When developing a route in the hilly area we need to frequently set the horizontal curve and sometimes it becomes difficult or impossible to set the curve following normal geometric standards of design.
When inscribing a curve inside the turning angle, the length of the route will be substantially reduced, which results in steep gradients. In such circumstances, it is preferable to round off the route not by inscribing but by circumscribing the curve around the turning point. Such compound curves are called hairpin bends or reverse curves.
Figur shown below shows two different types of symmetrical hair bends consisting of main curve C reverse curve Cr and tangents (Straights) m. The acute angle of bend is alpha(a). The main curve with the radius R has a total length of C and subtends the angle Gama(y) at the center.
Points AQ and B are located at the apices of the reverse curve. Between the ends of the reverse curve and the main curves of the bend, tangents must be introduced for the transitions of the superelevation and extra width in the curves.
A hairpin bend is located on the hill section having a minimum cross slope and maximum stability. It must be against landslides and groundwater seepage.
For the design and layout of hairpin bends elements such as radius of the main curve and reverse curves (R and r) and length of the tangent (m) are initially selected based on the site situation comfortably with the required geometric standards.
The design of hairpin bends then basically consist of establishing the value of turning angle beta (B) at point A and B which satisfies the pre-selected parameters of the bend. For this purpose following simple expression may be derived based on the geometry of hairpin bends as shown in the figure below.
Tangent length of reverse curve T = r tan(B/2)
T = Tangent length
r = radius of a reverse curve
B = Deflection angle
The distance from the apex of reverse curve angle to the commencement of the main curve is,
AE = BF = T +m
From triangle AOC or BOF, It will be found that,
TanB = OE/AE = R/(T+m), Where R is the radius of the main curve.
From trigonometry, it is also known that,
Substituting this expression for Tan B in preceding expression, solution of Tan(B/2) becomes,
Hence, the angle B to correspond to R, r, and m can be easily determined. The distance from the apex of the reverse curve to the center of the main curve is determined by,
AO = OB = (T+m)/CosB = R/SinB
The central angle gamma(y) corresponding to the main curve of the bend is equal to gamma (y) = 360 – 2(90-B)- alpha(a)
And the length of the bend is,
Hence the total length of bend is,
S= 2( Cr +m)+C
Where Cr is the length of the reverse curve.
Having obtained these parameters, the hairpin bend can be plotted on the contour map or set out on the ground.
These expressions given above are for symmetrical hairpin bends having reverse curves with equal angles and of equal radius. If owing to land conditions, these curves should differ. In which case these are referred to as unsymmetrical hairpin bends. the bend is designated by the same method.
The bends described so far above, which have reverse curves situated with their convexities in opposite directions are called hair bend or reverse curve loop of the first type. these configurations are suitable in cases with more or less straight contours of the hill slope.
In bends of the second type, which may also be either symmetrical or unsymmetrical, the reverse curves have their convexities facing toward the same side.
These bends are introduced at a place with the contours representing shallow drainage basin or flat hill nose. whatever be their forms, hairpin bends are introduced along the road that goes up to cross a mountain pass, where the route is to be developed on the same side of hill slope in order to change the direction of the route.
There could be a series of hairpin bends in one stack. The distance between the ends of the reverse curves of the first hairpin bend should be as large as possible. Recommendations regarding the separation distance of two bends vary widely.
In the former USSR, two adjacent bends are required to be separated by at least 200 m. This appears to be too high for the types of the rugged hilly terrain of the region. IRC recommendation in this regard is 60 m.
Design parameters of hair pin bends (Comparison)
|Designed Speed||20 km/hr||20 km/hr|
|Minimum radius of main curve||14 m||15 m|
|Maximum length of transition curve||15 m||20 m|
|Maximum gradient within bend||2.5%||4%|
|Super elevation in curve portion||10%||6%|
|Widening of carriageway||4 m||3 m|
In stacking hair pin bends, care should be taken to ensure that the branches of the road in hair pin bends could be accommodated in the given site. Sighting should be checked at the neck with respect to the cross-sections of all branches plotted together.
Hair pin bends are not desirable elements of hill roads. in these bends, speeds have to be restricted substantially. The cost of construction also increases substantially because of the extensive volume of earthwork and retaining walls, so also vehicular operation costs.
When designing hill roads, several alternatives routes are investigated and preference is given to one having the least number of hair pin bends.
I hope this article on “ Hair Pin Bend ” remains helpful for you.
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