2. Exercises for Practice

2.29 Show the various elements of a simple circular curve on a neatly drawn sketch.

This section explores the elements of a simple circular curve and emphasizes the importance of accurately sketching these elements.

2.30 Explain the following terms for a simple circular curve: (i) Back and forward tangents, (ii) Point of intersection, curve and tangency, (iii) Deflection angle to any point, and (iv) Degree of curve

This section explains key elements of a simple circular curve such as back and forward tangents, points of intersection and tangency, deflection angles, and degree of curvature.

2.31 Show the various elements of a compound curve.

This section outlines the key elements involved in a compound curve used in road design.

2.32 Draw a neat sketch of a reverse curve provided to join two parallel straights.

This section emphasizes the importance and method of sketching a reverse curve that connects two parallel lines.

2.33 Draw the neat sketches to differentiate between simple, compound and reverse curves.

This section focuses on understanding the differences between simple, compound, and reverse curves through detailed sketches and descriptions.

2.34 List the requirements to be satisfied in setting out a transition curve.

The section outlines the essential requirements for setting out a transition curve in engineering.

2.35 What is a transition curve and where is it used? What are its advantages?

A transition curve is a gradual change from a straight to a curved path, commonly used in roadway and railway design to enhance safety and comfort.

2.36 What is the need of super-elevation and how it is determined?

Super-elevation is essential in road engineering to counterbalance the lateral forces acting on vehicles during turns, improving safety and comfort.

2.37 Give any five general requirements of a transition curve.

This section outlines the five general requirements of a transition curve in highway and railway alignment design.

2.38 State the conditions to be fulfilled by a transition curve introduced between the tangent and circular curve.

This section outlines the critical conditions necessary for the effective implementation of a transition curve in road design, connecting a tangent to a circular curve.

2.39 What are different types of vertical curves? What is the use of having a vertical curve as parabola and not a circle?

This section discusses the various types of vertical curves used in road design and explains the advantages of using parabolic curves over circular curves.

2.40 Why are parabolic curves not generally used for horizontal highway curves?

Parabolic curves are not commonly used for horizontal highway curves due to concerns regarding safety, stability, and structural efficiency compared to circular curves.

2.41 What is meant by rate of change of grade on vertical curves and why it is important?

The rate of change of grade on vertical curves refers to how quickly the vertical alignment of a road changes from one slope to another, which is crucial for ensuring driver safety and comfort.

2.42 Explain why the second differences of curve elevations are equal for a parabolic curve.

This section explains the equality of the second differences of curve elevations for parabolic curves.

2.43 Derive the formulae to calculate various elements to set out a simple circular curve.

This section focuses on deriving the formulae used to calculate various elements necessary for setting out a simple circular curve.

2.44 Establish the formulae to calculate various elements to set out the compound curve.

This section focuses on deriving the relevant formulae needed to effectively calculate various elements necessary for setting out a compound curve in surveying.

2.45 Derive the relationship between the several elements of the reverse curve.

This section focuses on understanding the relationships among various elements constituting a reverse curve in geometric design.

2.46 Discuss various types of transition curves. Derive an expression for the super-elevation to be provided in a transition curve.

The section discusses different types of transition curves and derives the expression for super-elevation in such curves.

2.47 A 4.56° circular curve is to be designed to fit between two intersecting straights. What is the radius of this curve? (Ans:1256.49 m)

This section covers the calculation of the radius of a circular curve based on a given deflection angle.

2.48 It was found, while setting a simple circular curve using offsets from the tangents, that for X =16 m, and Y = 0.28 m. Find the radius of the curve. (Ans: R = 457.28 m)

2.49 A right hand simple circular curve connects two straights AI and IB where A and B are the tangent points. The azimuth of each straight is 50° 43' 12" and 88° 22' 14", respectively. The curve passes through point C of coordinates (321.25, 178.1) m. If the coordinates of A are (240.40, 125.90) m, compute the radius of curve and degree of curve.

This section details the computation of the radius and degree of a simple circular curve connecting two straight roads, providing essential formulas and calculations for effective curve design.

