top of page
Writer's pictureAPSEd

Length of Valley Curve Based on Headlight Sight Distance & Comfort Criteria

Valley curves are a type of vertical curves used in the vertical alignment of highways. The length of a valley curve is calculated based on two criteria i.e., headlight distance (or stopping sight distance) and passenger comfort criteria.


Valley Curves Concept


As said, valley curves are a type of vertical curves used in the vertical alignment of highways. It is also called a sag curve.


Where is a Valley Curve Used?


A valley curve has upward concavity. Such a situation is possible only when a descending gradient meets the ascending gradient of a highway. Therefore, valley curves are located at places where a descending portion of the highway meets the ascending section of the highway.


Valley Curves
Valley Curves

The Shape of a Valley Curve


Generally, the cubic parabola is adopted for a valley curve. But, for small angles of deviations, all types of transition curves like a spiral, lemniscate, and cubic parabola are suitable.


Design Criteria of Valley Curves


Comfort Criteria


While traversing a valley curve, the centrifugal force acts downwards and exerts pressure on tyre. The tyre is now subjected to both the weight of the car and centrifugal force due to the valley curve. This causes discomfort to the passengers. Therefore, the length of a valley curve is designed so as to minimize the discomfort to passengers.


The comfort criteria can be satisfied only by transition curves which help in gradually increasing and decreasing the centrifugal force as the car traverses the valley curve. Therefore, the length of the valley curve as per comfort criteria is calculated as the length of two transition curves for descending and ascending sections of the highway.


Headlight Sight Distance Criteria


The headlight sight distance is the amount of highway that should be visible at any time in night conditions in order for the vehicle to stop before the obstacle. Numerically it is the same as the stopping sight distance.


In a valley, during the daytime, there is no problem in satisfying the sight distance. But during the nighttime, it becomes a problem. Therefore headlight sight distance is also considered a criterion.


Headlight Distance Criteria
Headlight Distance Criteria

Valley Curve Length Formula


Comfort Criteria


As said, the comfort criteria can be satisfied only by transition curves. Therefore, the length of the valley curve is calculated as the length of two transition curves for descending and ascending sections of the highway. The formula is given as,


L = 2 * Lt1 = 2 * ((V^3)*N/C)^(1/2)


where,


C = rate of change of centrifugal acceleration. Generally fixed at 0.6 m/s^3

N = |(±n1) - (±n2)|

n1 - descending gradient which is in -ve

n2 - ascending gradient which is in +ve

V - design speed of the highway in m/s


Headlight Sight Distance Criteria


Length of valley curve as per headlight sight distance is derived using basic trigonometry. The formula is given as,


For L > SSD


L = (N*S^2) / (1.5 + 0.035*S)


For L < SSD


L = 2S - ((1.5 + 0.035*S) / N)


where,


S - headlight sight distance (stopping sight distance)

N = |(±n1) - (±n2)|

n1 - descending gradient which is in -ve

n2 - ascending gradient which is in +ve

V - design speed of the highway in m/s


Initially, we don't know whether the length of the curve is greater or lesser than the sight distance. Therefore, it is calculated on a trial and error basis. The formulas are better illustrated below.

Valley Curve Length Formulas
Valley Curve Length Formulas

Example Problem


Question: For a portion of the highway, descending gradient 1 in 25 meets ascending gradient 1 in 20. The design speed is given as 90 kmph. Calculate the length of the valley curve (L) based on comfort and headlight distance criteria. Take S value as 153.66 m. Assume L is greater than SSD.


Solution:


N = |(±n1) - (±n2)|

N = |-1/25 - 1/20| = 0.09


Comfort Criteria:


L = 2 * ((V^3)*N/C)^(1/2)


L = 2 * (((0.278*90)^3) * 0.09 / 0.5)^(1/2)

L = 106.066 m


Headlight Distance Criteria:


For L > SSD


L = (N*S^2) / (1.5 + 0.035*S)


L = (0.09*153.66^2) / (1.5 + 0.035*153.66)

L = 308.96 m


Therefore, the length of the transition curve as per the comfort criterion is 106.66m and as per headlight sight distance is 308.96m. Usually, a higher value is adopted for design.


Practise Problem



That's all for this blog. Want us to cover a topic of your interest? Fill out the form below and let us know.







4 Comments


CBKM BOCU
CBKM BOCU
5 days ago

EPTU Machine ETPU Moulding…

EPTU Machine ETPU Moulding…

EPTU Machine ETPU Moulding…

EPTU Machine ETPU Moulding…

EPTU Machine ETPU Moulding…

EPS Machine EPS Block…

EPS Machine EPS Block…

EPS Machine EPS Block…

AEON MINING AEON MINING

AEON MINING AEON MINING

KSD Miner KSD Miner

KSD Miner KSD Miner

BCH Miner BCH Miner

BCH Miner BCH Miner

Like

CBKM BOCU
CBKM BOCU
6 days ago

EPTU Machine ETPU Moulding…

EPTU Machine ETPU Moulding…

EPTU Machine ETPU Moulding…

EPTU Machine ETPU Moulding…

EPTU Machine ETPU Moulding…

EPS Machine EPS Block…

EPS Machine EPS Block…

EPS Machine EPS Block…

AEON MINING AEON MINING

AEON MINING AEON MINING

KSD Miner KSD Miner

KSD Miner KSD Miner

BCH Miner BCH Miner

BCH Miner BCH Miner

Like

Quintan Barnes
Quintan Barnes
May 01

As a passionate driver and enthusiast of automotive safety, I found this article on the length of valley curves incredibly insightful. Understanding how headlight sight distance plays a crucial role in ensuring safe navigation through challenging terrain is paramount. It's discussions like these that reinforce the importance of choosing reliable vehicles, like those found on https://www.autobidmaster.com/en/search/salvage-cars/cadillac/. Their selection of salvage cars, including Cadillac models, offers a great opportunity for drivers to find quality vehicles at competitive prices, allowing us to prioritize both safety and affordability on the road. Thanks for the informative read!

Edited
Like

Hanna Ovr
Hanna Ovr
Sep 13, 2022

Regularly check your car for breakdowns, because safety is paramount! In case of a breakdown, contact the auto parts store, they only have quality auto parts and fast delivery, so I was satisfied.

Like
bottom of page