Drafter Selected Radius

# Surveying a Route

**10**
*Wednesday*
Feb 2016

Posted Reference, Right of Way

in
**10**
*Wednesday*
Feb 2016

Posted Reference, Right of Way

inMike asked an excellent question in the last post regarding how radii are laid out in the field. In the model world, we have the advantage of slipping some sectional track together, and wherever it lays, it lays, or for those using flex or hand laying, we draw a couple of straight lines representing where we want the track to go and we swing an arc using a pencil on a string secured by a nail.

A route preliminary survey doesn’t start much different than the latter. A couple of disclaimers first; I do not work for a railroad nor have I surveyed a route. The knowledge conveyed next is one of a few ways of inserting a radius in the field per my 1907 ICS Reference Library.

The Survey team will carry with them, among other things, an engineer’s transit, a 100 foot tape or chain, two transit poles, lots of stakes and a drafting board, scales, triangles, paper, pencils, radius protractors in the “office equipment.”

Let’s start with an example straight route, arriving from the left, as shown. The numbers represent staked stations, by 100, such that Sta. 246 is 24,600 feet from the origin of the route. Due to some obstacle, the route needs to diverge from its path at Sta. 248 + 25 (24,825 ft). Moving he transit to the last station, the Surveyor swings his transit about and notes an acceptable divergent route, Δ = 30° to the right of the previous path. Staking continues.

At the end of the day, the Surveyor conveys his notes to the draftsman, who translates the measurements onto a topographical map. At the divergence, the draftsman uses one of the radius protractors to select a suitable radius to be inserted.

Drafter Selected Radius

In this example, I have chosen to include a 6° curve, which equates to a radius of 955 feet, therefore the distance T is 256 feet. As mentioned in a previous post, the radius R can be found through 5730 / D, where D is the degree of curvature.

Using mathematical tables or geometry, the Point of Curvature (PC) and Point of Tangency (PT) are determined with respect to Sta 248 + 25, also known as the Point of Intersection (PI). For our reference, the equation to determine the distance T from PI to PC or PT for a given divergent angle (Δ) is R tan (Δ / 2), were the curve radius R is in feet and the angle Δ is in degrees.

When the Survey team returns to lay the final right of way, they will “backup” from the PI 256 feet, or advance from the prior station stake if they feel like doing a little more math that day (these distances shown as reference). The transit will be placed on the PC and swung in the direction of curvature ½ the selected degree of curvature, 3° in our example. A stake will be placed 100 feet out, representing the first chord.

With a pole at the PC, the transit is moved to the new stake placed 100 feet and 3° out. Using the preceding pole and the new stake, the transit is used to sight placement of the next stake, now a full degree of curvature (6° here) from the last chord. The remained of the chords will all be placed 100 feet and 6° divergent from the prior chord until it aligns with the PT on the divergent route.

Finally, with all stakes in place, the roadbed and rails can be centered on the stakes, thereby laying tracks along the desired routes with selected curves.

Thanks for the request Mike, and I hope this answers your question.

**08**
*Monday*
Feb 2016

Posted Historical, Layout Design, Reference, Right of Way

inDigging for information continues, and I have had my head buried in many old documents of late, a year’s worth of newspapers in the last three weeks actually, and that will continue for some time.

A few weeks back, at Terry Smith’s prompting, I dug out my copy of the 1888 Scientific America article on the B&SR and referenced a change in my layout design with respect to superelevation of the rails. At the same time I located a later article pertaining to the use of narrow gauge railroads on the front lines during war time. The B&SR was once again referenced.

Like the first (1888 Sci Am), the 1920 Proceedings of the American Society of Civil Engineers article references tight radii, at least per standard gauge standards. Scientific America mentions a radius of 20 degrees and the ASCE article states, on page 664, a radius of 36 degrees was in use on the alignment, in addition to the 20 degree, as well as an average speed of greater than 20 MPH.

The 36 degree curvatures has not, to date, matched any markings on the Valuation maps or the Harrison surveys, so I am thinking that this may have been the radius of the curve (or curves) into the Forest Mills facility. I am not sure if this spur constitutes “the alignment,” as the author states, if such references the main line only. The Harrison survey includes radii of less than 20 degrees, including a 23 degree radius as part of the Y compound curvature departing Bridgton yard and 25 degrees in the proposed village yard.

