Practice Question: Find the Middle Ordinate on a Horizontal Curve
NCEES Civil PE Specification Geometrics: Basic Circular Curve Elements
Problem
What is most nearly the middle ordinate “M” of the shown standard horizontal cure providing the following curve data:
\(R=1500\ ft\)
\(T=197\ ft\)
CORRECT ๐
INCORRECT ๐
% Students Correctly Answered:
81.1%
Solution
Answer: A) 13 ft
Refer to PE Civil Reference Handbook V 1.1 Section 5.2.1 basic curve elements:
\(M=R-R\cos\fracโ2\)
where:
\(\Delta=Intersection\ Angle\)
\(R=1500\ ft\)
\(T=R\tan\fracโ2\)
\(197=1500\tan\fracโ2โ โ =15\ degrees\)
\(M=1500-1500\cos{\left(\frac{15}{2}\right)}=12.8\ ft\)