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#21 ·
@kormsen:
....yes, that will work IF you have a wall nearby..:-D AND in germany we call it METERSTAB showing centimeters. The people calling a Meterstab "Zollstock" just want to annoy the "Meterstab-men".

@bunker:
i´d say you seem to be right. but ANY two points is wrong, they should be in a straight track-line, then it can be ANYTWO points. In the curve, you have to calculate.....
and for sure: GRADE is something that does not depend on length. each point of your layout has its own grade. and you WISH to be the grade in stations is "0" and on "grades" it should have a nearly constant grade of the amount u choose.
you have to be aware that badly layed down tracks may have a variety of grades, even though you meassured out an average grade. So to define an grade and level out our layout, i would choose to meassure most constantly, say every foot or max. every 2 feet. that asures you to have no badly "grade-holes" or "grade-hills" on your track.

example herefore:
i have layed some bricks as a basement for my trestle-bents. but i did too much packing and ramming, so the bricks came out some mm over the winter.
so, as my average grade from middle to upper station is nearly exact 3.96 %, i have on that way a "ramp" up to my trestle of about 5-5,5%, causing my loco at the edge of traction to slip...
leaving the trestle the grade is reduced....so the "hiking" of my brick-basement caused a "grade-hill" on my track, but it has not caused the average grade to be changed.


but even though you are right with your 2 degrees, my opinion is that its MUCH more accurate to meassure base(run) and rise.


regards

Frank
 
#22 ·
Image




That is my suggestion: easy to handle and nearly accurate:


CHOOSE a measuring Lenth, say....3 feet, 36 inches.


measure the underpinned rise (u need one right and one left to lay down the waterlevel, so just 1 bricklet  is the effective rise) 
it doesnt matter what u use for: wood, cd.covers, cylinders,   u just have to be able to meassure out how much u had to underpin to reach waterlevel.


then calculate like this in 3 steps:


you have a measuring length "L" in inches
and a underpin-rise of "R" in inches


so under waterlevel circumstances your grade in % is:


on a length of          "L" inches        a rise of        "R"   inches
on a length of          1    inch           a rise of        "R"  / "L"   inches
on a length of          100 inches       a rise of       ("R" / "L")     x    100  inches




examples:


 2 inches on 36 inches :


on               36 inches        a rise of     2 inches
gives on      1 inch              a rise of    2/36 = 0,055 inches
gives on      100 inches      a rise of    0,055*100  =  5,5 inches


so you have a grade of 5,55 inches per hundred inches what is a grade of 5,55 %.
 
 
OR


 
19 inches on 300 inches (as requested):


on               300 inches       a rise of   19 inches
gives on      1 inch              a rise of    19/300 = 0,063 inches
gives on      100 inches      a rise of    0,063*100  =  6,3 inches


so you have a grade of 6,3 inches per hundred inches what is a grade of 6,3 %.


...just wanted to add as a "exampled help".


regards


Frank 
 


 
 
#23 ·
Another manner of practical application for use in the short distances that you'll be encountering, is use a 2 ft. long spirit level and one or more straight edges of convenient lengths. On one end of the spirit level attach a piece of wood, metal, etc., that extends 1/4" below the bottom edge of the levels frame (i.e. this will only be 1/100 of an inch greater than it should be for a 1% grade (i.e. 0.25" instead of 0.24")). In use remember to always place the end of the level that has the 1/4" projection on the down hill side of the straight edge and make sure the levels bubble is equal distant between the lines (i.e. reading level) and you'll maintain pretty close to a 1% grade. Or use whatever off-set to the end of the level that's required for the % of grade you shooting for. Also don't forget to check for across grade (i.e. left - right) level frequently this is very important also.

Image


Or you could get fancy and buy one of the new LCD digital readout levels that displays % of Grade and forget the extension on the end.
Image


http://www.sears.com/shc/s/p_10153_12605_00948295000P?keyword=carpentry+level

or...

http://www.sears.com/shc/s/p_10153_12605_00979583000P?vName=Tools&cName=HandTools,Carpentry&sName=Levels%20&%20Protractors&psid=FROOGLE01&sid=IDx20070921x00003a
 
#26 ·
Posted By Biblegrove RR on 05/11/2009 7:40 PM
gotta climb 19 inches within 300 inches of track!

