The Big Helix: Designing a Helix (252)
Вставка
- Опубліковано 20 кві 2022
- Building a helix is a complex procedure that requires some fairly complex planning up front so as to avoid mistakes along the way. In this video we'll start by making some critical measurements and then use them to calculate the sizes of our loops, length of the helix, amount of track required, the slope of the loops, and the angle of the roadbed. Once we have all that figured out we'll be ready to move on in subsequent videos to build a stable base for the helix, install the loops, lay some track and get'er done!
The On30 file can be downloaded from my website larrypuckett.wordpress.com . Feel free to share the file with anyone who might be interested. You can email me at ljpuckett at me dot com if you are interested in an item. - Навчання та стиль
I wish my some of my math teachers explained geometry, trig, etc., as easy as you do. I actually understand it!
thank you for the great full detailed video
Thanks Larry, what an excellent Video working from first Principles, you make it so easy to follow. Best wishes.
Great video. Who would have thought math would come in handy in building a helix for a layout? looking forward to the helix build.
Grateful for the educational tips & tricks, Larry
Great video, Larry. I think I must have been doodling impossible trackplans or just plain asleep in school for the maths lesson when we did negative tans! I am a fan of using set track on helixes to eliminate any tracklaying issues.
After building helixes using timber supports, I've sworn that if I build another I'll go with a method I've seen in German railway modelling magazines, which uses threaded steel rods, and then you use nuts to support the trackbed, and of course you can adjust the nuts minutely to get get the gradient absolutely perfect.
That was a great video Larry. I am looking forward to watching the series.
Hello Larry
Great video as usual.
Most helix designs all seem to be circles, but don't forget the good old oval. This gives the potential of greater travel distance between curves, allowing more distance to rise, also helps reduce train drag, it may allow you to reduce the helix diameter if that's a construction issue , but of course you cant go to tight, certainly should be same as or larger than the tightest bend your train types/lengths can handle without derailing.
Just thought this would be a good idea for those of us with a tighter area.
I based mine around the calculations shown woodland scenic's slope = 4" rise requires 16ft distance to give a 2% slope ( I used just the calculation not the polystyrene product on my helix)
Mike
Larry Great info. I have a heix on my Layout and presently adding a third level which mean I need to extend my helix. I bought my helix kit from TrackSideScenery The product is very light and easy to work with Looking forward to seeing the progress on your helix.
You lost me at the first mathematic equation! I will still be following along with you.
Larry looks very interesting. I have not used trig since high school, plan to build a similar helix and staging yard on my new helix. Next week more progress
That was interesting. I tried the app on my iPhone previously and found supporting the phone to be a pain to deal with while making adjustments. So, I bought a digital torpedo level from Amazon that is 6 inches long and will fit between the levels of a helix and not fall over as it has a base a little wider than the HO track. I have seen 10” torpedo levels too. It works a lot better. You mentioned building the helix out from the corner and later moving it into place. If the floor is level under there, have you considered building a base on lockable casters? Build it so you can roll it out for maintenance, removing derailments, etc. Then roll it back in, lock down the casters, insert two pieces of rerailer tracks to join it to the levels. Helixes do eat up a lot of track. Imagine if you were building it double tracked? You might see if Tracksetta has a curved gauge to fit your needs and get one to help lay out the curved flex track. Joey at Trackside Scenery has a helix kit cut to your requirements using I think Gator Board. You should take a look at it before you start cutting up sheets of plywood. It is all black in color. Just another option. Don’t you have Avnet articulated steam engine? A Y6B? Will that be okay on your helix design?
I bought some of the lockable casters but in this case don’t plan to use them since I will also have to install uprights on the sides of the helix to support the uppermost level of the layout. So once installed it will not be moveable at all.
I’ve built two helix’s (helii?). On the first one I used flex track. Soldering all those joints around curves was a major headache. On the second one I used curved track soldered together (Kato). It went together so much better. Mine are both double track which makes it more difficult. I’m anxious to see yours come together!
Interesting video, Larry. Pretty good explanation of the grades and their calculations, with one glaring omission - you didn't talk at all about compensated grades. Your grade may be 1.86 percent, but with compensation for the grade on the curve, you're actually closer to an effective grade of 2.79%, using the LDSIG-modified John Allen formula of CG = G + 28 / R, where CG is Compensated Grade, G is actual grade, and R is the curve radius.
