cualculo de flechas en curvas ferroviarias
TRANSCRIPT
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 )