Hi Chris,
First, I would like to visit New Zealand one day. I've seen Zena, Hercules, and Legend of the Seeker. The scenery is awesome.
Second, from my civil engineering book:
[quote="station. The rod man has the rod over the point (usually a stake) The instrument man sights on the rod. This gives the instrument the line of sight of the line that is being laid out (the back-sight). The instrument sight glass has a 360º vertical rotation. So the instrument man flips the glass over and it is now showing the line to be staked in the forward direction (the fore-sight). The rod man walks out about 100 feet plus a bit so that the instrument man can direct him to place the rod on-line. Once on line, the two chain men take the 100 foot chain (or tape - the original measuring device was a physical chain with each link being one inch long) and pulling it taught between the stake the instrument is set up over and the direction to the rod main to get the chain on-line. Once on line, a stake is driven on-line at the end of chain and the staked line has been lengthen by 100 feet. (The other type of surveying chain is a Gunter chain that is 66 feet long - it is still found in public records of some public and farm lands).
On a curve, the back sight is on the 100 foot chord across the curve's arc. Once lined up, the sight glass is flipped. Now there is an extra step from the tangent. There is a deflection angle that has to be turned. This angle is the amount the curve turns in the 100 foot chord. So for a left turning curve of 3º, the sight glass is turned 3º to the left. Then the rod man is put on line and the chain men place the stake. This deflection angle is called the degree of curvature. Now the routine to set the curve is back sight, flip to fore sight, set the degree of curvature, rod no line, chain on line, and place the stake. (For a tangent, the degree of curvature is zero (0) degrees).
A skilled team can whip this out just as fast as they can run a straight line. The only issues are when a tangent to curve or a curve to tangent occur in the middle of an even station. The CE then has to calculate the deflection angles that are somewhere between a tangent 0º and the degree of curvature (3º in the above example). Eventually, the degree of curvature was tied to easements and super elevation.
[/quote]
All this gobblty gook reduces to:
radius (in feet) = 5730/(degree of curvature).
As some point out, this is the "railroad" or chord definition. Roads use the "highway" or arc defintion. The difference between the two is less than 0.01% (1 in 10,000) for a 1500 foot radius. For 0.1% (1 in 1,000) for a 600 foot radius. For 1.0% (1 in 100) for a 200 foot radius.
I hope this helps and does not seem like a bunch of dross. I find the history of technology as fascinating as science fiction - speculating on the future and learning from the past.
Doug vV
