# What's the grade?



## Biblegrove RR (Jan 4, 2008)

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?


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## Bunker (Feb 7, 2009)

Which prompts a question I have, "How does one calculate % of grade to degree of angle?


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## Guest (May 11, 2009)

3" in 300" would be 1%. 
19 divided by 3 is a bit over 6. 
so you are planning a 6.2% grade. 

better would be, to stay with less than 5%.


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## 6323 (Jan 17, 2008)

So, how would one figure the grade on a curve? 
I need to elevate my mainline, just enough to clear 
a potential yard lead below. Using either a tunnel, or a bridge. 
Haven't decided that yet. 

If it helps, I'm using 8 foot Diameter curves.


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## Biblegrove RR (Jan 4, 2008)

19 / 3 = 6.333333333333333333333333 

like I said, more switches and track for a switchback will be in order?


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## Biblegrove RR (Jan 4, 2008)

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!


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## Semper Vaporo (Jan 2, 2008)

Posted By Bunker on 05/11/2009 7:47 PM
Which prompts a question I have, "How does one calculate % of grade to degree of angle?


They ain't a "linear" relationship. i.e.: the angle of a 10% grade is not the same as some number times the angle of a 1% grade.

It is, however easy to calculate with a good calculator or a Trigonometric Tangent table in a book.

Percent of grade is "Rise divided by Run" times 100 to convert to percent. 

Which is the same as "Side Opposite divided by the Side Adjacent" in a right triangle which is the definition of Tangent...

So if you know the Percent of Grade, divide by 100 and look up the result in a Trig Tangent table:

5% grade = 0.05 = (about) 3 degrees (per my trig table... Tangent of 3-deg is 0.05241 which is as close as the table gets.)

Or use your calculator's ArcTangent function:

5% grade = 0.05 = 2.832405226 degrees (per my Calculator).


The OP scenaro: 19/300 = 0.06233 * 100 = 6.233% grade = arcTan(19/300) = 3.623892596 Deg.






(I hope!)


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## SteveC (Jan 2, 2008)




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## Bunker (Feb 7, 2009)

Okay, help me talk this out, 
in carpentry, a roof slope of 12/12 is a 45º angle, which is a 50% grade. 
A 6/12 slope is 22.5º angle or 25% grade? 
11.25º would be 12.5% 
~5.5º should be 6.25% 
~2.25º is 3.125% 

Am I missing something here?


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## Bunker (Feb 7, 2009)

P.S. I am asking because I can measure degrees of angle, but have never had to use "grade" before.


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## Guest (May 12, 2009)

Bunker, 
i think, your calculations are right.


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## Semper Vaporo (Jan 2, 2008)

45 degrees is 100% grade ...

Rise (12) divided by Run (12) = 1 *100 = 100%

90 degrees is infinite grade.


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## SteveC (Jan 2, 2008)

12" / 12" = 1.00 =100% Grade
6" / 12" = 0.50 = 50% Grade
3" / 12" = 0.25 = 25% Grade
1.5" / 12" = 0.125 = 12.5% Grade
1" / 12" = 0.083 = 8.3% Grade

1" / 100" = 0.01 = 1% Grade
or in other words
0.01" rise per inch of run, so on a run of 12" the rise would be 0.12" 
Another way to look at it is...
1% of 12" Run = ?
0.01 x 12 = 0.12"

Why is a 45 degree angle considered a 100% Grade?
*Edit:* _(I got this backwards, it's the slump angle that determined the maximum 45 degree angle for a 100% grade)_ Because it's the practical limit of traction, normally, also I believe it's the normal slump angle of un-compacted earth. Even if you compact the dirt and create an angle greater than 45 degrees you run the risk of slides, caused by nature trying to reach equilibrium.


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## Guest (May 12, 2009)

thinking again, what Steve explains makes more sense. 

Editing as well:
or it is called 100%, because it is 1 in 1 or 100 in 100 a full rise.


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## SteveC (Jan 2, 2008)

Korm

Yes sir, I'm sure that is true (i.e. the rise is equal to 100% of the run), but I believe that that relationship (i.e. where the maximum angle is 45 degrees) was decided on because of the observed natural maximum slump angle of dirt, of course this ideal natural slump angle would be dependent of many variables like the moisture content etc.etc.

