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Field Engineering by William H Searles Railway surveying NO BACK COVER
Field Engineering by William H Searles 16th edition NO BACK COVER
505 pages
Copyright 1880, 1907 printing
A handbook of theory and practice of railway surveying, location, and construction designed for classroom , field and office and conatining a large number of useful tables, original and selected.
CONTENTS
CHAPTER I RECONNOISSANCE.
2. Topographical considerations 1
6. Use of maps 3
7. Pocket instruments 3
9. Aneroids 4
10. Formulae for aneroid 4
16. Locke level 7
17. Prismatic compass 7
CHAPTER II. PRELIMINARY SURVEY.
18. Definitions 8
19. Engineer corps 8
20. Chief engineer 8
21. Assistant engineer 9
22. Chainman 10
24. Axeman 11
26. Topographer 11
28. Leveller 13
29. Rodmen 13
32. The compass 14
33. The chain 14
35. The level 15
36. The rods 15
88. The clinometer 16
39. The plane-table 16
40. The transit 16
42. Transit points 17
43. Transit flags 17
44. Obstacles to alignment and measurement 18
45. Parallel lines 18
46. Lines at a small angle 18
47. General problem 19
48. Lines at a large angle 26
49. Selection of angles 21
53. Rocky shores; Tie-lines 22
64. System of plotting map 23
CHAPTER III. THEORY OF MAXIMIM ECONOMY IN GRADES AND CURVES.
55. Choice of routes 24
56. Statement of the problem 25
57. Engine traction 25
58. Engine expense 27
60. Resistance to motion 27
61. Resistance due to grade 28
62. Resistance due to curve 28
63. Formulae for resistance 29
64. Formulae for maximum trains 30
65. Engine-stage 32
66. Graphical solution 33
67. Train load reciprocals 33
68. Reduction of grades on curves 33
69. Example 36
70. Assisting engines 36
71. Maximum return grades 37
72. Undulating grades 38
75. Comparison of routes 39
76. Value of distance saved 39
77. Conclusion
CHAPTER IV. LOCATION
78. General remarks 39
79. Long tangents 39
80. Leveller's duties; Profiling40
81. Establishing grade lines41
CHAPTER V. SIMPLE CIIRVES.