The load a loco may be able to pull might be rather disappointing if compensated grade isn't taken into account.
I have always been aware of the effects of curves as well as the grade but don’t remember ever seeing the formula you gave. The magic 2% grade that everyone tries to stay under seems to also incorporate the curve effect to some degree although it does not account for the degree of curvature. I’m sure a civil engineer could provide a real world formula but of course it would be incorrect for models. In his book John Armstrong says that model locos pull more cars on a grade than they should be able to so grades should be somewhat exaggerated but he doesn’t really address the curvature effect.
@@TheDCCGuy I don't remember where I found the formula, but it was apparently developed empirically by John Allen (THAT John Allen) through a series of experiments in the 1950's. The formula he developed was CG = G + 32 / R.
In the 1980's and 90's, the Layout Design Special Interest Group did another series of experiments and refined the formula to CG = G + 28 / R.
Compensated grade is also called equivalent grade.
Thank you for sharing. 👍👀
Thanks Larry.
Curious thing, I was just reading that exact same book. I'm also rereading the "Realistic Operation For All Scales, How to Operate our model railroad" by Bruce Chubb.
Apparently MR has pulled John’s book. I suspect they will have someone else do a major update as they had me do with Andy Sperandeo’s old wiring book.
Hi Larry, very nice video.
I want to add my sand grain, for the construction of the helix you will use plywood 12mm that it's ok, when you cut the helix from the plywood sheet there are a few different approaches, I saw a video where they use the octagonal principle for the helix base, this makes the cuts to be straight, easier to cut, joint the segments and less waste. each segment of the octagon is a trapeze that overlaps with the next section. I used to make a small helix and work very well. The circle is into the octagon.
Yes, I a, aware of that method and read through a long thread about it on the MRH forum. It does look intriguing and should cut plywood waste but it requires a lot more cutting and a lot more fitting and joining so I opted for the “traditional” circular loops. I may change my mind and try the trapezoidal approach for the second helix.
Really great explanation of how to figure the loops. However, I might suggest that when determining the distance between levels one should first determine how high the highest piece of rolling stock running on it will be. Then allow some extra "headroom" above that. Next, and this is a little different from what you said, take the thickness of the plywood or what ever you are using to support the track, PLUS any cork roadbed AND the thickness of the track itself. I think this will help avoid getting the levels too close together.
That’s what I meant when I said if you run modern double stacks you may need more than the 3-3.5” clearance.
I am seriously thinking of adding 1 helix maybe 2 to my layout expansion project, haven't decided yet. From experience purchase the digital level from the Jungle Web Site and not use the iPhone. I found it clumsy to use and unable to keep it upright while making adjustments. I am hoping that you don't go with a kit and build everything from scratch, it will be interesting to see you scientific approach to its construction.
The math is all good Larry but I am going to pick on the term "negative tangent". When you have the tangent value and you are calculating the associated angle it is in fact the arctangent. It is also sometimes called the inverse tangent as a result of the -1 exponent but the only correct trigonometric term is arctangent.
I did find it a bit odd that you chose to arbitrarily set the rise per loop at 3.5" rather than divide the total height change by the number of loops that could be determined from your track plan. The other thing I noticed from your track plan is that you could have started the inter-deck grade much further back reducing the overall climb accomplished by the helix itself helix thereby reducing helix length and the associated time a train spends in the helix itself and the amount of track (cost) in the helix itself. Perhaps a few feedback comments as to why you chose the arrangement you did as opposed to some of the other options available to you. Don't get me wrong, I am an ardent advocate of helices but at first glance and without knowing some of your other reasoning/constraints this one seems to be perhaps a full turn longer than absolutely essential.
The distance between the loops and height difference is what controls the number of loops not vice versa. You need to establish a standard height between the roadbed based on your rolling stock and roadbed thickness. For HO the standard for many years has been 3” as a minimum for most rolling stock. So that in turn controls the number of loops. You can’t just arbitrarily say you want 6 loops and divide the total height difference by that.
