### 10. Spirals and Coordinates

As with most surveying stake out operations, having point coordinates makes for more flexible field operation.

Starting with directions of the incoming and outgoing tangents along with the PI coordinates, the process to compute point coordinates are:

#### a.TS and ST coordinates, Figure E-17

 Figure E-17 TS and ST Coordinates

These are computed using Equations E-27 through E-31.

 Equations E-27 through E-29 Equations E-30 and E-31

#### b. Spiral point coordinates, Figure E-17

 Figure E-17 Spiral Coordinates

Using the deflection angle notes, spiral point coordinates can be computed using Equations E-32 through E-37. Right deflection angles are positive, left are negative.

 Entrance spiral Equations E-32 through E-34 Exit spiral Equations E-35 through E-37

#### c. Arc point coordinates, Figure E-18

 Figure E-18 Arc Coordinates

Arc points are computed using equations E-38 through E-40. Right deflection angles are positive, left are negative.

 Equation E-38 through E-40

Math check? The coordinates of the CS computed from the SC should match those computed from the ST.