A. Elementary Relations.
82. Limits to curves and tangents 42
83. Definition of terms 43
84. Radius and degree of curve 44
85. Measurement of curves 44
86. Approximate value of R 45
87. Central angle and length of curve 45
88. Definition of other elements 46
90. Formula for tangent distance T46
91. Formula for long chord C 47
92. Formula for middle ordinate M 48
93. Formula for external distance E 49
95. Formula for radius in terms of T and 50
96. Formula for external distance in terms of T and 50
97. Formula for radius in terms of E and
98. Formula for tangent distance in terms of E and 51
99, To define the curve of an old track 51
100. Other curve formula; Table III 52
B. Location of Curves by Deflection Angles.
101. Deflection angles 52
102. Rule for deflections 53
103. Rule for finding direction of tangent at any point 53
104. Subchords 54
105. Deflections for subchords 54
106. Correction for subchords 55
107. Ratio of correction to excess of arc 55
108. Transit work on curves 57
109. Field notes 58
110. Central angle in terms of deflections 58
111. Method by deflections only 58
C. Location of Curves by Offsets.
112. Four methods 50
113. By offsets from the chords produced 59
114. Do. beginning with a subchord 80
115. Formula for subchord offsets, approximate 61
117. By middle ordinates 61
118. Do. beginning with a subchord 62
119. By tangent offsets 82
120. Do. beginning with a subchord 64
121. By ordinates from a long chord 64
122. Do. for an even number of stations 65
123. Do, for an odd number of stations 66
124. Do. for an even number of half stations 67
125. Do. beginning with any subchord 67
126. Erecting perpendiculars without instrument 69
D. Obstacles to the Location of Curves.
127. The vertex inaccessible 69
128. The point of curve inaccessible 70
129. The vertex and point of curve inaccessible 70
130. The point of tangent inaccessible 71
131. To pass an obstacle on a curve 72
E. Special Problems in Simple Curves.
132. To find the change in R and E for a given change in T 73
133. To find the change in R and T for a given change in E 74
134. To find the change in T and E for a given change in R 75
135. General expression for elementary ratios 75
136. To find a new point of curve for a parallel tangent 76
137. To find a new radius for a parallel tangent 76
138. To find new P, C. and new radius for a parallel tangent 77
139. To find new tangent points for two parallel tangents 78
140. To find new R and P.C. for new tangent at same P.T 80
141. To find new P.C. for a new tangent from same vertex 81
142. To find new radius for a new tangent from same vertex 81
193. To find new B and P.C. for same external distance, but new 82
144. To find a curve to pass through a given point 83
145. To find new radius for a given radial offset 84
146. Equation of the valvoid 86
147. To find direction of a tangent to the valvoid at any point. 87
148. To find the radius of curvature of the valvoid at any point 88
149. To find the length of arc of the valvoid 88
150. To find new position of any stake for a new radius from same P.C 89
151. To find new radius from same P.C. for new position of any station 92
152. To find distance on any line between tangent and curve 93
153. To find a tangent to pass through a distant point 94
154. To find a line tangent to two curves 96
155. To find a line tangent to two curves reversed98
156. Study of location on preliminary map; Templets; Table of convenient curves 100
CHAPTER VI. COMPOUND CURVES.
A. Theory of Compound Curves.
157. Definition 102
158. The circumscribing circle 102
159. The locus of the point of compound curve 103
160. The inscribed circle of the principal radii 104
Cor. 2, Maxima and minima of the radii 104
B. General Equations.
161. Formula for radii, central angles, and sides 105
162. Given: S1 S2 and R2 to find 1, 2 and R2 106
163. Given: AB, VAR, VBA and R2, to find 2 1 and R1 107
164. Given: R 1 R2 2 to find the triangle VAB 108
16.5. Given: A , the radii, and one side to find the other... 108
166. Given: one side, radius and central angle to find the others 110
167. Remarks on special cases 111
168. Obstacles; the P.C. C. inaccessible 112
C. Special Problems in Compound Curves.
169. To find a new P.C.C. for a parallel tangent 113
170. To find a new P.C.C. and last radius for a parallel tangent 115
171. To find a new P.C.C. and last radius for the same tangent 118
172. To find a new F.C.C. and last radius R for new direction of tangent through same P.T 121
173. To find a new P.C.C. and last radius Rfor new direction of tangent through same P.T. 124
174. To replace a simple curve by a three-centered compound curve between the same tangent points 127
175. To find the distance between the middle points of a simple curve and three-centred compound curve 129
176. To replace a simple curve by a three-centred compound curve passing through the same middle point 129
I. The curve flattened at the tangents 129
II. The curve sharpened at the tangents 132
177. To replace a tangent by a curve compounded with the adjacent curves 134
I. When the perpendicular offset p is assumed 136
II. When the angle a or B is assumed 137
III. When the radius E, is assumed 137
IV. Locus of the centre 02 138
178. To replace the middle arc of a three-centred compound by an arc of different radius 140
I. When the radius of the middle arc is the greatest 140
II. When the radius of the middle arc is the least 141
III. When the radius of the middle arc is intermediate 142
CHAPTER VII TURNOUTS.
179. Definitions; Frogs and switches 197
180. Single turnout from straight track in terms of frog angle 198
181. Single turnout from straight track in terms of frog number 149
182. Double turnout, middle track straight, to calculate F" 151
183. Double turnout, middle track straight, and three given frogs 152
184. Double turnout on same side of straight track to calculate the middle frog, F" 158
185. Double turnout on same side of straight track with three given frogs 155
a. When the middle track is a simple curve 155
b. When the middle track is straight beyond F 158
c. When the middle track is reversed at F 159
186. Turnout on the inside of a curved track 161
187. Turnout on the outside of a curved track 163
188. Tongue switches 164
189. Tongue switch turnout from a straight track 164
190. Tongue switch double turnout to find F" 165
191. Tongue switch double turnout with three given frogs 166
192. Tongue switch double turnout on same side of straight track with three given frogs 167
a. The middle track reversed at F 167
b. The middle track compounded at F 168
c. The middle track straight beyond F 168
193. To find the reversed curve for parallel siding in terms of F and perpendicular distance p 169
194. To find the connecting curve from frog to parallel siding on a curve in terms of F and perpendicular distance p 170
a. The siding outside of main track 171
b. The siding inside of main track 171
195. To locate a crossing between parallel tracks 172
196. To locate a reversed curve crossing between straight tracks 173
197. To locate a reversed curve crossing between curved tracks 174
198. To find the middle ordinate m, for one station in terms of D 175
199. To find the middle ordinate mi for rails, in terms of rail and R 175
200. Curving rails; To find m1 in terms of rail and m 176
201. To find elevation of outer rail on curves 177
202. To find a chord whose middle ordinate equals the proper elevation 179
203. General remarks on elevation of rail 179
204. General remarks on coned wheels 180
CHAPTER VIII. LEVELLING.