I remember as a child, playing in the gravel piles and coal piles (I've never claimed to be smart







) in the respective storage yards of same (I guess this also confirms just what type areas it was I lived for a fair percentage of my childhood). Anyway, the slope of those piles were mostly very close to 45 degrees. Yes, my friends and I got chased and yelled at a lot by the watchmen and yard workers, they knew is was dangerous, all we knew it was a challenge and fun, seeing who could reach the top first.


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## Semper Vaporo (Jan 2, 2008)

Also, make sure you do not confuse the three terms that all have similar names.

Grad (without an "E")

Grade (with an "E")

Gradient 

These terms are somewhat "related" but are not interchangeable in meaning. 

"Grad" (without an "E") is a measure similar to degrees, but instead of 90 degrees in a right angle and 360 degrees in a full circle, there are 100 Grads in a right angle and 400 Grads in a full circle. It is a term used to define an angular displacement. Grad is a measurement of any angle without restriction to direction.


"Percent of Grade" (with an "E") is the Vertical distance (Rise) divided by the horizontal distance (Run) * 100 (to express it as "Percent"). (Rise over Run)

"Gradient" is the Horizontal distance (Run) divided by the Vertical distance (Rise). (Run over Rise)

They all have to do with an angular measurment, but Grade and Gradient have definitions specifically to do with the angular deviation from the horizontal on the Earth's surface (i.e.: the Slope).


Grade (not Percent of Grade) and Gradient are reciprocals of each other... i.e.: 

1 / Grade = Gradient 

1 / Gradient = Grade; 

1 / ( Percent of Grade / 100 ) = Gradient --- or --- ( 1 / Percent of Grade ) * 100 = Gradient

1 / ( Gradient * 100 ) = Percent of Grade --- or --- ( 1 / Gradient ) / 100 = Percent of Grade

One other error people make is to measure the "Run" along the Slope. This is not the "RUN". 

What you are working with is a "Right Triangle". The 90-degree angle is the point where the Rise and Run meet. 

The "Run" is the horizontal component of the triangle that is adjacent to the 90-degree angle (and the "Rise" is the vertical component). 

The side opposite the Right Angle (the "Hypotenuse" of the Right Triangle) is the "Track" of which you are measuring the slope (as Percent of Grade). 

For extremely small angles (low Percent of Grade) the Run and the length of track (Hypotenuse) will be nearly the same value, so the amount of error in expressing the Percent of Grade will be very small. As the angle gets larger, the error will become significant.

A Surveyor's Stadia table will tell you what the Rise and Run will be for given angles if the Hypotenuse is 100 units long.


Example: (Here are a few points from my Stadia Table)

If the Angle is 0.5 degrees and the track is 100 units long then the Rise will be 0.87 units and the Run will be 99.99 units, the Percent of Grade= 0.87%.

If the Angle is 1.0 degree and the track is 100 units long then the Rise will be 1.74 units and the Run will be 99.97 units, the Percent of Grade= 1.74%.
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%.
If the Angle is 4.0 degrees and the track is 100 units long then the Rise will be 6.96 units and the Run will be 99.51 units, the Percent of Grade= 6.99%.
If the Angle is 6.0 degrees and the track is 100 units long then the Rise will be 10.40 units and the Run will be 98.91 units, the Percent of Grade= 10.51%.


If the Angle is 22.5 degrees and the track is 100 units long then the Rise will be 35.36 units and the Run will be 85.36 units, the Percent of Grade= 41.42%.
If the Angle is 26.5 degrees and the track is 100 units long then the Rise will be 39.93 units and the Run will be 80.09 units, the Percent of Grade= 49.85%.
If the Angle is 45.0 degrees and the track is 100 units long then the Rise will be 50.00 units and the Run will be 50.00 units, the Percent of Grade= 100.00%. If the Angle is 90.0 degrees and the track is 100 units long then the Rise will be 100.00 units and the Run will be 0.00 units, the Percent of Grade= infinity.






Notice how little difference there is between the "Run" and the "length of the track" for small angles. 

Also notice how much the Percent of Grade is compared to the Angle.

