String Lining Curves

Review - Anatomy of a Curve

Direction of up Stationing

TS

SCCS

STThe 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, andif continued will make a full circle

TS

SC

CSST

SpiralSpiral

Body of Curve

30’ Cord

15’15’

R=50

0’

R=500’

MO

a

b c

Calculating an MOFrom 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 - bMO = 500 – 499.775

MO = 0.225’ = 2¾”

This is essentialfor string lining Curves

a

R = MOft

2 + a2

2(MOft)2

Review

Measuring Middle Ordinate on a Curve1.Mark out regular intervals on the rail2.Assign a number to each marking3.Place string on markings and pull tight4.Measure half way between markings5.Record data at each MO6.Create a graph showing tolerances

110

765

4

3

2 9

8

Basic Principles

Measuring Middle Ordinate on a Curve1.Mark out regular intervals at 1’ or ?2.Assign a number to each marking3.Place string on markings and pull tight4.Measure half way between markings5.Record data at each MO6.Create a graph showing tolerances

110

765

4

3

2 9

8

OR

String Line Measuring

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

Station # Measure 1/10 ths “

Station # Measure 1/10 ths “

1 0 10 152 2 11 143 3 12 164 5 13 115 7 14 86 13 15 57 16 16 38 16 17 19 17 18 0

String Line Measurements

TS

SC CS

ST

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 Excel3. Produce Graph in Excel4. Do trial & error exercise in Excel5. Layout Throws in Field

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

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

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

Step by Step

1. Eye ball beginning of spiral and label 02. Go string length back3. Measure stations and label on base of rail

Must be whole number when divided into string length4. Eye ball end of curve and go string length beyond5. Record all stations on form and base of rail6. Identify existing centerline of track (nail, stake etc.)

TS

ST

•

••

•••

•

•

•

•

•

•

••

•

•

Step by Step

7. Measure MO’s at each station8. Record on form as number of 1/10 ths of inch9. Document potential clearance issues, including track c-c10.Do trial and error methodology in Excel11.Create Graph in Excel12.Present throws to crew for correction

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 1190 30 60 90 1201 31 61 91 1212 32 62 92 1223 33 63 93 1234 34 64 94 1245 35 65 95 1256 36 66 96 1267 37 67 97 1278 38 68 98 1289 39 69 99 129

10 40 70 100 13011 41 71 101 13112 42 72 102 13213 43 73 103 13314 44 74 104 13415 45 75 105 13516 46 76 106 13617 47 77 107 13718 48 78 108 13819 49 79 109 13920 50 80 110 14021 51 81 111 14122 52 82 112 14223 53 83 113 14324 54 84 114 144

Date Recorder Name

String Line Data SheetTrack Designation Curve # Chord Length

Sample Data entry sheet

Record MO’s at each station

Note: TS, SC, CS, ST

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

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 8A A A A

-1 0 0 0 0 0 0.00 28.25TS 0 1 1 0 0 0 0.00 28.25

1 5 7 -2 -2 0 0.00 28.252 14 13 1 -1 -2 -0.40 28.653 16 20 -4 -5 -3 -0.60 28.854 26 26 0 -5 -8 -1.60 29.855 30 33 -3 -8 -13 -2.60 30.856 43 40 3 -5 -21 -4.20 32.45

SC 7 56 45 11 6 -26 -5.20 33.458 49 46 3 9 -20 -4.00 32.259 35 46 -11 -2 -11 -2.20 30.45

10 51 46 5 3 -13 -2.60 30.8511 49 46 3 6 -10 -2.00 30.2512 43 46 -3 3 -4 -0.80 29.0513 45 46 -1 2 -1 -0.20 28.4514 50 47 3 5 1 0.20 28.0515 49 46 3 8 6 1.20 27.0516 43 46 -3 5 14 2.80 25.4517 38 46 -8 -3 19 3.80 24.4518 50 46 4 1 16 3.20 25.0519 55 46 9 10 17 3.40 24.8520 33 46 -13 -3 27 5.40 22.8521 44 46 -2 -5 24 4.80 23.4522 50 47 3 -2 19 3.80 24.4523 47 46 1 -1 17 3.40 24.85

CS 24 48 46 2 1 16 3.20 25.0525 38 41 -3 -2 17 3.40 24.8526 37 34 3 1 15 3.00 25.2527 21 27 -6 -5 16 3.20 25.0528 18 20 -2 -7 11 2.20 26.0529 17 13 4 -3 4 0.80 27.4530 9 7 2 -1 1 0.20 28.05

ST 31 2 1 1 0 0 0.00 28.2532 0 0 0 0 0 0.00 28.25

1112 1112 0 0 21.6

Measured input from

Field

Revised Guess

Ordinates

Labe

l

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

0

5

10

15

20

25

30

35

40

45

50

55

60

Station

Offset

Before

0

5

10

15

20

25

30

35

40

45

50

StationAfter

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

Station

Throw

Throws

Tampers, Before Computers

Tampers, Before Computers

Tampers, Before Computers

For 62’ Chord1” = 1°

Tampers, Before Computers

Tampers, Before Computers

When projector gets to TS, start adding counts @ 1-count every 6-tiesWhen shadow board gets to TS there should be 7-counts in

Now add counts at a rate of 2-counts every 3-ties20’ before shadow board reaches SC you should have full counts in (94)

Keep 94-counts until shadow board is 40’ from CSThen decrease count @ 1-count every 3-ties

When shadow board reaches CS decrease @ 2-counts every 3-tiesWhen shadow board gets to 20’ before ST should be 0-counts

Adjust super @ ⅛” every 5-ties

TS

SC CS

ST1-Count

every6-Ties

7count2-Countevery

3-Ties 20’

40’

94 Count94count94count

1-Countevery

3-Ties 2-Count

every3-Ties

87count

0count

Add Super⅛ in 5-Ties

Super Out⅛ in 5-Ties

Full Super

Tampers, with Computers

LiftLine

Super Elevation Degree

OfCurve

Amountof

Raise

“V” System

TheyTroubleshootthemselves

Can beInstalled onMarc IV’sOr better

TampersContinuous Action (CAT) ( $2.4m )