205. Use of the engineers' level 181
206. The datum, how assumed 181
207. Benches, how used; B.M . 181
208. Height of instrument; HI 182
209. Reading of the rod 182
210. Elevation of intermediate points 182
211. Turning points; T.P 182
212. Rule for backsights and foresights 183
213. Form of field-book; proof of extensions 183
214. Profiles.... 184
215. Simple levelling; test levels 185
216. Errors in reading, due to the level; how avoided 185
217. Errors in reading, due to the rod; how avoided 185
218. Errors due to curvature of the earth 186
219. Errors due to refraction 187
220. Radius of curvature of the earth 187
221. Levelling by transit or theodolite 188
222. To find the H.I. by observation of the horizon 189
223. Stadia measurements; horizontal sights 191
224. Stadia measurements; inclined sights, vertical roda 193
225. Stadia measurements; inclined sights, inclined rod 195
CHAPTER IX. CONSTRUCTION.
226. Organization of engineer department 196
227. Clearing and grubbing 197
228. Test levels and guard plugs 197
229. Cross sections; Slopes 197
230. Cross sections, formulas for 198
231. Cross sections, staking out 200
232. Cross sections on irregular ground 201
233. Cross sections on side-hill work 201
234. Compound cross sections 202
235. Selection of points for cross sections 203
236. Vertical curves 203
237. Form of cross-section book 204
238. Extended cross profiles 205
239. Inaccessible sections 205
240. Isolated masses 206
241. Borrow-pits - 206
242. Shrinkage; Increase 206
243. Office-work 207
244. Alteration of line 207
245. Drains and culverts 208
246. Arch culverts 209
247. Foundation=pits; Bridge chords on curves 210
248. Cattle-guards 214
249. Trestle-work 214
250. Tunnels: Location; Alignment; Shafts; Curves ; Levels ; Grades; Sections; Rate of progress; Ventilation; Drainage 216
251. Retracing the line 222
252. Side ditches and drains 223
253. Ballasting 223
254. Track-laying; Expansion of rails; Sidings 223
CHAPTER E. CALCULATION OF EARTHWORX.
254. Prismoids; Choice of cross sections 225
255. Formules for sectional areas 227
258. Pfismoidal formulm for solid contents 229
257. Tables of quantities in cubic yards 229
258. Tables of equivalent depths 231
259. Formula for equivalent depth in terms of slope angle 232
260. Conditions necessary for correct results in use of tables 233
261. Method of mean areas; correction required 233
262. Exad calculation of content; examples 234
263. Wedges and pyramids 236
264. Side-hill sections, uniform slope - 286
265. Side-hill sections, irregular ground 237
266. Side-hill sections in terms of slope angle 237
267. Systems of diagrams 238
268. Correction for curvature In earthw 239
269. Haul; Centre of gravity of prismoid 243
270. Final estimate 245
271. Monthly estimates 246
TOPOGRAPHICAL SKETCHING.
272. General remarks 247
273. Artificial features 248
274. Natural features; Contours; Hatchings 248
275. Method of sketching 249
CHAPTER XII. ADJUSTMENT OF INSTRIIMENTS.
276. The transit 250
277. The level 252
278. The theodolite 258
CHAPTER XIII. EXPLANATION OF THE TABLES 253
TABLES.
I. Geometrical Propositions 271
IL Trigonometrical Form-nice 273
III. Curve Formulae 277
IV. Radii, Offsets, and Ordinates 280
V. Corrections for Tangents and Externals 288
VI. Tangents and Externals to a One-Degree Curve 289
VII. Long Chords and Actual Arcs 293
VIII. Middle Ordinates to Long Chords298
IX. Linear Deflections 301
X. Curved Deflections; Valvoid Arcs 302
XI. Frog Angles and Switches 303
XII. Middle Ordinates for Rails 304
XIII. Difference in Elevation of Rails. 304
XIV. Grades and Grade Angles 305
XV. Barometric Heights, in feet 307
XVI. Coefficient of Correction for Atmospheric Temperature 309
XVII. Correction for Earth's Curvature and Refraction. 309
XXIII. Coefficient for Reducing Stadia Measurements310
XIX. Logarithmic Coefficients, Stadia Measurements311
XX. Lengths of Circular Arcs312
XXII. Minutes in Decimals of a Degree 313
XXII. Inches in Decimals of a Foot314
XXIII. Squares, Cubes, Roots and Reciprocals 315
XXIV. Logarithms of Numbers332
XXV. Logarithmic Sines, Cosines, Tangents, and Cotangents359
XXVI. Logarithmic Versed Sines, and External Secants404
XXVII. Natural Sines and Cosines449
XXVIII. Natural Tangents and Cotangents458
XXIX. Natural Versed Sines and External Secants470
XXX. Cubic Yards per 100 Feet in Level Prismoids493
XXXI. Useful Numbers and Formulae 500
Corrections for Subchord Lengths297
PREFACE
Although the modern railway system is but about fifty years old, yet its growth has been so rapid, and the progress in the science of railway construction so great, as to render the earlier technical books on this subject inadequate to the needs of the engineer of to-day.
