight lines or The detector/low pass filter (LPF) demodulates the audio segments of great circle areas connecting radio navigation signal and sends the voice (audio) to the audio panel for aids and or points in space that can be located by means distribution to the crew headsets/speakers. of radio navigation aids. The accuracy and precision of At major airports during certain periods of the day, on-board navigation aids must be such as to permit flight the controlling authorities are exceptionally busy. The within 4 nmiles of the centerline of the airway. This is a controller is often continuously transmitting instructions, significantly lower requirement than the accuracy required pausing between successive calls to wait for a pilot reply of airport landing navigation aids. P1: FYD Revised Pages Encyclopedia of Physical Science and Technology EN001F-916 May 10, 2001 10:30

Aircraft Instruments 341

d The other vector is directed from the aircraft location } h toward the VOR station. The angle of this vector mea- sured clockwise (as viewed from above the aircraft) from R R + h magnetic north is known as the bearing (B) to the station. These angles are related by B = R + 180◦(modulo 360◦). A pair of vectors is also defined relative to the aircraft. The first of these is a vector pointed forward along the longitudinal axis of the aircraft. The angle measured from magnetic north clockwise (looking down) is known as the FIGURE 2 Illustration of radio reception range vs altitude. heading (H). Another vector is the ground velocity vec- tor. The angle measured clockwise from magnetic north is Navigation along the airways can either be by means known as the ground track angle or track (T ), and the mag- of radio-based or inertial platform-based equipment. We nitude of this vector is known as ground speed and is the consider radio-based equipment first. These, in turn, can speed of the aircraft relative to an Earth fixed coordinate achieve navigational measurements from land-based or system. The intended value for this angle is known as the satellite-based radar transmitters. course. Heading and track angles are generally different The land-based, cross-country (as opposed to land- except in a zero wind zero sideslip condition. It should be ing) radio-navigation system with the greatest accu- noted that the VOR radial and bearing are independent of racy utilizes transmitters operating with carrier frequen- bearing, track, or course. The VOR navigation equipment can locate an aircraft cies ( fc) in the very high frequency VHF band from along a given radial but does not, by itself, give the distance 108 ≤ fc ≤ 118.0 MHz. This system is known as the “Very high frequency—omni Range (VOR) navigation system.” yielding the aircraft two-dimensional (2-D) position or As this system operates with a VHF carrier frequency, map coordinates. This 2-D position can be found by using its propagation is essentially line of sight. Aside from re- any two VOR stations that are not colinear with the aircraft ceiver noise limitations, the range of the VOR system is position (as illustrated in Fig. 3) by triangulation. a function of aircraft altitude in the form of the distance An alternate method of measuring the aircraft 2-D po- from the aircraft to the local horizon. It can be seen with sition is possible with some VOR stations. These sta- reference to Fig. 2 that the range d for an aircraft operating tions, which are designated VOR-DME stations, incor- at altitude h above the Earth (radius R)isgivenby porate distance measuring equipment (DME) colocated √ with the VOR station. Of course, the aircraft must also be d = (2hR + h2)1/2 =∼ 2hR, equipped with the corresponding DME equipment. (DME is explained later in this section.)

where the approximation is valid since R h. IFR flight The operation of the VOR transmitting station can be is conducted at altitudes of 3000 ft or greater such that the understood with reference to the functional block diagram effective range is more than 65 nmiles. of Fig. 4. The VOR system in North America and Europe con- The instantaneous frequency fFM(t)isgivenby sists of a set of radio transmitters that are spaced in an

irregular grid covering the entire landmass. The average fFM = 9960 + 480 sin(60πt). spacing between VOR stations is about 60–80 nmiles (de- pending upon geographical region), permitting successful That is, fFM varies from 9480 to 10,440 Hz at a 30-Hz VOR navigation between any airport pair on each of these rate. This frequency-modulated (constant amplitude) sub- continents. carrier amplitude modulates the carrier yielding The VOR navigation system provides a means of { + φ } π , locating an aircraft position relative to a given VOR sta- 1 m sin[ F (t)] sin(2 fct) tion. This position is specified by two vectors. One vector projects from the station location and is directed radially where  away from the station. The angle measured clockwise t φ = π τ τ = . (looking down on the station) from magnetic north is F (t) 2 fFM( ) d total phase of subcarrier known as the radial (R). The VOR receiver in the air- o craft yields a measurement of the radial along which the The operation of the VOR system is strongly dependent aircraft is located. upon the transmitting antenna system. This antenna has a P1: FYD Revised Pages Encyclopedia of Physical Science and Technology EN001F-916 May 10, 2001 10:30

