Deflection Angle Method/Rankine's Method of Setting out of Simple Circular Highway Curve

Summary

This educational video introduces the deflection angle method for setting out a simple circular curve in surveying. It explains the basic data required, including the deflection angle and radius of the curve, and demonstrates how to calculate the deflection angle using the formula 90L/πR. The method involves marking points on the curve using a theodolite and a peg interval, which can be adjusted for accuracy. The video also highlights a crucial check to ensure the calculations are correct by comparing the total deflection angle with half of it. The presenter promises further examples and methods in upcoming videos.

Takeaways

• 📚 The video introduces a method for setting out a simple circular curve using the deflection angle method.
• 📐 Basic data for a simple circular curve, such as the deflection angle and radius, are always known and used in this method.
• 🔍 The point of intersection where the back tangent and forward tangent cross is crucial for setting out the curve.
• 📍 The deflection angle is measured using a theodolite to establish the forward tangent.
• 📈 The formula for the deflection angle is given as 90 * L / (π * R), where L is the chain interval and R is the radius of the curve.
• ⛓ The length of the curve is calculated using the formula π * R^2 / 180, which helps in determining the chain interval.
• 🔑 The chain interval (L1) is chosen to maximize the number of points on the curve for better accuracy.
• 📏 The theodolite is used to set the deflection angle by tilting the telescope and marking points on the curve at the specified distance (L1).
• 🔄 The process of marking points on the curve involves adding multiples of the deflection angle to maintain the station point without moving the theodolite.
• 📊 The final point on the curve may not be exactly at L1 due to the decimal values obtained from the curve length calculation.
• 🔍 A check for the accuracy of the calculations is provided by comparing the total deflection angle from PC to PT to half of the calculated deflection angle.
• 👨‍🏫 The video concludes with a promise to teach how to solve an example of setting out a simple circular curve in future videos.

Q & A

What is the main topic of the video?

The video is about learning the deflection angle method for setting out a simple circular curve in surveying.

What are the basic data required for the deflection angle method?

The basic data required are the deflection angle and the radius of the curve, which are typically known beforehand.

What is the point of intersection in the context of the video?

The point of intersection is where the back tangent and forward tangent are expected to cross each other.

How is the forward tangent determined in the deflection angle method?

The forward tangent is determined using a theodolite or any instrument capable of measuring horizontal angles once the basic data is known.

What is the significance of the tangent length in the deflection angle method?

The tangent length is crucial as it helps in determining the point of tangency and ultimately in drawing the center of the curve, given the known radius.

What is the formula for calculating the deflection angle?

The formula for the deflection angle is 90 * (L1/R), where L1 is the chain interval and R is the radius of the curve.

How is the length of the curve calculated?

The length of the curve is calculated using the formula πR^5/180, which involves the radius of the curve and the deflection angle.

What is a peg interval and how is it determined?

A peg interval is the distance between two consecutive points on the curve. It is determined based on the desired number of points on the curve and the length of the curve.

Why is it beneficial to multiply the deflection angle by 2 when marking points on the curve?

Multiplying the deflection angle by 2 is beneficial because it eliminates the need to change the station point, keeping the process consistent and time-efficient.

How can the accuracy of the curve setting be checked?

The accuracy can be checked by ensuring that the total deflection angle from the PC to the PT line is equal to half of the calculated deflection angle.

What is the purpose of the check mentioned in the video?

The check serves as a validation to confirm that the calculations for the curve setting are correct, ensuring the curve is accurately set out.

Why might the last point on the curve not be equal to the peg interval?

The last point might not equal the peg interval because the length of the curve is often a decimal value when calculated, making it difficult to maintain the exact peg interval on the field.

What is the final step in setting out the curve using the deflection angle method?

The final step is to calculate the last deflection angle using the formula with L2, which is the angle between the last two points on the curve, ensuring the curve is correctly set out.

