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A short class with Sarah and her students. The other ways are under More.
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Today, we’ll begin with calculating tangent lengths needed to connect two segments using circular curves. The formula for tangent length is T = R tan(Δ / 2). Can someone explain what each variable represents?
R is the radius of the curve, and Δ is the deflection angle.
Excellent! So if we had R = 300 m and Δ = 36°, what would the tangent length be?
We would calculate T using the formula, so T = 300 * tan(36/2).
Right! Let’s compute that value. Always remember the acronym 'TRD' for 'Tangent, Radius, Deflection' when working through these.
So that means T = approximately 97.48 m?
Spot on! Remembering the relation helps a lot in practical applications. Quick recap: Tangent length connects our straights to curves.
Next, let’s discuss how to calculate the length of the curve. The formula is L = RΔ(π / 180). Can anyone recap what we're calculating here?
It's the actual distance along the curve, right?
Exactly! If R = 300 m and Δ = 36° again, how would you find L?
L would equal 300 times 36 times π divided by 180.
Correct! And what would that give us?
The length would be 188.50 m.
Great job! Remember the acronym 'CLR' for 'Curve, Length, Radius' to help you with these calculations.
Let's dig deeper into the curve and discuss sub-chord lengths. If we have normal chords and need to determine lengths of sub-chords, what would that involve?
We calculate the length of each sub-chord based on the given intervals using the curve lengths and chainages.
Precisely! With normal chord lengths of, say, 20 m and your curves set, how would you approach finding these lengths?
We would assess chainages and subtract the calculated lengths to find the sub-chord lengths step-by-step.
Excellent approach! Now, let’s think of a mnemonic: 'CSL' for 'Calculate, Sub-chord, Length.' This can help remember this method in practice.
Got it! That's a great way to remember.
The distance connecting the last point of a straight line to the beginning of a curve.
A vital parameter for determining the size and fit of the circular arc.
Crucial for identifying the shift in direction between two straights.
Determines the distance along a curve needed for design and construction.
Essential in surveying to define distance along a project route.
To find the angle Δ, halved to see, helps us find tangent length, easy as can be.
Imagine two roads meeting, needing a curve, the tangent leads the way, so straight it can serve.
Remember 'TCR' for Tangent, Curve, Radius, when calculating layouts.
Use 'TDC' to remember Tangent, Deflection, Curve when setting angles.
Term
Tangent Length
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Term
Curve Length
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Term
Deflection Angle
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The length of the straight line extending from the point of intersection to the point where the curve begins.
The distance from the center of the circle to the curve at any point.
The angle subtended at the center of the curvature by the two tangents.
The length of the circular arc connecting two points on the curve.
A linear measurement of distance along a surveyed path or road.
A part of a chord that lies within the curve connecting two points of the curve.
This section discusses the calculation and setting out of circular curves connecting two straight lines, with practical examples illustrating the concepts.
The section provides a detailed overview of the geometric principles used in engineering to connect two straight roadways or railways through circular curves. It incorporates mathematical calculations for tangent length, curve length, and chainage, along with real-world examples that illustrate these calculations in various contexts.
In this section, we explore the geometric principles involved in connecting two straight segments AB and BC with circular curves. The calculations necessary for setting out these curves involve determining tangent lengths, curve lengths, chainages, and offsets. Using the provided formulas, we compute the chainages of key points and sub-chords along the curves.
Notably, several examples demonstrate practical applications of these calculations, guiding students in understanding the methodology required for road and railway design. Key formulas include:
Several worked examples elucidate these calculations further, including various scenarios such as deflection angles and different chord lengths while using the theodolite for precise measurements.