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A short class with Sarah and her students. The other ways are under More.
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Let's start by calculating tangent length, which is essential when setting out a circular curve. The formula we use is Tangent Length (T) = R * tan(Δ/2). Can anyone tell me what 'R' represents?
Is 'R' the radius of the curve?
Exactly! And Δ stands for the deflection angle. Now, if our radius (R) is 343.8 m and the deflection angle (Δ) is 32°, let's calculate T together.
So we would use T = 343.8 * tan(16°)?
Yes, that's correct! Calculate it out, please.
I calculated T to be approximately 98.58 m.
Well done! Remember: Tangent Length helps establish how far from the intersection point the curve begins.
Next, we will calculate the length of the curve (l). We use the formula l = πRΔ/180. Can someone explain how we would apply this formula?
We would need to substitute R and the deflection angle (Δ) into the formula.
Right! For our problem, R is 343.8 m and Δ is 32°. What’s our curve length?
So we have l = π * 343.8 * 32 / 180, which I calculated to be around 192.01 m.
Perfect! Knowing the curve length helps us plan for tracking the arc.
Now let's talk about calculating chainage. First, what is the chainage at the point of curve (T1)?
We need to subtract the tangent length from the chainage at the point of intersection.
Exactly! Can someone compute it if the chainage at the intersection is 1764 m?
If we subtract approximately 98.58 from 1764 m, the chainage at the point of curve (T1) would be 1665.42 m.
Correct! And how about the chainage at the point of tangency (T2)?
We would add the curve length to T1.
Exactly! So what is T2?
The calculation shows it's approximately 1857.43 m.
Great job! Chainage is crucial for marking positions along the curve in fieldwork.
Let's wrap up by calculating both the initial and final sub-chord lengths. Why do you think these are important?
They help ensure accurate positioning along the curve, right?
Exactly! The initial sub-chord (C1) is found by subtracting the chainage of curve from the next tangent.
And how do we find Cn?
Good question! Cn is calculated based on the chainage at the end tangent. Great teamwork in unraveling these calculations!
In Example 2.13, we calculate the tangent length for a curve radius of 343.8 m with a deflection angle of 32°, yielding a specific tangent length essential for curve alignment.
Length of the curve is computed using R = 343.8 m and Δ = 32°, demonstrating how to derive critical measurements for planning alignments.
To find a curve, remember T, R and Δ are key!
Imagine planning a road. You measure out the distance (chainage) and create smooth bends (curves) using formulas for tangent and arc length, imagining the path ahead.
To remember Tangent Length, think T = R * tan(Δ/2): 'Tangle the Radius with Tangents'.
CRTC: Curve Radius, Tangent Length, Chainage — the essential elements for curve setting!
Term
Tangent Length
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Term
Chainage
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The linear distance along a project from a reference point, often used in road and railway projects.
The distance from the point of intersection to the starting point of the curve.
The angle between the two tangents meeting at the point of intersection.
The amount of bending in a path or a curve.
The distance between two consecutive points on a curve.
This section outlines the calculations necessary to set out a simple circular curve connecting two straights based on given parameters.
In this section, we focus on Example 2.13, which provides a detailed solution for setting out a circular curve based on specific chainage and deflection angle parameters. The example highlights key steps, such as calculating tangent lengths, lengths of curve, and initial and final sub-chord lengths.
This section centers around Example 2.13, where two straights intersect at a chainage of 1764 m with a deflection angle of 32°. The radius of the curve is set at 50 m, and various calculations are conducted to derive necessary parameters for setting out the circular curve using the deflection angle method. Key calculations include:
The section emphasizes practical applications of these formulas and the importance of precise measurements in planning for curves in construction and civil engineering.