To invert the table for some Percent of Grade values:

1.00% = 0.57 Degrees
2.00% = 1.15 Degrees
4.00% = 2.29 Degrees
6.00% = 3.43 Degrees
10.00% = 5.71 Degrees
50.00% = 26.57 Degrees
100.00% = 45.00 Degrees


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## coyote97 (Apr 5, 2009)

Hi folks,


i think it´s important  to note that the angle in degrees is nothing you can really work with in practice.


The only thing the degree is good for is to see that the 45 degree angle means 100% grade.


The defination of a grade in percent gives more sense when we pull the word apart:


"per -cent"


the grade is the rise in every unit depending to 100 of that unit of the base (run).


its "one unit" "per" "cent-units".


Certainly in curves the base equals the bow of the curve. 
To make curves lesser difficult to drive through, you can e.g. take a 6 ft-waterlevel bringing it on two trucks on both ends. So because the waterlevel gives a straight line through the curve, the Curve itself has more length from truck to truck.
So while taking always the same grade on the waterlevel, the nominal grade of the curve is automatically reduced from the point one truck enters the curve. the tighter the curve gets, the more the nominal grade will be reduced, while the waterlevel always shows the same caliber
The length of the waterlevel defines the effect of grade-reducing through the curve.




 
To make the confusion perfect: 


in Germany we have another definition of grade:


"1:50" or "1:100" what is easy to translate in percent: 1:50 is 2 percent, 1: 100 is 1 percent.
The advantage of this for G-Scale is easy building in the garden: if you have a levelled ground, just underpin a wood of an inch for every 50 inches base...so you have a 1:50 or 2% grade.
for 4% you have just to put 2 inches under the track, or one inch of 25 inches base:   a 1:25 grade!
If you have no leveled ground, lay your waterlevel straight on the tracks and underpin the waterlevel on one side for the grade you wish: e.g. 1cm for a length of 50 cm(signed on the waterlevel--the points it lays on the track must be 50cm apart). now you just have to raise the track untill the waterlevel shows "even".


regards


Frank


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## Bunker (Feb 7, 2009)

...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?)


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## SteveC (Jan 2, 2008)

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.









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.


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## Guest (May 12, 2009)

...and I thought this was going to be easy. ??? 


it IS easy. we just complicate things by trying to explain them. 

i just started my layout with the easyest part. a gradE that manages a 2' rise. 
the only measuring tool i need is one of these folding sticks for carpenters. (in german we call them Zollstock(inchstick), because they show centimeters) 
i marked every hundred units a rise of five units on the wall, because i want 5%. where curves are planned i just mark 3 units rise for the same length. 
following these marks i build my benches now. 
when i have the track down, i will control it with a fishing line and will finetune any big bumps in the rise with some glued down coffeestirrers. 

that "system" worked before, and will work again. - even if i don't understand everything about grades, grads and gradients. (because i didn't graduate...)


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## coyote97 (Apr 5, 2009)

@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


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## coyote97 (Apr 5, 2009)

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


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## SteveC (Jan 2, 2008)

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.










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.









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


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## Biblegrove RR (Jan 4, 2008)

Holy Moly I sure opened a can of worms with this one! lol


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## SteveC (Jan 2, 2008)

Posted By Biblegrove RR on 05/12/2009 7:46 AM
Holy Moly I sure opened a can of worms with this one! lol
Yes, but look at all the stuff you're now aware of, scary isn't.


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## vsmith (Jan 2, 2008)

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.


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## SteveC (Jan 2, 2008)

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.


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## Biblegrove RR (Jan 4, 2008)

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!


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## SteveC (Jan 2, 2008)

John

I see that I was wrong about the rhetorical part.









Even with the additional 10 ft. (120") for a total of 420" to climb 19" that would still be a 4.5% grade wouldn't it?


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## Biblegrove RR (Jan 4, 2008)

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.


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## Guest (May 12, 2009)

at thre percent a 19" rise takes 633 inches length. = 52' 9"


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## SteveC (Jan 2, 2008)

I believe that a 19" rise over a 634" run would give you a calulated 2.99% grade.


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## Totalwrecker (Feb 26, 2009)

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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## Biblegrove RR (Jan 4, 2008)

What if I increase grade within the loop at 2%? That would give me about an extra 300" or 6" gain in height....


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## Guest (May 12, 2009)

with what diameter curves? 
and with what locos?


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## Biblegrove RR (Jan 4, 2008)

10' minimum Diameter and all types of locos etc.


