I know someone on this post has better math skills then I do. I need to know about what percent grade is a rise of 21 inches over 42 feet.
Thanks
21 inches divided by 12 inches/foot = 1.75 foot
1.75 foot rise in 42 foot run is 1.75/42 = .041666, which is just under 4.17 percent
3.753 % But I was an English major in school.
I converted 21 inches into feet: 21 inches = 1.75 feet.
You have the total radius of 42 feet.
A 1.75 foot rise in 42 feet is 4.17% of the total 42 foot radius distance.
There are 90 degrees of possible rise if the train rose 100% of the 42 feet within 42 feet.
So a rise of 4.17% of 90 degrees is a rise of 3.753 %…(.0417) X (90)
Can’t wait to see the responses I get on this one. That’s my answer and I’m sticking to it.
Jack
Slope % = rise / run x 100 (in the same units inches or feet)
1% slope = 1" rise over 100" run.
2% slope = 2" rise over 100" run.
Kurt
Where/how does a radius come into play?
Everybody but Jack is right. (Sorry, Jack.) The grade is the rise divided by the run. There are, however, two ways of doing this, depending on whether you divide by the distance along the (inclined) track or by the horizontal distance. The AREMA definition of grade is ambiguous on this point; and, in fact, for the grades normally found on railroads, it makes very little difference in the numbers.
To calculate the angle that the incline makes with the horizontal, which is what Jack was trying to do, you do not simply multiply the grade by 90 degrees. Instead you have to take the arc sine or the arc tangent of the grade (depending on which definition of grade you used). For railroad grades, this is very nearly the same as multiplying by 180 degrees, then dividing by pi. This is approximately the same as multiplying the grade by 57.3 degrees. The 21 inches in 42 feet example is indeed 4.17 percent. It is also 2.39 degrees.
Bob…you have to admit it was a pretty impressive display, albeit wrong. [:D] After I went to bed, I realized I overthunk it. That’s what happens after 42 years of not using the math stuff.
Jack
Hey All,
Ok I figured out what percent my grade is going to be, what I need to know is how steep can these trains climb what percent? I know it depends on the engine (How many motors it has, and if the traction rubber bands are on the drive wheels) and how many cars its pulling and weather or not its a straight incline or curved. But all that aside does Lionel have a maximum grade guideline that these engines can pull in general? The grade I am looking at is 6.25 percent. I want to rise 2 feet over a 32 ft run is this to steep?
BD…I may be wrong, but if I recall some of the archived discussions correctly, 4% seemed to be the maximum “practical” concensus (straight grade, no curves). I don’t recall a Lionel guideline being discussed. Your 6.25% grade may be a bit ambitious.
Jack
Jack,
Yeah, I refigured my calculations I got it down to a 4.06% grade thats a 16 inch rise over a 32 ft run. I was trying to do a 2 ft rise over a 32 ft run and thats 6.25% grade. Thanks for the input!
You don’t have to limit your grade to just your longest run. You could also figure in one of your shorter run as well as a curve. This would increase your run to over 32 feet thereby lowering your slope.
Jim
A 6% grade is insane unless you are running very short consists and the grade itself is fairly short. The longer the train, the greater the load. 4% is pushing your luck. It isn’t just the issue of traction/load you also need to be concerned about coupler failures and resulting breakaways.
Jack told me earlier that 4% would be maximum, I can play with the numbers somemore to get it down to lower grade % but, I dont want to go no lower then a 16 in rise…Guess I will just have to make the run longer… start the upgrade before the final curve and the 32 ft straight away…what would be a comfortable % to shoot for. I had it down to 4.06 from 6.25??
You want to get as much under 4% as possible. 3.5% is better than 4%, 3% is better than 3.5%. Like a real railroad, 2%-2.5% is what you would like to shoot for (yes, it does eat up a lot of real estate). This will minimize the stress on your equipment.
Black Diamond: If you really want trains 24" above the lower level, can you add an independant second level?
Kurt