Deflection Angle Method/Rankine's Method of Setting out of Simple Circular Highway Curve
Summary
TLDRThis 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
📐 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.
📏 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.
Mindmap
Keywords
💡Deflection Angle Method
💡Circular Curve
💡Radius
💡Tangent Length
💡Point of Tangency
💡Long Chord
💡Theodolite
💡Peg Interval
💡Deflection Angle Calculation
💡Total Deflection Angle
💡Setting Out
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
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