SME
Transportation Engineering · Problem type
Length of a crest vertical curve
Use this for “A +3% grade meets a −2% grade on a 100 km/h road with SSD = 183.1 m. How long must the crest vertical curve be?”
Diagram
The dashed grades meet at the PVI (dot).
A = |G₁ − G₂| = |3 − (−2)| = 5%.
S
<
L,
so
L
=
AS²
658
=
5
×
183
2
658
=
255
m.
With that L, the sight line at its worst place just touches the road: the curve is exactly long enough.
This is an example. Type your own values to start a new problem.
G₁
Grade in
example · %
G₂
Grade out
example · %
A
Change of grade
calculated · %
S
Sight distance
example · m
L
Length of curve
calculated · m
Formulas
A
=
|
G₁
−
G₂
|
5 = |3 − (−2)|
L
=
A
×
S
2
658
254.7539
=
5
×
183.1
2
658
Assumptions
•
AASHTO 2018: eye 1.08 m and object 0.60 m above the road, so 200(√h₁ + √h₂)² = 658.
•
A parabolic crest curve; G₁ and G₂ in percent, + uphill in the direction of travel.
•
Two cases: the sight line lies within the curve (S < L) or runs past both ends (S ≥ L).
Step-by-step
WE KNOW
G₁ = 3%, G₂ = −2%, S = 183.1 m
FIND
change of grade (A), length of curve (L)
Step 1 · Find change of grade (A)
Use A = |G₁ − G₂|
The change of grade in percent: how sharply the road turns over the top.
A
=
|3
−
(−2)|
A
=
|5|
A
=
5%
Step 2 · Find length of curve (L)
Use L = A × S² ÷ 658
AS²
658
comes
out
longer
than
S
,
so
the
driver
and
the
object
both
stand
on
the
curve.
183.1
<
254.7539:
S
<
L
L
=
5
×
183.1
2
658
L
=
5
×
33,525.61
658
L
=
167,628.05
658
L
=
254.7539
m
Check
Put the numbers back in. Both sides should match.
5 = |3 − (−2)| ✓
254.7539
=
5
×
183.1
2
658
✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
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