Lindsayts, on 27 September 2016 - 01:49 AM, said:
The line was laid out with a team of surveyors, pegging out the line using chains and a set of theodelites.
There are two things wrong with that statement: (1) A theodolite is used for measuring angles (vertical and horizontal planes) not distances, and (2) it is the chain (singular) that is used to measure distance -- horizontal distance.
As a pointed out on Monday, if you do a web search on "survey +grade" you'll find (1) run is measured along the horizontal, and (2) run is measured along the hypotenuse (the path the wheels roll). (The Wikipedia article "Grade (slope)" chooses Interpretation 1 but goes on to say, in railroading, it's Interpretation 2.) Then I said that for typical railroad grades, it's "macht nichts." Goku substantiated that.
I'm going to wax eloquent on this subject, but I need to establish my credibility.
- In 1957, I had a summer job working with a Pennsylvania Highway Department Surveying team. Among other things, we surveyed Interstate 80 in the Stroudsburg area. Well before the end of the summer, I was relieving the transitman and "running the gun."
- In the 1970s as an IBM engineer, I augmented an APL implementation of COGO with graphics output.
- With Open Rails, I proposed a "route designer" as a tool to accompany a route editor. The proposal went over like the proverbial "lead balloon."
I want to talk about three areas. The first two relate to surveying practice in highway and railway design and surveying. The third relates to an MSTS dirty little secret.
Route Design
Route design largely takes place in an office -- yesteryear and this year. Although CAD has supplanted the drafting table to some degree, it is 2D paper that will be used in the field. Most used are drawings in the horizontal plane. There, the route path is partitioned by stations. In the US, there is a whole-numbered station point every 100 feet. Also, there are construction points: start of curve, end of curve, intersection points, etc. that do not necessarily fall at 100-foot intervals.
The other type of drawing is the vertical profile of the route. Vertical profiles are plots of elevations (heights) of the route at distances along the route path. Given the relatively easy curves associated with highways and railways, the straight-line segments between segments are a reasonable approximation of the route path.
Field Work
Field work, done by surveying teams, is mostly stationing -- erecting stakes with pins at stations -- and leveling -- obtaining an elevation value to enable approximating the terrain.
Tools for stationing are the transit and chain. In 1957, a transit amounted to a small telescope on the top of a tripod. Also, there was a plumb bob centered beneath the scope, such that the scope could be located directly over the center of a pin or nail in a wooden stake marking a station. (As I recall, the head of the nail was 2 or 3 mm.) The base of the scope was levelable, and leveling was an important part of moving the transit from one point to another.
The preponderance of the distance measurements made with the transit were made in the horizontal plane. I only saw one measurement made along a slope all summer long. Trigonometric functions were acquired from a book of tables, and only the Party Chief carried one. Since calculation (multiplication) was long-hand and by the Party Chief, he rarely called for such a measurement. Measurements in the horizontal plane were done with the chain (graduated steel tape marked in feet and hundredthsin the US). One end was held on a stake nail with a plumb bob used at the other end. Occasionally, bobs could be used on both ends, but accuracy suffered.
Preliminary Summary
When railroads (real or virtual) are built with sectional track or rail of specific length it is only natural to use the length as the run. To do otherwise would require extracting a square root.
An MSTS Dirty Little Secret
A bunch of years ago when I first joined the Open Rails Development Team, I discovered that MSTS track sections are rigid bodies. That's an important realization for curves. Elevate a curve section at one degree say, and the outbound end of the curve is no longer level; it is only level at the pivot end. Of course curved sections are generally pretty short (short meaning limited angular span). So the tip is very slight.
However, dynamic track is different; you can make an angular span up to 90 degrees. Worse, dynamic track can have five subsections (straight, curve, straight, curve, straight), and the whole business is treated as a rigid section. Now (this will blow your mind), perform an experiment: Layout a single dynamic track section with subsections 0, R<90, 0, R<90, 0. That is, the straight sections are of zero length, and the two curved section are of radius R (whatever you want to make it) and 90 degrees in span. (Both curves have the same specification.) Finally, elevate the section at, say, 3 degrees. Question: If the height at the start of the section is H, what is the elevation at the end of the section? Answer: H. How can that be? Answer: The section (all subsections) is a rigid body. So what is the problem? We are led to believe the grade is constant (3 degrees) all throughout the path. It isn't. (The path does not follow the helical curve we expected.)
Open Rails, with its objective of matching MSTS behavior does just that. But, any new route editor should consider, in the future, handling curved sections the RIGHT way in addition to the MSTS way. (It would take an option setting, and that is the domain of Open Rails. It is important that the traveler and the geometry have the same behavior.)
Please forgive the length of this post.