This document discusses string lining curves to measure middle ordinate (MO) tolerances. It provides instructions on marking stations along a curve, measuring MOs, recording data, analyzing the results through graphing and trial-and-error in Excel, and determining any necessary track adjustments. Proper string lining ensures uniform curve geometry and helps identify problem areas that may not be visible otherwise.

1. String Lining Curves

2. Review - Anatomy of a Curve
Direction of up
Stationing
TS
SCCS
ST
The Spiral is the transition between tangent and curve
with no defined radius, hence the name spiral.
The Body of the Curve has a defined radius, and
if continued will make a full circle
TS
SC
CSST
Body of Curve

3. 30’ Cord
15’15’
MO
a
b c
Calculating an MO
From a known radius
a² + b² = c²
(15)² + (b)² = (500)²
225 + b² = 250,000
b² = 250,000 - 225
b² = 249,775
b = √249,775
b = 499.775’
MO = 500 - b
MO = 500 – 499.775
MO = 0.225’ = 2¾”
This is essential
for string lining Curves
a
R =
MOft
2 + a2
2(MOft)2
Review

4. Measuring Middle Ordinate on a Curve
1.Mark out regular intervals on the rail
2.Assign a number to each marking
3.Place string on markings and pull tight
4.Measure half way between markings
5.Record data at each MO
6.Create a graph showing tolerances
1
10
7
65
4
3
2 9
8
Basic Principles

5. Measuring Middle Ordinate on a Curve
1.Mark out regular intervals at 1’ or ?
2.Assign a number to each marking
3.Place string on markings and pull tight
4.Measure half way between markings
5.Record data at each MO
6.Create a graph showing tolerances
1
10
7
65
4
3
2 9
8
OR

6. String Line Measuring

8. 1” MO for 62” chord = 1° curve = 5,730 Radius

10. Station # Measure
1/10 ths “
Station # Measure
1/10 ths “
1 0 10 15
2 2 11 14
3 3 12 16
4 5 13 11
5 7 14 8
6 13 15 5
7 16 16 3
8 16 17 1
9 17 18 0
String Line Measurements

11. TS
SC CS
ST

12. Comments on String Lining
1. Divide curve into equal stations,
beginning and ending one
string length before TS and after ST
2. Record MO’s on form and input to Excel
3. Produce Graph in Excel
4. Do trial & error exercise in Excel
5. Layout Throws in Field

13. Comments on String Lining
• Saves on Geometry Car Mobes
• Indicates problems on sharp curves that can not be seen
• Throw at station = amount, adjacent = ½ the amount
• The sum of new MO’s must = original MO’s
• If throw is (-), then adjacent becomes (+)
Negative throw here gives positive MO at 

½α
α

14. Comments on String Lining
• Objective: All MO’s are within tolerance
& Uniform
• In Body of curve: MO’s are equal
• In spirals: Uniform increase & decrease
• Measure on outside rail gage face *
• Super elevation can be changed by throws
• OK, let’s get to it

15. Tools Required
•String Line (fishing line, coated steel leader)
•50’ steel tape (cloth if 3rd Rail)
•Keel
•Ruler with 1/10” increments
•Pad of forms and pencils
•Manpower, 1,2,3 or 4 depending on speed
Step by Step

16. Step by Step
1. Eye ball beginning of spiral and label 0
2. Go string length back
3. Measure stations and label on base of rail
Must be whole number when divided into string length
4. Eye ball end of curve and go string length beyond
5. Record all stations on form and base of rail
6. Identify existing centerline of track (nail, stake etc.)
TS
ST
•
•
•
•
•
•
•
  







•
•
•
•
•
•
•
•
•

17. Step by Step
7. Measure MO’s at each station
8. Record on form as number of 1/10 ths of inch
9. Document potential clearance issues, including track c-c
10.Do trial and error methodology in Excel
11.Create Graph in Excel
12.Present throws to crew for correction

18. Step by Step Sta # MO Sta # MO Sta # MO Sta # MO Sta # MO
-5 25 55 85 115
-4 26 56 86 116
-3 27 57 87 117
-2 28 58 88 118
-1 29 59 89 119
0 30 60 90 120
1 31 61 91 121
2 32 62 92 122
3 33 63 93 123
4 34 64 94 124
5 35 65 95 125
6 36 66 96 126
7 37 67 97 127
8 38 68 98 128
9 39 69 99 129
10 40 70 100 130
11 41 71 101 131
12 42 72 102 132
13 43 73 103 133
14 44 74 104 134
15 45 75 105 135
16 46 76 106 136
17 47 77 107 137
18 48 78 108 138
19 49 79 109 139
20 50 80 110 140
21 51 81 111 141
22 52 82 112 142
23 53 83 113 143
24 54 84 114 144
Date Recorder Name
String Line Data Sheet
Track Designation Curve # Chord Length
Sample Data entry sheet
Record MO’s at each station
Note: TS, SC, CS, ST