342 Aircraft Instruments

VOR station 2 0°

0° R 1 270° 90°

270° 90° R2 180°

VOR station 1 180° Actual aircraft position

FIGURE 3 Illustration of navigation by dual VOR stations.

unique directional pattern in which the signal strength E carrier. These two signals are separated by a pair of narrow varies with angle θ in the form band, bandpass filters at center frequencies 30 Hz (yield- θ = + θ . ing e1) and 9960 Hz. E( ) Eo(1 cos ) It should be noted that the phase of the 30-Hz signal The antenna system causes this pattern to rotate (elec- e1 is a function of the radial at the aircraft position. The tronically) at 30 revolutions per second. The effect of this 30-Hz signal e2 has a fixed phase that is chosen such that system is functionally equivalent to an antenna with a spa- the signals e1 and e2 are exactly in phase when the aircraft ◦ tially fixed pattern E(θ) that is mechanically rotated at 30 is along a 0 radial [i.e., directly north (magnetic) of the φ revolutions per second. The result is that at any given lo- VOR station]. Denoting as the phase angle of e2 relative cation the VOR signal is amplitude modulated at 30 Hz. to e1, The operation of the VOR receiver can now be under-  φ = e1, e2 = θ, stood with reference to Fig. 5. The output of the r-f tuner and amplifier is an AM carrier that is, this phase is equal to the radial along which the (at the carrier frequency to which the receiver is tuned). aircraft is located. This signal is amplitude modulated at 30 Hz due to the Navigational position measurements (θ) are made by rotating antenna radiation pattern and at the 9960-Hz sub- measuring phase angle φ. The measurement is accom- plished in conjunction with a special purpose display and a variable phase shifter. Although there are multiple prac- Transmitting tical implementations of this display function, we will antenna VHF oscillator Amplitude at carrier modulator and frequency fC R-F amplifier e R-F tuner AM Narrow band 1 and amplifier detector filter at 30 Hz f (t) Frequency FM modulator (subcarrier)

30 Hz 30 Hz Narrow band FM e oscillator filter at 9960 Hz demodulator 2

FIGURE 4 Functional block diagram of the VOR transmitter. FIGURE 5 VOR receiver block diagram. P1: FYD Revised Pages Encyclopedia of Physical Science and Technology EN001F-916 May 10, 2001 10:30

Aircraft Instruments 343

e Phase detector e Fixed p/2 a 1 phase shift

e e i eC 0 To/From P f LPF SGN (e ) LPF 0 indicator

Variable phase e2 shifter, f3 eb

D

90° P

0° 180° Movable course indicator

OBS 270°

Display FIGURE 6 Functional block diagram of a phase angle measurement system.

◦ illustrate the general principles involved, with a specific indicator calibrated for φs in degrees from 0 through 360 configuration as depicted in Fig. 6 that is, at least, repre- (module 360◦). This OBS is adjusted by the flight crew sentative of the functional operation of such a subsystem. until the pointer P (also known as the course deviation In Fig. 6, a hypothetical phase detector is shown con- indicator, CDI) is centered. This occurs for iφ = 0, which sisting of an analog multiplier (mult) and a low pass filter occurs for φs = φ. Since φ = θ = φs, the phase shift in- (LPF). Choosing the phase of e1 as the phase reference, troduced by the variable phase shifter when the needle we have is centered yields a measurement of the radial or bearing of the aircraft. This value is numerically indicated by the e (t) = sin 60πt 1 movable course indicator under pointer D. The pilot can E2(t) = e2 sin(60πt + φ) then read position from the point on the movable course indicator directly beneath the marker D. and   As long as the aircraft flies along the radial correspond- π φ = φ = θ ea = e1 sin 60πt + ing to s , the meter will remain centered. How- 2 ever, as the aircraft position deviates from the selected = π − φ + φ radial, the CDI deflects proportionately. The dots on ei- eb e2 sin(60 t s ) ◦    ther side of center correspond to 5 deviations for each π dot. This display reaches saturation for deviation of ±12◦ e = ke e sin 60πt + [sin(60πt − φ + φ )], p 1 2 2 s from the selected radial. where φ is the phase angle introduced by the variable phase There is an ambiguity in the radial corresponding to ◦ φ shifter. aircraft position of 180 , since there are two nulls for s at φ = φ and at φ = φ + 180◦. This ambiguity is resolved k s s = e1e2[cos(120πt − φ + φs ) + sin(φ − φs )] by a binary display indicating TO/FROM. As long as the 2 aircraft is located such that The LPF suppresses the 120-Hz component and generates current eφ: φs − π/2 <φ≤ φs + π/2, eφ = K sin(φ − φs ), This steady current passes through the coil of a gal- the indicator displays FROM. Otherwise, it displays TO. vanometer whose movable element deflects pointer P on A scheme for achieving the TO/FROM is depicted in the face of the display. The variable phase shifter is me- Fig. 6. The two signals from the VOR receiver are func- chanically linked to a knob known as the OMNI Bearing tionally multiplied and low pass filtered. The sign of the Selector (OBS) that is further linked to a movable course result drives the binary TO/FROM indicator. P1: FYD Revised Pages Encyclopedia of Physical Science and Technology EN001F-916 May 10, 2001 10:30