2.50 There are two tangents XI and IY for a railroad circular curve where X and Y are the tangent points having coordinates (240.4E, 125.9N) and (253.8E, 218.65N), respectively, and the coordinates of the mid-point on the curve is (60.13E, 195.89N). Compute the radius of curve, the deflection angle, and the length of the curve.

2.51 Two straights intersect at a chainage of 2500 m with an angle of deflection as 40°. The straights are to be connected by a simple circular curve...

This section focuses on the calculations involved in setting out a simple circular curve connecting two intersecting straight paths.

2.52 A right hand circular curve connects two straights AB and BC intersected at point B which has a chainage of 2000 m...

2.53 A straight BC deflects 24° right from a straight AB which are to be joined by a circular curve passing through a point P...

This section focuses on calculating various curve parameters linking two straight paths AB and BC that deflect at an angle, specifically using a circular curve passing through a given point P.

2.54 Two straights, which deflect through an angle of 60°, are to be connected by a circular curve of radius 80 m...

This section discusses the calculation and setting out of a circular curve connecting two straight lines with a specified deflection angle and radius.

2.55 Two straights, which meet at an intersection angle of 135°, are to be connected by a circular curve of radius 60 m...

This section discusses the construction of circular curves connecting two intersecting straights and calculations related to defining their geometry.

2.56 Two straights intersect making a deflection angle of 59°00'24"...

2.57 A circular curve of radius 900 m is to be constructed between two straights of a proposed highway...

This section covers the fundamental elements and calculations required to construct a circular curve connecting two straight segments of a highway.

2.58 The bearings of three successive intersecting straights AB, BC and CD along the centre line of a proposed highway...

This section explores the concepts of bearings and the calculations necessary for setting out curves connecting multiple intersecting roadways.

2.59 A circular curve has to pass through a point P which is 70.23 m from I, the intersection point...

This section discusses the design and calculation of circular curves in the context of road geometry.

2.60 A reverse curve is to start at a point A and end at C with a change of curvature at B...

This section explores reverse curves, illustrating their characteristics and how to set them out effectively using the two-theodolites method.

2.61 A circular curve of 1800 m radius leaves a straight at through chainage 2468 m...

This section focuses on calculating chainages and offsets for various curves, particularly involving transition curves in road design.

2.62 A composite curve consisting of two equal length transition curves and a central circular arc...

This section discusses the design and data requirements for a composite curve comprising two transition curves and a central circular arc.

2.63 A composite curve consisting of entry and exit transition curves of equal length and a central circular arc...

This section describes how to design a composite curve using entry and exit transition curves, connected by a central circular arc.

2.64 A road 7.30 m wide deflects through an angle of 18°47'26"...

2.65 A wholly transitional curve having equal tangent lengths is to be designed to connect two intersecting straights...

2.66 A 10 m wide road is to be deflected through an angle of 35°30'.

This section focuses on calculating the length of transition curves and the super-elevation for a road that is deflected through a specified angle.

2.67 A circular curve of 610 m radius deflects through an angle of 40°30'...

This section focuses on the calculations required to adjust a circular curve's radius and layout due to the introduction of smaller radius transition curves.

2.68 The centre-line of a new road is to be set out through built-up area...

This section focuses on setting out the centerline of a new road, particularly in a built-up area, addressing the necessary calculations and considerations.

2.69 A parabolic vertical curve is to connect a +3.1% gradient to a –2.3% gradient...

This section focuses on designing a parabolic vertical curve between two gradients for road design, emphasizing the calculations required for both overtaking and stopping visibility.

2.70 A parabolic vertical curve is to connect a –2.2% gradient to a +1.9% gradient...

This section focuses on calculating the necessary length of a parabolic vertical curve that connects specific gradients.

2.71 A road having an up-gradient of 1 in 15 is to be connected to a down-gradient of 1 in 20...

This section covers the design and analytical process involved in creating a vertical parabolic curve to connect two gradients.

2.72 A vertical parabolic sag curve is to be designed to connect a down-gradient of 1 in 20 with an up-gradient of 1 in 15...

2.73 A proposed road consists of a rising gradient of 2% followed by a falling gradient of 4%...

This section discusses the design elements involved in creating a road with a vertical parabolic summit curve connecting a rising and falling gradient.