What grade does this equate to besides TOO MUCH!?!?!?

I guess it's time for that switch back afterall eh?



But none of this math answers the basic question, how to climb 19" in 300" lenth

A Switchback IS one way but operationally I think it would get old really fast, could you work a helix loop AKA like the Tehachapi Loop? I am thinking where you could increase the run of track by adding a larger loop that crosses over itself, this alows a longer run of track and hence a lower gradient in roughly the same area of layout. It would also make a nice feature on the layout.
 
#27 ·
Vic

My interpretation was, that it was more of a rhetorical question than anything, the reason being if I'm not mistaken John stated that a helix was found to be impractical for his location in a previous topic.
Image
 
Discussion starter · #28 ·
Image


I can always reverse the loop. Here it shows outbound going around the loop and crossing the main line. I can put the switch where the crossing is and the crossing on the other end. This would give me an extra 10' to make the grade!
Image
 
Discussion starter · #30 ·
yeah you're right, 4.5%. Well... What if I push the loop on down the line, How much distance would I need to climb this grade at a doable 3%? this will determine where to put the crossing.
 
#33 ·
Posted By Biblegrove RR on 05/11/2009 8:21 PM
KCHahn, I am trying not to go over a 2% grade, especially in curves! Therefore it's 1" up for every 50 inches of track. or 2" per 100" of track...
8' circle has 96" multiply that by 3.14 (pie) = 301.44 inches
therefore in order to rise to a safe 12" for clearence of your yard lead, 12 divided by 3 would equal your grade.
4%

I may be wrong, it's been a long day in the yard!


Actually Blackberry 'pie' will give a different dimession than pumpkin..... sorry I couldn't resist
 
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#38 ·
Yes, its always a question of what duty shall be done.
In modelling and in prototypical business as well.


Trains with 100 cars or more need a matching way, so when these "worms" are driven through the land, you´ll need mainlines with less grades and big curve-diameters. Speed is also important! Mainlines must allow the best-possible speeds.


The other extreme is logging with shays: a bunch of switchbacks and grades of 8%, 9% or even more lead high into the mountains...but  not for heavy and long trains! Speed was no question, the problem was to bring the log out of the wood.


So there were following data to lean on:


Mainlines for the really "heavy duty" seldomly are more steep than 2 -2,5 %, which is  considered to be a "steep-track" with many problems in hauling, traction and speed.
Mainlines have regularly about 1-1,5% Grade, not more if possible.


Branchlines in standard gauge often reach grades of 3 %. Seldomly they had 4 or 5 % Grades. 
In Europe there were tests in the 1930s of which they decided to make a cut on a grade of 7 % for adhesive railroads. Steeper grades should be prepared with a rack.


Because of the weak engines, there were several lines with grades of 5-7 % that were formerly rack-track-railroads. After the tests the racks were removed, but the service was very hard both for the people and engines, even when they were changed to adhesive RRs.


The line named "Höllentalbahn" (Hells-Canyon-RR) in the black forest is such a former racktrack-line with a grade of about 5.55 %.


The shay-pushed development of industrial lines with grades up to  12 or 15% without a rack is totally unkonwn in europe. Inspectors would have had one heart-attack after the other.....
I dont know if our engineers ever really had a clue of the genius construction of the shay, but i fear they knew, but ignored it with much arrogance.


The most-known Nation to have steep mountain grades with narrow gauge is swizzerland. There are some lines going on nearly 7 % grade without rack. But you must see, that therefore u have just to use 2 or 3 cars with an old loco or use modern hauling-equipment for slightly heavier trains.