@@TheDCCGuy No kidding you can't just arbitrarily say 6 loops Larry! And while 3" clearance has indeed long been the standard that is very tight to access modern equipment if it derails but to each their own confidence level that they won't experience derailments requiring access inside the helix. But there is some iteration and trade off necessary during helix design. When I look at your track plan there appears to be 45 degrees (give or take) of curve between the approach tangent and the helix. There will also be 180 degrees at the top to "reverse" the direction of travel aligning to the upper level. So according to a quick read of the track plan there will be N+0.625 (give or take) helix turns - note that I did say number of loops determined from your track plan. Checking the options of N= 4, 5, and 6 the closest match is to your 3.5" climb per turn is 5.625 which conflicts with your calculated 5.42 loops but at 3.37" climb per turn that violates your minimum 3.5 inch climb per turn standard. This is why I noted the potential to start your inter-deck grade to the left of the helix as shown on the track plan at 10:55. If you made the helix 4.625 turns at 3.5 inch climb per loop you would obtain 16.19" of climb in the helix and get the remaining 2.81 inches on the approach. At the helix grade of 1.86% that would take 151" of grade so about 12 ft 7 inches.
While helices are great tools they have a number of nuances and are not necessarily the easiest things to design and build.
I was going to say I get a different answer for the inverse tan of 0.0186 but I realized I had my calculator set for rads, not degrees!
Great design and explanation. Instead of using flex track you could consider using set track curves to make the track laying easier. Maybe more expensive though.
One problem with set track is the curves only come in a few radii so it limits your helix design. For example I just checked the Atlas website and in HO they only make 15, 18, and 22 inch radii curves. I doubt you’d want a helix that tight.
Good explanation of the math, Larry, except that is the inverse tangent, not the negative tangent.
I think I must have worded it that way since that’s the way it looks on my calculator-I skipped trig in college.
Larry, instead of struggling to measure the angle, just measure the height between layers. It's much easier to measure it accurately just as you measured the total required rise. You can use math or a simple graphical method to figure the height of the bottom layer above the (presumed level) foundation bench work. Once you complete the first turn, make each additional layer the constant separation height above the one below it.
Have you considered the reduction in headroom at roadbed splices? If you follow the normal splice practice your headroom will be 2.5" at the splice plus there will be a nasty edge to dig into the back of your hands when you do track maintenance.
Linn Wescott suggested an overlapping type roadbed construction in Ch 7 of his book _How to Build Model Railroad Benchwork_ probably available at Kalmback.
A friend of mine is building a 3 track helix that I designed using that method. Tracks are 34, 36.5 and 39" radius with a total rise of about 21". It connects 4 different layers of his RR. We are using curved segments cut from 3/8" plywood and overlapped like bricks to form a continuous 0.75" thick roadbed about 4.75 turns long. It has 4.5" rail to rail separation or about 3.75" (minus track height) between layers. We are using threaded rods with nuts & washers to support the layers which makes for easy adjustment of height.
As you will see I have a way to creat a constant slope helix, be patient. And yes I have Linn’s book.
Strictly speaking, the length of track in one turn of your helix is a bit more that the circumference, but because the rise/height squared is negligable compared to the circumference squared, the change is on the order of rounding error and so is practically insignificant. Also, for small incline angles like the one in your case (or any practical model railroad helix I'd guess), the inverse tangent of x is approximately equal to the angle x expressed in radians so you don't even need a calculator--just convert from radians to degrees! This is given by x in degrees equals x in radians times the factor 180/pi which is about 57.3. In your case, 57.3 times 1.86% (0.0186) equals 1.06578 which rounds to your 1.066 degrees. Trust me, I'm a retired mathematician. :-)
There was an old joke where I worked. The director asked a biologist, a mathematician, and a statistician to tell him what 2+2 is. The biologist said something between 3 and 5. The mathematician immediately countered that is was exactly 4. The statistician craftily replied what do you want it to be? So the answer depends on your perspective! Now can you explain to me what a radian is?
@@TheDCCGuy Heh. Funny, because I also worked as a statistician for many years. A radian is another way to measure angles, and a full 360 degrees equals 2*pi radians. If you consider a sector cut from a circle, the arc length of the outer (curved) edge is equal to the radius times the angle in radians. For this reason it's considered more "natural" than degrees. Nearly all scientific calculators give you the option of using degrees or radians when doing trig stuff. Thanks for all your videos!
Exactly what I noticed when I was trying to replicate Larry's results while my calculator was set to radians, not degrees!
The difference in length (along the center line) is about 0.0325" or a little less than the width of the rail head (Atlas code 83 from about 1983). There's about a 4" difference between the length of the inner and outer rails. (retired engineer ;-)
Great, informative video. Thank you.