344 Aircraft Instruments

Antenna Interrogation Antenna

Response

Transmitter T/R Receiver T/R

Ranging Receiver Transmitter circuit

Delay Aircraft distance display Ground transponder Airborne DME (interrogation) FIGURE 7 Block diagram of a DME system.

IV. DISTANCE MEASURING EQUIPMENT V. LORAN

Distance measuring equipment (DME) is located with Another radio-based navigation aid that is used particu- VOR ground stations and provides a measurement of the larly by general aviation aircraft is known as the Long- distance of the aircraft user from the associated VOR sta- Range Navigation system or LORAN. LORAN is a hy- tion. A combination of VOR/DME measurements yields perbolic navigation system, so-called because it locates an the vector position of the aircraft relative to the VOR/DME aircraft along a hyperbola whose foci are a pair of radio radio station. The DME concept is based upon the prop- transmitter stations. The intersection of hyperbolas from agation time of pulses transmitted by the aircraft to a multiple pairs of stations determines the aircraft position transponder repeater located at the ground station and on along the Earth’s surface (i.e., yields the solution to the the known propagation speed of these pulses. A block di- navigation problem). agram of the system is depicted in Fig. 7. The current version of LORAN evolved from a system The aircraft interrogation equipment transmits a pair of developed in Europe before World War II and is known as pulses on one of 126 carrier frequencies spaced 1 MHz LORAN-C. LORAN-C consists of a system of 24 trans- apart in the range 1025 ≤ fc ≤ 1150 MHz. The pulse pairs mitter stations in North America and Russia that operate are 12 µs apart and have a duration of 3.5 µs. The pulse in groups forming so-called “chains.” Each chain consists pair repetition frequency is between 5 and 150 per second of at least three stations (although four is more common). and the peak power is between 50 W and 2 kW depend- One of these in each chain is a master and the others are ing upon the equipment design. The ground equipment secondaries. Transmitter power level P is in the range receives these pulses, introduces a fixed 50-µs delay, and (400 < P < 1000 kW). then retransmits them. The retransmitted pulses are on a Each chain transmits pulses of the very specific format carrier frequency fcr = fc ± 63 MHz. of a 100-kHz carrier frequency fc having amplitude such The aircraft equipment receives these pulses and mea- that the antenna current I (t)isgivenby sures the time delay t from transmission to reception   −2(t − τ) and converts the time delay to a distance measurement D: I (t) = A(t − τ)2 exp sin(2π f t + φ) t >τ T c D = c( t − 50 µs)/2, = 0 t <τ,

where c = speed of propagation of the modulated carrier where t = clock time wave. τ = envelope to cycle difference Each ground transponder is designed to handle at least T = 65 µs 50 but typically about 100 aircraft. The pulse repetition φ = phase code parameter (radians) rate is intentionally made variable, and the interrogator φ = is designed to respond only to retransmitted pulses 0 for positive phase whose pulse-repetition rate and phase are exactly those = πfor negative phase transmitted. A = amplitude parameter P1: FYD Revised Pages Encyclopedia of Physical Science and Technology EN001F-916 May 10, 2001 10:30

