How do I compute railroad spirals with iPOGO?

The C&O/B&O valuation maps were originally surveyed around 1916 and did not usually show spirals at that time. Rather the surveys were intended to locate right of way and improvements for filing with the Federal Government, and usually documented the centerline of right of way or ownership. The railroads had been granted a lot of freedom in the early days to encourage transportation development and commerce. The 1916 filings were to establish what the railroads had built to date for tax and ownership purposes.

Spirals on val maps are not conducive to right of way computations. Nor are they useful when you have to compute a track shift relative to the right of way. And the field location of a spiral will very seldom exactly match a val map.

The primary purpose of the spiral is to provide a gradually increasing rate of change in radius and superelevation so the train will not go flop. This rate of superelevation change is dictated by railroad standards based on formulas derived from speed and equilibrium. For example, many years ago the maximum rate of superelevation change was 1" in 62 feet when there was a maximum speed of 50 mph. The length of 62 feet was used because it worked well with the old method of "string-lining", which is another complete topic. Therefore, if your curve had to have a 3" superelevation for the speed of the train, your spiral length had to be a minimum of 184 feet long. But 200' feet is easier and quicker to stake in 10 chord spirals, so you usually go with even 100' lengths in design where you have the room.

Every season, the railroads send out maintenance production gangs to line and surface the tracks, and the spirals can be modified as necessary to accomodate faster trains or heavier traffic. Your best indications of track spirals in the field are the aluminum tags you see on the ties marking the T.S., S.C., C.S. and S.T. The values stamped on these tags are also used by the production gangs to set up their line and surface equipment.

By definition, a spiral is a curve with steadily increasing radius going from infinity (flat) to Dc (sharp). There is a unique 1/3 and 2/3 relationship in the deflection angles for these curves. The 1/3 delta applies at the flat end of the spiral and the 2/3 delta applies at the sharp end. This holds true for any two points on the spiral because there is a steadily increasing rate of change throughout the spiral. Likewise, the long tangent to the spiral PI on the flat end is twice as long as the short tangent to the spiral PI on the sharp end.

As mentioned above, the length of spiral is usually determined by the allowable rate of change. If a spiral is referenced on the val map, it is usually given as a rate of change in radius or "a" ("K" in some surveying texts) that has been predetermined to be acceptable for the degree of curve and operating speed. You can then calculate the length of the spiral by simply dividing the Dc by the rate of change. For example, a 4 degree curve (chd def) with a rate of change of 1.0 would yield a spiral length of 400'. This simple formula tells you that since there is a steadily increasing rate of change, you must go 100 feet to reach 1 degree of curvature, at 200 feet the radius equals 2 degrees, and so forth.

Once the length of spiral is determined by design, you then split the spiral in half at the original T.C. on the original alignment. From the original T.C., half of the spiral lies back on the tangent, and half of the spiral lies ahead on the curve. This in turn forces the original centerline alignment to shift down and in as you progress from the tangent through the spiral and onto the curve. This shift is termed the "O" or "throw" distance. The offset from the original alignment T.C. to the shifted spiral alignment will always be 1/2 of "O".

Click here for an iPOGO command file containing typical spiral formulas, computations and output.
(applies to iPOGO, 5.0, 06/30/2001)