CPR Galt Subdivision
Calculating Grades for Your Model Railway
Just like their full size cousins, model trains can become more interesting to watch and operate if they have to struggle up a grade, especially on curves around the side of a mountain or through rolling hills. While they can be challenging to include in small switching layouts, having grades on a medium or large layout sometimes allows modelers to include more track and have longer, more interesting runs for their trains.
We’re all familiar with the figure eight track configuration that comes with many train sets---one step up from an oval or circle of track. After setting up such a layout, it becomes apparent that the trackwork is more than a little unrealistic---the train goes round and round, up and down on grades that seem a little more than steep. Fun to watch for a short period of time, but a more sophisticated model railway soon becomes desirable. Having one with some grades will add some interest for the viewer and train operator.
Grades are usually expressed as a percentage, such as a 2% grade. Grades up to 3% are generally acceptable for model railways, depending on the type of equipment, length of trains, and the terrain being modelled. Grades above 3% can appear unrealistic, but they could be used in hidden tracks where it is necessary to reach a certain height. Using a 3.75% grade for the hidden track may enable you to use a 1.5% grade elsewhere in locations where the track is visible and will appear more realistic.
Technically speaking, grades are usually expressed as a percentage (Gradient) of the Rise (the vertical measurement) over the Run (horizontal measurement). Using the three variations of this relationship as outlined below, you can figure out whatever you need to know about the grades on your railway.
Sometimes you will you need to figure out how much of a grade exists between two points having a certain elevation change between them. To calculate this grade, divide the Rise by the Run and you will have the Gradient as a decimal percentage.
2 inches / 100 inches = .02 (= 2%)
½ inch / 100 inches = .005 (= 0.5%)
3 inches / 160 inches = .00187 (= 0.2% approx.)
Gradient (%) = Rise / Run
A 1% grade then, is 1 inch Rise in 100 inches Run.
If you need to figure out how much elevation change you can make for a specific gradient, multiply the Run by the Gradient. This will tell you the amount you can raise the track at that percent grade, given the length of track you have to create the grade.
100 inches x .02 (2%) = 2.0 inches Rise
150 inches x .03 (3%) = 4.5 inches Rise
125 inches x .015 (1.5%) = 1.875 inches (a little less than 2 inches of Rise)
Run times Gradient (%) = Rise
(100 inches Run x .01 Gradient = 1 inch Rise).
If you have an elevation change to accommodate, and want to know how much length of track you need to fit that amount of Rise and hold to a certain percent Gradient, divide the Rise by the Gradient.
4 inches rise / 2% grade (4 inches / .02) = 200 inches length of track
3 inches rise / 3% grade (3 inches / .03) = 100 inches length of track
7 inches rise / 1.5% grade (7 inches / .015) = 466.66 inches length of track
Rise divided by the Gradient (%) = Run
(1 inch Rise / .01 Gradient = 100 inches Run.)
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