Looking at the Valuation map V2-1 and map obtained from the Registry of Deeds, the radius of the ROW preceding the Forest Mills spur is about 14.5 degrees and, if the map is even close to being accurate, the radius departing the main line is *sharp*. Quite frankly, it looks tighter than 36 degrees, however I have not pulled out the drafting equipment yet to approximate the radius.

For those still pondering the question of how tight of a radius is OK for a 2-footer, the following real world examples may help, with approximate scale radii, keeping in mind that the tightest verified radius on the main line was 23 degrees:

- 16 deg = 358 ft = 89″ (O) = 49″ (HO)
- 20 deg = 286 ft = 72″ (O) = 40″ (HO)
- 23 deg = 249 ft = 62″ (O) = 34″ (HO)
- 25 deg = 229 ft = 57″ (O) = 32″ (HO)
- 36 deg = 159 ft = 40″ (O) = 22″ (HO)

There is anecdotal information that locomotive #7 had to back into the Harrison corn shop spur due to the tightness of the curvature. Whatever radii you choose for your line, make sure you don’t have to run Billerica and Bedford cab-forward, unless that’s your preferred style.

**08**
*Friday*
Jan 2016

Posted Historical, Layout Design, Reference, Right of Way

inIn the course of other on-going research, Terry Smith reminded me of the February 11, 1888 Scientific American article written about the Bridgton and Saco. I had been remiss in reviewing my copy of this publication prior to giving my MARPM presentation this year, as it would have allowed me to provide better information on the use of superelevation on the railroad.

For those researching designs and information for their own layouts, superelevation is the practice of making the outer rail higher than the inner rail, within a curve, in order to decrease or eliminate the lateral (outward) pressure on the rails and to avoid the danger of derailment. This can be accomplished with a very simple mathematical equation, which I provide an example of below.

Within the presentation, I had commented that I would build my layout using 45 MPH as the railroad’s design speed, with this number being drawn from a comment Ernest Ward made within his biography “My First Sixty Years in Harrison, ME” (pg 16):

Fastest speed recorded, Number 5 with two passenger cars – three and one-fourth miles in four minutes.

This equates to 48 MPH, therefore the use of 45 MPH. What is missing from the statement is where this show of speed occurred. It is unlikely that this was an average speed on the line, or even over the majority of the line. It is more likely this was exhibited on a (relatively) straight portion of the line.

The extra bit of information I was reminded of when reviewing the Scientific American (Vol. 58) article was in relation to an actual exhibition of the railroad’s capabilities to visitors from Central and South America:

The visitors were disembarked at the beginning of the 16 deg. curve, and, despite their fears and misgivings when Mansfield, who chaperoned the party, told them the train should round that sharp arc at a speed of 25 miles an hour, the thing was done before their very eyes.

The equation to calculate superelevation, from my 1908 reference book on railroad engineering is:

e = (G’ * v^2) / (g * R)

where,

- e = superelevation, in feet;
- G’ = horizontal distance between the rail head centers, in feet;
- R = radius of curvature, in feet;
- v = velocity of train, in feet per second;
- g = acceleration due to gravity (32.174 ft/s^2)

The distance between the rails for a two footer is 24 inches, and the rail head width for 30 lb ASCE rail is 1 11/16 inches, per LB Foster. This sets G’ equal to 2.14 feet. The radius of curvature given in the Scientific America demonstration is 16 degrees, or 358 feet radius, using R = 5,730/D, a fairly accurate conversion equation. The velocity of the train George Mansfield had run by was 25 MPH, or 36.7 ft/s.

We mix all of these numbers up in the equation and get a superelevation, in feet:

.25 ft = [2.14 ft * (36.7 ft/s)^2] / (32.174 ft/s^2 * 358 ft)

The rails on this particular curve referenced likely had 3 inches of superelevation, resulting in a “lean” into the curve of approximately seven degrees. This would equate to 1/16 inch rail elevation for those of us modeling in O scale, and 0.034 inches for those practicing the HO arts. Not too shabby.