Outlines

00:00

📐 Introduction to Deflection Angle Method for Circular Curve Setting Out

This paragraph introduces the deflection angle method for setting out a simple circular curve in surveying. It explains that the basic data required includes the deflection angle and the radius of the curve, which are known. The process begins at the point of intersection of the back tangent and forward tangent, and the curve's commencement point is identified. Using a horizontal angle measuring instrument, the forward tangent is established. Once the basic data is known, the tangent length, point of tangency, and curve center can be determined using the given radius. The paragraph also discusses the concept of the long chord and how deflection angles are calculated and used in setting out the curve, emphasizing the importance of the peg interval in determining the number of points on the curve for accurate curvature representation.

05:01

📏 Calculation and Application of Deflection Angles in Curve Setting Out

The second paragraph delves into the specifics of calculating and applying deflection angles for setting out a semicircular curve. It describes the formula for the deflection angle, which is 90 times the length of the curve segment (L) over the product of pi and the radius (R). The length of the curve is derived from the formula pi * R^2 / 180, which helps in determining the peg interval based on the desired number of points on the curve. The paragraph explains the process of marking points on the curve by using the theodolite to set horizontal angles and marking distances according to the peg interval. It also discusses the efficiency of not moving the instrument by adding deflection angles cumulatively and the importance of the final deflection angle calculation to ensure the accuracy of the curve's end point. The paragraph concludes with a method to check the accuracy of the calculations by comparing the total deflection angle with half of the angle between the PC and PT lines.

Keywords

💡Deflection Angle Method

The Deflection Angle Method is a technique used in surveying and civil engineering to set out a circular curve on a road or railway. It is central to the video's theme as it is the primary method being discussed for creating a simple circular curve. The method involves using the deflection angle and the radius of the curve to determine the points on the curve. In the script, this method is explained as an alternative to the offset from the long chord method, and the steps to calculate and apply the deflection angles are detailed.

💡Circular Curve

A Circular Curve refers to a segment of a circular arc used in the alignment of roads or railways to provide a smooth transition from a straight path to another. It is the main subject of the video, where the script discusses how to set out such a curve using the deflection angle method. The video script provides a step-by-step guide on how to determine the points on the curve, which is essential for the construction of the circular curve.

💡Radius

The Radius is the distance from the center of a circle to any point on the circumference. In the context of the video, the radius is a known value that is used to calculate the deflection angles and to draw the center of the curve. The script mentions that the radius is essential for determining the points of tangency and for calculating the length of the curve.

💡Tangent Length

Tangent Length is the distance from the point of tangency (where the curve starts or ends) to the center of the curve. It is a critical measurement in the deflection angle method as it helps in determining the points on the curve. The script explains that once the basic data is known, including the radius, the tangent length can be calculated.

💡Point of Tangency

The Point of Tangency is the exact location where a tangent line touches the curve without crossing it. In the video script, it is mentioned as the starting point of the curve. Identifying the point of tangency is crucial for setting out the circular curve using the deflection angle method.

💡Long Chord

The Long Chord is a straight line that connects the points of tangency at the beginning and end of the curve. It serves as a reference in setting out the curve and is mentioned in the script as a line that is between the PC (point of commencement) and PT (point of tangency). The long chord is used to help calculate the deflection angles.

💡Theodolite

A Theodolite is a precision instrument used in surveying for measuring angles in the horizontal or vertical plane. In the script, it is used to measure the deflection angles and to mark the points on the curve. The theodolite is essential for the practical application of the deflection angle method.

💡Peg Interval

Peg Interval, also known as the pack interval in the script, is the distance between the points marked on the curve. It is determined based on the desired number of points on the curve and is crucial for evenly spacing the points along the curve. The script explains how to decide the peg interval and how it affects the marking of points on the curve.

💡Deflection Angle Calculation

Deflection Angle Calculation is the process of determining the angle at which the curve deviates from a straight path. The formula provided in the script is 90 * L / (π * R), where L is the peg interval, and R is the radius. This calculation is fundamental to the deflection angle method and is used to find the direction for marking points on the curve.

💡Total Deflection Angle

The Total Deflection Angle is the sum of all the individual deflection angles used to mark the points on the curve. It is used as a check to ensure the accuracy of the calculations. The script mentions that if the total deflection angle is equal to half of the angle between the PC and PT lines, the calculations are correct.

