Fast Facts Home

Grade Chart

 

Grade is generally defined as the difference in elevation of track between two points and is expressed as Rise over Run. Where the Rise or Vertical Measure is Y and the Run or Horizontal Measure is X or X/Y. So if your track rises 3 inches over a distance of 100 inches the grade is 3/100 or .03 (3% grade).

Prototypical Grades:

On main lines, grades are generally 1 percent or less, and grades steeper than about 2.2 percent are not common.

Here are some current and historical exceptions:

Pennsylvania Railroad north of Madison, Indiana. The track rises 413 feet over a distance of 7012 feet which results in  a 5.89% grade.

Norfolk Southern  south of Saluda, North Carolina has a 4.7% grade

Burlington Northern Santa Fe’s Raton Pass in New Mexico has a grade of 3.3%

On the CSX Cranberry grade, the grade is 2.86% at Rodemer, West Virginia

And again on the CSX Cranberry grade, at Cemetery Hill. The section located between the M&K yard at Rolesburg, West Virginia and Terra Alta, West Virginia.has a grade of 2.6%

 

Modeled Grades:

In the modeling world and in particular in the three rail world grades often far exceed prototypical grades. This is made possible by the use of traction tires and magnetized trucks. However, each locomotive will have its own slippage and draw bar pull characteristics.  For both appearance and functionality it is a good idea to keep grades under 3%, but if your trains are capable of handling steeper grades go for it. One thng to keep in mind is that you should approach steeper grades with graduated grades. For example before starting a 3% grade start with a 1% and then a 2% grade. Some people use the rule of thirds if your final grade is 3% and 200" long approach the grade with a 2% grade that is 133" long and approach that grade with 1.33% grade that is 89" long. Also never start or stop a grade on a curved section of track.

To use the chart below select the rise from the top row and the grade from the left column. The value where the row and column intersect is the run or length of track (in inches) that you will need.

For example if you want to gain 5 inched in altitude using a grade of .025 (2.5%) you will need a 200" length of track.

Grade/Rise 1" 2" 3" 4" 5" 6" 7" 8" 9" 10" 11" 12"
0.01 100 200 300 400 500 600 700 800 900 1000 1100 1200
0.015 66.66667 133.3333 200 266.6667 333.3333 400 466.6667 533.3333 600 666.6667 733.3333 800
0.02 50 100 150 200 250 300 350 400 450 500 550 600
0.025 40 80 120 160 200 240 280 320 360 400 440 480
0.03 33.33333 66.66667 100 133.3333 166.6667 200 233.3333 266.6667 300 333.3333 366.6667 400
0.035 28.57143 57.14286 85.71429 114.2857 142.8571 171.4286 200 228.5714 257.1429 285.7143 314.2857 342.8571
0.04 25 50 75 100 125 150 175 200 225 250 275 300
0.045 22.22222 44.44444 66.66667 88.88889 111.1111 133.3333 155.5556 177.7778 200 222.2222 244.4444 266.6667
0.05 20 40 60 80 100 120 140 160 180 200 220 240

 

[Drawing Here]

Grade Calculator 

Gaining altitude: Helixes: (Under Construction)

A helix is a spiral of track where the track crosses over itself allowing a train to gain height in a relatively limited space. The grade of the helix is again subject to the types of trains that you are running. For a layout where the minimum curve has a 36 inch radius and a grade of 3%, a helix will allow you to gain 6.88 in a 6' 6" x 6' 6"* foot area as opposed to a 226" (18' 9") 'straight' run.

For the purposes of modeling you will most likely start with the height you want to achieve and the grade you want to use. Although it might be necessary to adjust the grade in order to ensure that the track meets.

For this example I am going to start with my tallest car which is a double stack measuring 5.25" talls and I need to gain 12 inches in height to get to the second level of my layout.

First I am going to add another .25" inches for clearance.

Then I will need to add the height of the helix structure beneath the roadbed to the height of the roadbed ties and track.

For me that is .375" + .25" + .375" or 1" and this is added to the height of the car and clearance for a total of 6.50". Which should be the height of rail top to rail top.

Now determine the minimum radius of the helix.

We need to detrmine the total lenght of track required first and then we can determine how many loops the helix will have to have in order to gain the necessary height.

For this example I am going to use a grade of 2.5%

12 / Y = .025 or Y = 12/.025

Y = 480" or 40' lets see if I can do this with 36" radius track.

Determine how many loops of track it will take.

Each loop is the circumference of circle with a 72" diameter.

c = 72 * π

c = 226

480/226 = 2.12 loops.

Okay we have a problem 2.12 * 6.5 (The minimum clearance) is greater than the final height. I have several choices, I can increase the height of the second level, have 1 loop of track and then a straight section with a grade, increase the grade or increase the radius of the track.

I am going to increase the diameter to 84"

c = 84 * π

c = 264

480/264 = 1.81 loops

This will work the, total height gained is now (1.81 * 6.5 ) 11.765 inches.

Here is the formula c = 2r * π

Where:

c = Circumference

r = radius π = 22/7 or 355/113 which is more accurate

c = 2Ï€r

The tallest car as of this writing is the .. double stack measuring inches from rail to the top of the ... So if you wanted to build a layout where you had one track crossing over another using a bridge or via duct you would need to start with the height of the tallest of you rolling stock and then add the height of the roadbed and structural work. So instead of just gaining 6 inches in elevation you may need to gain 8. *This assumes that the structure of the helix will add an in or two to the diameter of the curved track.

[Chart:]

Grade/Rise/Run

[Drawing 1]

[Drawing 2]

[Calculator]