Does anyone know of a website calculator that calculates riser heights! I have 216" run and 6.5" rise for a grade of 3% but what I want to know is the riser heights I will require at 12" intervals for my 18 risers…I will deduct the thickness of the roadbed base (1/2" ply) and foam roadbed!
At 12" increments, every riser needs to be 0.36" higher than the previous one for a 3% grade.
You should have a transition into the start and end of the grade. I’ll let someone else tell you how to figure that. If there is a curve involved, it effectively increases the grade, as far as locos being able to pull rolling stock.
For the vertical transition:
I chose a length of 12" (I wouldn’t go shorter–if I was running 89’ cars, probably longer)
I divided that into 2" segments
For the first segment, I assigned a grade of .5%
For the next, I assigned a grade of 1%
Etc, until the last grade was 3%
Then I added up all the rises from each segment: .01 + .02 + .03 + .04 + .05 + .06
Actually, since the last 2" are at 3%, I suppose the transition length is actually 10". But it’s still pretty much the same.
Doing that, I got a rise of .21" at the end of 12", instead of the .36" from the straight 3% grade.
If the grade levels out at the end of the distance, the number just “flips over”.
Ed
I agree with Henry’s math. However, in the interest of accuracy and ease in cutting the risers, I would go metric and that works out to 9.172mm. 9mm is close enough.
You need a transition into and out of the climb so that will skew these figures.
I did calculate a grade using a spreadsheet and the cosine function. Took a bit of messing around to get it to work, but it eventually worked out. Best part is that the transitions were included in the calculations!
Once you get the basic info into the sheet, it can calculate the riser spacing and their heights as well. It just requires a lot of calculations since you have to think in radians, and a grade is equal in length to the value of pi (3.14 radians).
Computers think in radians.
for a linear rise, the change in height of each riser is simply 6.5" / 18
1 12.00 0.36 3.01
2 24.00 0.72 3.01
3 36.00 1.08 3.01
4 48.00 1.44 3.01
5 60.00 1.81 3.01
6 72.00 2.17 3.01
7 84.00 2.53 3.01
8 96.00 2.89 3.01
9 108.00 3.25 3.01
10 120.00 3.61 3.01
11 132.00 3.97 3.01
12 144.00 4.33 3.01
13 156.00 4.69 3.01
14 168.00 5.06 3.01
15 180.00 5.42 3.01
16 192.00 5.78 3.01
17 204.00 6.14 3.01
18 216.00 6.50 3.01
if you add the vertical easements Ed suggested, your grade increases
1 12.00 0.06 0.50
2 24.00 0.18 1.00
3 36.00 0.62 3.65
4 48.00 1.06 3.65
5 60.00 1.50 3.65
6 72.00 1.93 3.65
7 84.00 2.37 3.65
8 96.00 2.81 3.65
9 108.00 3.25 3.65
10 120.00 3.69 3.65
11 132.00 4.13 3.65
12 144.00 4.57 3.65
13 156.00 5.00 3.65
14 168.00 5.44 3.65
15 180.00 5.88 3.65
16 192.00 6.32 3.65
17 204.00 6.44 1.00
18 216.00 6.50 0.50
Can you cut wood that accurately with typical tools? If you are using risers, I suspect you are using either open grid or some form of L girder with joists to attach those risers to. In which case - the length isn’t all that critical. You clamp them and check the resulting grade, once it’s right, you screw them on. If they overhang the bottom of the joist - just cut off the excess.
Everyone wants to do complicted math. I guess it’s nice to know, but it is entirely unnecessary. Just like for building a helix. Only the first and last turns need calculations tp get a smooth transition in and out. The risers/spacers for the intermediate levels will all be exactly the same size.
–Randy
I didn’t suggest using a .5% grade for a full foot. I suggested using it for the first 2 inches. For the next TWO INCHES, I suggested 1%. And increasing the grade by .5% every two inches until reaching 3%. And, yes, the run will be a bit longer if you stay with the 3%. But you will have the necessary vertical transitions.
