Profile longitudinally of a road

Definitions

Three elements make it possible to characterize the geometry of a road:

the profile transversely is a cut perpendicular to the center line of highway of the whole of the points defining its surface,
the profile longitudinally is a vertical rise in the direction in the axis in the road in the whole of the points constituting this one.
the alignment is a flat projection on a topographic Cartesian reference mark of the whole of the points defining the road alignment.

Elements of composition of the profile longitudinally

The profile longitudinally is deeply marked by the very low value of the slopes which one can give to the road to ensure suitable speeds of circulation and by the problems of visibility necessary to a nondangerous control.

The profile longitudinally thus consists of a succession of segments of right-hand sides and arcs of circles, more rarely of arcs of curve with progressive curve (clothoid) making it possible to connect between them the segments of right-hand sides.

Choice of the segments of right-hand sides

. The slope of the right-hand sides cannot exceed a certain maximum fixed for each category of road: 4 to 8% according to the categories.

In addition, null slope is normally never employed so that the water run-off is carried out easily. The following minimal gradients in general are adopted:

0,5% in the zones where the crossfall of the roadway is lower than 0,5%, if there is risk of glaze,
At least 0,2% in the long cut sections: so that the longitudinal work of drainage is not too deeply buried a face air-side;
At least 0,2% in the sections in fill envisaged with water descents.

The position of the right-hand sides compared to the original ground depends on several factors such as:

to avoid useless earthworks: position close to the surface of the original ground,
to balance the earthwork ones,
to minimize the movement of the Earths,
to accentuate the cut position to increase spoil of a useful material, to protect the environment (seen, noise…),
to accentuate the position in fill to avoid a bad material or a material of expensive extraction, to make more pleasant the road to the user, to avoid a floodplain.

These elements of right-hand sides reveal angles known as " saillants" or " rentrants" who correspond to the zones of connection per circle, possibly by arc of clothoid.

Choice of the circles.

The rays of the circles are primarily in relation to the visibility which one must ensure, possibly with a dynamic comfort. The sight distances necessary depend on the operation which one wants to ensure (to stop or pass a vehicle) and speed to which one can circulate.

Stopping distances and sight distances are thus defined.

stopping distance

It depends on the vehicle, the driver and the circulation terms. That is to say d0 the length of braking, where the driver does not intervene.

d0 = 4/1000*v2/F (V) where F (V) is a factor speed V. F (V) varies from 0,46 to 0,34 when V passes from 40 to 120 km/h.

The stopping distance is then:

in right alignment:

d1 = d0 + 0,55 V if V (speed of reference) is < 100km/h
d1 = d0 + 0,55 V + 0,5 V if V is > 100 km/h.

in curve.

d2 = d1 + 0,25 d0

For the braking distance, it is advisable to add the distance from to the reaction time of the driver. One will retain like stopping distances the following values: :

sight distance

3 sight distances are considered:

dD: sight distance of normal going beyond necessary to the normal going beyond (average power of the vehicle).
dd: minimal sight distance of going beyond which corresponds to a normal going beyond carried out by a more powerful vehicle.
dMd: sight distance of operation of going beyond (the exceeded vehicle brakes).

dMd < dd < dD: the most constraining the sight distance is thus dD, and one finds in the order of constraints decreasing dD, dd then dMd.

They are in relation to speed V: in particular dd = 4 V and dD = 6 V when V < 100 km/h if not 5 V and 7 V.

Note: the conditions of visibility suppose:

the eye with 1 m in height.
the vehicle: 1,20 m height
dangerous Obstacle: 0,15 m height.
permanent Obstacle: 0,00 m height (painting).

One must ensure the visibility:

everywhere for the
, stopping distance everywhere for the sight distance dMd preferably for Vr speed + 20 km/h,
for the distance dd on half of the way.

There exist relations between the rays of the curves of the profile longitudinally and the sight distances to observe the conditions of visibility necessary to control of the vehicles. RV = F speed, type of connection (projecting, returning)

In salient angle, one wants to ensure:

only the " possibility; of arrêt" on the one-way roadways (2 or 4 ways) since there is no problem of going beyond;
the possibility of going beyond relatively difficult (the exceeded vehicle brakes) or even to flux circulation on the bidirectional roads (2 or 3 ways).

In re-entrant angle, it is necessary to ensure only the visibility for the stopping distance, the visibility of going beyond being always assured. Their dimensioning is primarily function of considerations related on dynamic comfort, the conditions of night visibility and the conditions of ruissellement.

The presence of an overpass than the right of a re-entrant angle must be the subject of a particular examination.

In practice

Up to 70 km/h, it is the night constraint of visibility which is paramount:

On the basis of beam of headlights, horizontal axis located at 0,75m and 1 degree of opening, and for a stopping distance in curve D (in m), the ray is given by the formula: R = D ²/(1,5+0,035d)

For 80 km/h, it is the stopping distance in straight line which is retained.
Beyond that, the principal constraint concerns comfort and relates to the vertical acceleration undergone by the users.

Although comfort cannot be measured precisely because strongly depend on the system of suspension of the vehicle, of the flexibility of the tires and the load transported inter alia, the international standards admit a maximum centrifugal vertical acceleration of 0,3 m/s ² is approximately g/33. The resulting condition is:
R = V ² /3,9 with V expressed in km/h

This condition is the maximum recommended. However, for the roads with weak characteristics (difficult relief in particular), safety not being concerned, of the higher values of acceleration can be allowed but with the detriment of the comfort of the users. The possible maximum value can be increased to 0,5 m/s ².

In synthesis.

Internal bonds

Sources

"Installation of the Principales" Roads; - Recommendations for the design and the geometry of the road - SETRA - 1994,
To include/understand the principal parameters of geometrical design of the roads” - Sétra - January 2006.

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