grade

[Anonymous]

when garde is mention like 2.5%, what would that be in degrees?

wayne A new comer to the hobby

[Modelcar]

....I would figure 90 degrees {vertical}, ='s 100 % grade. and 45 degrees ='s 50 % grade and so on.....

[CSSHEGEWISCH]

Actually, a 45 degree grade would be 100%, 100 foot increase in elevation for every 100 feet horizontal.

[Hugh Jampton]

take the arcsin of the grade percentage/100
a 2.5 % grade would be asin 0.025 = 1.432543738 degrees

[Modelcar]

...Correction, my error...

[ajmiller]

If the formula is sin A = grade percentage / 100, then a 100% grade gives an angle A = arcsin(100/100) = arcsin(1) = 90 degrees.

So would a 1% grade be one foot increase in elevation for every 100 feet of horizontal distance, or one foot increase in elevation for every 100 linear feet of track? At small angles there's not much difference. The first definition implies that A = arctan(percent grade/100) and the second implies that A = arcsin(percent grade/100).

[mudchicken]

QUOTE: Originally posted by ajmiller

If the formula is sin A = grade percentage / 100, then a 100% grade gives an angle A = arcsin(100/100) = arcsin(1) = 90 degrees.

So would a 1% grade be one foot increase in elevation for every 100 feet of horizontal distance, or one foot increase in elevation for every 100 linear feet of track? At small angles there's not much difference. The first definition implies that A = arctan(percent grade/100) and the second implies that A = arcsin(percent grade/100).

AJ: Vertical Distance over Horizontal Distance......the distance along the track is the "slope distance" which means nothing until you look at a railroad ICC Val Map.

[jchnhtfd]

It's arctan. The definition of % grade used by engineers and surveyors is the feet of rise in 100 feet horizontal run. It's that horizontal run that can get you, although for most railroad grades the difference is insignificant (there are a few, though... like Mount Washington in New Hampshire, USA!). It may sound slightly odd, but the reason is that all surveying is done in terms of horizontal distances, not slope distances, and elevation changes.

[ajmiller]

I initially thought it was arctan. But then I thought, since I'm not a surveyor, that maybe Hugh posted the right formula.

[Modelcar]

...Let me take a new stab at our question...with this data.
That being: "How does one relate a % grade to an angle in degrees"....
* A 45 degree slope is a 100% grade. Us 45 as your constant and multiply by
percent grade expressed as a decimal.
Example: Convert a 20% slope to degrees
45 degrees times .20 = 9 degrees.
Example: Convert a 9 degree slope to a percent.
9 degree / 45 = .2 = 20%

[ajmiller]

QUOTE: Originally posted by Modelcar

...Let me take a new stab at our question...with this data.
That being: "How does one relate a % grade to an angle in degrees"....
* A 45 degree slope is a 100% grade. Us 45 as your constant and multiply by
percent grade expressed as a decimal.
Example: Convert a 20% slope to degrees
45 degrees times .20 = 9 degrees.
Example: Convert a 9 degree slope to a percent.
9 degree / 45 = .2 = 20%

The relationship requires trigonometry though. The angle is given by the arc tangent of the slope. The slope is rise over run, or for 20% grade, the slope is 0.2.
The arc tangent of 0.2 in degrees is 11.3 degrees, not 9 degrees.

A 100% grade has a slope of 1. The arc tangent of 1 is 45 degrees.

[MP173]

This is like college...

We have had economics (discussion of scrap metal rates), physics and chemistry (Nuclear fuel discussion), geography (Montana wheat rates), and now trig.

If I am self grading, I would give myself a 3.25 (2 A's, 1 B, 1 C).

ed

[Hugh Jampton]

Well that doesn't seem logical to me.
Surveyors measure the distance from the theolodite to the measuring stick along the ground (the hypotenuse) [they used to use a 66' chain] and sight to the height on the measuring stick (the opposite side), which makes the sin easier to calculate. To calculate the tangent they would have to mesure the distance from the theolodite to the measuring stick exactly horizontal (the adjacent side), which seems a load of hassle because of sag in the line and the difficulty of getting it level [perhaps nowadays laser measuring equipment does this simply, but railroads were built before the advent of these].
I'm not a surveyor, but I know some, and I'll certainly ask next time I see them, but if I were going to do it I'd certainly opt for the easy method.

