40 to 60
o
o
x
DME R
RV
OR
H - HVOR
Figure 5.12: The ‘Cone of Silence’
Another, more generally accepted, rule-of-thumb to determine the coverage of a
VOR station is [5]:
Range = 1.2
p
h +
p
hVOR
(5.29)
where Range expresses the VOR coverage in nautical miles, h is the height of the
aircraft above the ground, measured in [ft] (this differs from equation (5.28), which
expressed the altitude in meters above sea-level!), and hVOR is the height of the VOR
station above the ground, also measured in [ft]. The latter term is often neglected.
5.2.3 VOR accuracy
The nominal VOR signals become distorted by VOR noise and steady-state errors.
There are two types of systematic errors: ground station errors and airborne equipment
errors. Each of these errors comprises both the equipment and antenna errors
and site or location errors. ICAO has established the following rules [2, 7]:
1. the error of the airborne equipment must be smaller than ±2 at a distance
from the antenna of four times the wavelength and at an elevation-angle of 0
to 40, and
2. the maximum error for the ground station is ±3.5.
70 Chapter 5. Radio-navigation, sensors, actuators
Height [ft] VOR range [NM]
1000 50
5000 92
20000 182
30000 220
3000 75
5000 95
Table 5.3: VOR coverage based on two different flight tests [7]
Ref.[7] presents some data about ground equipment errors, obtained from actual
measurements. According to this source, the steady-state errors typically lay somewhere
in the range from ±1.4 to ±2.5. There are also other errors of a more random
nature, which are caused by e.g. variations of supply voltage of the ground and/or
airborne equipment, temperature changes, inaccurate instrument reading, etc. Flight
tests using commercial aircraft yielded the following approximative values for overall
VOR system error [7]:
# < ±1.7(68% of the tests)
# < ±3.4(95% of the tests)
# < ±5.1(99.7% of the tests)
Since ref.[7] is already somewhat outdated, modern VOR stations and receivers may
be more accurate than these figures suggest.
5.3 Other flight navigation systems
The equations from the previous section allow us to create a simulation model of
an aircraft that is operated in a conventional air-traffic environment, using VOR and
DME systems for guidance along airways, standard arrival routes, and standard departure
routes. However, in modern air-traffic control environments, it has become
increasingly common to define ad-hoc flight-paths along great circles1 between fixed
(sometimes arbitrary) waypoints, rather than fly along pre-determined airways, defined
by VOR radials.
The geometric position of modern airliners is computed by the Flight Management
System, using integrated information from DME stations (possibly VOR stations),
the Inertial Reference System (IRS) from the airplane, and sometimes also
navigation information from Global Positioning System (GPS) satellites. In this setup,
the IRS usually offers short-term position information, which remains accurate
even when manoeuvring, while the radio and/or satellite navigation signals offer
longer-term position updates which nullify the long-term IRS drift.
1A great circle is a circle on the surface of a sphere (thus on the surface of the Earth or the celestial
sphere) which is formed as the result of the inter-section of the sphere and a plane passing through the
center of the sphere.
5.4. Sensors, Actuators, Flight Control Computer 71
In the foreseeable future, the ILS is likely to remain in use as the main precision
approach system, even though in the late 1970’s ICAO declared the far superior Microwave
Landing System (MLS) to become the precision approach system for the
21st century. In practice, the MLS has only been applied in a few specialized locations
where operational requirements dictated a need for a combination of precision
and accuracy that, at that time, only the MLS could provide. Nowadays it seems
more likely that the role of the ILS will some day be taken over by satellite-based
landing guidance systems. Precision approach guidance using GPS is already feasible
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