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There are three main parts to Geometric roadway designing alignment profile and cross section Combined three factors engineers are provided information to create three dimensional design for whatever need of the facility alignment Combine with horizontal tangents and curves the alignment is the route selection of a road Generally speaking a horizontal curve is usually treated as circular for the sick of simplicity and beauty maybe a non circular shape would theoretically be more efficient and cost efficient a circular design is much easier to complete in practice For example in Figure 1 Important features radius R central angle Δ length L semitangent distance T middle ordinate M external distance E and chord C The curve begins at the tangent to curve point TC and ends at the curve to tangent point CT degree of curvature D Degree of curvature is defined as the angle subtended by a 100 ft arc or angle subtended by a 100 ft chord The relationship between R in feet and D is as shown below L of the curve is given by T of the curve is given by M of the curve is given by The chord C is given by Last but not the least E of the curve is given by The placement of the circular curves in the area is done by using the tangent to curve point TC with a transit and then establishing successive points by turning deflection angles and measuring chords as shown in Figure 2 The deflection angle in radians dx to a point on the curve at a distance x from the TC is given by There numerical feature of horizontal curves establish the minimum R and sometime their minimum L Minimum R of horizontal curve is mostly depended on the relationship between design speed maximum rate of superelevation and curve radius In other times these heigh would be changed for other reason than fictionality on the road like appearance standards save space for future development or geographical environment profile

With the horizontal layout defines the horizontal the profile defines the vertical aspect of the road including crest and sag curves and the straight grade lines connecting them Tangent grade is one of the key factors in the profile The tangent grade is referred to the tangent of the angle of the surface to the horizontal of a landform or liner It is a specific kind of the slope where zero indicates horizontality This feature is specially designed inroads to serve the purpose of slowing down vehicles according to the steepness and length of the grade to fit the need of the traffic Tangent grades of a road is designed according to the slopes of the surface So if we describe a surface with a function f x where the y-axis is horizontal to earth then it's target grades are based on f x

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