The bearings of three successive intersecting straights AB, BC and CD along the centre line of a proposed highway... - 2.58 | 2. Exercises for Practice | Surveying and Geomatics
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2.58 - The bearings of three successive intersecting straights AB, BC and CD along the centre line of a proposed highway...

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Interactive Audio Lesson

Listen to a student-teacher conversation explaining the topic in a relatable way.

Understanding Bearings

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Teacher
Teacher

Today we're going to learn about bearings and how they affect road design. Bearings help us understand the direction of each road segment. Can anyone tell me what a bearing is?

Student 1
Student 1

Isn't it like the angle measured from north?

Teacher
Teacher

Exactly! Bearings are usually given in degrees from the north direction. For instance, AB has a bearing of 103°29'24". Can someone explain why knowing this is important for connecting road segments?

Student 2
Student 2

We need it to design curves accurately and ensure safety on roads.

Teacher
Teacher

Great point! Accurately calculated bearings minimize abrupt changes in direction and improve driving comfort and safety. Remember: bearings = angles from the north, think of them as a compass that guides our road design.

Chainages and Tangent Points

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Teacher
Teacher

Now, let's talk about chainages. The through chainage for point B is 1097.65 m. What do you think a chainage represents?

Student 3
Student 3

It’s like the distance along the road from a starting point, right?

Teacher
Teacher

Absolutely! Chainages help us measure where to place curves accurately. Now, with the horizontal distance BC being 708.32 m, how would we find the chainage for the tangent points after calculating the curves?

Student 4
Student 4

We would add the radius and the distances!

Teacher
Teacher

Correct! For the first curve of radius 1500 m, we determine the tangent points by adding and subtracting the lengths and chainages correctly. This lets us set up the proper alignment for the road.

Calculating the Curves

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Teacher
Teacher

Let’s figure out the specific curves connecting our segments. We have to connect AB to BC with a 1500 m radius curve and BC to CD with a 900 m radius curve. How do we start this calculation?

Student 1
Student 1

I think we need to calculate each tangent point and the lengths.

Teacher
Teacher

Exactly! Each tangent point is critical for determining where our curves begin and end. Once you get the tangent points, the actual curve lengths can be derived using the radius and angle we calculated. Who can recall how we determine the tangent length for a curve?

Student 2
Student 2

It’s usually based on the radius and the deflection angle, right?

Teacher
Teacher

Precisely! Utilize the formulas you learned in previous lessons, and don't forget to keep track of your units.

Practical Applications and Importance

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Teacher
Teacher

Finally, why do you think these calculations are important for urban planning and safety?

Student 3
Student 3

If we calculate wrong, it could lead to dangerous road conditions!

Teacher
Teacher

Exactly! Proper planning avoids accidents and ensures smooth traffic flow. These are not just numbers; they represent real-life safety measures. Let’s remember: accurate calculations lead to safer roads.

Introduction & Overview

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Quick Overview

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

Standard

The section discusses the use of bearings in determining the orientation of road segments AB, BC, and CD. It also explains how to connect these segments using circular curves and calculate relevant chainages and tangent points for a new highway design.

Detailed

In this section, we analyze the bearings of three intersecting lines (AB, BC, and CD) that form part of a proposed highway. Bearings are specified as 103°29'24", 125°43'22", and 116°12'54", respectively, and the horizontal distance between points B and C is 708.32 m. The task involves calculating the connections using circular curves: a 1500 m radius curve between AB and BC and a 900 m radius curve between BC and CD. An important result is the through chainage of the intersection point (B) of 1097.65 m, with subsequent calculations leading to the determination of the chainages for the tangent points on both curves. This segment not only illustrates practical applications of bearings and distance in road design but also reinforces fundamental surveying principles that are essential for civil engineering and highway construction.

Audio Book

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Bearings of Intersecting Straights

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The bearings of three successive intersecting straights AB, BC and CD along the centre line of a proposed highway are 103°29'24", 125°43'22" and 116°12'54", respectively.

Detailed Explanation

In highway design, the term 'bearing' refers to the direction of a straight line in relation to the north (or magnetic north). Here, we have three bearings:
- Line AB has a bearing of 103°29'24".
- Line BC has a bearing of 125°43'22".
- Line CD has a bearing of 116°12'54".
These bearings are important in understanding how the lines intersect and orient the proposed highway.

Examples & Analogies

Think of bearings like giving someone directions. If you say 'Go 30 degrees east of north,' it's similar to giving bearings in the context of a map. The angles tell the driver how to navigate through turns and straight sections.

