At best, I'm only a lightly skilled survey hobbyist. A burning desire for insight & knowledge forces me to risk the possible intellectual embarrassment of asking silly questions.
If offset distance or something like water prevents you from using/finding the radius point for layout of a road, is there a math equation that could be fielded to set incremental points on a radius from one set point? (i.e. The beginning of the turn).
Intuitively, maybe something like: A given repetitive number of angular offset degrees that will intersect with a given (and incrementally increased) number of "so many feet forward and so many feet over"
Are there any books or skill pamphlets that would be useful for educating such a gentlemen survey practitioner?
Thank you guys for as much patient generosity in sharing knowledge you're able to spare!
Yes.
Occupy the PC and backsight the tangent then plunge and turn half delta then layout the chord distance is the classic way it was done. This can be done for the PT and intermediate POCs (using calculated deltas). The plans would state the degree of curve so that the Party Chief could easily calculate deltas by multiplication..
Chord and Middle Ordinate
It's possible to layout a curve without a radius point.
Any good surveying book will give you the basic formulas.
It's just a matter of using the central angle of the curve (the "delta") portion and the chord calculated for that portion.
The back tangent (the straight line leading up to the beginning of the curve) can be used as a backsight, the other end of the curve, or any point on the curve can be used as a starting point. Any number of points along the curve can be set this way.
It's simpler than it sounds.
You got some correct replies, but they probably don't tell you much except that it is possible. Most curves (unless very small) are, in fact, laid out without a radius point being marked on the ground.
The terminology and abbreviations are daunting the first time you encounter them. You need to find an basic surveying book in your library or on line, and read about curves to get a fuller explanation.
One key concept is that the central angle is also the angle by which you change direction in going through the curve. From that and some other geometry, the equations follow.
Here's a summary of the formulas:
https://dl.dropboxusercontent.com/u/25124076/CurveFormulas.doc
and a calculator application
https://dl.dropboxusercontent.com/u/25124076/CurveCalc.exe
Recognize from the outset in your reading that older books pushed the Railroad approximations, which are not exactly self-consistent at very precise levels. The highway or arc formulas are mathematically consistent. A curve has one radius, which corresponds to either of the "degree of curve" definitions (like one temperature can be given as Fahrenheit vs Celsius).
I pondered that when I started surveying. I assumed they chained all the way to the radius point, maybe 4800 feet away, then all the way back again to lay out the curve. Sounds laughable now but at the time I knew nothing of coordinate geometry.
The classic method I learned in school was by deflection. Basically the curve gets divided up by stations and the proportianate deflection of the curve's delta is turned to the next station backsighting the previous station, basically just laying out short chords. Sort of divide and conquer. The total number of deflections will add up to the curve's overall delta. You'll find the method outlined in most survey manuals but is rarely used any more with the advent of datacollectors. Just another tool in the bag if ever needed.
By deflection, backsighting the rear tangent: The deflection to any point on curve is the degree of curvature divided by 200 multiplied by the length of arc in feet.
5729.58 divided by the radius of the curve you are dealing with equals the degree of curvature.
Degree of Curve x 0.3 will give you the factor for 1' of deflection, i.e. for a 1° Degree Curve = 1 x .3 = .3, for 25' of arc, the deflection = 0°07'30", for 50' of arc, the deflection = 0°15'00", etc. Also the chord length needs to be determined between stations, either the short chord berween stations or long chords from the stakeout point. The formula for the chord length is: 2 x the Radius x Sin ½ the Delta (the deflection angle).
degree of curve
A good designer will construct a curve by making it have an even number degree of curve. This way the layout crew can layout the centerline of the curve without complicated calculations. A 1 degree curve can be laid out by setting on the pc and deflecting 1 degree and pulling 100 feet, then 2 degrees and pulling 100 feet, repeat until the curve is done. A two degree curve the same process first 100 feet, a two degree deflection, then 4 then 6 and so on. One of the more annoying things I see now are engineers designing curves with even radius distances making the degree of curve awkward numbers. There are curves with arc or chord definitions which will make the distance pull slightly smaller for the arc definition curve
"Wiggle In" on a Curve
Slightly off topic but...
We have all done a "wiggle in" on line between two points.
One of my most head slapping moments was when an old Party Chief showed me
that you can "wiggle in" on a Curve too!
Instead of just plunging the scope (i.e. 180), you apply the proper deflection angle.
I still have that moment vivid in memory. Never saw that in any book.
That's the way I learned it.
lol..hey if the radius is say <50' or so, sometimes I still set the RP and pull my tape back and set points on the radius for a contractor...its just faster and easier.
> lol..hey if the radius is say <50' or so, sometimes I still set the RP and pull my tape back and set points on the radius for a contractor...its just faster and easier.
That's what I do, then I take it a step farther with RTK and just stake out to the radius point and hold the radius HD to stake a curve if stationing isn't that critical. Bit like swinging a really long tape. When you end up back at your starting point, you know you've gone just a bit too far. 😉
degree of curve
Isn't the deflection angle for 100' for a 1° curve, 0°30'?
