Chapter 7
AIRCRAFT NAVIGATION
Keywords. Navigation, Dead-reckoning, Position-xing, Celestial naviga-
tion, LORAN, VOR
7.1 INTRODUCTION
Navigation may be considered as the art of directing the movement of a
vehicle from one place to another. It is an art practiced by all who travel
but its development is rooted rmly in the fundamental laws of science. In
todays context it can be formally dened as the determination of a strategy
for estimating the position of a vehicle along the ight path, given outputs
from specied sensors.
In the early days, when man-made vehicles were surface bound (either
on land or in the sea) and they seldom ventured far beyond easily recogniz-
able landmarks, the act of navigation could be carried out by humans using
their senses to determine direction distance, speed, and position. As vehicles
became more and more sophisticated and their eld of operation expanded
to realms beyond the perception of limited human senses sophisticated nav-
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igation instruments became necessary. Instead of known landmarks these
instruments used information learned from celestial bodies, certain distant
objects on the surface of the earth, and many other sources of information
to carry out the job of navigation.
In these lecture notes we shall exclusively focus on the navigation of
aircraft. Whenever a purposeful change in location has to take place for an
aircraft the following questions must be asked and answered:
Where is the aircraft now?.
(or, more specically) where is the aircraft now with respect to where
it should have been?
These questions are answered by a navigation system. There are a number
of reasons why sophisticated navigation systems have become so important
in modern times. Some of them are.
Time lags between measurement and decision needed to be reduced.
Number of aircraft in a given airspace has increased manifold in the
past few decades.
Safety requirements have become crucial.
A navigation system may provide information in a variety of forms, ap-
propriate to the needs of the aircraft. If the information is primarily for
the benet of the crew. it involves some type of display. other outputs,
however may involve steering signals sent directly to the autopilot or digital
information sent to a central computer. However in the modern context one
would consider these systems as navigation-cum-guidance systems. Some of
the forms that this information takes are given below.
Position Information: The basis of virtually all navigation outputs is po-
sition. position can be given in geographic coordinates-geodetic latitude (),
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geodetic longitude (), and altitude (h) - as in en-route navigation for long
distance ights, or as polar coordinates with a ground-based navigational aid
as the origin, as in terminal areas.
Steering Information : Due to crowding of the airspace one of the major
tasks that an aircraft pilot has to perform is keeping out of the way of other
aircraft. The technique widely used now-a days involves the assignment, to
each aircraft, of a block of air having established dimensions called lateral,
longitudinal and vertical separation. The exact dimensions depend on the
instruments in use, the speed and character of the aircraft and the ight
environment too. This block moves at the speed indicated in the aircrafts
ight plan. It is the task of the pilot to remain within this block. Conse-
quently the pilot needs to know, at any time, where he is with respect to
this block of air. The desired output is a continuous, real-time indication of
where the aircraft is with respect to the center of the assigned block. With
intermittent xing (in which intermediate checking points are established),
the total error for which the system must allow consists of the error in posi-
tion determination, plus the accumulated error between measurements and
action based on determination of position and interpretation of results.
Displays : Navigational information must be made available to the pilot
in a form suitable for his use. when navigation was mainly a manual opera-
tion, the usual display consisted of a chart, or plotting sheet, on which lines
of position and xes were plotted with higher speeds and increased trac
density, such a display is no longer adequate. Modern displays are basi-
cally computer-based and depend on some kind of CRT display, or advanced
at planar color displays. HUD (Head Up Display) is one such electronic
and optical instrument which provides the pilot with such essential functions
as aircraft performance information, navigation and landing guidance, on a
single display in symbolic form.
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7.2 TYPES OF NAVIGATION
All position-determination schemes can be classied as either dead reckoning
or Position xing.
