SPECIAL PUBLICATION NO. 225 NOAA Repri.nt for Triangulation BY WILLIAM MUSSETER National Geodetic Survey Rockviiie, Md. September 1977 Reprinted December 1985 U.S. DEPARTMENT Of COMMERCE National Oceanic and Atmosplrer(c Admirrktrath National Ocean Survey NOAA Reprint Manual of Reconnaissance for Triangulation BY WILLIAM MUSSETER National Geodetic S,wey RockviUe, Md September 1977 U.S. DEPARTMENT OF COMMERCE National Oceanic and Atmospheric Administration National Ocean Survey PBEI'ACE TO BEVISED (-1 EDITION Since the hat printing of thls manual in 1951 the speeltlcatlons for dnt- and mnd-order triangplation have been made more exacting. FImt-order work bas been #paratad lnto three ciorures and seeoad-order Into two clam Specfd- catlons uader these classes appear on page 4 in the revised table whfcb has been cupfed at reduced scale from Special hbllcatlon No. 247, ,"M~anualof Geodetfc Trian#ulatlon." The only other changes in thh editlon, doe to the revlston of the upedflcatlona, appear OB pages 3 to i. CONTENTS p8m 1 3 3 4 8 7 8 9 10 10 11 12 13 14 14 16 16 17 X8 18 20 21 25 . 23 28 30 32 33 33 . 36 38 38 39 40 43 44 56 41 4a 50 50 50 52 amp* 2-contfnud ks heating positions on work ah&. ............................... sa Spssdometer-compess travene- ............................. 34 Tmmm notes.. .......................................... 56 Curvature eht-.- ............................................ 85 Correction for earth’s curvature and Rfraction ................ 55 Formula for curvature and tion..... ................... 50 Eumplw of correctioM........................ ........... 57 Rebation charactmidcar of lines. ............................... 5a cle!amnce of lines.... ...................................... 60 Avoidance of obatructioas...................................... 61 Meaauring hei’ghtu of ....................................... 01 Setation of station .t.... ..................................... 68 Inwrviewa with property o.ers.... ............................ 84 rstbrs to property oanen.................................. 66 Descriptiom of statio^ ........................................ 67 Temporwp nuukin gs.... ................................... 69 BeeonnWnce sketch. ........................................ io Standard symbols ......................................... 72 Party organization and outfit ................................... 74 Instnrments.............................................. 74 Gened property- ......................................... 75 cb.ptsr 3. Specid prOb1. ........................................ 70 Erne lines. ................................................... 70 Ehit b...... ........................................... 70 . atskcd ............................................... 18 &aa nets ..................................................... 79 Recovery of old atationL ..................................... 81 Conaectiona to mrka of other surveys.... ....................... aa Connectioaa to trmverse ........................................ 84 Supplamenul stations.. ........................................ 86 Stations on buildings,,.,,, ..................................... 88 Boundam surveps. ............................................ 87 N.ngs..o ns..... .......................................... 88 ULozTrRATIONS mmn 1. Differenttypea of Bgureo used in triangulation ..................... 13 2. Elbow 6gure... ............................................... 14 3. Area triangulation.............................................. 15 4. Example of horizon sketch,,,,.,,,,,,,,,-.--,,,,;,,,,,,,^^^, 21 8. Tppid reconnaissance problem,,.,,,,,,,-,,,,,,,,,,,,,,,,,,,,,,. 26 6. Relative eleuatioaa by reciprocal vertical antlm .................... 39 7. Relative elevations by nonriciprocd vertical angla. ............... 41 8. Datermination of obstruoting height .............................. 41 9. Example of compound profiling. ................................. 48 10 . Obstructing height determined by vertica1 anqies and altimeter,,.,., 4i 11. Indirect profiling. .............................................. 4s 12 . Checking clearance of line from side point. ca8e 1.................. 45 13 . Checking clearance of line from side point. me2 .................. 46 14. &ample of indirect profiling .................................... 46 16. Detennination of obstructing height by method of “least favonrble” condidon ................................................... 48 10. Distance determination by “prrrallruing” .......................... 