Introduction
1.5 The regulations
accident damage. The courts' interpretation of all rules and regulations is governed by an accumulated body of national and international case law. In recent years, the thrust in many jurisdictions has been to stress the responsibility of senior management to provide appropriate tools for the job and to ensure by formal procedures that they are safely and correctly used by trained personnel.
Imagine a fishing vessel (FV) has collided with a coaster. The evidence of its officer of the watch, confirmed by the voyage recorder, is accepted that although diligently observing the radar, which was correctly set for the severe sea clutter, the FV was undetectable. Apportionment of blame might depend on the court's findings on these questions.
• Was the radar capable of detecting the target?
• Ought the coaster owners to have known by how much the long feeder to the high scanner would degrade the radar's performance?
• Ought they to have known that this radar outfit with its small high scanner was unsuited to the small targets and rough weather prevalent in the coaster's trading area?
• Should the skipper have known that his inferior radar reflector, incorrectly mounted, would jeopardise his vessel's detectability?
2. IEC 60936-2, Maritime navigation and radiocommunication equipment and systems - Radar - Part 2: Shipboard radar for high speed craft (HSC) - Perfor- mance requirements - Method of testing and required test results. This standard is, in effect, an extension of the above, and describes the additional require- ments for radar which are to be fitted to HSC. The minimum range and range discrimination requirements are more demanding and the antenna rotation rate is higher (40 rpm minimum). This standard also details the scenarios that the associated ATA or ARPA must comply with.
3. IEC 60936-3, Maritime navigation and radiocommunication equipment and systems - Radar - Part 3: Radar with chart facilities - Performance requirements - Method of testing and required test results. This standard is new, published in 2002. It details the testing standards and test results required for radars with charting facilities. It also defines what information can be displayed: in effect, it is only selected parts of the system electronic navigation chart (SENC) that may be shown. The most important point to make here is that it is a radar, not a chart display system, and it is vital that the radar information should not be masked or degraded in any way when the chart information is added to the display.
4. IEC 60872-1, Maritime navigation and radiocommunication equipment and systems - Radar plotting aids -Automatic radar plotting aids (ARPA) - Methods of testing and required test results. This standard details the minimum number of targets we have to track, the tracking accuracy to be achieved, alpha-numeric data to be displayed for the tracked targets, details on guard zones and acquisi- tion zones, operational warnings, trial manoeuvre details, interfacing, symbols and other specifications. [Based on IMO Resolution A.823:1995, performance standards for automatic radar plotting aids (ARPAs).]
5. IEC 60872-2, Maritime navigation and radiocommunication equipment and systems - Radar plotting aids -Automatic tracking aids (ATA) - Methods of test- ing and required test results. The ATA specification is very similar to that of the ARPA, except that the ATA has to track a minimum of 10 targets compared to the ARPA's 20. Also, for the ATA, trial manoeuvre and history dots are not required.
6. IEC 60872-3, Radar plotting aids - Electronic plotting aids (EPA) - Methods of testing and required test results. This is the simplest of the three plotting standards. EPA is a manual plotting system. Again, the standard defines how many targets are to be manually plotted, how the information is to be displayed, symbols to be used, accuracy to be required and other specifications.
7. IEC 60945, Maritime navigation and radiocommunication equipment and systems - General requirements - Methods of testing and required test results.
This standard deals with issues such as environmental testing for heat, cold, humidity, vibration and corrosion. It also deals with electromagnetic emis- sions and susceptibility to electromagnetic interference, illumination of controls, compass safe distance, equipment manuals and acoustic noise.
IMO's 2004 radar review will doubtless lead to the amendment of IEC 60936 and IEC 60872.
1.5.2 Radar for craft outside SOLAS
These radars, carried voluntarily, may comply with a recent performance specifica- tion, IEC 62252 EDl Maritime navigation and radiocommunication equipment and systems - Radar for craft not in compliance with IMO SOLAS Chapter V - Per- formance requirements and methods of test and required test results. Summarising, three classes of radar, A, B and C, are recognised and may use the 3 or 9 GHz bands.
Scanner first sidelobes should not exceed -2OdB (class A) otherwise — 18dB. When mounted at 7.5m, with normal propagation and no clutter, the radars should pick out the following targets on 8 out of 10 scans:
Ground rising to 60 m: Class A 9 nmi; classes B and C 5 nmi.
Ground rising to 6 m: Class A 5 nmi; classes B and C 3 nmi.
Radar reflector, RCS 400 m2 at height 7.5 m: Class A 5 nmi; classes B and C 3 nmi.
Radar reflector, RCS 10 m2 at 3.5 m: Class A 2 nmi; classes B and C 1 nmi. Minimum ranges: Class A 50 m, class B 60 m, class C 75 m.
Radar reflector, RCS 5 m2 at 3.5 m: Class A 1 nmi, classes B and C not applicable. In sea clutter a target of 200 m2 (class A) otherwise 400 m2 should be detected at 100 m to 1 nmi on 5 of 10 scans.
