Comments on Double-Theodolite Evaluations
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322 BULLETIN AMERICAN METEOROLOGICAL SOCIETY Comments on Double-Theodolite Evaluations ROBERT O. WEEDFALL AND WALTER M. JAGODZINSKI U. S. Weather Bureau (Original manuscript received 7 May 1960; revised manuscript received 26 August 1960) 1. Introduction After reading an article [1], in the May 1959 issue of the Bulletin of the AMS wherein Mssrs. Hansen and Taft describe another method of computing double-theodolite runs, it was realized that a method developed at the AEC installation at Yucca Flat, Nevada is even more efficient than any previous method and could be of great value in speed and saving of man-hours to those wind- research installations that use the double-theodo- lite method. Further, it does not need special plotting boards but utilizes the standard Weather Bureau equipment with a few ingenious adaptations. FIG. 1. Winds-aloft plotting board, showing position of three distance scales. (360-deg intervals not indicated.) 2. Materials needed (1) Winds-aloft plotting board (fig. 1). A 3-ft-square board with distance scales running from the center to the bottom, with a movable circular piece of plastic attached to the center of the board, whose outer edge is marked off in 360-deg intervals. (2) Circular protractor (fig. 2). A 10-inch- square piece of clear plastic divided into 360-deg intervals. (3) Appropriately marked scale in the shape of an "L" (fig. 3). (4) Scotch tape, rubber band and short piece of string. (5) Winds-aloft graphing board (fig. 4). A rectangular board 2 X 2% ft marked with height FIG. 2. Clear plastic protractor, 10 inches square. scales along the edges and with an attached (Divisions into 360-deg intervals around outer edge of movable plastic rule with degree and velocity circle not indicated.) calibrations. 3. Procedure Depending on wind velocities, the appropriate scale on the winds-aloft plotting board is selected and the circular protractor (fig. 5) is taped onto the board with its center at 1500 m (or whatever distance theodolite position #2 is located from theodolite position #1) and is properly ori- entated toward position #1, which is the center FIG. 3. Appropriately marked scale, about 6X9 inches. Unauthenticated | Downloaded 09/23/21 12:28 PM UTC VOL. 42, No. 5, MAY, 1961 323 FIG. 4. Winds-aloft graphing board. Height scales run vertically. Degree and velocity scales run hori- zontally on movable plastic ruler. of the board and is usually where the balloon is released. Theodolite position #2 is the center of the circular protractor. A knotted rubber band or string has been secured through the center of the protractor prior to its being taped to the board. FIG. 5. "O" is theodolite position #1. "P" is the- To figure out the balloon's horizontal distance odolite position #2. "A" is any plotted point. for each time interval that readings of the azimuth String or rubber band from center of and elevation angles were taken, the azimuth circular protractor. angle of theodolite position #1 is lined up ver- —. —. — String from "O" to "B" indicating an eleva- tically at the bottom arrow of the winds-aloft tion angle of 35 deg corresponding to plotted point "A". plotting board, and the corresponding azimuth Distance "A" to "B" is height corresponding angle of position #2 is located with the rubber to time interval at point "A" and is measured with band on the circular protractor. Where these scale (fig. 3). lines intersect, a point is plotted in ink. Points are plotted for each succeeding time interval. From these plotted points, the wind direction and stick or ruler is laid off from the center of the velocity is computed in the same way as for board to the appropriate elevation angle ob- single theodolite pibals. served from theodolite position #1, correspond- The advantage so far over the method out- ing to each plotted point. (One board was lined by Mssrs. Hansen and Taft in the AMS adapted by drilling a hole in the center and Bulletin is that a special plotting board is not using a weighted string.) The right-angled dis- necessary. However, in their method, they now tance from each plotted point to the ruler (or use a slide rule to compute the height of the weighted string) is then measured, using the balloon at the appropriate time intervals. The appropriately marked "L"-shaped scale. This balloon's horizontal distance out for each time reading gives the height of the balloon at the interval has to be measured, and this distance appropriate time interval. The previously com- multiplied by the tangent of the corresponding pute wind directions and velocities are then elevation angle. This time-consuming step is plotted against their corresponding heights on eliminated in this new method by graphically the winds-aloft graphing board. computing the heights from each of the plotted points in the following manner. 