19. Step by Step Produce Graph from Data Sheet
0
5
10
15
20
25
30
35
40
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
ID Problem areas

20. Step by Step
Trial and error column #3
Input from Field Column #2
The rest is auto calculated
Column 3 Total must Equal Column 2 Total
If total of throws is positive:
maybe not enough Rail
If total of throws is negative:
maybe to much Rail
Difference
Sum of
Differences
Half Throw
1 2 3 4 5 6 7 8
A A A A
-1 0 0 0 0 0 0.00 28.25
TS 0 1 1 0 0 0 0.00 28.25
1 5 7 -2 -2 0 0.00 28.25
2 14 13 1 -1 -2 -0.40 28.65
3 16 20 -4 -5 -3 -0.60 28.85
4 26 26 0 -5 -8 -1.60 29.85
5 30 33 -3 -8 -13 -2.60 30.85
6 43 40 3 -5 -21 -4.20 32.45
SC 7 56 45 11 6 -26 -5.20 33.45
8 49 46 3 9 -20 -4.00 32.25
9 35 46 -11 -2 -11 -2.20 30.45
10 51 46 5 3 -13 -2.60 30.85
11 49 46 3 6 -10 -2.00 30.25
12 43 46 -3 3 -4 -0.80 29.05
13 45 46 -1 2 -1 -0.20 28.45
14 50 47 3 5 1 0.20 28.05
15 49 46 3 8 6 1.20 27.05
16 43 46 -3 5 14 2.80 25.45
17 38 46 -8 -3 19 3.80 24.45
18 50 46 4 1 16 3.20 25.05
19 55 46 9 10 17 3.40 24.85
20 33 46 -13 -3 27 5.40 22.85
21 44 46 -2 -5 24 4.80 23.45
22 50 47 3 -2 19 3.80 24.45
23 47 46 1 -1 17 3.40 24.85
CS 24 48 46 2 1 16 3.20 25.05
25 38 41 -3 -2 17 3.40 24.85
26 37 34 3 1 15 3.00 25.25
27 21 27 -6 -5 16 3.20 25.05
28 18 20 -2 -7 11 2.20 26.05
29 17 13 4 -3 4 0.80 27.45
30 9 7 2 -1 1 0.20 28.05
ST 31 2 1 1 0 0 0.00 28.25
32 0 0 0 0 0 0.00 28.25
1112 1112 0 0 21.6
Measured
input from
Field
Revised
Guess
Ordinates
Label
Correction Sheet
Cumulative
of
Differences
Full Throw
in inches
Gage to
Centerline in
inchesCol 2 - Col 3
Cumulative
& Inclusive
Stations
Body of curve same # if practical
Then reduce to 0

21. 0
5
10
15
20
25
30
35
40
45
50
55
60
-10
-7
-4
-1
2
5
8
11
14
17
20
23
26
29
32
35
38
4
Offset
Before

22. After

23. -6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
-10
-7
-4
-1
2
5
8
11
14
17
20
23
26
29
32
35
Throw
Throws

24. Tampers, Before Computers

25. Tampers, Before Computers

26. Tampers, Before Computers
For 62’ Chord
1” = 1°

27. Tampers, Before Computers

28. Tampers, Before Computers
When projector gets to TS, start adding counts @ 1-count every 6-ties
When shadow board gets to TS there should be 7-counts in
Now add counts at a rate of 2-counts every 3-ties
20’ before shadow board reaches SC you should have full counts in (94)
Keep 94-counts until shadow board is 40’ from CS
Then decrease count @ 1-count every 3-ties
When shadow board reaches CS decrease @ 2-counts every 3-ties
When shadow board gets to 20’ before ST should be 0-counts
Adjust super @ ⅛” every 5-ties
TS
SC CS
ST
1-Count
every
6-Ties
7count
2-Count
every
3-Ties
20’
40’
94 Count94count
94count
1-Count
every
3-Ties
2-Count
every
3-Ties
87count
0count
Add Super
⅛ in 5-Ties
Super Out
⅛ in 5-Ties
Full Super

29. Tampers, with Computers
Lift
Line
Super
Elevation Degree
Of
Curve
Amount
of
Raise
“V” System
They
Troubleshoot
themselves
Can be
Installed on
Marc IV’s
Or better

30. Tampers
Continuous Action (CAT) ( $2.4m )