Deflection Angles

passpepasspe · Oct 19, 2010

I am looking for sample problems regarding the geometric design with reference to deflection angles...anyone has a reference that tackles understanding the deflection angles best?? I just don't understand them.

maximus808 · Oct 19, 2010

do you mean finding the station along a horizontal curve with deflection angles? Most cases, the deflection angle of two tangents are given. Most text refer to this angle as I or delta. If given bearings, you will need to use the bearing of both your forward and back tangent to find the deflection angle by subtracting by 180 degrees. Geomtrics is a lot of geometry and trigonometry.

Ambrug20 · Oct 20, 2010

passpepasspe said:
I am looking for sample problems regarding the geometric design with reference to deflection angles...anyone has a reference that tackles understanding the deflection angles best?? I just don't understand them.

In surveying, a horizontal angle measured from the prolongation of the preceding line to the following line. Deflection angles to the right are positive; those to the left are negative.

Or you can say that deflection angle is turned to the right or left starting at the backsight point or to the right or left looking forward 180 from the backsight.

if you look on the figure 78.1 p.78-2 CERM, the angle "I" between PI and tangent is deflection angle.

hope it helps

passpepasspe · Oct 21, 2010

Tanya said:
passpepasspe said:

I am looking for sample problems regarding the geometric design with reference to deflection angles...anyone has a reference that tackles understanding the deflection angles best?? I just don't understand them.

Click to expand...

In surveying, a horizontal angle measured from the prolongation of the preceding line to the following line. Deflection angles to the right are positive; those to the left are negative.

Or you can say that deflection angle is turned to the right or left starting at the backsight point or to the right or left looking forward 180 from the backsight.

if you look on the figure 78.1 p.78-2 CERM, the angle "I" between PI and tangent is deflection angle.

hope it helps

thanks both, yes i was looking for the stuff that is hte cerm. Found examples of calculating deflection angles and chord leghths from the chelapati manual.

maximus808 · Oct 21, 2010

Yes, I have that manual too and it helped me greatly improve my understanding of geometrics (horz and vert curves)

armenterosjl · Oct 21, 2010

passpepasspe said:
I am looking for sample problems regarding the geometric design with reference to deflection angles...anyone has a reference that tackles understanding the deflection angles best?? I just don't understand them.

Deflection angles is not an objective in this exam ( I think)

maximus808 · Oct 21, 2010

isn't deflection angles the angle intersection the back and front tangent?

armenterosjl · Oct 21, 2010

maximus808 said:
isn't deflection angles the angle intersection the back and front tangent?

I represent intersection angle, central angle of curve or deflection angle between back and forward tangents...It is part of the problem in Horizontal Curves. See prob.78.1 CERM. Also page 78-2 CERM

passpepasspe · Oct 21, 2010

armenterosjl said:
maximus808 said:

isn't deflection angles the angle intersection the back and front tangent?

Click to expand...

I represent intersection angle, central angle of curve or deflection angle between back and forward tangents...It is part of the problem in Horizontal Curves. See prob.78.1 CERM. Also page 78-2 CERM

Look at example 404.1 in Goswami book

armenterosjl · Oct 21, 2010

passpepasspe said:
armenterosjl said:

maximus808 said:

isn't deflection angles the angle intersection the back and front tangent?

Click to expand...

I represent intersection angle, central angle of curve or deflection angle between back and forward tangents...It is part of the problem in Horizontal Curves. See prob.78.1 CERM. Also page 78-2 CERM

Click to expand...

Look at example 404.1 in Goswami book

Yes. It is the same concept.....

PEin2010 · Oct 24, 2010

Is it true that the deflection angle is the angle subtended at the center divided by 2?

civilized_naah · Oct 24, 2010

PEin2010 said:
Is it true that the deflection angle is the angle subtended at the center divided by 2?

For a chord of a circle, the angle made with the tangent is half the angle subtended at the center. The deflection angle is the angle between the chord and the tangent.

ptatohed · Jun 20, 2013

The term, Deflection Angle, when used with Hor Curves, has always bothered me. Some sources regard the Def Ang as equal to I and some regard it as equal to I/2.

Two examples found with a quick internet search:

Defines Def Ang as I/2

Defines Def Ang as I

If you are lucky, the problem statement will clarify by stating “The Def Ang b/t Fwd Tan and Long Chord” (I/2) or “The Def Ang b/t Fwd Tan and Bck Tan” (I). But many times, the problem statement will simply state “The Def Ang is 30^”. Arrgghh!