💡Setting Out

Setting Out refers to the process of marking the exact positions of construction elements on the ground, such as the points on a circular curve. It is the practical application of the theoretical calculations and is the main activity being described in the video script. The term is used throughout the script to describe the steps taken to apply the deflection angle method.

Highlights

Introduction to the deflection angle method for setting out a simple circular curve.

Understanding the basic data required: deflection angle and radius of the curve.

Identifying the point of intersection where back tangent and forward tangent cross.

Joining points of intersection to establish the back tangent.

Using a theodolite to measure the forward tangent with the given deflection angle.

Calculating the tangent length and point of tangency with known basic data.

Drawing the center of the curve using the known radius.

Discussion on the calculation of deflection angles as horizontal angles.

Estimation of deflection angles using a third light SPC (Start Point).

Formula for calculating the deflection angle: 90 * L1 / (π * R).

Understanding the formula for the length of the curve: (π * R^2) / 180.

Determining the peg interval for maximum points on the curve.

Procedure for marking points on the curve using the peg interval and deflection angle.

Advantages of not changing the station point to save time.

Layering deflection angles to form the curve by repeating the procedure.

Challenge of measuring decimal peg intervals in the field.

Using whole numbers for peg intervals to simplify field measurements.

Calculating the last deflection angle with L2 for the final curve point.

Verification of calculations by checking if the total deflection angle equals half of the deflection angle from PC to PT.

Conclusion summarizing the deflection angle method for setting out a simple circular curve.

Upcoming tutorial on solving examples using offsets from the long chord and deflection angle method.