61 pase 51 52 54 57 37 58 39 59 80 $0 85 89 MAIWAL OF RECONNAISSANCE 'FOR TRLANGULATXON GENEBAL STATEMENT During the past few years, such progress has been rnade in th methods of executing tisnguistion that it is desirable to revise some- what the treatment of the subject of reconnaissance aa given in Spe- cial Publication Xo. 98, "Reconnaissance and Signal Building') and Specid Publication No. EO, "5Ianual of First Order Triangulation." It ia with this in mind that the following out.line of present practices ia writtsn. This manual is primarily a guide to engineers of the United States Coast and Geodetic Survey, and, BS such. presupposes some familiar- ity with triangulation methods of the Bureau. Them methods arc fully cowred by various manuals published by the Coast and Geo- detic Surpey. The changes introdaced by the us of the porfabb steel tower signals and the multiple-unit observing partieq and by the closing in of the triangulation net, have made increasing demands upon the reconnaissance both in accuracy and in scope of information desired. At the stme time, the use^ of new instruments, including the altimeter, has dected the methods emplopd. The use of the steel tower signal, first introduced in 1st. has revolutionized contml surveys in flat and timbered regions. It has enabled the reconnaisscmcs engineex to specify signals of greater heights without involving undue espense, and has dted in the use of triangulationz to the exclusion of traverse. for nearly all hori- zontal control. It has permitted triangulation to be carried into regions where this type^ of survey was considered impossible 8 few yeg~ago. Since high signa& me now readily available, t.he demand for signal height has rapidly increased and frequently the full height of the steel towem ii necessary. h these regions, the clearance of linm owrobstructions is about assmall aa formerly, and since the size and cost of sted@ppcd triaquktion parties sre large, this makes accurate reconnaissance very desirable. Also the use of the steel towers require3 that greater attention be paid to accessibility in the selection of stations to guard against hauling difficulties. The econ- omy of the steel signal favors the establishment of many estn, or supplemental, points for local use and os t.ies to surveys of other or- ganizations. The arailabilitF of steel towers and the low cost of 1 additional stgtions make it possible to plan stronger figures than formerly, and this results in better control of the area. Triangulation parties now consist of from two to nine observing units and the limit has bp no means been reached. Monthly espensea of these parties ~ulltu high 85 315.000. compared with $1.500 to !B,OOo for single-unit parties of several years ago. Hence, delay caused by an obstructed line. or other failure of the reconnaissance. is more expensive than formerly. It is now imperative that reconnaissance parties reduce such failures to a minimum. .ne rapidity of pmg- mss of the triangulation parties requires'that they be furnished with aII information obtainable concerning roads and local conditions. With the completion of the major Imp of triangulution has come the procesa of bteaking dom the enclosed areas, filst by am with 60-mile spacing. and then by arcs with %-mile spacing. This spoic- ing has reduced the latitude for departing from the ideal rdute to very meager limits. Fornierlp it opm common practice to follow lines of least resistance br following valleys and keeping in contact with arteries of tmnsportat.ion. At present. triangulation must fol- low an host straight course between termini. orercominp lrnp ob- stdes it may encounter. On this account.. it is often necessaq to cover areas that ore conves in profile, or otherwise difficult, for con- siderable distances. All of these factors combine to require a greater degree of accuracp and wider scope of information for the recon- naissnnce than was necessary o few 'pears ago. The problems of reconnaissance differ for almost every arc. and no gemera1 instructions can corer all the peculiar conditions fntmd in the field. In the folIowing paragmphs an attempt will he made to consider and explain tlie principles of recannuisance and give some tTpical es,miples of the operations inrolvd. To snme readers the methods outlined may appear unneces~arily' elaborate and expensive for tlie proper requirements of the recon- naissance. However. a careful inredgation of the records shows that when skill and energy are used in prosecuting the work. the costs are no higher than were those of earlier and less precise meth- ods. For manp yeam before the stel signals came into usit mas the custom of the reconnaissance engineer to rely more on his omer- perienca and native ability than oil instnimental work. Cery good results were thus .secured and they frilly met the requirements of the time. However. on& ii mall pmportion nf the trimmilation em- cuted during that period was in difficult tini1)erecl regions. and t.he few men engaged on reconnaissance were t