CAPTAIN WEIR'S AZIMUTH DIAGRAM
By Lieutenant E. R. McClung, U. S. Navy
Captain Weir's azimuth diagram as furnished to ships bears an explanation of only one of the several solutions of the astronomical triangle which can be performed with more facility by using this diagram than by any other method. Directions for solving problems in addition to the usual one of simply finding the azimuth where latitude, declination and hour angle are known are here printed in condensed form, with a view to removing the page, and, after cutting it in two pieces, pasting these pieces on the blank margin of the diagram. Any doubt as to the theory and method involved in these solutions will be removed by consulting the references to Muir and U. S. Naval Institute Proceedings.
No explanation of the proper sign to choose is here attempted as this will be made clear only by practice. Therefore, it is well to solve a sample problem under each case, assuming the same values for all, so that the results will, themselves, be a check on the work.
The cases are numbered with reference to the case already explained on the diagram as Case I. The following small table offers a ready means of selecting the known and unknown quantities and should also be cut out and pasted on a blank space of the diagram. Subscripts a and t indicate arc and time respectively, and the quantity in parentheses is the one to be found by the solution.
Use as | Case I | Case II | Case IIIa | Case IIIb | Case Iva | Case IVb |
Hour angle | t | ta | (ta) | t | ?2 – ?1t | Ct |
Latitude | L | L | L | L | L1 | L’ |
Declination | d | (h) | h | (d) | L2 | (D) |
Azimuth | (Z) | Zt | Zt | Z | (C) | ?2 – ?1t |
Directions for Solving Additional Problems by Weir's Diagram
(See Muir, 1911, Appendix C, page 756, and U. S. Naval Institute Proceedings, December, 1908, page 1253.)
In all solutions reckon azimuth from elevated pole.
Case II.—Given L, d and t to find h and Z (to predict position of body, particularly a star). Find Z in usual manner by Case I, then convert Z into time and consider as an hour angle. Convert t into arc and consider as an azimuth. Use given latitude as latitude, and on declination scale read off true altitude, h.
Case III.—Given L, Z and h to find t and d (for star identification).
(a) Convert azimuth into time and consider as an hour angle. Use given latitude as latitude. Consider altitude as declination. On horizon circle read off body's H. A., expressed in arc and converted into time.
(b) Use known values of latitude, azimuth and hour angle as such and work backward to obtain declination.
Case IV.—(a) To find course to destination: Use latitude of place of departure as latitude. Consider difference of longitude converted into time as hour angle. Consider latitude of destination as declination, and on horizon circle read off Z—initial course required.
(b) To find distance to destination: Use latitude of place of departure as latitude. Consider difference of longitude as azimuth. Consider course converted into time as hour angle. Then on declination scale read off D, and distance to destination = 90° = D. Reduce this value to minutes of arc = nautical miles.
The following hints will make the use of the diagram very easy and convenient:
Make a number of pins after this fashion.
Place new numerals along horizon circle as follows:
From equator (90°) to south pole, add, in red ink, numerals from 90 to 180, at every fifth graduation opposite to black numerals running from 90 down to 0, thus:
90° | … |
85° | 95° |
80° | 100° |
75° | 105° |
Etc. | Etc. |
From north pole to 105° and from south pole to75°, place in black ink at each fifth division the value of hour angle equivalent to the degrees of arc, thus:
H.A. | Arc |
0 | 0° |
0:20 | 5° |
0:40 | 10° |
1:00 | 15° |
1:20 | 20° |
1:40 | 25° |
2:00 | 30° |
Etc. | Etc. |
Each degree on the horizon scale being equal to four minutes of time, with these numerals to aid the eye, time can be converted into arc, and the reverse operation performed, instantly.