angle in horizontal curve obstruction formula

[ketanco]

I saw this formula in CERM in the section for calculating the sight distances when an obstruction is present in a horizontal curve

M=R(1-Cos(teta))

what is the angle Teta here?

they dont give a description

 

[JMT]

Look at the horizontal curve elements (figure 79.1) on page 79-2.

 

[ptatohed]

Depending on the edition, the CERM has flipped flopped with calling M, HSO and vice versa. To me there is a clear distinction.

M is the Middle Ordinate (the distance from the midpoint of the curve to the midpoint of the long chord) (has nothing to do with stopping sight distance)

HSO is the Horizontal Sight Line Offset (the distance from the point on the curve perpendicular to the midpoint of the cord formed by the sight line from driver to object) (see 79.9 CERM13 for a graphical depiction) (used to determine the stopping sight distance along a curve with an obstruction)

I think ketanco is asking about HSO and JMT is talking about M.

The theta in the HSO = R(1 - cos theta) is equal to the degree of curvature x the stopping sight distance / 200 but you don't need to know that. They are just showing you how they derived the formula you do need to know: HSO = R x (1 - cos (28.65 x S) / R )

 

[ketanco]

got it thanks.