Within my MARPM presentation, I used scale radii (48″, 60″, 72″, etc.) converted to real world curvatures (a 72″ scale radius equals a real world 20 degree curve). In light of this “new” information, I will recalculate my curvature elevations using a 25 or 30 MPH design speed, rather than the “more modelgenic” numbers I had created using a 45 MPH design speed.

**31**
*Thursday*
Dec 2015

Posted Historical, Layout Design, Reference, Right of Way

inThe Forest Mills Company was a good customer of the railroad; taking receipt of coal and exporting “any or all products of wool or cotton or both in the town of Bridgton,” according to the 1768-1968 Bridgton history book.

As the facility grew, additional energy was needed to supplement that which was coming from the Eighth and Ninth power sites, on which the Mills were situated. A siding and coal trestle were stated to have been built to deliver the fuel around 1900 (Jones, 55) to “facilitate the unloading of coal and other factory supplies.”

Jones mentions (pg 67) 1,200 tons of coal were delivered to the Company in 1905. As the Company shed the wood working leases at the very end of the 1800’s, it is possible, likely, that all of this coal was destined for the woolen mills located at the corners of Kansas, Mill (also Kansas, current day) and Oak streets.

The railroad used half as much coal as the Mill did within the 1905 year to power five locomotives, running six days a week. I am not sure if the Mill ran six or seven days a week, but they did run eleven hours a day, according to the 1880 insurance map documents in the American Textile History Museum’s collection.

So how much is 1,200 tons? Assuming Bituminous coal has an average bulk density of 50 lb/cu ft (it runs from 42 to 57 lb/cu ft), it was 48,000 cubic feet (1,778 cu yd), or the equivalent of 127 modern day triaxle dump trucks (@ 14 cu yd/full capacity) making a visit throughout the year.

So one of those problems I have been struggling with has been the distance from the Mills which the sidings were built. Taking a moment to reference Google Maps and plot out a path to Mill #2, which had the boilers, was approximately 2,000 feet from the coal trestle. There has been much stated about shoveling coal from a standard gauge car to two or three narrow gauge “gondolas” right beside it, but who wants to drag that much coal 0.4 miles from the trestle to the Mill?

Well, the answer may have materialized during my searches yesterday. I was searching for a copy of the original Harrison extension map referenced by Bill Jensen in his *“Harrison Interlude”* article (Short & Narrow Rails #15) within the Maine Registry of Deeds and, not only did I come away with a digital copy of that map, I also located a Forest Mills map.

Likely generated when the Forest Mills facilities were shuttered and put up for sale in 1911, per the 1768-1968 Bridgton history, the deed map of that year shows a rail line extending from just westward of the trestle and siding to Mill #2 along the ~100 ft wide sliver of property Forest Mills retained when it sold the areas around the complex for residential and other business.

I am on the hunt for some corroboration. The Sanborn insurance maps from 1907 and 1914 do not show this spur, but the insurance maps are known to be incorrect in some details. The 1916 valuation map shows the siding and trestle, and the Forest Mills property intersecting the ROW, so the spur may have been removed prior to 1916, possibly shortly after the deed was created as the railroad no longer had a reason to maintain the switch and spur.

It also may not have been included on the valuation map because it is entirely on Forest Mills property, with the exception of the switch, of course, but this is unlikely. USGS topographical maps covering the Harrison extension area, the Norway 15 minute quadrangle, are only available for 1896 and 1949, missing the period I’m after (he Quads do show the railroad on other maps, so if you are curious, the collection is available for review here).

The Forest Mills facilities were acquired by and served the American Woolen Company around 1918 per the June 1919 copy of “United States Investor” and produced cassimere (old spelling of cashmere), which is mentioned in their 1921 publication, possibly a company annual report of sorts. They may not have needed the energy coal supplied and could get by with just water power in producing the lighter weight material, also a reason to have pulled up the tracks, if they still existed, or not have them relaid.

I don’t have all of the answers, but this map gives me more sound information on moving that much coal to the Mill, and this is prompting me to change my track plan. I like the notion of another company-specific spur on the narrow gauge. The Hall & Hamblin grist mill, later Ingalls & Morrison feed mill, in the Bridgton yard had its own spur to provide coal service, so why not the woolen mills?

Now how did Pondicherry get their 2,200 tons of coal…

Have a good new year, everyone.