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A short class with Sarah and her students. The other ways are under More.
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Today we're going to talk about Rankine's method of setting out circular curves. Can anyone tell me what they think 'tangential angles' refers to?
Is it the angle between the tangent line and the curve?
Exactly! The tangential angles are critical as they help define the curve's geometry. Rankine's method calculates these angles to set out the curve accurately. Remember the acronym RCD — Radius, Chord Length, and Deflection Angle. You can use it as a mental checklist!
How does this method actually work?
We begin by determining the length of the chords and then calculating the deflection angle using the formula. For example, using the relation δ = 1718.9*C/R gives us the necessary angle for the first chord. What do you think happens to the angle if the radius is very large?
The angle would get smaller, right?
Correct! Larger radii lead to smaller angles. Now, can you explain how we set the angles in the theodolite?
We set the theodolite to zero at the first tangent and then adjust it for each deflection angle!
Great! To recap, Rankine's method focuses on calculating tangential angles to set points on a circular curve accurately, using RCD as a guide.
Now let's shift our focus to the Two Theodolite Method. Can someone explain why we might use two theodolites instead of just one?
Maybe it’s for measuring angles without needing to move the theodolite a lot?
Exactly! It allows us to simultaneously measure angles at points T1 and T2. This technique is useful, especially when the ground is uneven. Who can describe how we actually set this up?
We set up both theodolites at T1 and T2, set initial readings, and measure the angles for each point on the curve.
Yes, and we calculate deflection angles just like with Rankine's method. It's critical to ensure the readings are accurately set to establish precise intersections. Remember, the angles for the curve must be subtracted from 360 for left-hand curves. Can you tell me why that matters?
Because it changes the direction we measure? We want to go counter-clockwise for left curves!
Exactly! As a summary, the Two Theodolite Method is a powerful alternative that accommodates difficult terrain by allowing simultaneous angle measurements, which can enhance accuracy greatly.
Using Rankine’s method, if a curve has a radius of 50 meters and a chord length of 10 meters, the deflection angle calculated would be δ = 1718.9 * 10 / 50.
In the two theodolite method, if the deflection angles are calculated to be 5 degrees for point D and 10 degrees for point E, the measurements from both theodolites should intersect at these points.
Tangent to the curve is the place we sway, Rankine’s angles guide our way!
Imagine a traveler on the road, using Rankine’s method to find the best route through a winding valley, adjusting angles as they go to ensure a smooth journey.
Remember 'RCD' for Rankine’s method: Radius, Chord length, Deflection angle!
Two Theodolites = '2T' for 'Two Targets' on the curve!
Term
Rankine’s Method
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Term
Deflection Angle
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Term
Two Theodolite Method
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Term
Curvature
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The angle between the tangent line and the radius at a given point on the curve.
The angle that measures the angle turned off from the tangent to the curve direction.
The straight line distance between two points on the curve.
An instrument used for measuring angles in horizontal and vertical planes.
The fixed distance from the center of the curve to any point on the curve.
Angular methods provide techniques for setting out circular curves using instruments and calculating angular measurements.
This section details two primary methods of setting out circular curves using angular measurements: Rankine’s method and the two theodolite method. Each method relies on calculating deflection angles to accurately establish curve points along tangent lines.
In highway and railway engineering, setting out curves is crucial for ensuring safe and efficient transitions between straight paths and circular arcs. This section introduces two angular methods for setting out simple circular curves: Rankine's Method and the Two Theodolite Method. Rankine's method utilizes tangential or deflection angles with a theodolite and tape to determine curve points by following a straightforward calculation process based on the radius and chord lengths. The two theodolite method, on the other hand, allows for the precise location of curve points without direct distance measurements, relying instead on the geometry of circles and the player's description in the workspace. Together, these methods facilitate accurate and effective curve setting in practical engineering applications.