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## Guest (May 12, 2009)

that should work out, if you do not insist to use Bachmann big howlers with long trains.


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## coyote97 (Apr 5, 2009)

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


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## Semper Vaporo (Jan 2, 2008)

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.


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## RimfireJim (Mar 25, 2009)

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.









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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## Semper Vaporo (Jan 2, 2008)

Posted By RimfireJim on 05/12/2009 2:23 PM
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.









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.)



Well, now... what kind of "grade" (pun intended) do we give you...???? ???









You have confused a "Percent of Grade" value with a "Distance" measurement... that 3.49 is in "Units" (as in inches or milimeters or furlongs) not "Percent of Grade".

Also, it makes no difference where the transit is, as long as the measured angle is 2 degrees, the distance between the two points is irrelevant. The Percent of Grade will also be 3.5 Percent, too, regardless of distance. The difference in elevation (Rise) will be 3.49 units if the "Run" is 100 units. That 3.49 is not just some rounding error in expressing 3.5. One (3.49) is in Units and the other (3.5) is Percent of Grade and other than being close in numerical quantity they have no relation to each other outside of the 100 unit distance given.

I can't give you a "F" because you are absolutely right about the need for a drawing board to point at and wave your hands in front of whilst talking about this stuff!

It would be so easy to explain it if we could "interact" in each other's presence instead of this 'slow motion' communication in text in a media called a Forum.


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## Guest (May 12, 2009)

coming back to the practical application of our gathered knowledge: 
i just found a grave difference between an upwards grade and an downwardsgrade. 
the difference i found lies in the state of testcars used. 
shoving a car up a grade, it stays in good condition. letting it roll down it derails and falls to the floor, when it hits the bumper at the end.


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## Biblegrove RR (Jan 4, 2008)

HERE'S AN EASY ONE FOR YOU PROFESSORS... 

I am sticking 3 10' sticks of PVC together to make close to a 10' diameter circle, it's a little more (even better) What Diameter would 40' be? 
480" circle


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## vsmith (Jan 2, 2008)

I was thinking something like this, use your existing grade to your advantage, still its a bit of engineering


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## Semper Vaporo (Jan 2, 2008)

Posted By Biblegrove RR on 05/12/2009 3:44 PM
HERE'S AN EASY ONE FOR YOU PROFESSORS... 

I am sticking 3 10' sticks of PVC together to make close to a 10' diameter circle, it's a little more (even better) What Diameter would 40' be? 
480" circle


Circumfrence divided by Pi = diameter

40-ft / 3.1415 =n 12.73-ft = 12' 8.78"


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## Biblegrove RR (Jan 4, 2008)

My smallest Diameter loop is 9.5 foot and hope this is enough for all Engines out there?








This is what I am dealing with, having to get up to the small switchyard / Dairy Plant.








I can do without the loop here but want to have a trussed line to the pool so I can back in refreshments etc.


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## Semper Vaporo (Jan 2, 2008)

9.5 ft DIAMETER is big enough for many engines, but not "ALL" engines. The Aster Mike is specified as needing a 2 meter RADIUS, which is 6.56 Ft RADIUS which is 13.12-ft DIAMETER (I have run mine on a 6-ft Radius (12-ft Diameter) but not fast!). 

Many other of the "Bigger" engines require even larger curves.


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## coyote97 (Apr 5, 2009)

oh, i like what i see, biblegroove!
that looks good, really!


what holds you back to spend another foot or two with the diameter?--will look even better and gives you both more wide curve and more tracklenght for the grade.




regards


Frank


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## Mike Reilley (Jan 2, 2008)

While I don't think figuring the grade in a plan is hard, I've found SETTING a grade outside can be a challenge. You can set a grade VERY accurately with a water level...and the math that's been discussed in this thread...but it's a real pain in the butt. A little more direct way to do this is to buy a level that measures grade...directly. I bought this Craftsman level and have been very pleased so far.

http://www.sears.com/shc/s/p_10153_12605_00948292000P?keyword=digital+level#reviewsWrap 

The laser on it helps a ton...as you can use it to measure the grade of the land you are starting with. Put it on a camera tripod...measure the height of the laser beam coming out of it, and point it at a equal height above the ground, and it reads out the grade from the level to the target.


