What tools and methods are used to calculate RR and highway grades to the hundredth of a percent? [?]
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How far does the track rise in 100’? If it rises 6", the grade is 0.5%.
The tool of choice would be a transit, I’m sure… Unless you have another point of reference, grade significant to the railroad is almost imperceptible.
First off, you have to decide which two points you’re measuring the grade between-- there is no such thing as grade at a point, except theoretically. Once you’ve got the two points: is the track between them straight or curved? If it’s straight you could measure the inclination directly, setting up the transit or theodolite directly over the railhead and measuring the vertical angle to a rod held vertically atop the railhead at the other end of the line (correcting for earth curvature if necessary). Accuracy of 0.01% won’t be too hard unless the heat waves are a problem.
But more likely you’ll set up a level (or transit or theodolite) alongside the track and have your assistant hold the rod vertical atop the railhead at each end of your line, thus getting the elevation gain between them. Then you’ll have to measure the distance between them. If your line is a couple hundred feet long you can get the elevation gain to a small fraction of an inch, which again allows you to get the grade to better than 0.01%.
If the track is curved the horizontal distance neasurement might take a little thought. After that you have to decide whether your “grade” figure is to include an allowance for curve resistance.
…Mentioning the “earth’s curvature” factor above…{Timz}, prodded me to wonder about such railroad constructors building the Cascades Tunnel back about 1929…Would they have figured the “curvature” factor in their calculations in building that tunnel…Such as starting from both ends and meeting precisely on point whenever they “broke thru”…? Just curious…and of course the same goes for much longer tunnels such as some in Japan that are in the area of 30 miles in length…
I don’t think timz meant the Earth’s curvature, seems more like goin up a hill around a bend.
But the answer to your question is no, the curvature of the Earth is not factored in. This is because surveyor’s equipment is initially levelled by a spirit level or a plumb bob. Both of these work due to gravity, and therefore point automatically to the centre of the earth. As an example you could survey a completely level line all the way round the World, and wherever you put a spirit level it would show that it was level, but looking at it from space you would plainly see it was curved.
…And I thought later after asking the question…Both surveyors would be using the same process from both ends so I suppose no compensation would be needed anyway…
You’re better off using a survey level & 100 ft. surveyor’s chain as opposed to a transit.
(It’s faster and trig levels have a penchant for inconsistencies)
Railroads calculate vertical curves by mathematical formula (it’s actually more of a parabola, but…)…and you connect different grades together with those vertical curve for a smooth transition/ no kinks. You folks (timz & co.) are making something relatively easy into something difficult and could use some exposure to what surveyor’s equipment is really used for. Earth curvature is so slight that for figuring grades, we all are card carrying members of The Flat Earth Society. (Hugh, is that you I see grinning?)
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…Is the earth curvature ever a factor in ANY railroad building surveying process…?
I suspect not if you are using a 100 ft chain. It must take a longer distance for that to show up.
I always found that grading on the curve worked better for me.[:D]
I guess since you said ANY, it is a factor in the design and installation of the railroad long distance microwave communication systems but that has nothing to do with the track.
…Now that’s a pretty strong point…!
…We do have a figure {it varies a very small bit}, of 8" per mile from flat for each mile traveled forward and when one discusses the process of surveying I began to wondering if that had to be considered when doing measuring of great distances such as long railroad tunnels.
…We do have a figure {it varies a very small bit}, of 8" per mile from flat for each mile traveled forward and when one discusses the process of surveying I began to wondering if that had to be considered when doing measuring of great distances such as long railroad tunnels.
Sorry for repeat…system messed up trying to post…
“8 inches per mile” is almost right-- the earth’s curvature drops 8 inches below a horizontal line in one mile, but it’s proportional to the square of the distance. So 32 inches in two miles, etc.
And yes, the Cascade Tunnel should be curved. As I recall you should be able to see through a 7.79-mile tunnel, but a person standing at one end of a ten-mile constant-grade tunnel probably can’t see the other end.
…Ok, and if we’re measuring and digging from both ends to meet in the center… by theory…No compensation {because of the earth’s curvature} is needed in keeping the tunnel bore lined to meet in the center…?
If you want to know the average grade over a mile-long stretch of straight track, the quickest is unquestionably the transit/theodolite, as long as the heat waves aren’t bad and accuracy to 0.01% is good enough. (Don’t forget that 8-inch correction for earth curvature.)
If you need accuracy to 0.001% then use the level.
Can you tell I’m not a surveyor? You’re lucky I didn’t suggest a theodolite. I’ve set them up before, and they are a total pain. Tool notwithstanding, I think we are talking the same basic principle.
Has GPS gotten accurate enough to use for these calculations?
…Commerical GPS units avail. to us I’ve seen in operation tell position within a few feet…Is that useful for position in surveying…Doesn’t seem like it to my judgement. But professional equipment seems to be ready for the job…Remember the 9 miners trapped a few years ago in Pennsylvania near Somerset…{Near my home}…The 30 inch drill was positioned with great help by GPS and they broke through right where the men were trapped 240 ft. below the surface and a mile plus from the mine entrance.