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LORAN pulse signal where C = speed of propagation of LORAN signal 1.0 D = separation of master and secondary 0.8 For any given TD, the above equation describes the lo- 0.6 cus of points (LOP) for constant TD. The curve ±y(x) 0.4 satisfying this equation is a hyperbola. That is, a single 0.2 measurement of the TD for a master and any one of its 0 secondary transmitters (i.e., X, Y , and Z) locates the air- –0.2 craft along a hyperbola. Amplitude A second measurement of the time delay between the –0.4 master and another secondary TD2 results in the location –0.6 of the aircraft along a second hyperbola. In principle, the –0.8 aircraft x, y coordinates can be found by solving a pair of –1.0 equations in these two unknowns (i.e., the intersection of 0 20 40 60 80 100 120 140 160 180 200 the hyperbolas). In practice, a LORAN receiver performs Time (microsecond) optimal statistical analysis on multiple measurements of FIGURE 8 LORAN signal waveform. the TD from multiple master-secondary stations. The time of arrival of a pulse from a given transmit- ter within a chain is taken as the positive zero crossing Figure 8 depicts a typical LORAN current pulse. These of the pulse on its third cycle (i.e., approximately 30 µs pulses are periodically transmitted at an interval known as after pulse initiation). A modern aircraft LORAN receiver the group repetition interval (GRI), which interval identi- is under control of a microprocessor and associated pro- fies the chain. Each transmitting station in a chain has a grams. Under program control the receiver operates in four specific signal format consisting of the number of pulses modes: (1) initialization, (2) acquisition, (3) pulse group in a group, pulse spacing in a group, carrier phase code time reference (PGTR) identification, and (4) tracking. of each pulse, time of transmission, time between repeti- During initialization, the receiver sets parameters that will tion of pulse groups, and delay of secondary station pulse generally optimize its performance. This process also may groups relative to the master. include adjustment/tuning of dynamically programmable The LORAN-C signal propagates along the Earth’s sur- interference rejection filters. Acquisition is the process of face for relatively large distances. At the relatively low car- searching for and locating signals that have been identi- rier frequency employed, the phase and group velocities fied during initialization. Essentially, the receiver “locks can differ substantially owing to the complicated nature on to” a set of pulses such that the TDs between master and of the propagation velocity. The corresponding velocity secondary are obtained with the greatest possible accuracy variations result in temporal variations in the pulse time available at the operating conditions. The PGTR mode es- of arrival that have diurnal and seasonal components. sentially minimizes various propagation errors. Tracking In addition, the local Earth spatial conductivity varia- is the process of maintaining a fixed synchronization of the tions result in propagation time errors. Conductivity vari- receiver with the PGTR for each signal being tracked. Ad- ations of 3 or 4 orders of magnitude occur for signal paths ditional details of the operation of LORAN can be found over seawater or over arid landmasses. It is beyond the in Refs. (2–4). scope of this article to further discuss the propagation er- rors or techniques for their partial compensation. Inter- ested readers should consult Ref. (1) for a more complete VI. AUTOMATIC DIRECTION FINDING discussion. LORAN operation is based upon measurements of the One of the earliest radio navigation methods is radio di- time delay of the signal arrival from the master to the ar- rection finding. This method is based upon the directional rival time of the corresponding pulse from the secondary sensitivity of a loop antenna. Consider an antenna consist- transmitters. The LORAN receiver determines the propa- ing of a loop of conductor in a vertical plane. For a given gation time difference (TD) between these two signals. In radio transmitter at a specific distance the antenna termi- the absence of any error source and within the validity of nal voltage is proportional to cos θ where θ is the angle the planar approximation of the Earth’s surface, we have measured in a horizontal plane from the plane of the coil

      to a line through the coil center and transmitter location. 2 2 1 D D Direction finding was accomplished in an early aircraft TD = + x + y2 − − x + y2 , C 2 2 (as well as in ships) by manually rotating the antenna until P1: FYD Revised Pages Encyclopedia of Physical Science and Technology EN001F-916 May 26, 2001 14:6

