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highway agencies has come only recently. This is understandable. Railroad trains must follow the precise alignment of the tracks, and the discomfort described here can be avoided only by adopting easement curves. On the other hand, the motor-vehicle operator is free to alter his lateral position on the road and can provide his own easement curves by steering into circular curves gradually. However, this weaving within a traffic lane (but sometimes into other lanes) is dangerous. Properly designed easement curves make weaving unnecessary. It is largely for safety reasons, then, that easement curves have been widely adopted by highway agencies. For the same radius circular curve, the addition of easement curves at the ends changes the location of the curve with relation to its tangents; hence the decision regarding their use should be made before the final location survey. They point of beginning of an ordinary circular curve is usually labeled the PC (point of curve) or BC (beginning of curve). Its end is marked the PT (point of tangent) or EC (end of curve). For curves that include easements, the common notation is, as stationing increases: TS (tangent to spiral), SC (spiral to circular curve), CS (circular curve to spiral), and ST (spiral go tangent). On two-lane pavements provision of a wilder roadway is advisable on sharp curves. This will allow for such factors as (1) the tendency for drivers to shy away from the pavement edge, (2) increased effective transverse vehicle width because the front and rear wheels do not track, and (3) added width because of the slanted position of the front of the vehicle to the roadway centerline. For 24-ft roadways, the added width is so small that it can be neglected. Only for 30mph design speeds and curves sharper than 22°does the added width reach 2 ft. For narrower pavements, however, widening assumes importance even on fairly flat curves. Recommended amounts of and procedures for curve widening are given in Geometric Design for Highways.

B Grades

The vertical alignment of the roadway and its effect on the safe and economical operation of the motor vehicle constitute one of the most important features of road design. The vertical alignment, which consists of a series of straight lines connected by vertical parabolic or circular curves, is known as the “grade line.” When the grade line is increasing from the horizontal it is known as a “plus grade,” and when it is decreasing from the horizontal it is known as a “minus grade.” In analyzing grade and grade controls, the designer usually studies the effect of change in grade on the centerline profile. In the establishment of a grade, an ideal situation is one in which the cut is balanced against the fill without a great deal of borrow or an excess of cut to be wasted. All hauls should be downhill if possible and not too long. The grade should follow the general terrain and rise and fall in the direction of the existing drainage. In mountainous country the grade may be set to balance excavation against embankment as a clue toward least overall cost. In flat or prairie country it will be approximately parallel to the ground surface but sufficiently above it to allow surface drainage and, where necessary, to permit the wind to clear drifting snow. Where the road approaches or follows along streams, the height of the grade line may be dictated by the expected level of flood water. Under all conditions, smooth, flowing grade lines are preferable to choppy ones of many short straight sections connected with short vertical curves. Changes of grade from plus to minus should be placed in cuts, and changes from a minus

grade to a plus grade should be placed in fills. This will generally give a good design, and many times it will avoid the appearance of building hills and producing depressions contrary to the general existing contours of the land. Other considerations for determining the grade line may be of more importance than the balancing of cuts and fills. Urban projects usually require a more detailed study of the controls and finer adjustment of elevations than do rural projects. It is often best to adjust the grade to meet existing conditions because of the additional expense of doing otherwise. In the analysis of grade and grade control, one of the most important considerations is the effect of grades on the operating costs of the motor vehicle. An increase in gasoline consumption and a reduction in speed are apparent when grades are increase in gasoline consumption and a reduction in speed is apparent when grades are increased. An economical approach would be to balance the added annual cost of grade reduction against the added annual cost of vehicle operation without grade reduction. An accurate solution to the problem depends on the knowledge of traffic volume and type, which can be obtained only by means of a traffic survey. While maximum grades vary a great deal in various states, AASHTO recommendations make maximum grades dependent on design speed and topography. Present practice limits grades to 5 percent of a design speed of 70 mph. For a design speed of 30 mph, maximum grades typically range from 7 to 12 percent, depending on topography.

Wherever long sustained grades are used, the designer should not substantially exceed the critical length of grade without the provision of climbing lanes for slow-moving vehicles. Critical grade lengths vary from 1700 ft for a 3 percent grade to 500 ft for an 8 percent grade.

Long sustained grades should be less than the maximum grade on any particular section of a highway. It is often preferred to break the long sustained uniform grade by placing steeper grades at the bottom and lightening the grade near the top of the ascent. Dips in the profile grade in which vehicles may be hidden from view should also be avoided.

Maximum grade for highway is 9 percent. Standards setting minimum grades are of importance only when surface drainage is a problem as when water must be carried away in a gutter or roadside ditch. In such instances the AASHTO suggests a minimum of 0.35%.

C Sight Distance

For safe vehicle operation, highway must be designed to give drivers a sufficient distance or clear version ahead so that they can avoid unexpected obstacles and can pass slower vehicles without danger. Sight distance is the length of highway visible ahead to the driver of a vehicle. The concept of safe sight distance has two facets: “stopping” (or “no passing”) and “passing”.

At times large objects may drop into a roadway and will do serious damage to a motor vehicle that strikes them. Again a car or truck may be forced to stop in the traffic lane in the path of following vehicles. In dither instance, proper design requires that such hazards become visible at distances great enough that drivers can stop before hitting them. Further more, it is unsafe to assume that one oncoming vehicle may avoid trouble by leaving the lane in which it is traveling, for this might result in loss of control or collision with another vehicle.

Stopping sight distance is made up of two elements. The first is the distance traveled after the obstruction comes into view but before the driver applies his brakes. During this period of

perception and reaction, the vehicle travels at its initial velocity. The second distance is consumed while the driver brakes the vehicle to a stop. The first of these two distances is dependent on the speed of the vehicle and the perception time and brake-reaction time of the operator. The second distance depends on the speed of the vehicle; the condition of brakes, times, and roadway surface; and the alignment and grade of the highway.

On two-lane highways, opportunity to pass slow-moving vehicles must be provided at intervals. Otherwise capacity decreases and accidents increase as impatient drivers risk head-on collisions by passing when it is unsafe to do so. The minimum distance ahead that must be clear to permit safe passing is called the passing sight distance.

In deciding whether or not to pass another vehicle, the driver must weigh the clear distance available to him against the distance required to carry out the sequence of events that make up the passing maneuver. Among the factors that will influence his decision are the degree of caution that he exercises and the accelerating ability of his vehicle. Because humans differ markedly, passing practices, which depend largely on human judgment and behavior rather than on the laws of mechanics, vary considerably among drivers. To establish design values for passing sight distances, engineers observed the passing practices of many drivers. Basic observations on which passing sight distance standards are based were made during the period 1938-1941. Assumed operating conditions are as follows:

1. The overtaken vehicle travels at a uniform speed.

2. The passing vehicle has reduced speed and trails the overtaken one as it enters the

passing section.

3. When the passing section is reached, the driver requires a short period of time to perceive

the clear passing section and to react to start his maneuver.

4. Passing is accomplished under what may be termed a delayed start and a hurried return

in the face of opposing traffic. The passing vehicle accelerates during the maneuver and its average speed during occupancy of the left lane is 10 mph higher than that of the overtaken vehicle.

5. When the passing vehicle returns to its lane there is a suitable clearance length between it

and an oncoming vehicle in the other lane.

The five distances, in sum, make up passing sight distance.