vertical alignments and vertical curves

Question 1

Stopping sight distance

Answer 1

perceive + react + stop = ssd
percieve + react time = PRT = 2.5s

• in horiz design, ssd can govern radius where walls and barriers inhibit a drivers lateral view
• in vert design, ssd is related to sight limitations caused by topography

Question 2

vertical allignments

Answer 2

straight line gradients (tangents) that closely follow the terrain

these tangents are connected by parabolic curves

the design speeds effect on driver comfort and or SSD will determine the parabolic shape

size of the parabolic curve is given by its horizontal length L

Question 3

vertical curves

Answer 3

vertical curves are skewed parabolas, the rate of change of grade w-r-t hz length is constant

this constant is the k factor of the parabola and is equal to the hz length required for a 1% change in grade

eg k = 50 so it takes 50m for grade to change by 1%

available sight distance is constant throughout the parabola

k=L/A - A as a percentage

L is rounded up to the nearest 10m typically

Question 4

grades

Answer 4

expressed as either a percent or a ratio (m/m). positive if it is rising in direction of increasing stations

notes on grade values
- incoming and outgoing (g1 and g2) refers to chainage
- all values, G, g, A, and a need signs in front, +/-

G1 ang G2 - incoming and outgoing grades as percentages, i.e. G1 +6%
g1 and g2 - incoming and outgoing grades expressed as a rise/run ratio, i.e. g1 = +0.06
a and A - outgoing grade minus incoming grade as either a decimal or percent, i.e. +0.03. A decides if curve is crest or sag

max and min grades
G min 0.5% generally for urban roads
G absolute min 0.3%
G min 0 percent for rural without curbs, water will follow the cross slope and enter ditch

grade = generally longitudinal slope
slope = generally transverse slope. note: x=0 at crown, so negative normal sloped road crown means reg cross slope. road crown is the shape of the driving surface

Question 5

curves diagram and formula

Answer 5

delta = VPI = vertical point of intersection
delta y = dif in elev between curve and tangent at a chainage
k factor = vert curve parameter
vpi is horizontaly centred between the BVC and EVC
y is elev at a horizontal distance (x) from the BVC