CONTENTS
1. Operations in location
1
2. Reconnoissance 1
3. Nature of examination
1
4. Features of topography 2
5. Purposes of reconnoissance 3
6. Elevations, how taken 3
7. Pocket instruments used 4
8. Importance of reconnoissance 5
CHAPTER II.
PRELIMINARY SURVEY.
9. Nature of preliminary 6
10. Grades 6
11. Importance of low grades 7
12. Pusher grades 7
13-14. Purposes of preliminary 8
15. Nature 9
16. Methods 9
17. Backing up
10
18. Notes 11
19. Organization of party
11
20. Locating engineer
11
21. Transitman ; also form of notes 12
22. Head chainman
13
23. Stakeman
13
24. Rear chainman 14
25. Back flag 14
26. Axeman 14
27. Leveler ; also form of notes 14
28. Rodman 15
29. Topographer 16
30. Preliminary by stadia 17
CHAPTER III. LOCATION SURVEY.
31. Nature of "location" 18
32. First method
18
33. Second method
19
34. Long tangents 19
35. Tangent from broken line of preliminary 19
36. Method of staking out location
CHAPTER IV. SIMPLE CURVES.
37. Definitions 20
38. Measurements 2020
39. Degree of curve 21
40-41. Formulas for degree and radius 21
42. Approximate method
22
43. Tangent distance T
22
44. Approximate method
23
45. External distance E
23
46. Middle ordinate M
23
47. Chord C 24
48. Formulas for R and D in terms of T, E, M, C, I 24
49. Sub-chord c
24
50. Sub-angle d
26
51. Length of curve L
27
52. Method of deflection angles 27
53. Example; application to parabola 27-28
54-55. Deflection angles for simple curves 29
56. Field-work 30
57. Example 30
58. Caution 3
59. Field-work when curve cannot be laid out from P.C. 31
60. Second method
32
61. Field-work of finding P.C. and P.T 33
62. Example 33
63. Form of transit book for curves 34
64. Curves with metric system 35
65. Circular arcs, with example 36
66. Method of offsets from the tangent 37
67. Field-work
37
68. Deflection distances, with field-work 38
69. Approximate computation of offsets 39
70. Offsets between two curves 39
71. Deflection distances for curve beginning with sub-chord 40
72. Example 40
73. Approximate solution of right triangles 41
74. Field-work for method of deflection distances 41
75. Caution 42
76. Deflection distances when first sub-chord is short 42
77-78. Middle ordinates 43
79. Ordinate at any point 43
80. Middle ordinate, approximate formula 44
81. Example 44
82-83. Any ordinate, approximate formulas 41 15
84. Example 45
85. Find a series of points by middle ordinates 46
86-88. Substitute new curves to end in parallel tangents 46-48
89-90. Curve to join tangents and pass through given point 48-49
91-92. Find where curve and given line intersect 49-50
93. Approximate method
50
94. Find tangent from curve to given point 50
95. Approximate method 51
96-99. Obstacles in cases of curves 52-53
CHAPTER V. COMPOUND CURVES.
100. Definitions 54
101. Field-work 54
102. Data 55
103. Given Rt, Rs, It, Is; required I, Ti, Ts 55
104. Given Ts, Rs, Rt, I; required Is, It, Ti 56
105. Given Ts, Rs, Is, I; required It, Ti, Rt 56
106. Given Ti, Ts, Rs, I; required It, Is, Rt 56
107. Given Ti, RI, Rs, I; required h, It, Ts 57
108. Given Ti, Rt, It, I; required Is, Ts, Rs 57
109. Given Ti, Ts, RI, I; required Is, It, Rs 57
110. Given, long chord, angles, and Rs; required It, L, I,
Rt . 58
111. Given, long chord, angles, and Rr; required II, L, I,
R., . 58
112. Substitute for simple, a compound curve to end in
parallel tangent 58
113. Example
59
114. Change P.C.C. so as to join parallel tangent 60
115. Substitute for simple, a symmetrical curve with
flattened ends 61
116. Substitute curve with flattened ends to pass through
middle point 62
117. Substitute simple curve for curves with connecting
tangent 63
CHAPTER VI. REVERSED CURVES.
118. Use of reversed curves 64
119-122. Between parallel tangents, common radius 64-65
123-124. Between parallel tangents, unequal radii 65-66
125-126. Find II, 72, 7'2 when I, TI, RI, R2 are given 66-67
127-128. Find common radius to connect tangents not
paralle1.67-68
CHAPTER VII. PARABOLIC CURVES.
129. Use of parabolic curves
69
130. Properties of the parabola 69
131. Lay out parabola by offsets from tangent 70
132. Field-work
71
133. Parabola by middle ordinates 72
134. Vertical curves, where used 72
135. Method for vertical curve 200 feet long 73
136. General method
74
137. Example
76
138. To find proper length of vertical curve 76
CHAPTER VIII. TURNOUTS.
139. Definitions 77
140. Find frog angle from number of frog 78
141-142. Description of split switch 79
142. Find radius of turnout for split switch 80
143. Radius of turnout for split switch and straight frog 81
144. Turnout beyond frog 82
145. Methods of connecting parallel tracks by turnouts 82-83
146-148. Formulas for simple cases 83-84
149. Reference curve 85
150. Comparison of radii, reference curve and split switch 86
151-152. Additional cases of parallel tangents with turnouts 88-89
153-154. Formulas for a series of parallel tracks 90
155. Examples 91
156. Crotch frog for split switches 92
157. Modified reference curve defined 92
158. Radius for modified reference curve inside 93
159. Approximate formula for above 94
160-161. Modified reference curve outside 95-96
161. Example of case § 161 96
162. Bending process described 97
163. Find radius of turnout curve from frog to parallel
curved track outside ; also approximate method 98-99
164. Example of precise method 99
165. Example of approximate method 100
166. Radius of turnout curve from frog to parallel curved
track inside 100
167. Special case of turnout outside 101
168. Cross-over between parallel curved tracks 101
169. Stub switch described 102
170-171. Stub switch formulas, including crotch frog 103
CHAPTER IX. "Y
" TRACKS AND CROSSINGS.
