Self Assessment 17

§ 57 – 61

262. What are the four main categories of a pocket calculator and which of these are the most useful for navigation?

Main Categories of Pocket Calculator are:

Simple (arithmetical functions only)

Scientific (full range of mathematical functions)

Programmable Scientific

Specialised Programmable (‘dedicated’ to a specific subject, e.g. Navigation, Engineering).

263. What is a calculator ‘logic system’ and which ones are in common use?

The Logic System of a calculator is the method by which data are received and processed, i.e., the key sequence necessary to perform calculations. The three logic systems in common use are: simple algebraic, full hierarchy algebraic, and reverse polish notation (RPN).

264. What are the ‘trigonometrical functions used in a scientific calculator?

265. What key sequence displays the tangent of 47º?

266. What key sequence displays the angle corresponding to cosine 0.90631?

Trigonometrical Functions involve the ratios between the sides and angles of a right-angled triangle and are the tangent (tan), sine (sin) and cosine (cos).

With the calculator in degree mode, the most usual key sequence to display the tan of 47º would be, 4︎⃣  7︎⃣  TANG which would display: 1.07236871. (NB: some calculators with EOS use the  TANG  key before entering the number of degrees).

To display the angle corresponding to cosine 0.90631 the most usual key sequence would be:

.  9︎⃣  0︎⃣   6︎⃣  3︎⃣  1︎⃣  INV cos which would display 24.999 (or 25º) (NB: some calculators would use the  ARC  or the  cos-¹ key instead of  INV  ).

267. What is the difference between sexagesimal and decimal notation for angles

268. Which of these notations is used in a calculator?

269. How is one of these notations corrected to the other?

Sexagesimal Notation means the expression of angles in degrees, minutes and seconds, e.g., 33º 48’18”, whereas Decimal Degree Notation means the expression of angles in degrees and decimals of a degree, i.e., 33º 48’18” would be expressed as 33º .80 5 in decimal degree notation.

A pocket calculator can only calculate in decimal degree notation, therefore it must be possible to convert an angle from sexagesimal notation to decimal degree notation and visa versa.

To convert say 87º 24’36” to decimal degrees usually uses a key marked DMS.DD  but this can vary from make to make so the manufacturer’s manual must be consulted. In this case, the DD will be 87º .41.

To convert decimal degrees (say 35º .27) to sexagesimal usually uses INV   DMS.DD  but individual calculators may differ. This example gives 35º 16’12”.

270. Explain the difference between polar and rectangular coordinates.

271. What is the ‘polar to rectangular conversion’ function in a calculator?

272. How is rectangular to polar conversion performed with a calculator?

Polar Co-ordinates define a point by an angle and a distance, e.g., point B is on Course 045º and 10 miles from A.

Rectangular Co-ordinates define a point by the length of its vertical axis from the starting point (navigationally, the D Lat) and the length of its horizontal axis from the starting point (navigationally the Dep).

The polar to rectangular function on a calculator converts polar co-ordinates to rectangular ones, e.g., a course and distance can be converted to D Lat and Dep.

To convert rectangular co-ordinates to polar ones, reverse the uses  ﷯?  key by pressing the  INV 


273. What are the two principal American satellite navigation systems and their Russian equivalents?

274. Are these systems compatible with each other?

275. What is the American/European GEOSTAR system?

American NNSS or TRANSIT system     = Russian TSIKADA system.

American NAVSTAR GPS system            = Russian GLONASS system.

None of these satellite systems is compatible with any of the others.

The GEOSTAR satellite navigation system is a joint American/European commercial venture comprising 2 satellites linked to powerful land—based computers which are in turn linked to a user’s transceiver. Range measurements from the satellites are calculated by the central computer to determine the user’s position and transmit it back to the user. This transaction can be completed in under one second and is claimed to have an accuracy of about 1 metre.

276. With reference to SV’s (space vehicles), what is the difference between: –

a. an orbit and a trajectory?

b. injection velocity and escape velocity?

c. orbital inclination and satellite elevation?

An orbit is the path of a spacecraft when it follows a closed curve such as a circle or an ellipse; a trajectory is the path of a spacecraft when it follows a parabola or a hyperbola and escapes from the Earth’s gravitation.

injection velocity is that velocity required to place a spacecraft in orbit while escape velocity is that velocity required to place a spacecraft into a trajectory or space probe.

orbital inclination is the angle between the western end of the Earth’s equatorial plane and the orbit of a satellite; satellite elevation is the angle between the SV and the Earth’s surface tangent at any instant of time.

277. Explain briefly how a GPS position fix is achieved.

278. What is the potential accuracy of a GPS fix for: –

a. military use

b. civilian use?

A GPS fix is achieved by the precise measurement of the distance between the SV and the boat’s receiver at any instant. The intersection of the position lines from three such ranges from three SVs provides the fix. GPS fixes are continuously available.

Accuracy of GPS fixes is (i) 5-10 metres for military use only, (ii) 50 metres intentionally downgraded to 100 metres for civilian users.

279. In addition to displaying Lat. and Longitude, what are the other main functions available on a GPS receiver?

GPS Navigator Functions include waypoint facility, bearing and distance of next waypoint, speed made good and ground track (course made good).

280. What chart datum is used for NAVSTAR GPS?

281. What is ‘datum shift’, where will this value be found and how should it be applied?

Chart Datum for GPS is World Geodetic System T984 (WGS 84)

Datum Shift is the discrepancy between the datum on which a chart is based and WGS 84. Its value is printed near the Title of Admiralty charts and is the amount by which the satellite fix must be moved to agree with the chart.

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