The Ohio State University Autumn 2019
Assignment #4: Sight distance on vertical curve (20 points, including 5 points for technical
communication)
Date handed out: Tuesday, October 1, 2019
Date due: Tuesday, October 15, 2019
Always make a copy of your solution before submitting.
Use the values of the elevation of the beginning of the vertical curve Yo, grades G1 andG2, and design
sight distance SD distributed to you by e-mail. Use present design values for height of the driver’s eye
h1 and height of the object to be seen h2 for stopping sight distance.
1. Determine the minimum length of vertical curve L
min that would provide the SD value. Present the
length of curve in the body of the report, and show your calculations neatly below this stated value in the
body of the report.
2(a) Assume that the curve is to be designed using the length of curve L
min found in part 1, the driver is
located at the beginning of the vertical curve (X = 0), and that the object to be seen is located SD from the
beginning of the vertical curve (X = SD). What are the coordinates (X,Y) of the driver’s eye and the
object to be seen? Present the coordinates in the body of the report, and show your calculations neatly
below the coordinates in the body of the report.
(b) Using numerical values, present the equations for the elevation of the vertical curve Yvc and the
elevation of the sight line Ysl as a function of the distance X from the beginning of the vertical curve.Us
Present the equations in the body of the report and describe or illustrate how you derived the equations.
(c) Determine the location X of the minimum difference Ysl(X) – Yvc(X) and the value of this minimum
difference. Determine this location to the nearest foot and the difference to the millionths of a foot (i.e.,
n x 10-6
ft). Present the location and the difference in the body of the report.
Below these presented values, present a table of the distance X, sight line elevation Ysl(X), vertical curve
elevation Yvc(X), and difference Ysl(X) – Yvc(X) for 21 values of X in one-foot increments “encompassing”
the minimum Ysl(X) – Yvc(X) value as discussed in class. Specifically:
 Determine the values Ysl(X) – Yvc(X) in 10-ft increments of X beginning at the location of the
driver and ending at the location of the object to be seen
 Determine the location of the 10-ft increment with minimum Ysl(X) – Yvc(X) value; call this
location X
10-ft
 Form the 21 one-foot increments from X = X10-f t
– 10’ to X = X10-ft+10’.
(d) What is the grade (slope) of the vertical curve (VC) at the X value determined in part (c)? How does
this compare to the slope of the sight line?
3(a)-(c) Repeat part 2, but design the curve with length L
min
– 50’.
(d) What does the value of the minimum difference Ysl(X) – Yvc(X) indicate?
4(a)-(c). Repeat part 2, but design the curve with length L
min + 50’.
(d) What does the value of the minimum difference Ysl(X) – Yvc(X) indicate?
5. What is the point I am trying to make with these calculations? In addition to the sentence “covering the
point” presented in class, provide an additional one to three sentences illustrating what you learned.
6. The calculations you performed were all conducted with the “driver’s eye” being located at one X
value. Assuming that you used a spread sheet or computer program, briefly explain how you would
investigate whether sufficient sight distance is provided throughout the curve using the formula to
determine the length needed.