Vertical curve length or radius

[Cajonpassfan]

Lost in all this seems to be the question as to why a railroad would ever go from a 2% downhill to a 2% uphill grade without a flat section inbetween; that's just asking for trouble and broken knuckles
In the real world, crossing a valley or a terrain depression would involve some kind of drainage structure at the bottom of the grade, a bridge or a fill with a culvert, and those would typically not be built on vertical curves with a 4% delta. Just sayin'...
Otto K.

[CNR5529]

Lost in all this seems to be the question as to why a railroad would ever go from a 2% downhill to a 2% uphill grade without a flat section inbetween; that's just asking for trouble and broken knuckles
In the real world, crossing a valley or a terrain depression would involve some kind of drainage structure at the bottom of the grade, a bridge or a fill with a culvert, and those would typically not be built on vertical curves with a 4% delta. Just sayin'...
Otto K.

 

Agreed, going from a -2% grade to +2% grade is probably an exaggeration for most railroads, but there is more than likely a prototype for it in NA. The question though is how would a vertical curve of a fixed radius going from 0 to 2% cause any more or less damage to couplers on the same radius over a different change in gradient? The radius and equipment is the same, only the length of the curve has changed. If the coupler was going to break on the curve of a given radius from -2% to +2%, it would also break on the curve that levels off to 0 grade with the same radius: it means that the radius is wrong.

[ Guests cannot view attachments ]

[jagged ben]

Lost in all this seems to be the question as to why a railroad would ever go from a 2% downhill to a 2% uphill grade without a flat section inbetween; that's just asking for trouble and broken knuckles
In the real world, crossing a valley or a terrain depression would involve some kind of drainage structure at the bottom of the grade, a bridge or a fill with a culvert, and those would typically not be built on vertical curves with a 4% delta. Just sayin'...
Otto K.

Of course the area I'm trackplanning for is a behind the scenes staging area.   

Fair point for discussion though...   Is there any important reason I need a flat section in the middle?  For the moment I'm persuaded by CNR5529's argument.

[John]

Of course the area I'm trackplanning for is a behind the scenes staging area.   

Fair point for discussion though...   Is there any important reason I need a flat section in the middle?  For the moment I'm persuaded by CNR5529's argument.

well .. you don't ..

[Cajonpassfan]

Agreed, theoretically you don't, and if it's behind the scenes, who cares if it doesn't look quite prototypical. I would just mock it up using some common sense and see if it works. My gut tells me that using free rolling cars, a-2% to +2% transition will create some unpredictable forces in the sag that may or may not be a problem. A lot of that depends on the length of your trains, curvature, smoothness of locomotives and train speed, quality of track work, a dirt spot in the wrong place, etc. Testing is the only way to feel certain IMHO...
Otto K.

[nkalanaga]

Otto is probably right that the transition directly from down to up would cause some unusual stresses, but as far as the curve itself, no, you don't need the flat section.  And, unless your flat was longer than the train, you would still have part of the train going each way.  That's a common situation on the prototype, as very few railroads are truly flat.  Such short ups and downs are usually less than 2%, though...

In fact, the flat would also require two more transition sections, this increasing the complexity, while a continuous curve would allow everything to go smoothly through the entire curve. 

[randgust]

There's an awful lot of theory here and not a lot of practice.

Back on Page 1 there's a great comment on truck-mounted vs body-mounted couplers - that's a much bigger factor here than a lot of math.  As  proponent of truck-mounts, this is one reason why - the vertical alignment of coupler centerline is on a far shorter 'lever' than the body and also stays in the centerline.

The other significant issue here that I don't see mentioned is coupler performance - consistent precision of vertical alignment, and the presence of ANY horizontal curves on the section - all of which can cause slack run-in on the sag and result in false uncoupling if any side force is developed.   I've learned in my own layout that even horizontal curves on a consistent downhill 1.5% can have nasty slack run-in on long trains and force couplers apart as the slack pulls back out.   As the slack runs out, you'll also want to be aware that RDA couplers will 'try' to recenter vertically as force increases, non-RDA heads will re-lock in a new off-center alignment, and you may have more pull-aparts elsewhere.

