Curve Radius Question

Inkaneer Oct 17, 2019

  1. Inkaneer

    Inkaneer TrainBoard Member

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    I was pondering how to convert the radius of a curve from the prototypes measurement in degrees to the model railroad measurement of inches. I wondered if there was some formula to convert degrees to inches. I read in Model Railroader's book on Mid-sized and Manageable Track Plans where the Montour RR mainline had curves of 6-7% which the author, lain Rice, likened to 24 inches in HO. Horseshoe Curve near Altoona, PA is two curves of 637 feet and 609 feet radii and is listed as having a curvature of 9 degrees 15 minutes. I wanted to convert these to approximate N scale measurements,

    So I googled it because, after all, google is your friend. Turns out there is a formula to convert one to the other and it is as follows:


    R = 5,729.651/D where D = degree of curve and R = radius in feet

    There is also a table of curves from 1 degree to 90 degrees here:

    http://www.railwayeng.com/Track/Curves.htm

    Turns out that Horseshoe Curve radii in N scale are 47.75 inches and 45.675 inches while the Montour's alleged 6-7%, which the book says approximates 24 inch HO radius, scales out in HO to about 120 inches. A 17 degree curve according to the table would scale out to 44 inches in HO and 24 inches in N scale while a 33 degree curve would scale out to about 24 inches in HO and about 13 inches in N scale.
     
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  2. bremner

    bremner Staff Member

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    9.75" radius=130' radius
    11" radius=146' 8" radius
    17" radius=226' 8" radius
    a REAL F7 minimum radius is 274', which is 20.55" in N Scale.
     
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  3. Hardcoaler

    Hardcoaler TrainBoard Member

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    I match bremner's calculations. I have some old notes that record a Baldwin RF-16 Shark also required a 274' radius, just like the F7 that bremner converted to 20-1/2" in N Scale.

    Interestingly, going smaller, a real Baldwin S-8 Switcher needs 133' radius, which is 10" in N. A real GE 44 Tonner needs 125' radius, which is 9-3/8" in N.
     
    Last edited: Oct 18, 2019
    acptulsa likes this.
  4. RBrodzinsky

    RBrodzinsky Staff Member TrainBoard Supporter

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    That linked table makes no sense. The radius, which is a linear measure, is irrespective of the angle. I can set up 90 degree turn with any radius one wants; and a 15 degree arc with the exact same radius. Or is this for a fixed length of track (arc length)? (I haven’t bothered trying to do the geometry to calculate what this table is based on)
     
  5. NtheBasement

    NtheBasement TrainBoard Member

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    Sort of. Degrees of curvature refers to laying out track beds and such in the real world, where unlike on plywood they can't stake a center point and scribe around it with a chain of length X. Per wiki though I'm not sure I get it:
    In the United States, the measurement of curvature is expressed in degree of curvature. This is done by having a chord of 100 feet (30.48 m) connecting to two points on an arc of the reference rail, then drawing radii from the center to each of the chord end points. The angle between the radii lines is the degree of curvature.[7] The degree of curvature is inverse of radius. The larger the degree of curvature, the sharper the curve is. Expressing the curve in this way allows surveyors to use estimation and simpler tools in curve measurement. This can be done by using a 62-foot (18.90 m) string line to be a chord to connect the arc at the gage side of the reference rail. Then at the midpoint of the string line (at the 31st foot), a measurement is taken from the string line to the gauge of the reference rail. The number of inches in that measurement is approximated to be the number of degrees of curvature.[5]
     
    Last edited: Oct 18, 2019
  6. mtntrainman

    mtntrainman TrainBoard Supporter

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    All very interesting...thanks (y)

    Then there is reality in our modeling in n scale. If most of us can afford the real estate for say a 32x80 HCD....with 2 inch 'buffers' on all sides for derailment safety...we could get by with maybe 14 inch radius track for an outside curve. Those with less real estate may be running 24 inch wide layouts....thats about a 10 inch radius. Yet we run our BIG locomotives around those curves at the 'turn around' points.

    To dream of 48 inch radius (8 feet diameter) trackwork to turn em around is a pipe dream for most. :whistle:

    I realize making track work out on the flats with larger radius curves swinging through areas can be done on almost all layouts. Its those pesky turn around points that makes us cringe...lol:LOL:

    Me... I try NOT to look at my trains when they turn around to come back. Yes...it looks unrealistic...but its a necessity of the hobby. :D:D:)(y)(y)
     
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  7. jimfitch

    jimfitch TrainBoard Member

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    It's all academic.
     
  8. Hardcoaler

    Hardcoaler TrainBoard Member

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    I hide my tightest curves in tunnels where nobody can see them. :D
     
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  9. Inkaneer

    Inkaneer TrainBoard Member

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    That is one of the benefits of joining a club. That is why I joined a Ntrak club. I wanted to run long trains on a large layout with broad curves which I could not do in my home. Having done so I will never go back to the old 4x8 sheet of plywood layout. Even now the three foot corners we use with radii of 27, 25.5 and 24 inches seems small and four foot corners with radii of 39, 37.5 and 36 inches are being contemplated.
     
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  10. mtntrainman

    mtntrainman TrainBoard Supporter

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    The only 'club' around here is a bunch of HO guys who built a gigantic HO layout in one of the spare rooms at the local museum. I feel like Tom Hanks...stuck on an uninhabited island by myself with just my N scale layout I'll call "Wilson"....
    :cry::(:cry::cry::cry:
     
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  11. Maletrain

    Maletrain TrainBoard Member

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    I have often wondered if there could not be something like a cross between N-trak and T-Trak, where easy-to-handle modules were built with larger minimum radius, to be joined together in friends' rec room floors on a monthly rotation.
     
