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.
Henry
COB Potomac & Northern
Shenandoah Valley
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.
Brent
"All of the world's problems are the result of the difference between how we think and how the world works."
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
greg - Philadelphia & Reading / Reading
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
Modeling the Reading Railroad in the 1950's
Visit my web site at www.readingeastpenn.com for construction updates, DCC Info, and more.
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.
rrinker 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
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.
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".
7j43k if you really try, you can cut it to about .01" tolerance without using machine tools.
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.
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?
7j43k 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
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.
rrinkereither 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.
rrinkerAnother 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.
+1
Layout Design GalleryLayout Design Special Interest Group
7j43kI didn't suggest using a .5% grade for a full foot.
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.
Dave H. Painted side goes up. My website : wnbranch.com
dehusman 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.
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.
rrinker 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.
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.
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.
gregc 7j43k I didn't suggest using a .5% grade for a full foot. 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.
7j43k I didn't suggest using a .5% grade for a full foot.
Greg,
Very neat.
If I'm getting this right, what you found is that, if you add an extra foot to each end of the grade, and only raise (lower) the first riser 1/4 of the "standard" riser differential, that the transition curve is established.
So, in this case, the total run would grow by two feet. The number of risers would go to 20. The first riser from each end would b 1/4 of .36, or .09". And all the other riser increments would be based on the .36 number.
Beautiful,
7j43kNote 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.
The seam in the plywood run should have already been joined with a splice plate. Easy. One adds a few intermediate risers, clamped, and then evens out the whole thing. Easy and quick. Model railroaders have been doing it successfully since the days of the slide rule.
But if folks want to figure things to within a millimeter, more power to ya’.
7j43kSo, in this case, the total run would grow by two feet.
That, of course, is the rub. Usually the run can't "grow", and so the grade ends up steeper than one hopes once the necessary vertical transitions are added.
For a 3.5+% grade, not sure 1 foot of transition will be enough for long cars and engines. The steeper the grade, the longer the vertical transition. But I don’t think we know what the OP plans to run.
cuyamaBut if folks want to figure things to within a millimeter, more power to ya’.
Measure it with a micrometer, mark it with chalk, cut it with an axe.
I have the right to remain silent. By posting here I have given up that right and accept that anything I say can and will be used as evidence to critique me.
Usually, the term "chainsaw layout" means one you build to learn from and then tear apart with a chainsaw. But what the heck, how about cutting all the wood with a chainsaw.
rrinkerWhile technically correct, it is just a much more difficult way to do things....
If you want to fool around with calculations, have at it. However, I agree with Randy that there are easier ways to accomplish this without all the falderal with numbers.The grade from my single level layout up to the partial second level is laid out on multiple curves totalling about 45' in track length. I used 3/4" plywood for the sub-roadbed, cut into curves or straight sections as needed, then spliced together.I knew that the track needed to rise 15.5", so jacked-up the upper end and put a riser under it, clamping the bottom end to a crossmember in the open grid benchwork. Next, I added a riser at the mid-point of the grade, raising the roadbed half the amount of the upper one. Next risers were added at the 1/4 and 3/4 points of the run. Any sag between these supports was easily discernible by-eye, and risers were then added where needed, with any humps or sags adjusted as necessary.The area from the level track at the bottom of the hill and transitioning into the grade also got risers/supports, but they were simply fastened to the roadbed and benchwork using the natural transition of the plywood roadbed.
After the risers were all in place, I marked each one with a pencil line corresponding to the top of the joist to which they were clamped.The clamps were then removed, and a train placed on each of the various curves. I then manually raised the riser at the mid-point of the train within that curve to its marked position, then pushed the bottom of the riser towards the outside of the curve, ensuring that the inner end of the pencil line was still at the proper height. Naturally, the outer end of the line was higher than the riser to which I then clamped it: superelevation in one simple move. I manually adjusted the tilt until the train on the curve "looked right", then fastened it in place. The beauty of doing it in this manner is that the entire curve has a naturally-formed vertical easement in-to and out-of the superelevation. All that's need is to then raise the other risers so that the inner end of the pencil line aligns with the top edge of its respective joist, taking care to not push or pull the bottom of the risers from the offset naturally induced by offset of the mid-point riser.
Wayne
7j43kDave 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.
No I didn't.
I said take a 24" level and put a 3/4" piece of wood under the low end, then raise the roadbed up until its level. I didn't say you have to level the entire grade in one whack. I'm assuming that he will temporarily install risers over the length (C clamps) and then adjust the grade using the level. Trying to level an 18 ft long pece of 1/2 in plywood by just doing the top and the bottom wouldn't work.
He can set the top one because he knows where that one is supposed to be. Then just eyeball in the intermediates or even every other intermediate using clamps. Start at the bottom and work your way up. Set the first and second riser. Then move the level up a couple feet and try again. It takes seconds to go back and check your progress. Its itterative but very quick and easy.
Since that is more or less how every prototype grade in the US was set, I'm pretty sure it will work.
If he wants to get fancy, he can get a digital level, that reads out in percent grade and put it on the plywood and dial it in to whatever % grade he wants using the same process.
dehusman 7j43k 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. No I didn't.
7j43k 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.
I do see that on re-examination. My apologies for misreading.