Dead Reckoning
Dead reckoning consists of extrapolation of a known position to some
future time. It involves measurement of direction of motion and distance
traveled. The actual computation is performed by taking the last known
position and the time at which it was obtained, noting average speed and
heading since then and the present time. The speed is usually resolved to
get North and East components and each is multiplied by the time elapsed
since the last position to get distance traveled. This can be added to the
initial position to get the present position. To perform all these functions the
Navigation system requires the following instruments: (1) A speed measuring
device (2) A heading sensor (3)A timer and (4) A computer.
Measurement of speed is usually done using an air-speed meter (which
measures the aircrafts speed relative to the air and does not take into account
the speed of the air relative to the surface of the earth), or by measuring the
ground speed using doppler eect (this is done by transmitting three or four
beams in dierent directions toward the ground and measuring the aircrafts
relative velocity along these beams - see Problem 1 at the end of the chapter).
Heading can be measured using a simple magnetic compass, a gyro-magnetic
compass, or a gyrocompass.
The dead-reckoning computations are done as follows: Assume that the
measurements of ground speed Vg and true heading T has been done accu-
rately. Then, with reference to Fig. 7.1,
t
Vnorth = Vg sin T Y Yo = Vnorth dt (7.1)
o
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t
Veast = Vg cos T X Xo = Veast dt (7.2)
o
where, t is the measurement interval and (Y-Yo ) and (X-Xo ) are the distances
Figure 7.1: Dead-reckoning computations
traveled due north and due east during this measurement interval. Notice
that a simple integration of unresolved ground speed 1/Vg would give curvi-
linear distance traveled but would be of little use for determining position.
Thus, one must integrate the velocity.
The above equations are extremely simplied and are given only to impart
an idea of the principle on which the dead reckoning system works. In reality
the actual dead reckoning computer must also account for cross winds, the
kinematics of the aircraft, its angular orientation, the geometry of the earth
and its attendant gravitational eects, and many other factors before it can
extrapolate in a reasonably accurate manner.
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Position Fixing
In contrast to dead reckoning, position xing is the determination of the
position of the craft (a x) without reference to any former position. There
are three basic methods of xing position : (1) Map reading (2) Celestial
navigation and (3) Measuring range and/or bearing to identiable points.
Map reading involves matching what can be seen of the outside world
with a map and is the traditional method of position xing on land and is
also used by general aviation in clear weather. Modern systems adopting this
technique uses a radar to obtain a picture of the ground from the air and a
computer matches it with a map stored in the form of a digital land mass
database. These system are called terrain referenced navigation aids.
Celestial navigation has been used by mariners for centuries. The basis
of celestial navigation is that if the altitude of a celestial object (measured in
terms of the angle between the line-of-sight and the horizontal) of a celestial
object is measured then the observers position must lie on a specic circle
Figure 7.2: Celestial navigation
(called the circle of position) on the surface of the earth centered on the
point on the earth which is directly below the object. This is shown in
Fig.7.2. If the time of observation is noted and the celestial object is a star
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then this circle can easily be found using astronomical tables and charts.
Sightings on two or more such celestial objects will give two or more such
circles of position, and their intersection will give the position of the craft.
Though in the early days some aircraft did use celestial navigation this has
been abandoned nowadays in favour of better navigational aids. However, we
shall show that its basic principle (that of intersection of circles of position
to determine the exact position) will be used in a more general form in more
advanced navigation system.
Range and bearing navigational techniques are the basis of most modern
position xing systems. They use modern electronic equipment for doing this
kind of measurement. Through individual measurements of range and bear-
ing, a line of position a line on which the craft is presumed to be located-is
established. In principle, it is somewhat similar to celestial navigation. The
line might be a small circle, great circle, hyperbola or some other curve con-
stituting the intersection of the surface of the earth (or a concentric surface at
the altitude of the aircraft) with a plane or a cone or a hyperboloid etc. The
common intersection of two or more nonparallel lines of position constitutes
the x. If the lines are determined at dierent times, then one or more of
them must be adjusted for the assumed motion during the interval provide a
running x. Occasionally, an actual position is not needed, a line of position
being adequate to ensure safety. This is called homing. The method is not
suitable when other aircraft are in the vicinity and a means of avoiding them
is not available.
