Vertical Curve Length from a Design K-Value
Vertical Curve Length from a Design K-Value
Where two roadway grades meet, a parabolic vertical curve smooths the transition so sight distance and rider comfort stay within design limits. Rather than re-deriving sight-distance geometry every time, designers use a tabulated K-value — length of curve per percent of grade change — that already bakes in the design speed and stopping sight distance requirement.Using too short a curve length (below the K-value minimum) can hide an oncoming hazard just over a crest or create a harsh, uncomfortable dip, so checking L against K·A is a routine but essential step in profile design.
The minimum curve length is L = K·A, the design K-value times the algebraic difference in grades. where K is the design K-value (length per percent grade change) and A is the algebraic difference between the two grades, in percent.
Inputs
K_des := 45 m=45 m
A_g := 4=4
Multiplying the tabulated K-value by the grade break directly gives the minimum curve length that satisfies sight distance.
L_vc := K_des·A_g=180 m
Results
A result around 150–200 m is typical for a moderate grade change on a high-speed road; sharper grade breaks or higher design speeds push L up quickly since it scales linearly with both K and A. Any curve shorter than this value fails the sight-distance check and must be lengthened, usually by shifting the PVI or the approach grades.
Assumptions & limitations
- K-value already embeds a specific design speed and SSD.
- Crest and sag curves use different K tables; this uses whichever K is given.
- Symmetrical parabolic curve assumed.