It's small enough to place on a flatcar...and roll along your track so that you can measure the instantaneous grade the train sees. I've seen lots of GRRs with "2% grades" that have 4% dips or hills in the middle of a grade. This helps locate them and measure them....and that helps you decide whether you need to do something.


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## coyote97 (Apr 5, 2009)

Hi Mike,


there is a point where i agree: its difficult to BUILD a constant grade while laying it, measure, levelling and so on.
And perhaps its accurate enough to use such a level u bought.


But my experience is that it is NOT accurate to use it.


Dont get me wrong, maybe its good enough...but not good.


Why?--The digital measurements  have some problems "built-in", the older "analog-reading" refers to an accurate eye.... While the digitals often have an accuracy-tolerance of 5% or even worse (the cheaper they are, the worse they work), they do an additive fault, too: the last "digit" is not defined.


so its easy happening to have a  sign of 1,0 till 1,3 degrees for a 1,146 degree grade (what is 2%). Vice versa you can have a grade from 1,75 % to 2,27% while the level shows e.g. 1,1 degree.




For accurate measuring i use the following tec:
-use a tripod and a laser-level.
-DONT count on the accuracy of the level
-hold a yardstick upright to the track and point it with the laser. 
-turn arround the laser 180 degrees and point a second time
-the "waterlevel"-fault of the laser and tripod is now shown in the difference between the two amouts.
-the REAL amount lies exactly in the middle of both.


this method was used by the first surveyors with their old equipment. by taking 2 (or even more) amounts and doing a mathematical "middling" the measurment gets accurate. Using this method accurately they got faults of just some inches on measuring lengths of many miles.


so you can level nearly your whole layout from one point on (what is  important for accuracy). 
You just have to define constant length-pionts on the track. ...say every 100 inches. so for a 2% grade you have to be 2 inches higher after roling 100inches on trck. i too do agree that the difference between "run" and "track" is marginal on angles up to 10 degrees (what you´ll never reach with an adhesive railroad-grade).


What helps a lot is the measuring-logistic. Adding one measuring point after another can lead to a big failure, because every small fault is added and added and so on.


Its much better to measure to start and the end of a grade. then on half way of the grade to define the middle height. after this, you take the next two mesurments in the middle of each half. 
Like this, you can difine the grade for the whole tracklength, and then step by step bring it to the shorter distances




regards


Frank


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## Biblegrove RR (Jan 4, 2008)

thanks guys, I am using a Craftsman laser level based on that wing wall you see in the background. Bigger circle is better but... I am planning one even bigger a little ways on down the line in order to run track up to the very top of that hill by the house. I am debating whether to just use it for both but hten I would not have the line to the pool, that's no big deal though, just a switch and allot of truss work!


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## noelw (Jan 2, 2008)

Posted By Mike Reilley on 05/13/2009 12:35 AM
While I don't think figuring the grade in a plan is hard, I've found SETTING a grade outside can be a challenge. You can set a grade VERY accurately with a water level...and the math that's been discussed in this thread...but it's a real pain in the butt. A little more direct way to do this is to buy a level that measures grade...directly. I bought this Craftsman level and have been very pleased so far.

http://www.sears.com/shc/s/p_10153_12605_00948292000P?keyword=digital+level#reviewsWrap 

The laser on it helps a ton...as you can use it to measure the grade of the land you are starting with. Put it on a camera tripod...measure the height of the laser beam coming out of it, and point it at a equal height above the ground, and it reads out the grade from the level to the target.


It's small enough to place on a flatcar...and roll along your track so that you can measure the instantaneous grade the train sees. I've seen lots of GRRs with "2% grades" that have 4% dips or hills in the middle of a grade. This helps locate them and measure them....and that helps you decide whether you need to do something.


.................................................................................................................................................

We did the same thing like Mike Reiley did... I convienced Joe H. in our group when re-doing his layout is to get one Sears level to work with... 
They really work great on a flat car like he said.. I found so many places that had more dips that the 1 percent grade was more than we want it to be.. Sure helped to keep it the way we wanted it.. We went around his back yard 4 time to get the layout from 4 foot off the ground to about 1 foot above the ground going over a pond and back up again.. Kind like what the Wesern Pacifice did going up the Feather River Canyon in Calif. Noel


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