172. Definition
104
173. Main track tangent, "Y" track curved, and turnout
curved 104
174. Main track tangent, ." Y" curved, turnout
curved with tangent 105
175-176. Main track tangent and curve " Y "
curved, turnout curved 106
177. Crossing of tangent and curve 107
178. Crossing of two curves 108
CHAPTER X. CUBIC
SPIRAL EASEMENT CURVE.
179. Necessity for; also elevation of outer rail 109
180. Equations for cubic parabola and cubic spiral 110-111
181. Discussion of character of easement curves 111
182. Deflection, angles, spiral angles, and properties of
spirals 112
183. Values of y in terms of 1 and Rc 113
184. Values of p and q in terms of x, y, Re, and se 113
185. Tangent distances, with example 114-115
186. Laying out when Dc and p are given, with example 116-117
187-188. Laying out when D, and 1,, are given ; also
field-work 118
189. Laying out cubic spiral by offsets, with example 119
190-191. Deflection angles from intermediate points 120-121
192. Spirals for compound curves 122
193. Example ; also field-work 123
194-196. Substitution of curve and spiral for simple
curve..124-126
CHAPTER XI. SETTING
STAKES FOR EARTHWORK.
197. Data 127
198. What stakes and how marked 127
199. Method of finding rod reading for grade 128
200. Example
129
201. Cut or fill at center
129
202. Side stake for level section 130
203-206. Side stakes when surface is not level 130-132
207. Slope-board or level-board 132
208-210. Keeping the notes 133
211-212. Form of note-book 134-135
213. Cross-sections; where taken 136
214-215. Passing from cut to fill 136-137
216. Opening in embankment 137
217. General level notes
137
218-21. Level, three-level„ five-level, irregular sections 138
CHAPTER XII. METHODS
OF COMPUTING EARTHWORK.
222. Principal methods used
139
223. Averaging end areas
139
224. Kinds of cross-sections specified 140
225. Level cross-section 140
226. Three-level section 141
227. Three-level section; second method 142
228. Five-level section 143
229. Irregular section 143
230. Planimeter 144
231. Comment on end area formula 144
232. Prismoidal formula
144
233. Prismoidal formula for prisms, wedges, pyramids 145
234. Nature of regular section of earthwork 146
235-237. Prismoidal formula applied where upper surface is
warped 146-148
238. Wide application of prismoidal formula 148
239-240. Prismoidal correction 149-150
241. Where applicable; also special case 151
242. Correction for pyramid
152
243. Correction for five-level sections 152
244-245. Correction for irregular sections 152-153
246. Value of prismoidal correction 153
247. Method of middle areas
154
248. Method of equivalent level sections 154
249. Method of mean proportionals 154
250. Henck's method
154
251. Formula 155
252-254. Example 156-157
255-256. Comment on Henck's and end area methods 157-158
257-263. Example comparing the various methods 158
CHAPTER XIII. SPECIAL
PROBLEMS IN EARTHWORK.
264. Correction for curvature 159
265. Correction where chords are less than 100 feet 161
266. Correction of irregular sections 161
267. Opening in embankment 162
268. Borrow-pits 164
269. Truncated triangular prism 164
270. Truncated rectangular prism 165
271. Assembled prisms 167
272. Additional heights 168
CHAPTER XIV.
EARTHWORK TABLES.
273. Formula for use in tables 170
274. Arrangement of table 171
275. Explanation of table 171
276-277. Example of use, including prismoidal correction
table 172
278. Prismoidal correction applied for section less than 100
feet 173
279. Tables, where published 173
280. Tables of triangular prisms 173
281. Where published 173
282. Arrangement of tables of triangular prisms 174
283. Example of use
175
284-285. Application to irregular sections 176
CHAPTER XV. EARTHWORK
DIAGRAMS.
286-287. Method of diagrams
177
288. Forms of equations available for straight lines 178
289. Method of use of diagrams 178
290-291. Computations and table for diagram of prismoidal
correction 179
292. Diagram for prismoidal correction and explanation of
construction 180
293. Explanation and example of use 182
294. Table of triangular prisms 182
295-298. Computations and table for diagram of three-level
sections 183
299-300. Checks upon computations 187
301. Explanation of diagram ; also curve of level section 187
302. Use of diagram for three-level sections 188
303. Comment on rapidity by use of diagrams 189
304. Special use to find prismoidal correction for irregular
sections 189
CHAPTER XVI. HAUL.
305. Definition and measure of haul 190
306-307. Length of haul, how found 190
308. Formula for center of gravity of a section 191
309-310. Formula deduced
192
311. Formula modified for use with tables or diagrams 194
312. For section less than 100 feet 194
313. For series of sections
195
CHAPTER XVII. MASS DIAGRAM.
314. Definition
196
315. Table and method of computation 196
316. Mass diagram and its properties 198
317. Graphical measure of haul explained 199
318. Application to mass diagram 201
319. Further properties 201
320. Mass diagram; showing also borrow and waste 203
321. Profitable length of haul 203
322-323. Example of use of diagram 205
324. Effect of shrinkage on mass diagram 206
325. Discussion of overhaul 206
326. Treatment of overhaul by mass diagram 207
TABLES AND DIAGRAMS 208-220
