SHORT AND/OR SMALL-RADIUS CURVES
Short and/or small-radius curves such as for kerb lines, bay windows or for the construction of large templates may be set out by the following methods.
Offsets from the tangent:
The position of the curve (in Figure 10.16) is located by right-angled offsets Y set out from distances X, measured along each tangent, thereby fixing half the curve from each side. The offsets may be calculated as follows for a given distance X. Consider offset Y3, for example.
Thus for any offset Yi at distance Xi along the tangent:
Offsets from the long chord:
In this case the right-angled offsets Y are set off from the long chord C, at distances X to each side of the centre offset Y0.
An examination of , shows the central offset Y0 equivalent to the distance T1A on ; thus:
Offsets from the tangent
Offsets from the long chord
Similarly, DB is equivalent to DB on Figure 10.16, thus: DB = R − (R2 − X2 1 )12 and offset Y1 = Y0 − DB ∴ Y1 = Y0 − [R − (R2 − X2 1 )12 ] and for any offset Yi at distance Xi each side of the mid-point of T1T2:
Therefore, after computation of the central offset, further offsets at distances Xi, each side of Y0, can be found.
Halving and quartering:
Referring to :
(1) Join T1 and T2 to form the long chord. Compute and set out the central offset Y0 to A from B (assume Y0 = 20 m),
(2) Join T1 and A, and now halve this chord and quarter the offset. That is, from mid-point E set out offset Y1 = 20/4 = 5 m to D.
(3) Repeat to give chords T1D and DA; the mid-offsets FG will be equal to Y1/4 = 1.25 m. Repeat as often as necessary on both sides of the long chord.