346 Aircraft Instruments    a null terminal voltage was obtained. Of course, there is a(1 − e2) 3 ◦ =   =∼ + 2 2 − an ambiguity of 180 in this angular reading since the Rm 3/2 a 1 e sin FT 1 1 − e2 sin2 F 2 transmitter can be anywhere along the line orthogonal to T the coil when the terminal voltage null is obtained. In and   early receivers the transmitter location was obtained by a e2 = =∼ + 2 , triangulation with a second receiver. Rp   / a 1 sin FT 1 − e2 sin2 F 1 2 2 In a modern Automatic Direction Finding (ADF) re- T ceiver the single rotatable loop can be replaced by a pair of where FT = the geodetic latitude at a given location on coils in orthogonal vertical planes. An ADF receiver sys- the Earth’s surface. This latitude is the angle between the tem measures and displays the bearing of a station relative normal to the meridian ellipse and the equatorial plane and to the aircraft axes without operator intervention (other is the latitude used on maps. The longitude λ is the angle than tuning the receiver to the desired station transmitting measured from the prime meridian (through Greenwich, frequency). The predecessor to ADF required an operator England) to the meridian at any given point. to perform several manual steps to achieve this result. The The two radii of curvature (Rm and Rp) relate horizontal transmitter location can be found by a comparison of the components of velocity to the angular coordinates: relative amplitudes of the terminal voltages from the two ◦ VN coils. The 180 ambiguity is resolved by the use of a sep- F˙ T = R + h arate sense coil that provides a carrier phase reference to m uniquely locate the transmitter. VE λ˙ cos FT = , Rp + h where V is the component of horizontal velocity north, VII. LONG-RANGE NAVIGATION N VE is the east component of velocity, and h is altitude. For navigation using Earth-based radio systems, ordinary charts that represent navigational coordinates on a flat VIII. NAVIGATIONAL COORDINATE plane approximation are adequate. Such navigation takes SYSTEMS place over sufficiently short distances that this approxi- mation is valid. There are numerous coordinate systems for atmospheric Long-range navigation using satellite-based navigation flight navigation. The Earth centered-Earth fixed (ECEF) systems or inertial platforms require a more accurate rep- system is a set of Cartesian coordinates yi ,(i = 1, 2, 3) in resentation of the three-dimensional (3-D) geometry of which y3 lies along the spin axis and y1 lies in the prime the Earth. meridian. These coordinates are typically used in satellite- The Earth is essentially an ellipsoid of revolution about based navigation systems. its spin axis. The semimajor and semiminor axes (a,b)of Another major coordinate system is the Earth centered the Earth are inertial (ECI) system which is similar to the ECEF ex- a = 6378.137 km = 3443.918 nmiles cept that y1 is nonrotating relative to the fixed stars. This system is normally used in implementing an inertial nav- = . = . b 6356 752 km 3432 371 nmiles igation system. In this system, Newtonian mechanics are The ellipticity f and eccentricity e are valid and angular coordinates of stars are tabulated in ECI coordinates. a − b = , , f = = 0.003353 Geodetic spherical coordinates Zi (i 1 2 3) are a spherical coordinates in which Z1 is longitude λ, Z2 is and geodetic latitude, and Z3 is directed radially outward from √ the best fitting meridianal circle. a2 − b2 e = = 0.08182. a In navigational problems, it is common to define the IX. SATELLITE-BASED NAVIGATION radii of curvature Rm and Rp, where Rm is the meridian SYSTEM radius of curvature of the best fitting circle to a merid- ian section of the ellipsoid (i.e., along a plane through the Radio-based navigation is also based upon the use of spin axis) and Rp is the prime radius of curvature which is signals transmitted from satellites. There are two such the radius of the best fitting circle to a vertical east–west systems in service: (1) the U.S. Department of Defense section of the ellipsoid. These radii are given by (DOD) NAVSTAR global positioning system (GPS) and P1: FYD Revised Pages Encyclopedia of Physical Science and Technology EN001F-916 May 26, 2001 14:6

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(2) the Russian Federation global orbiting navigation In addition to estimations of position and clock bias, satellite system (GLONASS). The GPS system consists GPS receivers also estimate user velocity and clock drift of 24 satellites arranged in groups of 4 in each of 6 or- rate. These additional estimates are required on an air- bital planes inclined at 55◦ spaced 60◦ apart in longitude craft application since, in this case, the GPS receiver is and at a nominal altitude of 11,000 nmiles above the local presumed to be moving and to have changed its posi- surface (i.e., semimajor axis ≈26,600 km). tion considerably during the time required to obtain the Each satellite carries a precise (atomic) clock and repet- pseudo-range measurements. itively transmits its position and time. The user equipment The procedure for estimating aircraft position and clock consists of a receiver along with its own precise clock. By bias is to assume an initial position for the receiver and measuring the time difference δt from transmission of the clock bias (xo, yo, zo, Bo) and to find the aircraft estimated signal to its reception, the receiver obtains a measurement position at time tk (tk = kT, k = 1, 2,...): of the transit time from satellite to receiver, which yields         xo xo δx x˙ range R.           yk   yo  δy   y˙  2 2 2   =   +   + (k − 1)T   , R = Cδt = (x − xs ) + (y − ys ) + (z − zs )  zz   zo   δz   z˙ 

