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 E10, 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_{TSIi}
 Stake point j
 Rotate to deflection angle of j, a_{j}.
 Measure distance L_{ij}
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 E10 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 E11 Deflection Angle Geometry 
For any spiral point i:
Equation E16  Arc distance  
Equation E17  Spiral radius  
Equation E18  Spiral angle, radians  
Equation E19  Spiral angle, degrees  
Equation E20  Deflection angle, degrees 
Although not needed for the traditional deflection angle method, the tangent distance and offset to a curve point, Figure E12, can be computed using Equations E21 and E22.


Figure E12 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 E13 and Equation E23.
Figure E13
Radial Chord

Equation E23 
As with the pointtopoint condition, generally the arc distances can be used as radial chord distances. We see this shortly in an example.