Before we go on to describe some widely used navigational aids we would
like to discuss a few important points. Dead reckoning has been characterized
as the basis of all navigation with position-xing constituting a method of
updating it. Actually, dead reckoning and position xing complement each
other, each providing an independent means of checking the accuracy of the
other. Where position xing is intermittent with relatively long intervals
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(often hours) between xes, dead reckoning is appropriately considered the
primary method. If xes are available continuously or at very short intervals
(e.g., once each minute), the primary method might then be either dead
reckoning or position xing or an integrated output of both.
Another classication of navigation may be according to the portion of
ight involved. Usually, this classication is done as En-route phase and
terminal phase.
In the en-route phase a series of ground-referenced short distance aids
with relatively high accuracy but with coverage limited to line-of-sight dis-
tances may be used. The International Civil Aviation Organisation (ICAO)
recommends, as standard short-distance aids the very-high-frequency omni-
directional range (VOR) and distance measuring equipment (DME). Over
oceans and underdeveloped land areas such as polar regions (having no dis-
tinguishable land marks), long distance aids which are of lower accuracy than
short distance aids are used. In most cases they provide intermediate accu-
racy xes for use with dead reckoning. But with the increasing density of air
trac in such regions, automatic dead reckoning units of greater accuracy
become increasingly important.
In the terminal phase when an aircraft approaches terminal and proceeds
to a landing , it enters an area of converging tracks and high density traf-
c where high accuracy both horizontally and vertically becomes essential
with continuous indication. Navigation requirements become accentuated as
visibility limits are lowered , to provide service in virtually any weather.
In the next few sections we shall discuss a number of navigation systems
currently in use for aircraft navigation.
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7.3 THE LORAN SYSTEM
The LORAN (Long-Range-Navigation ) is a position xing aid. It operates
on a single frequency of 100 Khz and has a long range (greater than 1200
km). The latest version of this system called LORAN-C is very widespread,
having many chains throughout the continental USA, much of Europe and
the Middle East. The European countries, as well as the Russians have
conrmed their intention to use and expand LORAN-C (and the Russian
equivalent called Chayka)as a primary radio-navigation source. On August
6 1992, six nations in the European Community signed a treaty to expand
LORAN-C coverage. Installations of LORAN-C chains by the governments
of India and China indicate the worldwide interest in LORAN.
The basic principle of LORAN is simple. Each LORAN chain consists of
a master station and two, three or more slave stations. The aircraft receiver
must be tuned to select a chain (of master and slave stations) by manual or
by computer selection.Each chain transmits a sequence of pulses. First the
master and then after a xed coding delay, the slaves (Fig.7.3). Each slave in
a chain has a unique coding delay that allows the aircraft to receive its signal
before any other slave transmits. Usually the masters signal is received by
the slaves and retransmitted after the specied coding delay. The number of
pulses (eight or nine) and the coding delay identies the master and slaves of
a given chain. the navigation computer in the aircraft is fed with the position
information of the master and slave stations in a chain.
The receiver in the aircraft measures the dierence between the time of
arrival of the pulse from the master station and the slave stations. The
time dierence is measured using the third RF cycle in each pulse as the
reference point (see Fig.7.3). The locus of points of constant time dierence
is a hyperbola-like line-of-position on the reference ellipsoid which models
the surface of the earth. By using the master and a second slave a second
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Figure 7.3: The LORAN-C pulses
hyperbola is obtained. The two hyperbolas intersect at the aircrafts position
and at an ambiguous second point(Fig.7.4). The ambiguity can be resolved
by using another slave and obtaining a third line-of position. However, the
use of too many lines-of-position can lead to a possible region of location
of the aircraft rather than a single point. this region is called a cocked hat
in the marine terminology (Fig.7.5). This can also occur when a number of
navigation aids are used (multi-sensor navigation). Due to the hyperbola-like
lines of position LORAN is also called a hyperbolic navigation system.
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Figure 7.4: LORAN lines-of-position
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Figure 7.5: The cocked hat
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