4. Accuracy The lower right quadrant of the winds-aloft It must be remembered that there are certain plotting board is measured off in 10-deg intervals, inherent errors in double-theodolite observations with zero at the bottom (see fig. 5). These regardless of the method of evaluation. Errors intervals may be linked onto the board and accumulate rapidly with large balloon range rela- preserved with scotch tape. The balloon's hori- tive to base-line length. Errors also accumulate zontal distance out (which has been plotted for when the balloon travels parallel to a line be- each time interval and is still on the board) is tween the two theodolite positions. Having a brought into line with the zero-degree reading third theodolite position or using a remote release (vertical line from the center of the board). A can overcome this source of error. The theodo- Unauthenticated | Downloaded 09/23/21 12:28 PM UTC 324 BULLETIN AMERICAN METEOROLOGICAL SOCIETY lites should be located at the same elevation or 5. Speed another source of error is introduced [3]. It is If one considers a 30-interval run, using this only within the scope of this paper to comment new method takes about 25 min to complete, con- on the accuracy between the method described in trasted to 70 min when using the Circular "O" Weather Bureau Circular "O" [2], the method method, a saving of 45 min. When one compares described in the previously mentioned article in this new method to the one developed by Mssrs. the Bulletin of the American Meteorological Hansen and Taft, it would seem the times used to Society, and this new method, which could be compute the wind direction and velocity are about called the tangential-graphing method. the same. However, to measure the distance out A series of 12 runs was recently evaluated, from each plotted point, figure the tangent of using both the Circular "O" method and this new the elevation angle on the slide rule and multiply method. By using the Circular "O" method, the the two by the slide rule would take at least points were painstakingly measured and the 15 to 20 min longer than this new method. heights computed by slide-rule. The differences in the results were negligible. 6. Conclusion Regarding the accuracy of plotting points for The time-saving advantage over the Circular the successive time intervals, it seems the Circular "O" method is obvious. Although the time saved "O" method would be slightly more accurate is not as important a factor when comparing this than the method developed by Mssrs. Hansen new method to the method developed by Mssrs. and Taft, since they use what appear to be two Hansen and Taft, its versatility is its paramount circular protractors about 2 ft in diameter to advantage. And, since it gives the same results, determine the intersection of the azimuth angles the use of this new method appears to be justified. from the theodolite positions, and their method This paper has been written in the hope that it in turn would be more accurate than this new may save time and effort at all stations where method, since the circular protractor used is low-level or meso-scale wind research is being only 9 inches in diameter. conducted. In figuring the heights, this new method by which the height is measured graphically would REFERENCES naturally be less accurate than using a mathe- 1. Hansen, F. V., and N. H. Taft, 1959: Another method of evaluating double-theodolite runs. Bull. Amer. matical computation with the help of a slide rule. meteor. Soc., 40, 221-224. However, the maximum error should be less 2. U. S. Weather Bureau Circular "O". than 3 per cent, and would seem justified in view 3. Middleton, W. E. K., and A. F. Spilhaus, 1953: Meteorological instruments (3rd ed.). Toronto, of the time saved. Univ. Toronto Press, p. 186. (Continued from NEWS and NOTES, page 321) The morning ceremony in the main conference hall was attended by many eminent personalities including January SCIENTIFIC AMERICAN. Meteorologists will find the 18 members of the WMO Executive Committee and this review of the works of one outstanding meteorologist representatives of many of the diplomatic missions in by another leader in the meteorological profession most Switzerland. WMO Secretary-General D. A. Davies interesting and informing.—Dale R. Harris, Washing- opened the ceremony by welcoming the distinguished ton, D. C. gathering to the new building. Other speakers were P. P. Spinelli, director of the European Office of the Dedication of WMO Headquarters United Nations, and representatives of Swiss Federal It was an important occasion in the life of the World authorities and the local government. The brief cere- Meteorological Organization when the official inaugura- mony closed with an address by WMO President A.