Display effective diameter: Class A 150 mm, class B 85 mm, class C 75 mm.
1.6 Theory and calculations
1.6.1 Sources
No book of this sort could be written without reference to several good textbooks such as those by Barton [15], Kingsley and Quegan [16] and Skolnik [17]. These and numerous papers treat detection as part of radar or communications theory.
Our text references all sources of important quantitative data, but it is impossible to reference every qualitative statement, many of which have been absorbed by the author over the years. Readers needing more depth should go to the relevant textbook chapters. The textbooks are generally well indexed and contain extensive bibliogra- phies, routing interested readers to the specialist literature, which is voluminous but often difficult for the layman. Unfortunately, most textbooks either generalise by including aircraft, military jammers and other problems of no interest to us, or demand deep prior knowledge of electronics and mathematics. We shall consider only factors likely to have some practical significance, mentioning matters of purely academic interest only where necessary as a step to solution of some practical problem. We have aimed always to give sufficient theory to highlight what actually happens, the conditions under which results are valid and the likely residual error in calculations, and have tried to be consistent in terminology. Readers wishing to brush up on their basic understanding of electronics may find Bishop [18] or Hagon [19] useful.
Detectability depends on aspects of radar engineering, navigation, meteorology, oceanography and statistics. We have tried to give a straightforward account assuming no prior knowledge of these subjects. All of them abbreviate their common techni- cal statements using jargon, which we shall explain as we go along. For example, the navigator might ask 'At what range should our X-band radar raise a panamax
bulker loaded to her WNA marks?' and the engineer might answer ' 12 miles assum- ing four-thirds Earth and RCS 4OdB square metres.' The value of this jargon is shown by the long-windedness of these technical sentences in plain speech: 4At what maximum range should our radar lying in the marine 9 billion cycles per second frequency band display the radar reflection of a ship whose size is the maximum allowable in the Panama Canal and designed for carriage of bulk cargo, when laden to the winter North Atlantic load-line mark on her hull?' and 'At 22 km, assuming the rate of change of refractive index with height of the atmosphere is such that if the Earth were assumed to have | its actual radius radar rays would travel in straight lines, and she reflects equivalently to a metal sphere of silhouette area 10 thou- sand square metres.' The more important jargon terms are defined in the Glossary, Appendix 1.
1.6.2 Mathematics and units
We have tried our best to keep the inevitable mathematics of the calculations as simple as we can. This approach leads to a few differences from the standard treatment of some topics, indicated in the text. Some of the other possible treatments give slightly higher accuracy at the cost of more difficult mathematics, but the uncertainties surrounding the environment between the radar and its targets, as well as those within some of the targets, usually swamp any approximations of our approach. Refer to Chapter 13 for comments on accuracy of calculations. Wide use will be made of decibel (dB) notation, explained in Chapter 2, Section 2.1.7.
Scientific writing uses SI (Systeme International des Unites) units,12 formerly called the rationalised metre-kilogram-second (MKS) system, whose base units are: length (metre, symbol m), mass (kilogramme, kg), time (second, s), electric current (ampere, A), temperature (kelvin, K = degree Celsius + 273.3); also amount of substance (mole, symbol mol) and luminous intensity (candela, cd), which do not concern us. The radian (rad) of plane angle and the steradian (sr) of solid angle are supplementary units. Derived units for all other physical quantities use the above in a manner which minimises constants of proportionality. Examples are the newton, the measure of force, dimensions m kg s~2, and the volt, the measure of electric potential, m2k g s "3A -1.
We retain some everyday non-SI units: 1° = 27r/360rad ~ 0.001745 rad, 1 foot = 0.3048 m. The nautical mile remains in widespread marine use, including radar display scaling (although kilometres are preferred for river radar), and is often abbreviated n.m. but to avoid confusion with nanometres (10~9m) we prefer nmi. 1 cable is 0.1 nmi, its use generally inferring an approximation. Relationships are: 1 nmi = 1 min of latitude. Napoleon's savants defined the metre as 10~7 the distance from the North Pole to the Equator, through Paris; by which 1 nmi — 107/(60 x 90) m = 1851.85 m. (The metre has since been redefined as the dis- tance travelled by light in vacuum in 1/299 792 458 s and 1 nmi as 1852 m exactly).
12 Units and Symbols for Electrical and Electronic Engineering, an IEE Guide (Institution of Electrical Engineers, London, 1997).
If once upon a time a foot represented 0.01 s of latitude, the modern foot is 1.3 per cent short. The statute mile is 5280 ft, 0.869 nmi or 1.609 km. Our calculations will usually prefer km to nmi to minimise tedious conversion factors.
Bearings are either True (relative to the North Pole) or relative to some stated reference such as ship's head (i.e. centreline). With wide use of gyrocompasses, Magnetic North is less used. A point (of the compass) is 360/32 = 11.25°, used by mariners for rough estimates. Grads, 400 to a circle, milliradians and circular mils (6400 to a circle) are not used in civil marine.