  12. Inkaneer

    Inkaneer TrainBoard Member

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    You can but the problem is with the corners. You need four of them unless you are running point to point. Relying on more than on e person to bring the corners is problematic in that life sometimes gets in the way. That's why most modular clubs own the corners outright so they are always available. Also the larger the radius the larger the corner module both in length as well as width.
     
  13. bremner

    bremner Staff Member

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    just make 4 custom corners...
     
  14. BarstowRick

    BarstowRick TrainBoard Supporter

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    Oh Gosh. Here we go again. That was my first thoughts when, I read the lead in by Inkaneer. Sorry about that.

    Okay, but this is different from "What's the Tightest Radius Curve I can Use?" When working in a hobby shop, I wish I had a dollar for each time I heard that. My thoughts, un-verbalized at the time was, "Wrap it around your little finger, what the heck!"

    As already stated by Inkaneer and elaborated on by Nthebasement (Interesting handle). Railroads, the 1:1 foot scale use degrees to measure the radius of curves. 10 degrees, 9 degrees, 8 degrees, and not so popular the tighter 6 degrees. Which provokes the question how does that translate into inches? There is a calculator and graph that does the calculations for you. I just don't have my finger on it right now.

    Unfortunately this is true. Space constraints has worked against me in the past. One of the reasons despite a fairly large HO scale layout. Fun to operate and build but the curves were way to tight. I read in one of the model railroad wig wags of my time where 36" radius curves was ideal. Or so they thought. Looking at my HO layout with 19", 22" and 24" radius curves. Then it hit me an 18" radius curve is the rough equivalent to a 36" radius curves in N scale. Hummm? Light bulb, a blinder! I wonder! 24" radius curves is the rough equivalent of 48" radius curves. Do you see where this is leading?

    George, just hasn't figured it out yet. If and when he looks at his layout in the enlightenment of the above equivalents. Looking at the radius of curves he used. Do you get it? I thought you'd see where this is going!

    Some of the answers given here I've done but with little to no satisfaction. I don't want to hide my curves and hidden tight radius curves isn't the answer either.

    I haven't answered the degree question. There is a chart or graph out there. We need to pull an oogle google search to see if we can find it.

    By the way George, blind scale is the best scale to the Nth degree. o_O:):cool:
     
  15. RBrodzinsky

    RBrodzinsky Staff Member TrainBoard Supporter

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    OK, cool. So this is based on a chord of 100'. I can see how it would be practical for a survey crew to carry a 100' length chain. But, to state a radius is equivalent to a certain arc, without specifying the chord length, is a very confusing process for someone who does not work on a 1:1 railroad (or survey team)
     
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  16. Inkaneer

    Inkaneer TrainBoard Member

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    The degrees expressed is not the number of degrees the track turns but rather the number of degrees the track deviates from a straight line. This is the angle of deflection or deviation from the straight path. For example, you have a track that runs straight from east to west which on a compass would be from 90 degrees to 270 degrees. Now if that track would have a curve in it so that it would be running from 90 degrees (East) to 265 degrees it would have a deviation of 5 degrees from the straight path of from 90 degrees to 270 degrees. Any 5 degree curve, no matter how far it curves from 1 -90 degrees has the same radius of 1146.279 feet. A 10 degree curve has a radius of 573.686 feet. In a 10 degree curve the radius is shorter because the angle of deviation is greater. I hope that helps
     
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  17. BarstowRick

    BarstowRick TrainBoard Supporter

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    Last edited: Oct 19, 2019
  18. acptulsa

    acptulsa TrainBoard Member

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    Those links certainly simplify things. But it's possible to figure it out even if you can't find a chart or formula.

    First figure out what a hundred feet is. In HO, 1200 inches divided by 87.5 is about 13.7 inches.

    Then figure out what the circumference of the circle of track is. 22" radius makes for a 44" diameter. Multiply by pi and your circumference is about 138".

    Then figure out what fraction of the circle's circumference is one hundred scale feet. One hundred HO scale feet around a 22" radius circle is an arc of about 1/10th of the whole circumference (13.7÷138 and a little bit of fudge factor).

    So, how many degrees are there in a whole circle? 360, of course. And how many degrees does a locomotive turn through going around? 360, of course.

    Now, how far does it deviate from the straight and narrow going through 1/10th of a circle?

    1/10 x 360 = 36°

    The chart eliminates the fudge factor, and comes out 36.102°. Not too far off.
     
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  19. BarstowRick

    BarstowRick TrainBoard Supporter

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    Acptulsa, on my next project I will be depending on you to assist with the math on my grades and curvatures. Nice job.

    I was figuring a linear foot was close to 100 scale foot with a bit of a fudge factor. Not a box of fudge sitting on the train table although at one time that might of been true. More likely a box of See's Candy and now we all know why I'm diabetic. Sigh!
     
  20. mtntrainman

    mtntrainman TrainBoard Supporter

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    I barely passed Algebra in high school ! My head hurts now ! I am a simple son of a gun. I needed to get from point 'A' to point 'B'. I grabbed some Unitrack 'turnouts' and track pieces and snapped em together until I got to 'B' without it looking all wonky. It works for me. Like I said "I am a simple son of a gun"....:ROFLMAO::whistle:;)

    BUT...I'm liking this conversation even if the math eludes me :LOL:

    I am going to have to grab a bag of microwave popcorn however for when I come back to this thread ! (y)(y):sneaky:
    .
     
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