One more consideration is if you're planning to leave the trip-pins in:  that vertical re-centering of couplers out of the sag may lower the pin clearance as well on non-RDA heads.  I've had fits with that one and that is the #1 reason I stay with truck mounts and have modified ever single head to RDA.

Nothing against math here, but I'd take a  1/4"  x 2" piece of plywood about four feet long with track secured to it and some C-clamps, stick some wood blocks under the ends, jack the ends up to simulate what you need to do, clamp the center down, and see how it behaves with real cars including mixes of short and long cars with body mounts.  If this is in hidden trackage or staging, and starts dropping cars due to false uncoupling where you can't see it, you've created a real mess here that will haunt you.

My son the computer scientist has several great sayings, one of which is 'the problem with variables is that they can change', and that really applies here.   Lots of variables.   

I have great respect for John Armstrong, but what I suspect is that he reverse-engineered it, i.e. this is what actually worked in practice in O scale and probably HO, now go measure it mathematically and make a recommendation.   

[GaryHinshaw]

Couldn't agree more Randy.  The theory is just for fun (and some rough guidance).  There is no substitute for building and testing.

I also agree that a continuous curve between the up and down grades should be fine.  Slack action might be an issue with long trains, but that would be the case whether or not there was a flat section in between, assuming the train spanned the full transition section.

I'm not going to touch the body mount vs. truck mount issue.  There are pros and cons on both sides, and it really boils down to what operating factors are most important on your own layout.

[peteski]

Couldn't agree more Randy.  The theory is just for fun (and some rough guidance).  There is no substitute for building and testing.

I also agree that a continuous curve between the up and down grades should be fine.

How about adding some super-elevation (for even more mathematical and practical fun)?!   

[jagged ben]

There's an awful lot of theory here and not a lot of practice.
...   

The point of starting the thread was to establish a rough lower bound on the length required to make the plan feasible.  Too much length in theory and it wouldn't even be worth building a mockup or finishing the rest of the plan.    I'm satisfied with the theoretical answer, which suggests that the 18" I was contemplating should be more than adequate.

Some good points have been raised about other factors.  Fortunately the sag can be on entirely straight track, and although it's a staging area ot is not hidden from operators or in any way inaccessible.  I'm leaning towards an alternative that does not have a crossover (s-curve) within a few inches of the sag.

Anyway, thanks guys.    I'm ready to move on with the project.  Ya'll are more than free to keep discussing the theoretical though.   

[randgust]

Good, sounds like you're there, particularly if you've moving a crossover!

My own last 'theory v. practice' exercise was this one.    The  switchback line 'up the hill' is a consistent 4% - through that Peco #4 turnout.  So to then get to the log-load passing siding on the top, I had to build a 'dip' down out of that 4% switch, vertical curve back up 2%, and vertical curve off the 2% to get to the flat two-track siding area on the top.  A vertical "S" curve.

All I'm running on it are very short 25' logging cars and the longest locomotive is an Atlas Shay.   I still had to tweak the heck out of it because the trip pins on the shay were hanging on the diverging stock rails on the turnouts, and also hitting the points on the switches.  Pushing it right to the limits, I only have 42".

This is an extreme design case, but even here, I had to 'back off' the vertical curve well beyond the top turnout, where I originally thought I could top it off right at the frog.   In order to keep cars from rolling back into the sag, I had to put two Tortoise machines on the top with vertical 'sprags' that essentially put a wire barrier up through the log car axles - more or less handbrakes applied.   Cars stay coupled and trip pins clear, we're good, but I've violated every imaginable design theory.  Just like a logging railroad would, if it didn't derail, it must be right.

[jagged ben]

Randy, thanks for additional comments.  Fortunately we have a bit more space than that!    One concern I have is keeping the sag an adequate distance from a trailing point turnout to avoid any trip pin ramifications, not so disimilar to your situation.  So I think there will need to be at least 7 inches from the frog that we must endeavor to keep totally free of vertical curve, before starting the transition going back up the other way.  However if the sag only needs 12 inches or so we should have enough room for that.  And I'm not worried about trip pins on straight track away from the turnout given the math above and the .055" to work with between railhead and ties.  Just want to keep those issues away from the turnout.