We do not follow a forthcoming ISO standard, ISO 19018, which defines many navigational terms in a consistent manner. It includes the nautical mile (NM, but abbreviated as M on charts) as the fundamental length; 1 NM = 1852 m. 1/10 NM is 1 cbl (cablelength, also named cable). The unit of speed is the knot (kn): 1 kn = 1 NM/hr. The standard uses abbreviations RM, H up, C up, N up for relative motion, ship's head up, . . . course up, . . . north up of displays. For details see Junge,13 on which this paragraph is based.
For convenience, we often use practical units; ranges in kilometres, wavelengths in centimetres, antenna beamwidths in degrees, transmitter powers in kilowatts, pulse- lengths in microseconds. But except where definitely stated, our formulae always express angles in radians, lengths (wavelength, range, etc.) in metres and times in seconds. That is, we use SI except where other measures are widespread - an example is rainfall rate, quoted in mmh"1 rather than kgm~2 s"1. Always remember to make appropriate conversions', for example, in calculations 1OkW (10000 W) transmitter power must be written 104 W or preferably in scientific notation as 10 x 103 W, and
1.0° scanner beamwidth must be put as 0.01745 . . . rad.
The basic units often give inconveniently large or small numbers, for example, frequency 60000000 s"1, or current 0.0007 A. These zeros and 'damned dots' are a fruitful source of error - the result of a calculation may be dead accurate apart from being a thousand times too big! Prefixes are applied every 103: giga (G) = 109, mega (M) = 106. The smaller multipliers use lower-case letters: kilo (k) = 103, milli (m) = 10~3, micro (|x = mu) = 10"6, nano (n) = 10~9, pico (p) = 10"12. Other multipliers in common use are the centimetre (cm), 10~2m; decibel (dB), 10"1 bel, and for atmospheric pressure the hectopascal (hPa), 102 Pa.
Inadvertent use of mixed units is productive of error in calculations and unfortu- nately not all information sources clarify their units. The author has been caught out often enough to make no apology for insertion of units after equations - especially when non-SI - for avoidance of doubt, when purists would deem them unnecessary.
Where no units are stated, SI units are to be understood.
The electrical units - volt, amp, ohm, watt, farad, henry, etc. - form a coherent set within the SI system, so when we write V = IR we do not need to add that the answer is in volts when current / is in amperes and resistance R in ohms. The fly in the ointment is frequency, where 2n often sneaks in. Radian frequency (co = 2nf) merely
H. Junge, "Harmonisation of navigational terms. Synopsis of ISO/19018/Final/draft." Seaways, the International Journal of the Nautical Institute, April 2004 p26.
transfers 2TT to formulae involving wavelength, so we generally retain conventional (cyclic) frequency, generally referred to simply as 'frequency', / (Hz) and put up with a sprinkling of 27rs in expressions.
We write log(jc) for the common logarithm log 10 Qt), having base 10, of a quantity x; and ln(x) for the natural logarithm of x9 base e. So In (JC) is identical to log£(jc), where the Euler number e = 2.71828...; Iog10(jc) = 0.4343 . . . In (JC); ln(jc) = 2.3025... log(;c). Only when there is specific need to emphasise the base would we add the subscripts. Scaling of graphs within figures is always linear except when axes are specifically indicated as, for example, 'log scale'. Many of our graph axes run between non-zero quantities, with suppressed zero.
1.6.3 Basis of performance calculations
Equipment manufacturers rarely divulge the exact strategies they use for the various steps of the detection process, particularly now that maintenance is by exchange of printed circuit boards or other lowest replaceable units containing high levels of functionality and many functions are carried out within custom-made, digital application-specific integrated circuits (ASICs) whose workings are not divulged.
We therefore proceed by noting the performance available within the published 'data sheet' limits of transmitter power, scanner gain, prf, etc. and making reasonable allowance for shortfalls likely to arise in practical designs. The validity of the approach depends in part on the competitive nature of the industry; what can be done soon is done, and woe betide those firms who do not keep up!
1.6.4 Spreadsheet calculation
The equations needed for calculation of system performance are presented in forms convenient for generation of personal computer (PC) spreadsheets. Chapter 14 gives full listings and operating instructions. Having entered radar, target and environmental parameters, the spreadsheets, available on the IEE website (www.iee.org), deliver results such as maximum detectable ranges and indications of how well detectability is maintained as range closes, with graphs linking such parameters as detectability and range. It is then easy to explore the effect of radar, environmental and target parameters on performance. This approach informs judgement of how worthwhile the various parameters may be in a given situation or the robustness of a configuration against clutter and other environmental uncertainties. The spreadsheets should also help design trials of radars and aids to detection for minimum error from unwanted environmental effects, which was not always possible in the past.
1.6.5 Approximate methods
Full calculation is often complex and may not be justified for the task in hand, so we often include alternative approximate methods, sometimes using graphs. Rough approximations should not be despised, their uses include the following.
• Highlighting the major factors in play, separating the wood from the trees.
• Explaining principles to others.
• Getting 'orders of magnitude' for preliminary work.
• Not least, checking for blunders.