In the course of his practical experience as a railway engineer, the author was strongly impressed with the want of a more complete hand-book for field use, and finally concluded, at the solicitation of his friends, to undertake the preparation of the present volume.
The aim in this work has been:
First-To present the general subject of railway field work in a progressive and logical order, for the benefit of beginners.
Second-To classify the various problems presented, so that they may be readily referred to.
Third-To embrace discussions of all the more important practical questions while avoiding matters non-essential.
Fourth-To employ throughout the work a uniform and systematic notation, easily understood and remembered, so that after one perusal the formula may be intelligible at a glance wherever referred to.
Fifth-To express the resulting formula of every problem in the shape best adapted to convenient numerical computation.
Sixth-To furnish a large variety of useful tables, more complete and extended than any heretofore published, especially adapted to the wants of the field engineer.
An elementary knowledge of algebra, geometry and trigonometry on the part of the reader has been taken for granted, as a command of these instrumentalities is deemed essential to the education of the civil engineer. The few references to mechanics, analytical geometry, optics and the calculus may be assumed correct by those not conversant with these branches.
Many of the problems in curves are new, yet there is hardly one that has not presented itself to the author in the course of his practice. The investigation of the valvoid curve is original, and though the mathematical discussion is somewhat difficult, yet the resulting formula, taken in connection with Table X, are exceedingly simple and convenient for the solution of a certain class of problems.
The treatment of compound curves is novel and exhaustive.
A, few general equations are established, which, by slight modifications, solve all the problems that can occur.
No discussion of reversed curves is given, because these are inconsistent with good practice, except in turnouts, under which head they are noticed.
The chapter on levelling includes a discussion of stadia measurements, with practical formulae. The chapter on earthwork contains a review of several methods for calculating quantities, and states the conditions under which these succeed or fail in giving correct results.
Among the tables, numbers 3, 5, 6, 10, 18, 19, 26 and 29 are original. The adoption of versed , sines and external secants throughout the work, wherever these would simplify the formulae, rendered necessary of preparation of tables of these functions. The table of logarithmic versed sines and external secants has been computed from ten-plane logarithmic tables of sines and tangents, so that the last decimal is to be relied on, and no pains have been spared to make the table thoroughly accurate.
Tables numbers 4, 7, 8, 9, 11, 12, 13, 14 and 30 have been recalculated, enlarged, and some of them carried to more decimal places than similar tables heretofore published. The intention has been to give one more decimal than usual, so that in any combination of figures the result of calculation might be reliable to the last figure usually required.
The tables which have been compiled and rearranged are numbers 1, 2, 15, 16, 17, 24, 25 and 31. The tables of log. sines and tangents here given are the only six-place tables which give the differences correctly for seconds. The table. of logarithms of numbers is accompanied by a complete table of proportional parts, which greatly facilitates interpolation for the fifth and sixth figures.
In all the tables, whether new or old, scrupulous care has been taken to make the last figure correct, and the greatest diligence has been exercised by various checks and comparisons to eliminate every error. It is, therefore, hoped and believed that a very high degree of accuracy has been obtained, and that these tables will be found to stand second to none in this respect.
The preparation of this work has extended over several years, as time could be spared to it from other engagements. It is, therefore, the expression of deliberate thought, based on experience, and as such is submitted to the judgment of brother engineers. If it shall prove to have even partially met the aim herein announced, and so shall serve to smooth the way of the ambitious student, or to assist the expert in his responsible duties, the labors of the author will not have been in vain. WM. H. SEARLES, C.E.NEW YORK, March 1st, 1880.
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