5. Deflection Angle Method

The traditional method of staking a spiral is by measuring a deflection angles at the TS and chords between curve points. In Figure E-10, the process to lay out the first two points after the TS are:

• Instrument at TS, sighting PI.
• To stake point i
  • Rotate to deflection angle of i, a_i.
  • Measure distance L_TSI-i
• Stake point j
  • Rotate to deflection angle of j, a_j.
  • Measure distance L_i-j

The arc distances between the points (ie, Sta_j - Sta_i) are used as chords. While this does introduce some error, because of the spiral's geometry, the error is relatively small.

Figure E-10 Deflection Angle Method

General calculations are based on these spiral properties for any point referenced to the flat end:

• Radius is inversely proportional to distance along the spiral.
• Spiral angle is proportional to the square of the distance
• Deflection angle is closely proportional to the square of the distance
• Tangent offset is closely proportional to the cube of the distance.

Figure E-11 Deflection Angle Geometry

For any spiral point i:

	Equation E-16	Arc distance
	Equation E-17	Spiral radius
	Equation E-18	Spiral angle, radians
	Equation E-19	Spiral angle, degrees
	Equation E-20	Deflection angle, degrees

Although not needed for the traditional deflection angle method, the tangent distance and offset to a curve point, Figure E-12, can be computed using Equations E-21 and E-22.

	Equation E-21 Equation E-22
Figure E-12 Tangent Distance and Offset

Tangent distances (x_i) and offsets (y_i) can be used to compute radial chords from the TS to the respective curve point, Figure E-13 and Equation E-23.

Figure E-13 Radial Chord

Equation E-23

As with the point-to-point condition, generally the arc distances can be used as radial chord distances. We see this shortly in an example.