I just visited a site called "Geometry for Morons Like Us". Guess what? It didn't help me a whole lot. I am in the middle of planning an expansion and do not want to wind up with grades that are too steep, as in my Atlas N-18 current layout whereat steam engines need a helper up the grades. I have a few questions after you guys stopped shaking your heads in amazement. 1. Is grade = angle ? 2. In really simple terms (with perhaps a formula or two formulas if angle and grade are different) how can I figure out how long I need to make the hypotenuse of the right triangle to make it rise 3 or 4 inches above level with a 2% grade?
Mark: A 2 % grade will rise almost two inches every eight feet. So to go up 4 inches, you need about 16 feet. On the JJJ&E, the 2 % grade rises 7 1/2 inches in 36 feet and takes 36 feet to get down. That's about as easy as I can make it for you. A WS 2% riser takes 8 feet to go up two inches. Have fun... Stay cool and run steam....
To put it in more exact linear terms; to go up two inches, it will take 100 inches which is a 2% grade. (8 feet 4 inches). Stay cool and run steam......
Mark: Grade is pretty easy to understand... If you have a stretch of track 100 inches long and it rises in elevation by 1 inch, it has a 1% grade. 2 inch rise over 100 horizontal inches means 2% grade. 3 inch rise over 100 horizontal... You get the idea. 4% is the most severe grade, and those are rare. Most grades are 2% or less. Hope this helps!
Mark, Grade is simply percentage, not degrees of angle. It is just units of rise divided by units of run x 100 1" rise for 50" run is 2% 2" rise for 100" run is 2% 2" rise for 50" run is 4% 2" rise for 100" run is 4% In Bob's example, he has a 1.7% grade. 7.5" rise divided by 432" run = .01736 x !00 and rounded off you get 1.7% grade. Actuall units do not matter, it can be feet, inches, yards, miles, millimeters etc. as long as you are using the same for both run and rise.
Let me see .573 degrees per 1% rise times 2 equals a 2% grade. I think two inches every 100 inches is alot easier to figure out. Stay cool and run steam..... [ February 11, 2006, 05:30 PM: Message edited by: Powersteamguy1790 ]
In the for what it's worth collum: Since the grid in most track planning is 1 foot squares I think in terms of 1/2 inch per foot. Edit As pointed out (below), by Chriss- 1/4 inch per foot is correct and the easyest way for me count it. The hard part is calculating how long a curve is. I keep it simple and think an other 1/8 inch per 90 degrees of the curve. Works for me but I'm open to suggestions. Other factors: 1) Try to start the grade beyond 4"s of a turnout 2) For short distances and short trains with non-accumate couplers steeper grades can be considered. I concede that factor 2 is controversial. Both of my 2-6-0s and my 4-4-0 will ascend a 3 foot long 4 percent grade with three 39 foot passenger cars. My Atlas GPs will haul five 40 foot box cars up this grade without hesitation. Some of the steam locos out there probably could not haul themselves up that grade. [ February 11, 2006, 08:43 PM: Message edited by: Grey One ]
Just divide the height by the distance. Make sure they are both the same unit. going up 1/2" in a foot: 0.5 divided by 12 = 0.041666666666666 Move the decimal over 2 places and you get 4.1% grade. So lets say you wanna go over another track at 2" and keep the grade at 3%. How long will it take to get there? 60" is 3.333333% grade 65" is 3.07% grade
This is not correct. A %100 grade is 45 degrees, not 57.3 degrees. (Anyway, I don't think thinking in terms of degrees is of any great help to us model railroaders.)
mark... whenever there is a "%"...a "per cent"... just think of it as "per hundred" or "over 1 hundred" so...2% would be...2 per 100 (or 2 over 100) in our case thats usually 2" (up) per (over) 100" (distance). with that in mind...you can make smaller more manageable ratios... 1" over 50" (just over 4 feet) 1/2" over 25" (just over 2 feet) 1/4 over 12.5" (just over a foot)
As I said before, a 2% grade is a rise of 2 inches for every 100 inches in length. Two inches for every 8.4 feet equals a 2% grade. It's as easy as that. Don't make it difficult. I don't need angles, degrees, hypotenuses' and whatever. Better yet, buy a WS 2% riser set and they have it all figured out for you. If you want to go up eight inches, buy four WS 2% risers and plateau each set higher. KISS.... Stay cool and run steam.......
Gentlemen: Thank you. I now have enough to go on. Remember, I was the guy who computed an 18% grade last January.
To make this even simpler check the MicroMark catologue for thier grade measuring devices. They have two listed in the current one. The one is real easy to use. Just set it on the board and adjust angle of rise til you get the grade you want. Simple meter device easy to read.
I think that some people get confused when thinking of gradient in relation to angles. Jagged Ben states the perfect example that 45 degrees is a 100% grade. Some people intuitively think of a 100% grade as being straight up or 90 degrees. Once they realize this, it all becomes relative!
Once again for the mathematically challenged. Hopefully link to a useful tool. http://www.ares-server.com/Ares/Ares.asp?MerchantID=RET01229&Action=Catalog&Type=Product&ID=82280
And for the folks looking for a little more high tech and moving parts. http://www.ares-server.com/Ares/Ares.asp?MerchantID=RET01229&Action=Catalog&Type=Product&ID=60646
I typed this up yesterday and then it got lost... Grade is not angle. Grade is "rise" (height change) divided by "run" (distance travelled) expressed as a percent (multiplied by 100). Therefore, these formulas let you figure out grade, rise, or run if you know the other two. ( / is divide on your caculator, X is multiply) To figure out the grade of a planned rise and run: rise / run X 100 = percent grade To figure out the required run for a desired rise and maximum allowable grade: rise / percent grade X 100 = run And to figure out the maximum rise for a given run and maximum grade: run X percent grade / 100 = rise (Incidentally, don't worry about the difference between the hypontenuse (length of track) and the long leg of the right triangle (distance on the map). At a 2 percent grade, these would vary by only 2 hundredths of an inch for a 100 inch run. You can measure the "run" either as a line on the map, or the track on the layout.) Print that out and keep it by the calculator...
