Railroad ROW w/ Searles Spirals

@bill93

Trivia note.

This particular "route" covered 116 miles, and included 63 curves (33 w/ spirals & 30 w/o spirals).

A tabulation of the spiral curves used [central curve degree, Spiral Delta & # chords x chord length]:

3?ø, 4?ø57' 11x30 18 times (36)

4?ø, 9?ø00' 15x30 5 times (10)

4?ø, 4?ø12' 7x30 1 time (2)

3?ø, 2?ø15' 5x30 1 time (2)

2?ø30', 3?ø22'30" 9x30 5 times (10)

2?ø, 2?ø06' 7x30 3 times (6)

So in theory, only 6 solutions were needed going in, a 6 going out.

Non-spiral(ed) curves:

1?ø30' 8 times

1?ø00' 19 times

1?ø20' 1 time

0?ø30' 1 time

2?ø00' 1 time

😉

Calculated Centerline to existing tracks

Considering that 110 years have passed between construction and the retracement, I think this looks pretty good.

Record alignment TO tracks

Tangent PT 383+87.7
0.05 R
0.04 R
0.08 R
0.08 R
0.06 R
0.05 R
0.01 R
0.03 L
0.02 L
0.01 R
0.06 L
0.04 L
0.07 L
0.06 L
0.02 L
0.06 L
0.00 
0.03 L
0.02 R
0.00
0.03 R
0.00
0.01 L
Spiral PS 405+63.9
0.14 L
0.28 L
0.19 L
0.18 L
0.14 L
0.10 L
0.12 L
0.22 L
Curve PSC 410+13.9
0.43 L
0.54 L
0.56 L
0.56 L
0.57 L
0.55 L
0.48 L
0.44 L
0.38 L
0.36 L
0.28 L
0.25 L
0.28 L
0.21 L
0.17 L
0.15 L
0.14 L
0.14 L
0.17 L
0.19 L
0.15 L
0.18 L
Spiral PC 422+38.9
0.22 L
0.19 L
0.25 L
0.21 L
0.22 L
0.02 R
Tangent PT 426+88.9
0.25 R
0.31 R
0.25 R
0.20 R
0.01 R
0.01 L
0.30 L
0.29 L

@loyal

I've located and checked many miles of track around here and have yet to find any r/w monument and your findings run true to the average of what I've found for the location of existing tracks in the last 50yrs.

@loyal

Like your work Loyal.

If Bill93 would read some survey books he would fine out how the Spirals were done in the field.

If he would look at  Surveying Theory and Practice by R. Davis,F. Foote, J. Anderson and Edward M. Mikhail, 6th edition, chapter 17

starting on page 678 would help him. Also an internet search will give him all he ever wanted to know.

JOHN NOLTON

The 6th edition of the book I referenced above is year?ÿ1981. Another book would be

The Transition Spiral and its Introduction to Railway Curves, by A.L. Higgins?ÿ(1921)

JOHN NOLTON

Posted by: @john-nolton

If?ÿBill93 would read some survey books he would fine out how the Spirals were done in the field.

I have 4 survey textbooks that might have covered the topic, 2 of which each give a method of defining and laying out spirals but neither is the Searles definition.

Posted by: @loyal

Calculated Centerline to existing tracks

I haven't calculated anything it, but the fact the circular curve is consistently off in one direction makes me wonder if the curve was used for one of the rails and not the centerline.?ÿ I've heard that was common for some companies.

@bill93

That is certainly possible, I have also heard of that as well.

Loyal

Posted by: @loyal

So in theory, only 6 solutions were needed going in, a 6 going out.

So there was some economy of design effort. Still, I don't know why one spiral design to go with each degree of circular curve wouldn't have sufficed.

The Money Shot(s).

I didn't get involved with this until my client asked about the ƒ??spirals,ƒ? and after looking at the data, I visited the site with my client (County Surveyor) and we did some additional field work to verify the data supplied by the contract surveyor. Several ReBars, NGS Bench Marks, and a couple of PLSS Corners were observed, as well as about a dozen of the Concrete Fence posts. The ƒ??monumentsƒ? checked ƒ??spot on,ƒ? but the Concrete Fence Posts varied as much as 0.5 feet. We determined that the Fence Post Shots were NOT observed on the same face of the posts each time (centerish, outside face, inside face, etc.). This was confirmed by the contract surveyor.

My experience with this particular Railroad indicates that the OUTSIDE FACE (away from the tracks) is nearly always the best indication of the ROW Limit as intended by the Railroad. So (not surprisingly) many of the fence shots are a little on the ƒ??short side.ƒ?

Be that as it may, the whole shoot'in match (Record, Tracks, Fences) comes together pretty well. IMO the fences (ROW Posts) FIT the spirals pretty damn good.

Record to Concrete Fence Posts

Tangent 383+87.7 PT (100 ft. ROW)

49.4 L

50.2 L

49.3 R

50.0 L

49.1 R

50.0 L

48.8 R

49.7 L

49.3 R

50.1 L

50.2 L

49.9 L

49.1 R

50.4 L

51.1 L

48.9 R

50.4 L

49.2 R

50.8 L

49.5 R

50.2 L

50.0 R

49.8 R

50.3 L

50.1 R

49.4 R

50.1 L

49.7 R

50.5 L

49.4 R

50.2 L

50.0 R

49.8 L

49.7 R

49.9 L

50.1 R

50.0 L

50.2 R

50.0 L

50.5 R

Spiral 405+63.9 PC AND WIDTH CHANGE (150 ft. ROW)

75.9 R

75.5 L

74.7 R

75.2 L

74.7 L

73.8 R

74.7 L

74.4 L

73.7 R

74.9 L

75.0 L

73.8 R

73.7 R

74.8 L

Central Curve PCC 410+13.9

74.6 L

74.3 R

74.8 R

75.1 L

75.1 L

74.3 R

74.8 L

75.0 R

74.9 L

74.4 R

74.6 L

74.4 R

75.2 L

74.3 R

75.3 L

74.8 R

72.9 L

75.0 L

74.2 L

75.3 R

74.0 L

73.5 L

75.4 R

75.3 R

72.9 L

73.6 L

ROW WIDTH CHANGE @ SECTION LINE (250 ft. ROW)

125.5 R

125.4 R

125.0 L

124.5 L

Spiral 422+38.9 PCS

126.4 R

125.5 L

124.4 R

124.7 L

124.6 L

124.3 L

Tangent 426+88.9 PT

124.4 R

124.3 L

124.0 R

124.8 L

124.7 L

ROW WIDTH CHANGE (100 ft. ROW)

50.2 L

50.1 R

50.3 L

49.3 R

48.9 L

49.5 R

50.1 R

50.6 L

50.5 R

50.4 L

50.3 L

49.8 L

50.8 R

?ÿ

Loyal

Posted by: @bill93

I think I have it (within hundredths) in this spreadsheet

Download (Loyal_spiral.xls)

I would hate to have to do this without the spreadsheet, like the original designer did.

I never did figure out what the 51?ø 50' means.

The 51?ø50' is the angle between the "centerline" @ POC 419+76.8 and the Section Line between Sections 15 & 22.