Horizontal Distance Between Straights

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The horizontal distance BC is 708.32 m.

Detailed Explanation

This horizontal distance directly refers to the length of straight line BC on the proposed road. It is crucial for calculating the layout of curves and identifying how long the road will stretch in that section before transitioning to a new straight segment or curve. This kind of measure is typically used for planning road width, construction materials, and land acquisition.

Examples & Analogies

Imagine measuring the distance from your house to the park. If you know how long the road is between these points (like the 708.32 m distance), you can plan how much time it takes to walk there or how many resources are needed to maintain the path.

Connecting Curves between Straights

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It is proposed to connect AB and BC by a 1500 m radius curve and BC and CD by a 900 m radius curve such that there is an intervening straight on BC between the end of one curve and the start of the other.

Detailed Explanation

The design proposes using smooth curves to transition between the straight sections of the highway (AB to BC and BC to CD) to create safer and more comfortable driving conditions. A curve with a 1500 m radius is gentler than a curve with a 900 m radius. This could influence traffic flow and safety, as larger radius curves allow for higher speeds without skidding or losing control.

Examples & Analogies

Think about riding a bike. If you are turning sharply (like a small radius), you need to slow down significantly to avoid falling. However, if you're turning gradually (like a large radius), you can maintain speed and maneuver more easily. Similarly, the highway design considers these dynamics to ensure safety.

Through Chainage of Intersection Point

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The through chainage of intersection point B is 1097.65 m and chainage increases from A to D.

Detailed Explanation

Chainage is the measurement of distance from a defined starting point along the road. The value given (1097.65 m) indicates where B is located along the proposed highway in relation to the starting point A. Understanding chainage helps in mapping out the highway, ensuring proper spacing between turns, curves, and straight sections.

Examples & Analogies

Picture a ruler laid on the ground, where the starting point represents one end of the ruler. As you measure out the distance to another point, each mark along the ruler represents a chainage point. Knowing the exact position of point B helps plan for anything from signage to road maintenance.

Calculating Chainages of Tangent Points

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Calculate the through chainages of the four tangent points on the two curves.

Detailed Explanation

The tangent points where the curves meet the straight sections (tangent to the curves) need to be calculated. These points are critical for ensuring smooth transitions for vehicles moving from a curve to straight roadways. Accurate calculations ensure the highway can handle expected traffic loads and speeds safely.

Examples & Analogies

Imagine driving a car approaching a roundabout. You need to know exactly how much distance you’ll travel on the curve before transitioning smoothly back onto the straight road. Calculating the positions of these transitions is just as important for highway safety and functionality.

Definitions & Key Concepts

Learn essential terms and foundational ideas that form the basis of the topic.

Key Concepts

  • Bearings: The angle measurements from the north used to navigate and orient roads.

  • Chainage: A crucial metric in surveying that measures distance along a proposed roadway.

  • Tangent Points: Points where the curvature meets a straight road segment, important for road safety and alignment.

  • Radius: Key to curve design, impacts how gently or sharply a road turns.

Examples & Real-Life Applications

See how the concepts apply in real-world scenarios to understand their practical implications.

Examples

  • A construction crew measures the bearing of 130° to determine the direction for a new road section.

  • A land survey uses chainage measurements to accurately mark out a road layout, ensuring safety and proper alignment.

Memory Aids

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🎵 Rhymes Time

  • Bearings guide the roads we pave, without them, turns can misbehave.

📖 Fascinating Stories

  • Imagine a truck driver relying on a compass. He sees a bearing of 103° for his route. This number leads him down the smoothest path, avoiding all bumps on the way. Without bearings, he'd be lost on the road.

🧠 Other Memory Gems

  • BCT = Bearings, Chainage, Tangent. Remember how to lay out curves!

🎯 Super Acronyms

BCT for Bearings, Chainage, Tangents to help design highways properly.

Flash Cards

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Glossary of Terms

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  • Term: Bearing

    Definition:

    The direction or path along which something moves or along which it lies, measured in degrees from the north.

  • Term: Chainage

    Definition:

    A measurement of distance along a certain line, frequently used in construction and road design.

  • Term: Tangent Point

    Definition:

    The point of contact on a curve where a tangent line touches the curve; crucial for road design.

  • Term: Radius of Curve

    Definition:

    The distance from the center of the curvature to any point on the curve, essential for designing the path of road curves.

  • Term: Circular Curve

    Definition:

    A segment of a circle that connects two straight lines, commonly employed in road design.