where C is the speed of propagation of the satellite- Bk Bo δB B˙ transmitted signal and where x , y , z are the coordi- s s s δ δ δ δ nates of the satellite. If the receiver and satellite clocks where x, y, z, B are errors in the initial estimates, were perfectly synchronized then, in principle, measure- (x˙, y˙, z˙) are the estimated user velocity vector components, ˙ ment of δt would yield the range from the receiver to the and B is the user clock drift rate. (known) satellite position. A set of three measurements The GPS navigation problem can now be formulated as to three satellites could ideally yield the solution for the a state estimation problem in which the state vector, X,is user position (x, y, z) from these measurements. However, X = [δx,δy,δz,δB, x˙, y˙, z˙, B˙]. it is, in practice, impossible to exactly synchronize these two clocks. The actual measured time difference between The standard method for solving this problem is to lin- satellite (i) clock and receiver clock time yields an esti- earize the pseudo-range equation: mate of R (denoted R ) called pseudo-range. Because of i = + α δ + α δ + α δ + δ , the receiver clock uncertainty, at least four measurements Ri Rio i1 x i2 y i3 z B are required to estimate position and receiver clock error. where The pseudo-range model is given by  = − 2 + − 2 + − 2 + , Rio = initial pseudo-range estimate Ri (x xi ) (y yi ) (z zi ) B  2 2 2 where B is a bias resulting from the receiver clock error = (xo − xi ) + (yo − yi ) + (zo − zi ) + Bo tc: and where B = Ctc, ∂ R x − x  α = i = i that is, tc is the error between true GPS time as car- i1 ∂ − x R Rio Bo ried by the satellite and the receiver clock time and C is o ∂ − propagation speed. Ri y yi αi2 = = The user position can be determined (i.e., the navigation ∂y R − B Ro io o problem can be solved) by measurement of the pseudo- ∂ − range to at least four satellites by triangulation or trilater- Ri z zi αi3 = = ∂z R − B ation. However, the accuracy of this position solution is Ro io o influenced by many factors, including the geometry of the The parameters α , α , α are the direction cosines of the satellites in relation to the user and various error sources. i1 i2 i3 angles between the line of sight from the user to satellite These errors include intentional degradation by DOD (sig- i and the coordinate axes. The linearized pseudo-range nificantly reduced in the year 2000) meant to reduce the ac- equation can be written in terms of δR where curacy to unfriendly users, propagation errors, clock ran- i dom errors, orbital perturbations, and satellite ephemeris δRi = Ri − Rio = αi1δx + αi2δy + αi3δz + δB. errors. Consequently, many more than four measurements are made to reduce errors. It is beyond the scope of this Figure 9 is a simplified illustration of the geometry for article to discuss the details of these error sources, and an aircraft moving at a constant velocity beginning at true interested readers should consult Refs. (5–7). position, xT , yT . P1: FYD Revised Pages Encyclopedia of Physical Science and Technology EN001F-916 May 10, 2001 10:30

348 Aircraft Instruments         y xk xo δx x˙ S         1     δ   ˙  yk = yo + y + − y S       (k 1)T   R01 2  zk   zo  δz   z˙  vT Bk Bo δB B˙ R02 v X0,Y0 for aircraft moving at a constant velocity vector v = d T y Predicted user position [x˙y˙z˙] . For maneuvering aircraft the solution involves time-varying estimates of V . d x xT,yT x The recursive solution to the GPS navigation problem FIGURE 9 GPS navigation geometry (simplified). is a Kalman filter which continuously estimates X. The th k estimate of X (i.e., Xk ) is based upon K previous mea- surements and estimates and is of the form The measurement model for the aircraft traveling at a Xk = Xk−1 + Kk (δRk − Hk Xk−1), constant speed from an initial estimated position (xo, yo, zo) for four satellites is given by where Kk is the Kalman filter gain and δRk is defined above. The Kalman filter gain is completed in a multistep δR = HX + e, process that is derived from known statistics of process where and measurement noise, the basic dynamics of the aircraft  T motion, and the relationship between the state and the δR11 δR21 δR31 δR41   measurements in the zero noise ideal case. The details of δ = . . R  .  these relations can be found in Refs. (8–10). δRn1 δRn2 δRn3 δRn4 In this expression n is the number of measurements made X. THE GPS SYSTEM STRUCTURE to each of the four satellites, and the matrix H is given by where The structure of the GPS navigation system consists of   three major segments: (1) the space segment (the satel- H1   lites); (2) the control segment; and (3) the user receiver  H  H =  2  , systems. The satellite must be capable of transmitting its  ···  position and the correct GPS time continuously. A ma- Hn−1 jor function of the control segment is to periodically up- load to each satellite data from which this position can be where   computed. Periodic updates to this ephemeris data are re- α11 α12 α13 1 kTα11 kTα12 kTα13 kT quired owing to orbital perturbations and changes due to   lunar–solar perturbations, air drag, asphericity of Earth’s α21 α22 α23 1 kTα21 kTα22 kTα23 kT Hk =   gravitational potential, and magnetic static-electric forces α α α 1 kTα kTα kTα kT 31 32 33 31 32 33 in obit. α α α α α α 41 42 43 1 kT 41 kT 42 kT 43 kT The control segment configuration is depicted in k = 0, 1,...,n − 1. Fig. 10. The monitor stations receive the GPS signals (same as the user). These signals can be used to evalu- The state vector X is given by ate ephemeris errors and satellite clock errors. These sta- X = [δx δy δz δB x˙ y˙ z˙ B˙ ]T , tions are located at Colorado Springs, Kwajalein, Diego Garcia, Ascension Island, and Hawaii. These stations mea- and e is the 4 n × 1 dimensional error vector. sure pseudo-range values from the satellites as they come The solution to this problem for finding X can be ob- into view. These measurements are used to determine tained in a “batch” mode, in which data is collected for n ephemeris and clock errors. In addition, these stations samples and found as the ordinary “least-squares” (OLS) monitor local meteorological data that is useful for cor- solution, or the solution can be found recursively. The OLS recting for tropospheric delays. The data and corrections solution is given by obtained by these monitor stations are sent to the master − control. X = (H T H) 1 H TδR. The master control uploads navigation messages to the Once a solution has been reached for X, the position of satellites via the stations at Ascension, Diego Garcia, and the aircraft for all time xk , yk , zk )isgivenby Kwajalein. The satellites are continuously controlled via P1: FYD Revised Pages Encyclopedia of Physical Science and Technology EN001F-916 May 10, 2001 10:30

