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Aviation History
1938
1938 - 1720.PDF
598 FLIGHT.. JUNE I6, 1938. Fig. 18. (2) (3) (4) (5) (6) Let us on 4th March, 1938, in D.R. (2) We to fa) G.H.A. r , 22hre . .(b) oim 15 .. (c) S.H.A. ;-;:r- '<•--.-.. Sum — G.H.A. .. = now apply Longitude, get the L.H.A.(Subtract, because W) Long W = 132 0 259 39T 00 00 04 23 27 From Main Table„ Auxiliary Table.Main Table (This is the 1st Mental Operation) 12 I^.H.A. . . . . =391 15 (2nd Mental Operation) (3) In this case, we can sub- tract 3600 : It makes no difference to the L.H.A 360 L.H.A. =031 15 (3 r d Mental Operation : not always necessary.) We have now found the included angle ZPX of the formula. (4) Set this down .. .. 310 15' (5i Put Lat. below it . . ., 510 32' N. (6) Put Dec. below .. .. 160 38 S. Air Almanac.) (7) Add Lat. and Dec, as they are of " different " names. If they were of the " same " name, you would subtract . . .. 68° 10' (4th Mental —- Operation.) This is all the working before we start looking up Tables. (5) Look up " Log hav." for . . 310 15' It is : 8.86060 (9) Log. Cos." .... 51 32 „ 979383 (10) . •' Log. Cos." „ . . 16 38 „ 9.98144 ill) Add up the above 3 logarithms .. 8.63587 (5th Mental Operation.) i2j Look up the " Nat. Hav." corresponding to " Log. hav." 8.63587 , . . . It is : .04324 (13) Look up " Nat. Hav." of (68° 10' is the mysterious 6) (14) Add the two Nat. Havs. . . 68° itr" It is: (6th Mental Operation) (15) Look up the angle corresponding to a Nat. Hav. of .35729. We find it is 730 25'. This is the " Calculated Zenith Distance." All this may sound very long, but with practice and the use of forms, it can be easily done in under two minutes. In practice, the calculation would look something like this: 132° 00' o 04 259 23 What is " PX " ? It is (900 — Dec. of X). The Dec. of X will be given in the A ir A Imanac. Sin (00 — Dec.) is also Cosine Dec. If this is not seen, just take it on trust for the time being. What is " PZ " ? It is (900 — Lat. of Z) ; Z is your D.R. Latitude ; Sin (90 — Lat.) is also Cosine Lat. What is " ZPX " ? The Local Hour Angle. It is the" difference between the G.H.A. of X, and the D.R.. Longitude. What is " hav. 8 " ? Don't worry. We can make use of it without knowing. What is " ~." ? This means that if Lat. and Dec. are of the same name, i.e., both N, you subtract the lesser from the greater in part of tlie working, Tf Lat. and Dec. are of different name, i.e., one N and the other S, you will have to add them in one part of the working, take a concrete example. At 22hr0 oim 15' G.M.T., /510 32'N. the mean Sextant \oo° 12'W. Altitude of the Star Sirius was 160 38'. Index Error 1' +. A bubble sextant was'used. (T) First find the G.H.A., from the Air Almanac. As it is a Star, it is made up of several steps :— > _-.-: G.H.A. Long. L.H.A. Lat. .. •„:. ...£:.' ;:. ip,»'," cr,' f;,f.,-'r*:'v.j.": 391 391360 31 16 m 27 12 W. 15 32 N. 38 S. 10 -; V T.. hav. L. cos. L. cos. Cak ZD = 8.86060 9-793839^)8144 8.63587 .04324 •3 H°5 •35724 73° 25' And, don't forget, this is the long method. Has " spherical trigonometry " worried us much ? In practice, all this -would be done on a form. In the preceding paragraph, we were given a mean bubble sextant altitude of 16° 38' for Sirius. The Index Error given was iy +. We have just found the " Calc. Z.D." to be 730 25'. To find the intercept : <i) Set down the Sextant Alt. ..„.• .. 160 3S' (2) Apply Index ETTOT . . •;,*'' .. 1 -f (3) Apply Refraction, from Table at back of Air Almanac .. 16 39 Tf) the So 160 36' is the Obs. Altitude. Now (90 — Alt.) = Z.D. Hence 730 24' is the Obs. Z.D. But 730 25' is the Calt. Z.D. So the intercept is 1' towards. From Azimuth Tables. True Bearing is 5? 1500 W, or 2100 T. The sight was taken under favourable conditions, on the ground. If taken in the air, the intercept would probably have been larger, partly because of the greater difficulty in using the sextant, but mostly because the D.R. position would not have been so accurate. In air navigation, owing to the difficulty of keeping a very accurate D.R., and to the use of tables for which one "assumes" a position, large intercepts are quite common and not necessarily inaccurate. Many clever people have used their knowledge of spherical trigonometry to devise quick ways of obtaining the Calculated Z.D. or Calculated Altitude, without going through the " long " logarithmic procedure. There is, luckily, no need to know anything about spherical trigonometry oneself when using the various tables produced for this purpose ; all that is needed is to do as ons is told in the explanation. The majority of the tables give Altitude, and some give the Azimuth as well. As the G.H.A. system is new (at least in this country) for navigational work, it will be found that the majority of the tables show the L.H.A. in Time, not Arc. It is, however, understood that a set of Altitude and Azimuth Tables is being prepared in Great Britain, for use with the Air Almanac ; all the data will be in Arc. Some of the best-known tables are : Ageton's Dead Reckoning Altitude and Azimuth Tables ; Aquino's Altitude and Azimuth Tables ; Ball's Altitude or Position Line Tables ; Davis' Alt- Azimuth Tables ; Dreisonstok's Navigation Tables for Mariners and Aviators ; Gingrich's Aerial and Marine Navigational Tables ; Ogura's New Altitude and Azimuth Tables ; Smart & Shearme's Position Line Tables ; U.S. Hydrographic Office's Tables of Computed Altitude and Azimuth; and Weem's Line of Position Book. There are many other aspects of Astronomical Air Navigation that have not even been mentioned in this short explanation ; but it is not really a difficult matter in theory or in practice, thanks to the work of H.M. Nautical Almanac Office in preparing the Air Almanac,
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