My opinion is that if a problem only gives you the “Deflection Angle” with no other clarification, it should be I/2 (Ex. A Def Ang of 30^ equals an I of 60^)

civilized_naah · Jun 20, 2013

The term deflection angle can indicate any angle between two horizontal rays. When you are referring to an overall alignment, as in "the circular curve provides a transition from a back tangent to the forward tangent, with a deflection angle = ...", then ""deflection angle" refers to the horizontal angle measured from the back tangent to the forward tangent (deflects right if the angle is clockwise, deflects left if the angle is counterclockwise).

On the other hand, when laying out a curve by deflection angles, you are using the back tangent as your reference direction and laying off various CHORD LENGTHS at specific angles with respect to the back tangent. In this case, each deflection angle is the angle between the back tangent and a CHORD and therefore, is half the the angle subtended at the center.

ptatohed · Jun 20, 2013

civilized_naah said:
The term deflection angle can indicate any angle between two horizontal rays. When you are referring to an overall alignment, as in "the circular curve provides a transition from a back tangent to the forward tangent, with a deflection angle = ...", then ""deflection angle" refers to the horizontal angle measured from the back tangent to the forward tangent (deflects right if the angle is clockwise, deflects left if the angle is counterclockwise).

On the other hand, when laying out a curve by deflection angles, you are using the back tangent as your reference direction and laying off various CHORD LENGTHS at specific angles with respect to the back tangent. In this case, each deflection angle is the angle between the back tangent and a CHORD and therefore, is half the the angle subtended at the center.

Correct. I understand everything you said. My problem is in the (rare but not totally unlikely) case where the problem statement simply states "The Deflection Angle is XX^". Here's an example:

A horizontal curve has a deflection angle of 45o with the PI at Station 900.00 and a long chord of 500 m. What is the station of the Point of Curvature (PC)?

In this example (and others like it), I would say that the deflection angle they are referring to is b/t the back tan and long chord (I/2) (not b/t bck and fwd tangents) and thus, I would consider I (delta) to be 90^ (not 45^).

Is this how you see it? Thanks.

civilized_naah · Jun 20, 2013

Actually, given that language, I would interpret it as I = 45. So, that makes your point right there - that there is enough ambiguity in the language, to go either way.

dana · Jul 20, 2013

The question said that the deflection angle of 45 degrees, this is I. Long Cord=500 m is another data of the problem.

MWC PE · Jul 22, 2013

It has to be I.

Its not a horizontal curve question but a geometry question, or rather a question to see if you understand the geometric principles in horizontal curves. If you know that T is the same on both sides and you know that the station for the PI is measured along T and not along the curve then all you have is a question asking you how long the line T is which you can use to PC = PI - T

One equation for T is T = (LC)/(2cos(I/2))

ptatohed · Jul 22, 2013

MWC PE said:
civilized_naah said:

Actually, given that language, I would interpret it as I = 45. So, that makes your point right there - that there is enough ambiguity in the language, to go either way.

Click to expand...

dana said:

>The question said that the deflection angle of 45 degrees, this is I.

Click to expand...

MWC PE said:

It has to be I.

Click to expand...

Perhaps you guys are right. But the way I looked at it is if the term "deflection angle" is used, with no further description, it is not the def ang b/t the back/forward tangents at the PI - it's the def ang b/t the back tan and cord at the BC....... because...... there are several terms for the former (I, Delta, Intersection Angle, Central Angle), but no terms (that I know of?) for the latter. Thus, my logic is the problem writer could (should!) have easily selected a well-known term/symbol if he meant I, therefore he must mean I/2 when he says "deflection angle". Maybe I am thinking too hard.

S

jt74 · Mar 3, 2014

Here's a problem from the 2011 NCEES Water Resources and Environmental breadth practive exam (problem #125) where I ran into this definition issue. How am I to know which definition of deflection angle to use? (Or do I just solve for both defintions and see which one matches the solution set?)

Code:

The following information is for a proposed horizontal curve in a new subdivision:
PI station         12+40.00
Degree of curve    10d
Deflection angle   12d 30m

The station of the PT is most nearly:
A) 12+79.80
B) 12+80.10
C) 13+02.00
D) 13+64.75

Deflection Angles

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