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Handover AFSCF Satellite data MCS data link Master Time Monitor control USNO coordinates station station

Data DMA

Upload stations

Control segment configuration FIGURE 10 Control segment configuration.

the master control to avoid cumulative errors that would pressure of water vapor in an approximate relationship occur in the absence of this control function. [Refs. (11 and 12)] as represented by index of refraction, n: There are numerous error sources in GPS navigation so-   K K Pw lutions, including satellite ephemeris errors, propagation n =∼ 1 + 1 P + 2 errors and uncertainties, and clock errors. These errors are T T exacerbated by poor geometry, which increases the uncer- where P = atmospheric pressure tainty in position. Such uncertainty is represented quan- T = absolute temperature titatively by a parameter known as geometric dilution of Pw = partial pressure of water. position (GDOP). K1,2 = constants The ephemeris errors result from imperfect prediction of satellite position. Propagation errors and uncertainties The path length change due to refraction L is given result from ionospheric and tropospheric refraction varia- by  tion. The ionospheric refraction is determined largely by R free-electron density and carrier frequency. The index of L = (n − 1) ds, refraction, n, for propagation through the ionosphere is o defined as C where R = distance to the satellite n = , ∼ vφ = pseudo-range s = coordinate along the propagation path where vφ is the phase velocity. At any carrier frequency, f , the index of refraction is This expression can be rewritten approximately in terms given by φ of altitude h and elevation angle o to the satellite:    2 H fc n − 1 n = 1 − , L = dh, f φ ho sin o

where fc is the plasma frequency where H is the satellite elevation above the Earth. If the atmosphere is assumed to be exponential, then 2 1 Nee ∼ ∼ −bh fc = = 9 Ne n − 1 = (no − 1)e , 2π mεo where (for a standard day)

3 =∼ . where Ne = electron density (number/m ) no 1 00032 = e electron charge b =∼ 0.000145/meter. m = mass of electron εo = permittivity of free space Typical values are L =∼ 2.2 m for φ = 90◦ On the other hand, tropospheric refraction is indepen- o ∼ ◦ dent of carrier frequency, but is influenced by the partial = 25 m for φo = 5 , P1: FYD Revised Pages Encyclopedia of Physical Science and Technology EN001F-916 May 10, 2001 10:30

