Deflection Angles

[civilized_naah]

Stated like this, deflection angle means the angle between the two tangents, often referred to as either I or delta. This angle is EQUAL to the angle at the center.

On the other hand, when referring to a point on the curved and its location with respect to the back tangent, the deflection angle is the angle between the back tangent and the CHORD at the end of which the point lies. This angle is HALF THE ANGLE (subtended by the chord at the center)

 

[ptatohed]

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?)


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

Not only does this problem not tell you which two lines form the "deflection angle", but it also doesn't tell you if the Degree of Curve is arc basis or chord basis. I assumed the deflection angle was equal to I and the Degree of Curve was arc basis and I got 13+02.25, answer C. I then looked at the solution and they are treating the Def Ang as I and they are treating the D of C as arc basis and they got the same answer - answer C. But, I just noticed this today..... they use the symbol for Degree of Curve chord basis (DCo) instead of the correct symbol for arc basis (DAo)!!

 

[Predgw]

Most survey books state the intersection angle and deflection angle are the same thing. The thing to remember with a problem like this, more so because it is a breadth problem, what are they asking for? They want the station of the PT. There is no mention of laying out a specific station on a curve. This is not a curve layout question. The deflection angle term for layout would be labled as such;

layout the curve using the deflection angle method, or the tangent offset method.