Can anyone tell me the formula for determing the % of a grade. My elementary school math has eluded me.
Divide the distance that the track rises (rise) by the distance taken for that rise (run) and multiply by 100.
So suppose your tack rises 2 inches in a run of 24 inches the percent grade would be: 2/24x100=8.3%. I know that this is an extreme grade but it serves as an example.
Joe
In 100" of run a 1" rise is equal to a 1% grade, a 2" rise is 2%, a 3" rise 3%, etc. However, since there must be a gentle transition from flat to rise and rise back to flat, total tackage necessary to complete the grade must be about 25% longer than this basic calculation suggests.
CNJ831
Inches of rise per 100 inches of run. If the tangent track is short, just extrapolate, i.e., 1" rise in 24" would be 100 divided by 24 (run) equals 4.166 times 1 (the rise), grade is 4.17%, rounded. Also, don’t forget that railroads don’t work in a perfectly geometric world. Due to the easements required to keep the wheel on the tracks and the cars coupled a theoretical 4% grade might have a 6% section in the middle if the run isn’t real long. Have fun.
Lou
CNJ831 brings up an excellent point that is often forgotten and can lead to a lot of heartache in the train room.
Joe
One other thing to keep in mind, if you have the room. Vary the grade along the way if you can. My long 45’ climb is 2% tops but it has some spots along the way that are less. I think it makes for a more realistic climb up through the mountains. Plus my Locos get a bit of a breather.[C):-)]
Brent
Rise over run. (height change divided by horizontal travel along the bench.) Make sure the units match in both figures. Move the decimal two places to the right on your calculator’s display result. Read the two integers to the left of the decimal as a whole number, and they are the percentage you are looking for.
As CNJ points out, if you have a finite space to achieve both the rise and the run, your grade will end up being about 1.5" steeper along its central portion because you must build a vertical curve, or transtion, at each end. Failure to do this will result in pilots or snow plows bottoming against the rails ahead of the engine at the very onset of the rise, or couplers will come uncoupled.
Count on about 8" of vertical curve for every change of grade of 1%.
-Crandell
Do make sure that during your track planning you allow for tranisions for the up esing into the grade and the over easing at the top. This should be at least 1 1/2 car lengths (longest stock). This will help stop any unwanted uncoupling or even bottoming out plows/ pilots into the grade.