350 Aircraft Instruments

The influence of satellite geometry is given via the are then transmitted to all users in the vicinity of that GDOP. The GDOP can be computed from the matrix of receiver. LAAS, if implemented, should yield much higher th direction cosines to the satellite, Hi , where the i row of accuracy than WAAS, although it will require a larger H is infrastructure investment. H = [α α α − 1] i i1 i2 i3  −  = T 1 . XIII. GPS INTEGRITY AND AVAILABILITY GDOP trace Hi Hi Then the rms error is given by It has been proposed that GPS be used as the sole naviga- tion means for the U.S. national airspace system. In order σ = GDOP σ , o for this to be achieved, there are several major issues to where σo is the minimum position error that results for be considered, including (1) accuracy, (2) integrity, (3) optimal satellite geometry and is due to the error sources availability, and (4) continuity. The accuracy must be suf- listed above. ficient to safely achieve the navigational function, partic- ularly with respect to instrument approaches in inclement weather. System integrity is the capability of the system XI. WAAS to detect anomalous signals that could cause errors in ex- cess of that allowed for safe use of the system. Availabil- The accuracy of GPS navigation can be improved by a ity means that the signal is present at a level necessary to scheme that, at least partially, corrects common errors provide the navigational function for the entire duration of (bias errors) due to causes outside of the receiver. These the relevant portion of the flight. Continuity means that the error sources include (1) errors that are intentionally in- navigational signal is present at the required level without troduced by the DOD, (2) ionospheric delays, (3) tropo- interruption during the flight. spheric delays, (4) ephemeris errors, and (5) satellite clock At the present time, GPS by itself does not satisfacto- errors. rily resolve these issues. However, the FAA has defined three types of services related to GPS: (1) a multisensor system, (2) a supplemental system, and (3) a required nav- XII. GPS ACCURACY AUGMENTATION igation performance (RNP) system. In a multisensor navi- gation system, GPS with any available augmentation (e.g., The accuracy improvement is achieved via a method DGPS) can be used for navigation only after it has been known as differential GPS or (DGPS). The concept for compared for integrity with another approved navigation DGPS involves a reference GPS receiver located at a pre- system (e.g., VOR) on board the aircraft. In a supplemental cisely surveyed site that can calculate errors in pseudo- system, the GPS (with augmentation) may be used with- range and pseudo-range rate. These errors can then be out comparison to another approved navigation system, transmitted via a suitable carrier frequency to all partici- but another approved navigation system must be available pating users within a specific geographic area. on the aircraft and usable in case GPS is not available. DGPS methods are commonly known as augmentation An RNP system is one that satisfies all requirements for schemes and are generally divided into two types depend- the navigation phase without the need for any other navi- ing upon the size of the geographic area covered by the gation equipment on board. An RNP system may include system. These DGPS augmentation systems are (1) wide one or more navigation systems, e.g., GPS with inertial area augmentation systems (WAAS) and (2) local area navigation (see next section). augmentation systems (LAAS). The WAAS system consists of a master station (WMS), several reference (monitoring) stations (WRS), and a num- XIV. RECEIVER AUTONOMOUS ber of geostationary communication satellites (GEO). The INTEGRITY MONITORING (RAIM) reference stations all continuously track the GPS and GEO satellites and relay tracking information (via land links) One of the important requirements for the GPS system to the master station. Error corrections are determined by to provide independent (stand-alone) navigation is the calculation and are relayed to users via the GEO. In this need for the system to continuously monitor the signal system, the corrections are transmitted on one of the GPS integrity. The method for achieving this is known as re- carrier frequencies. ceiver autonomous integrity monitoring (RAIM). The goal LAAS augmentation involves a multitude of receivers, of RAIM is to detect and isolate an out-of-tolerance signal each serving a local area. Errors detected by these receivers that causes a navigational error in excess of that allowed P1: FYD Revised Pages Encyclopedia of Physical Science and Technology EN001F-916 May 26, 2001 14:8

Aircraft Instruments 351  for the phase of flight in progress. It is assumed that the t ω = ω τ τ + ω navigation solution has been obtained and that five or more i ˙ i ( ) d i (0) 0  satellites are in view. t The RAIM algorithm is based upon error residuals from φi = ωi (τ) dτ + φi (0) i = 1, 2, 3 the least-squares (or Kalman filter) solution. These error 0 residuals have been denoted X above and are used to cal- culate the sum of squared errors (SSE). whereω ˙ i = angular acceleration about axis i ωi = angular velocity about axis i = T X , SSE X W φi = position about axis i where W is a weighting matrix that is normally chosen in the design of the receiver (note: W could be selected The implementation of inertial navigation is dependent to be the identity matrix). The SSE is a scalar error that upon the choice of navigational coordinates, as well as generally is small for reliable signals and relatively large the aircraft altitude in relation to these coordinates, and in the event of an anomalous signal condition. The GPS the coordinates of the accelerometers. The navigational system has sufficient integrity for use if coordinates most commonly used for inertial navigation are the geodetic wander azimuth coordinates (GWA).This SSE < threshold value Cartesian coordinate system has z3 vertically up and z2 at an angle α relative to true north with z1 z2 forming a and is not suitable for use if tangent plane to the Earth reference ellipsoid. Inertial navigation systems operate by having a stabi- SSE > threshold value lized platform that maintains a fixed orientation in inertial where the threshold value depends upon the phase of flight space isolated from angular motion of the aircraft. The in progress. That is, the threshold for approach and landing platform is either maintained physically via gimballed phases is smaller than for enroute navigation phases. gyroscopes or analytically via computations made from gyroscopes (known as “strapdown” gyroscopes) that are physically attached to the aircraft structure. For a gimballed gyroscope platform, the accelerameters XV. INERTIAL NAVIGATION have axes of known orientation. For strapdown systems, an equivalent platform orientation is computed from cal- Inertial navigation is a method of calculating the position culated coordinate positions. and velocity of an aircraft based upon measurements of Transformation of coordinates is via a matrix C of di- acceleration. Such a system can operate without external rection cosines. For example, the transformation of any measurements from Earth or satellite radio signals, but vector V from ECEF coordinates to GWA coordinates is it does require initialization along and around all axes. given by Velocityand position components are found by integrating 