But, oh boy, those imperial measurements???
I made all the calulations in metric and it suddenly becomes sooo much easier. 😃
The inverse function(-1) can be read as "the angle whose tangent is . . . " and of course it also works for other functions as well.
Your calculations were pretty well explained - I'd quibble that tan-1 is really an inverse tangent not to the power of -1! - but your assumption about using complete circles is a bit of an error/simplification. You should include the start and end angles of your helix in your calculations somehow to get it completely correct.
Those approaches can actually be anything from flat sections to the same angles as the helix. That will allow vertical easements to be incorporated as needed.
Great video. I'd also split the hair about the inverse tangent :)
Dear Larry, checking the Kalmbach book listings, I find that this book is out of print and scheduled to be discontinued.
Too bad, it was there last week. I guess they figured that the other design books will fill the bill. It would be hard to find someone to do an update to John’s original. I had the honor of doing the wiring book as an update/replacement for Andy Sperandeo s version after getting his blessing to take it on. That one has been updated numerous time by a string of authors.
Great subject for a video series. I'm really looking forward to this. Do you have any plans to superelevate the outside rail? I remember reading about it years ago but you never hear about it nowadays. Thanks Larry
Super elevating track works great for the prototype but has little practical use for models. However on long sweeping curves it can be quite eye pleasing. The main purpose AFAIK on the prototype is to allow trains to sweep around curves at speed with reduced chance of derailing, but on a helix we usually creep up the slope so it is a complication that is not needed.
John Allen did some observations/calculations. He came up with a 32" curve will produce the effect of a 1% grade.
Yes but that was based on equipment available to him in the 50s and 60s. Modern equipment is much more free rolling so the effect is not as drastic. Still significant but not as much as it was then.
helix is not too hard to build, just have to use top quality wood, and I painted both sides of the wood to kind of seal it. threaded rod makes it easy to adjust. I have a 9 level helix on my level.
one other thing to think of for height is if you are using any kind of road bed as well. 1/2 cork will change the measurements
I have thought of using the threaded rod method as it allows fine tuning adjustments but always wondered how stable it is. Does it wobble at all if bumped?
@@TheDCCGuy I believe Charlie Bishop used the threaded rod method. He built one a few months ago. Keep safe Frank.
@@frankwhittle4364 IIRC Charlie also used a more robust looking spirit level tool. I wouldn't put a lot of trust in the accuracy of a phone's accelerometer.
@@chrisridd9423 Chris I think he really meant an Inclinometer, I don't want to put words in his mouth but that's what I would have called it
@@frankwhittle4364 you could be right. Angle measuring thingy :)
Hi Larry,
I have absolutely no experience of constructing a helix, but 2 things struck me when viewing your video. 1. the circumference that you calculated is based on the diameter of the helix being 60", but the circumference of your track will be less (unless the track is hanging off the edge of the helix). If you allow, say 1" between the track and the edge, that reduces the diameter to 58" (though the circumference may need to be measured from the centre of the track, so reducing the diameter even further). 2. It seems that you have a couple of feet of straight track before entering the helix, so why not use that to commence the climb on one line and the descent on the other?
I hope these comments are useful.
Stephen
First, I based my calculations on the center of the track and the roadbed will be cut to those measurements with 2.5” on either side. So yes the inner and outer edges of the roadbed will be slightly shorter and longer than the center but it won’t affect the outcome. The approach tangents will be sloped in order to make any vertical adjustments as needed.
@@TheDCCGuy Sorry Larry, I thought the diameter of 60" referred to the size of the helix and, therefore, the roadbed rather than the track and, yes, of course the inner and outer edges will have a different diameter.
I still enjoyed the maths lesson, though.
Regards,
Stephen
If you can afford a phone and levelling app, you can afford a digital spirit level
I already have the iPhone and the app is free.
Your assumption that plywood is exactly ,5 inches thick may be problematic with your calculations.
I have an ace in the hole on that one as I have two long approach sections to the helix and they can either be flat or sloped. So if need be I can accommodate any small deviations like that.
Nice and very informative video Larry. I’ve been meaning to ask if you’ve got Facebook or not. If not then I highly suggest making one to join the southern railway system modelers group to share your interests and great work. I’d also like to be able to message you directly if that would be ok.
Although I have or at least had a Facebook account I never use it anymore as I find it a time sink that I just don’t have time for.