If you choose to keep the overall run constant, the max grade will increase, but not as much as the 3.65% described above.
Ed
Henry said: “You should have a transition into the start and end of the grade. I’ll let someone else tell you how to figure that.”
I thought it would be fun to figure out the figuring out. If you’re using plywood, you can probably do it automatically.
As far as cutting wood, if you really try, you can cut it to about .01" tolerance without using machine tools.
Ed
Since the OP is from the North, he can deal with metric better than most 'mericans.
He doesn’t really need support for most acceptable roadbed materials every 12".
Since I don’t have a tape that measures in the hundredths of an inch, I’m going to round off to the nearest tenth. That will not cause, what one poster called the “usual undulations” in his thread about unwanted uncoupling.
As for sines and cosines, I had a CRC book once upon a time, and I’ve forgotten all that. Maybe because that was in the late 60’s
But you’re the guy who specified .36" in the second post of the topic.
Instead of going to .1" accuracy, why not go to 1/32"? That’s easy to do with a regular tape measure.
Ed
Another reason to just measure it at the end - as in, don’t rely on the accuracy of the riser length to set the grade. Make one accurate measurement as you clamp each riser, and you should avoid those nasty undulations. You should probably do that even if yoou cut each riser in a highly accurate manner - so you cut the wood to length within .01", but how do you make sure the riser attaches to the benchwork within .01" in oder to maintain that tolerance? ANd if you are going to just adjust the riser as needed to get the roadbed surface level or in a nice smooth vertical curve, why bother cutting the riser to such accuracy?
–Randy
Guilty as charged
I had one of those triangular drafting rulers that measured in 1/10’s
He doesn’t have to measure every one, if he has 3’ level or sheet rock t=square. With a 3’ level install the 0" and 36" risers and put the level on top and bring the 12 and 24" risers up to meet the level
There’s a lot of ways to build a grade on a layout.
The OP asked about riser heights. He got those. For frosting on the cake, he got the transition heights, too.
He didn’t ask how to build it.
Ed
+1
sorry Ed
so i looked at what radius curve would be necessary to transition from flat to the angle of the grade at the first riser after which the grade is constant.
i found that that there is a natural (constant radius) curve over a two riser interval distance, if a riser were 1/4 the height of the first riser at the mid-point. this appears to work for various grades.
This seems like a simple approach once the riser heigth and interval are determined. Of course this this requires an extra riser interval at both ends of the grade.
I don’t recall reading about building a vertical easement this way.
If you have 18 joists and a riser on each joist, why are you even wasting your time calculating the height of the risers?
Don’t bother with that. Totally unecessary.
Get a piece of 3/4 in wood and a 24" level. Set the 3/4" wood under the low end of the level, sitting on the roadbed to be raised. Raise the roadbed under the high end of the level until the level is level. That is 3% grade. Then run the risers up from the BOTTOM until they touch the roadbed, clamp and screw them to the joists underneath. The risers only need to be trimmed to the nearest 1/2 in or so.
No math, no precision cuts, one thing to look at, just keep the bubble level.
One reason that comes to mind is that the run is 216", which is longer than a piece of plywood.
Another could be that, if you have a curve in the sheet, the rise can get funny.
Another is that there will be a sag in 96" of 3/4" plywood. In 216": spectacular!
And another is because it answers the question the OP asked.
Ed
While technically correct, it is just a much more difficult way to do things. If there are 18 risers over a 216" run, that’s a riser every 12" - if that results in too much sag, you must be using wet noodles and not plywood. There’s just no point in making 18 ultra-precision cuts. You can just cut them all to some approximate size and line them up as they are attached.
–Randy
Dave said to position each end of the grade (top and bottom) tightly, and then run the risers up from the bottom to meet the grade.
Note that there are not yet the 18 risers installed. That is what he is setting up to do So the wet noodle run is 216". Not the 12" you seem to be assuming.
Do you REALLY think 216" of plywood won’t sag?
Ed