Transcripts

hello everyone in this video we are

going to learn another method of setting

out of a simple circular graph

previous video we have learned a method

by which we have taken the offset from

the long chord but in this video we are

going to learn setting out of simple

circular curve using deflection angle

method

so let's discuss the deflection angle

method

we know that the basic data the

deflection angle and radius of the curve

for a simple circular curve is always

known to us let's say that this is a

point where the back tangent and forward

transient is going to cross each other

the point of intersection and we know

that there's a point where the curve is

going to start at this point of

commencement

so joining them together we will be

having the back tension

since the deflection angle is given to

us using any instrument that can make

your horizontal angle we can have the

forward tangent and once the basic data

is known to us then we can have the

tangent length and ultimately the point

of tangency and also we can draw the

center of the curve as the radius is

known to us and there is another line

which is in between PC and PT which is

long chord

now let's discuss how the deflection

angles would be calculated and how they

can be used in setting out of the

semicircular curve so deflection angles

are actually the horizontal angles and

whenever there is a horizontal angle

there should be an estimate with the

help of which we can measure the

horizontal angle and in this case let's

say we are taking a third light SPC is

the start point so we are going to place

the theodolite at PC point now the point

of discussion here is how we can

calculate the deflection angle the

formula for the deflection angle is 90 L

over pi r so in this formula L1 is

actually a bag interval and R is the

radius of the curve now L is a pack

interval and that is to be calculated

depending upon the length of the curve

so we know the formula of the length of

the curve which is pi R5 over 180 so

this will involve radius of the curve

and reflection angle so using this we

can calculate the length of the curve

and let me tell you that length of the

curve is actually the distance from PC

to PT mirrored along the curve now once

we have calculated the length of the

curve depending upon that we can decide

the tag interval now Peg interval is to

be decided in such a way that we can

have the maximum points on the curve so

that a curvature can be found let's say

that we have calculated the length of

the curve and that came out to be 100

now it depends how many points we want

on the curve we can decide the pack

interval like let's say that we want 10

points or 9 points in between PC and PC

then we are going to decide the pack

integral as 10. similarly depending upon

your value you can decide any pack

interval now once the peg interval is

being decided now we can calculate the

deflection angle and let's say that we

have calculated the deflection angle and

that came out to be any value which is

being shown on this sketch let's say

that this is the deflection angle that

we have calculated using this formula

now what we are going to do using the

theodolite we will first point it

towards the pi telescope and then we

will Mark the horizontal angle as zero

then whatever is the deflection angle

that is calculated using this formula we

will tilt that amount of telescope

rightward by this magnitude so then we

can point out the direction like the one

which is being shown on this black line

now how we can mark the point on the

curve so now we know the direction and

we also are familiar with the pack

integral so we can mark the distance as

L1 let's say the distance is up to here

the one which is being shown with a

black dot so then this point can be

marked and this point will be the one

which is on the cup the peg interval is

really constant but again it depends

upon you you can vary the peg internal

but once you are keeping in the tag

interval constant then your calculation

will become easy let's say we are moving

forward with the same pack interval then

we can Mark another point on the curve

by taking the same Peg interval L1 and

once we are going to calculate the

deflection angle so that will be another

deflection angle from this black line

but in order to keep things simple let's

multiply deflection angle with the 2

then we can have the same magnitude now

we will be having benefit of doing this

benefit is we don't need to change the

station point the station point would be

same that will be PC so once we have the

twice of the deflection Angle now we can

point it again with the help of a black

line now we can Mark another point and

that point would be the distance of L1

from this point not from the start point

from this point and on the curve so

let's say this is the point so this

distance and this distance are C so now

we have Mach 2 points and those two

points are the the points on the curve

now let me tell you that you can also do

in this way that placing the third light

over here and doing the same that we

have done with the previous point but

that will be a very difficult job you

know that shifting the instrument is a

difficult job and that will also consume

more time so in order to save time we

are actually adding the deflection angle

with the previous one the same can be

done for the next Point as well like we

can have the three times the deflection

angle and that will be that this

reflection angle and again we can point

out from the pseudolite as the one which

is being shown on this black line and

again we can mark the point on this

black line with the help of L1 distance

from the previous point this point

so then this will be the point

so all these angles are actually being

layered from PC to Pila because we made

it to zero when we have started from the

first point moving on further we can

have the four points of the deflection

angle pointing it towards that again we

can have the fourth point and again that

will be the distance of L1 the peg

interval from the previous point which

is this one and this point would be over

here

so now you can see there is a formation

of the Curve similarly five times are

the deflection angle repeating the same

procedure six times of the deflection

angle sixth point

seven times of the deflection angle

seventh point

eight times of the reflection angle and

eighth point now the last point is not

necessary to be equal to L1 because we

are calculating the length with the help

of this formula which involves Y which

is actually have not exact value that

has a value of 3.14 so we are always

going to get the length of the curve in

decimals and we can convert that into

the exact number of Peg intervals but

again when we are dividing the length of

the curve in equal distances then we are

going to get a peg interval in decimals

and once we are getting a peg interval

in decimals then to keep the same

distance on field will become difficult

because that will have decimal values

and to measure the decimal values with

the help of tape if you are carrying

that so that will be a difficult job so

that's why most of the time what we are

going to do we are actually taking a

whole number that could be 5 meter that

could be 10 meter any whole number so we

are usually taking that point but so

once we are using that whole number then

at the end we are not going to have that

whole number so let's say that at the

end we are having a l constants in the

last distance so for that we need to

calculate the deflection angle the last

reflection angle using the same formula

but in this case we will have L2 and

that is actually the angle between this

line to this line This angle and since

our instrument is at that point so we

need to have an angle from this line to

this line so that can be measured by

adding a times deflection angle 1 with

the deflection angle true

so this is total deflection a deflection

angle one plus deflection angle 2 and if

we have done our calculation correctly

we have one check available

but before I tell you about the check

let me tell you what we have made

you can see by connecting these black

dots we have formed a simple circular

curve and and now the check is when we

have this total deflection angle the

angle is from PC to Pi line to PC to PT

line so this angle would be equal to the

half of the deflection angle

so if this is equal to half of the

deflection angle it means we have done

our calculations correctly if it is not

it means there is an error involved in

the previous calculations

so this is all from this video we have

learned setting out of the simple

circular curve by deflection angle

method and next videos I am going to

teach you how we can solve an example of

setting out of the simple circular curve

by taking offsets from the long chord

and also by the deflection angle method

so this is all from this video thank you

for watching this video