Regards


Frank 
 
#39 ·
Because curves will make the length of the slope longer, they lower the Grade between two points. So just measuring between two points in a straight line gives a false (too high) indication of Grade. Example: two points 50 inches apart with a difference in elevation of 2 inches is a 4% grade, but if there is 100 inches of track between the points in one big curve then the grade is actually closer to 2% (of course this assumes the track is one long uniform slope).

In an earlier post, I said that measuring the length of the track is the wrong value to use for the "Run" to get an exact calculation of the Grade. But if the grade is small, the amount of error in the calculation is pretty small so it really doesn't matter much unless you are really pushing the limits of your trains and if you are doing that, it is better to back off and rethink the layout.

If you have 100 inches of track in a curve and the difference in elevation of 2 inches then the Percent of Grade is ABOUT 2%. The "true" RUN would be close to 99.9 inches so the actual grade would be more like 2.002%. You will probably have more error than that in small undulations in the track along the slope!

There are a couple of other considerations to keep in mind.

You will probably want to measure the grade over as long of a distance as you can to improve the accuracy of the calculations, but you need to be sure there are no short segments where the grade exceeds the max you are shooting for within the distance you are measuring. The "end points" might be at the exact same elevation (0% Grade), but have a hill between them that is way too high to get the train over. This is why most people limit the Run measurement to about 2 ft. Besides being more convenient and easier to manipulate, you are more likely see any elevation undulations between the endpoints.

Curves allow one to reduce the Grade, but they also add rolling resistance such that the effective Grade is higher than a straight line between two points. Sharp curves raise the rolling resistance considerably. Using 1000 inches of track to cover a 100 inch distance in one big curve is good, but squeezing it into a squiggly series of "S" curves of 1-ft diameter won't work at all for most RR rolling equipment.


Another thing is to know the length of the train you want to work over variations in grade. I remember a riddle of something along the lines of:

How can it be necessary for a train of 50 cars to need a helper engine on a particular route when another train of 100 cars on the same route would not, given that all the cars are the exact same weight and all the engines have the exact same capability? (I seem to remember that this is a real circumstance on a RR somewhere in New England, but I don't remember which one.)

The answer is that the route has several up and down grades and the longer train would have part of the train on a down grade while the engine is pulling the front of the train up a steep grade, whereas the shorter train would all be in the valley between the grades when the engine is on the uphill grade to leave the valley.
 
#40 ·
Posted By SteveC on 05/12/2009 5:14 AM
Posted By Bunker on 05/12/2009 4:42 AM
...and I thought this was going to be easy. ???

If I am using a builder's transit and I measure the angle between any two points along my track bed and my result is 2 degrees of angle, then my grade would be 3½%, regardless of the length of track?

(Is my grade an A or an F for this answer?)
Yes sir, that just about covers it. One "A+" and a "Gold Star" for you.
Image


Or as C.T. stated from his tables above.
"If the Angle is 2.0 degrees and the track is 100 units long then the Rise will be 3.49 units and the Run will be 99.88 units, the Percent of Grade= 3.49%."

A long as the angle of inclination remains constant the percent of grade will remain the same. Of course taken to the extreme (i.e. with the transit remaining stationary) the curve of the Earth will cause the angle to change (i.e. increase as the Earth falls away), which would require filling to maintain the true horizontal base (i.e. "run") and angle. Just as any intervening hills would require cuts to be made. If you move the transit from survey to survey point and do the requisite back sites, then the percent of grade between any two points would remain constant.


Steve, I think you mistakenly gave Bunker an A+ instead of an F. He asked, "...between any two points", indicating an unknown length of run. As you pointed out in your own answer, 2 degrees equaling 3.49% grade is valid ONLY for a run of 100 units.

Yes, a track that is at 2 degrees of angle with respect to the horizontal is at 3.5% grade, but I don't think that is what Bunker meant.

It's also not clear where Bunker has his transit relative two either of his two points. Measuring an angle between two points relative to the transit is NOT the same as measuring the angle between the two points relative to horizontal, unless the transit is directly over one of the points.


(Man, I wish I could turn this computer screen into a whiteboard! Nothing more frustrating than trying to write mathematics.)
 
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