[ajmiller]

I didn't know what a theolodite was, but when I looked it up online, it asked me if I ment theodolite which is defined as: a surveying instrument for measuring horizontal and vertical angles, consisting of a small telescope mounted on a tripod. It's a synonym of transit. I always thought that transit was a strange name since to me transit means transportation system.

[tree68]

Boy - we better not get into degrees of curvature....

[Modelcar]

...Sure glad all the old timers of about a hundred years or so ago knew what they were doing....and were all on the same page...I hope.

[ajmiller]

QUOTE: Originally posted by tree68

Boy - we better not get into degrees of curvature....

There was a thread on that awhile back.

[dehusman]

Which is why grades are measured in % not angles. It is way easier to figure with percentage.

Dave H.

[mudchicken]

QUOTE: Originally posted by ajmiller

I didn't know what a theolodite was, but when I looked it up online, it asked me if I ment theodolite which is defined as: a surveying instrument for measuring horizontal and vertical angles, consisting of a small telescope mounted on a tripod. It's a synonym of transit. I always thought that transit was a strange name since to me transit means transportation system.

It is a transit because you could "transit" the telescope, i.e. flop the scope direct and reverse...Transits do not necessarilly have a vertical component to measure angles, theodolites do. Try looking up "Parkhurst Theodolite" and Total Station now.

[jchnhtfd]

QUOTE: Originally posted by Hugh Jampton

Well that doesn't seem logical to me.
Surveyors measure the distance from the theolodite to the measuring stick along the ground (the hypotenuse) [they used to use a 66' chain] and sight to the height on the measuring stick (the opposite side), which makes the sin easier to calculate. To calculate the tangent they would have to mesure the distance from the theolodite to the measuring stick exactly horizontal (the adjacent side), which seems a load of hassle because of sag in the line and the difficulty of getting it level [perhaps nowadays laser measuring equipment does this simply, but railroads were built before the advent of these].
I'm not a surveyor, but I know some, and I'll certainly ask next time I see them, but if I were going to do it I'd certainly opt for the easy method.

Hugh -- you are so right.[:D] Precise surveying in the bad old days with chains or steel/invar tapes was a hassle; that's when I started in the trade. Not only did you have to get the chain tension right (spring balances were used) but, for really good work, you had to properly support the chain (or tape) and compensate for its temperature (even with invar tapes) (there was a thermometer which measured the temperature of the tape. That gave you slope distance. You also measured -- with your transit or theodolite (MC -- I'll bet my transit is older than yours!) -- the horizontal angles from some reference, and the elevation difference (in precise work, you used a level for the elevation difference -- which is another pain in the...[:(]. At that point, with all your notes collected, you were ready to go back to the office (you hoped) and do your sums, which amounted to correcting all slope distances to horizontal distances, and correcting those to sea level and adjusting the whole survey (properly done surveys never go from x to y, unless the locations of x and y are both known to much better accuracy than the survey you are doing -- they go from x to y and back to x, and the idea of the adjustment is to make the location you found for the second x the same as the location you started from...). Once you were done with that, you were done for small surveys -- but for larger ones you had to adjust the whole mess for the curvature of the earth, which is why I have a set of seven place log tables for trigonometric functions on a shelf somewhere.

Yes it is a pain. But for those who like the work, getting the whole thing right, really right, gives a real feeling of accomplishment!

The newer 'total stations' take a lot of the fun out of it, since they record vertical angle, horizontal angle and distance -- measured electronically -- all at the same time, and convert the distance into horizontal distance and elevation change automatically.

But you still have to adjust the results, and you still have to be a fanatic about precise work in the field to make it all work right.

[Modelcar]

...A very interesting subject. I do have a difficult time understanding how surveyors figure a course, one starting from both ends of a tunnel...a long one, and meet in the middle. I understand the theory but don't understand how that actual surveying...going through the actual work of measuring and carrying the figure on for miles, etc...and then meet in the middle of many miles {for some bores}, within inches of center....All that without the errors adding up to be too much error over such distance.....