Re: Measuring curves

What Bruce Pryor provided and PRSL explained is a good explaination of a simple way to find a degree of curvature.
The situation is that railroads used surveyors who used 100' long engineering chains (not to be confused with 66' long land surveyor's chains) to locate the track sturcture. Thus construction stations were located every 100 feet [sta 113+57 means a location 57 feet beyond engineering station 113 or 11,357 feet from the starting point].
These same engineers and surveyors decided to measure curves by degrees of deflection instead of by feet of radius. Highway construction and often modern railway construction uses feet of radius.
A curve is defined by the central angle of a 100' long cord of the arc (or center line of the curve). This angle is also equal to the deflection between adjacent 100' cords. So this becomes a geometry and trigonometry problem.
A surveyor would set up his transit at the start of a curve and turn an angle equal to the desired curvature and where that angle and a 100' chain intersected would be a point on the curve. He could then move the transit to the new location and do the same thing. Or he could do more trig computations and figure how to location points without moving the transit until the end of the curve.
Brian Norden