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# Set Back Distance:

It is clearance distance, required from the centre line of pavement/road to the obstruction in ode to maintain the adequate sight distance to the curve.

The set back distance or clearance required from the centre line of horizontal curve depends upon.

• Required sight distance (SD)
• Radius of horizontal Curve (R)
• Length of curve(LC)

Note: This topic is part of the second chapter of Highway Engineering. I suggest reading this topic in the context of the complete chapter: Geometric Design of Highway. If you want to read the entire Highway Engineering, click here: Highway Engineering.

# Calculation Of Setback Distance

There are two cases in the calculation of setback distance:

## Case 1: When the length of horizontal curve greater than the sight distance (LC>SD).

(a) For Single Lane:

In single lane road the sight distance is measured along the centreline of the road.

 Set back distance (m)= OD CD=AC=R m=CD–CO In Δ ACO$$cos\frac{\alpha }{2}=\frac{CO}{AC}$$ $$CO=R· cos\frac{\alpha }{2}$$ $$m=R-R· cos\frac{\alpha }{2}$$ $$\frac{\alpha }{2}=\frac{SD}{2R}(Radians)$$ OR $$\frac{\alpha }{2}=\frac{180}{\Pi }\frac{SD}{2R}(Degrees)$$

(b) For Multi lane:

In multi lane road the sight distance is measured along the centreline of the inner lane and the set back distance is measured from the centre of road.

Let “d” be the distance between the centre line of road & centre line of the inside lane.

 $$d=\frac{W+W_E}{4}$$ $$\frac{\alpha }{2}=\frac{SD}{2(R-d)}(Radians)$$ OR $$\frac{\alpha }{2}=\frac{180}{\Pi }\frac{SD}{2(R-d)}(Degrees)$$ Set back distance (m)= OD DC=R m=DC–OC In Δ ACO$$cos\frac{\alpha }{2}=\frac{OC}{AC}$$ OC= AC$$cos\frac{\alpha }{2}$$= (R-D)$$cos\frac{\alpha }{2}$$ $$m=R-(R-d)cos\frac{\alpha }{2}$$

## Case 2: When the length of horizontal curve less than the sight distance (LC<SD).

(a) For Single Lane:

 Set back distance (m)= FO= FG+OG FG=FC-GCFC=RGC=R$$cos\frac{\alpha }{2}$$FG=R-R$$cos\frac{\alpha }{2}$$ OG=DI=AD$$sin\frac{\alpha }{2}$$AD=$$\frac{SD-L_C }{2}$$OG=($$\frac{SD-L_C }{2}$$)$$sin\frac{\alpha }{2}$$ $$m=R-R· cos\frac{\alpha }{2}$$+($$\frac{SD-L_C }{2}$$)$$sin\frac{\alpha }{2}$$ Here $$\frac{\alpha }{2}=\frac{L_C}{2R}(Radians)$$ or $$\frac{\alpha }{2}=\frac{180}{\Pi }\frac{L_C}{2R}(Degrees)$$

(b) For Multi lane:

$$m=R-(R-d)· cos\frac{\alpha }{2}$$+($$\frac{SD-L_C }{2}$$)$$sin\frac{\alpha }{2}$$

Here

$$\frac{\alpha }{2}=\frac{L_C}{2(R-d)}(Radians)$$

OR

$$\frac{\alpha }{2}=\frac{180}{\Pi }\frac{L_C}{2(R-d)}(Degrees)$$

Note:

Sēt back distance from central line of inner lane= m-d.

Sēt back distance from centre line of outer lane= m+d.

Sēt back distance from central line of inner edge= m-2d.

Sēt back distance from centre line of outer edge= m+2d.

In all above case two lane road is considered.

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